index int64 0 999 | image stringlengths 4.4k 871k | question stringlengths 189 2.04k | answer stringclasses 4
values | category stringclasses 6
values | subfield stringclasses 26
values | reasoning_type stringclasses 20
values | embedding listlengths 4.1k 4.1k |
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700 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIkAiQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A disk mass \(M\) that rotates on an axis passing through its center. Find the moment of inertia of a circular disk.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: $\frac{2}{3}MR^2$ B: $\frac{1}{3}MR^2$ C: $\frac{1}{2}MR^2$ D: $\frac{1}{2}MR$ | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
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701 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAH6A0YDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Luis uses a wrench to turn a nut. The wrench handle is tilted above the horizontal, and Luis pulls straight down on the end with a force. How much torque does Luis exert on the nut?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: -15Nm B: -17Nm C: -19Nm D: -21... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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702 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEqAswDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The \(500\,\mathrm{kg}\) steel beam shown in figure is supported from the right end. What is the gravitational torque about the support?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 3720N B: 3820N C: 3920N D: 4020N | C | Mechanics | Statics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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703 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAKkA84DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The tunnel is rigid and its mass is much less than that of either rocket. The rockets start their engines simultaneously, each generating thrust in opposite directions. What is the structure's angular velocity after \(30\,\mathrm{s}\)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g.,... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0291748046875,
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704 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHQAewDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The engine in a small airplane is specified to have a torque of \(60\,\mathrm{N\,m}\). This engine drives a propeller. On start-up,how long does it take the propeller to reach \(200\,\mathrm{rpm}\)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 5.0s B: 4.8s ... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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705 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIMAzQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows a piece of a large machine. A disk turns on an axle. A vertical cable attached to the edge of the disk exerts a force but, initially, a pin keeps the disk from rotating. What is the initial angular acceleration of the disk when the pin is removed?Please directly answer the question and provide the correct ... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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706 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIQAcIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A bucket is attached to a massless string that is wrapped around a \(4.0\,\mathrm{cm}\)-diameter cylinder. The cylinder rotates on an axle through the center. The bucket is released from rest \(1.0\,\mathrm{m}\) above the floor. How long does it take to reach the floor?Please directly answer the question and provide th... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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707 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFMAfYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The biceps pulls the forearm up against the upper arm at the elbow, so the force \(\vec{F}_{\mathrm{elbow}}\) on the forearm at the elbow—a force due to the upper arm—is a downward force. What is the magnitude of \(\vec{F}_{\mathrm{elbow}}\)?Please directly answer the question and provide the correct OPTION LETTER ONLY... | C | Mechanics | Statics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.027099609375,
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708 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHuBDIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Suppose the earth suddenly came to a halt and ceased revolving around the sun. The gravitational force would then pull it directly into the sun. What would be the earth's speed as it crashed?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: $5.13\times10^5\,\ma... | C | Mechanics | Work and Energy | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.034423828125,
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709 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAMQAyIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A ladder leans against a frictionless wall.The coefficient of static friction with the ground, that prevents the ladder from slipping. What is the minimum value of \(\mu_s\)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.35 B: 0.23 C: 0.29 D: 0.41 | C | Mechanics | Statics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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710 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJ2BBADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A typical can of food is \(7.5\,\mathrm{cm}\) in diameter. What is the tallest can of food.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 8cm B: 10cm C: 13cm D: 15cm | C | Mechanics | Statics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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711 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFqBQYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two equal masses are at the ends of a massless rod. The rod spins about an axis through its midpoint. Suddenly, a compressed gas expands the rod out. What is the rotation frequency after the expansion?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 0.80rev/s ... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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712 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCARoAroDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A solid disk is rotating. A circular loop is dropped straight down onto the rotating disk. Friction causes the loop to accelerate until it is riding on the disk. What is the final angular velocity of the combined system?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OP... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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713 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAKqA+QDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A block hangs from the end of a rod, together forming a pendulum that swings from a frictionless pivot at the top end of the rod. A bullet is fired horizontally into the block, where it sticks, causing the pendulum to swing out. What was the speed of the bullet?Please directly answer the question and provide the correc... | C | Mechanics | Momentum and Collisions | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
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714 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADMAzoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A 1000\ \mathrm{kg} rocket is fired straight away from the surface of the earth. The rocket need to escape from the gravitational pull of the earth and never return. Assume a nonrotating earth. What speed does the rocket need?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C... | C | Mechanics | Work and Energy | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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715 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJSAjADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A inventor wants to launch small satellites into orbit by launching them straight up from the surface of the earth at very high speed. By what percentage would your answer be in error if you used a flat-earth approximation?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D.... | C | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Implicit Condition Reasoning'] | [
0.0081787109375,
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716 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJUA5wDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Astronomers discover a binary star system with a period of \(90\,\mathrm{days}\). Both stars have a mass twice that of the sun. How far apart are the two stars?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: $8.3\times10^{10}\,\mathrm{m}$ B: $9.3\times10^{9}\... | C | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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717 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHYAkwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | At \(t=0\,\mathrm{s}\), a \(500\,\mathrm{g}\) block oscillating on a spring is observed moving to the right at \(x=15\,\mathrm{cm}\). It reaches a maximum displacement of \(25\,\mathrm{cm}\) at \(t=0.30\,\mathrm{s}\). At what times during the first cycle does the mass pass through \(x=20\,\mathrm{cm}\)?Please directly... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Predictive Reasoning'] | [
0.006744384765625,
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718 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHeA6wDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An student hangs from a bungee cord with spring constant. The student is pulled down to a point where the cord is \(5.0\,\mathrm{m}\) longer than its unstretched length, then released. What is his velocity \(2.0\,\mathrm{s}\) later?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A... | C | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
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719 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJYAwYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A pendulum consists of a massless, rigid rod with a mass at one end. The other end is pivoted on a frictionless pivot so that the rod can rotate in a complete circle. The pendulum is inverted, with the mass directly above the pivot point, then released. The pendulum later undergoes small-amplitude oscillations at the b... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0162353515625,
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720 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGMAqYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A \(10.0\,\mathrm{cm}\)-diameter suction cup is pushed against a smooth ceiling. The object can be suspended from the suction cup without pulling it off the ceiling? The mass of the suction cup is negligible. What is the maximum mass of an object?Please directly answer the question and provide the correct OPTION LETTER... | C | Mechanics | Statics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.025634765625,
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721 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGsAk4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Water fills the tube shown in figure. What is the pressure at the top of the closed tube?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 1.02atm B: 1.12atm C: 1.06atm D: 1.14atm | C | Mechanics | Statics | ['Physical Model Grounding Reasoning', 'Implicit Condition Reasoning'] | [
0.01080322265625,
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722 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFEAg4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A \(10\,\mathrm{cm} \times 10\,\mathrm{cm} \times 10\,\mathrm{cm}\) block of wood with density \(700\,\mathrm{kg/m^3}\) is submerged in water. What is the tension in the stringPlease directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 3.5N B: 3.2N C: 2.9N D: 3.8N | C | Mechanics | Statics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0296630859375,
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723 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEeAs4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | You need to determine the density of an unknown liquid. You notice that a block floats in this liquid with 4.6\ \mathrm{cm} of the side of the block submerged. When the block is placed in water, it also floats but with 5.8\ \mathrm{cm} submerged. What is the density of the unknown liquid?Please directly answer the ques... | C | Mechanics | Statics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.038330078125,
0.01416015625,
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0.005523681640625,
0.003082275390625,
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0.017578125,
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0.032470703125,
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724 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHQAxgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The water's speed through the lower pipe is \(5.0\,\mathrm{m/s}\) and a pressure gauge reads \(75\,\mathrm{kPa}\). What is the reading of the pressure gauge on the upper pipe?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 4.4kPa B: 4.8kPa C: 4.6kPa D: 5.0kPa | C | Mechanics | Dynamics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
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0.017... |
725 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAG6AoADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In one such plant, the intake tube in the base of the dam is below the reservoir surface. The water drops through the tube before flowing into the turbine through a nozzle. By how much does the inlet pressure differ from the hydrostatic pressure at that depth?Please directly answer the question and provide the correct ... | C | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01409912109375,
0.0079345703125,
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... |
726 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAI8AaYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Believe it or not, you can estimate the radius of the Earth without having to go into space. Suppose you climb a stepladder and discover that when your eyes are $10$ $ft$ ($3.0$ $m$) above the water, you can just see the rocks at water level on the opposite shore. From a map, you estimate the distance to the opposite s... | C | Mechanics | Geometrical Optics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.023193359375,
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0.002349853515625,
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0.00811767578125,
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727 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGKAzQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An astronomical unit ($AU$) is equal to the average distance from Earth to the Sun, about $92.9 \times 10^6$ $mi$. A parsec ($pc$) is the distance at which a length of $1$ $AU$ would subtend an angle of exactly $1''$. A light-year ($ly$) is the distance that light, traveling through a vacuum with a speed of $186000$ $m... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0257568359375,
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0.056640625,
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728 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE8AmADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows a general situation in which a stream of people attempt to escape through an exit door that turns out to be locked. The people move toward the door at speed $v_s = 3.50\ \text{m/s}$, are each $d = 0.25\ \text{m}$ in depth, and are separated by $L = 1.75\ \text{m}$. The arrangement in figure occurs at time ... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.033203125,
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0.002166748046875,
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729 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADmA9gDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An abrupt slowdown in concentrated traffic can travel as a pulse, termed a shock wave, along the line of cars, either downstream (in the traffic direction) or upstream, or it can be stationary. Figure shows a uniformly spaced line of cars moving at speed $v = 25.0\ m/s$ toward a uniformly spaced line of slow cars movin... | C | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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730 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIcBHgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | When a high-speed passenger train traveling at $161\ km/h$ rounds a bend, the engineer is shocked to see that a locomotive has improperly entered onto the track from a siding and is a distance $D = 676\ m$ ahead. The locomotive is moving at $29.0\ km/h$. The engineer of the high-speed train immediately applies the brak... | C | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0380859375,
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731 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEIA8oDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A pilot flies horizontally at $1300\ km/h$, at height $h = 35\ m$ above initially level ground. However, at time $t = 0$, the pilot begins to fly over ground sloping upward at angle $\theta = 4.3^\circ$. If the pilot does not change the airplane's heading, at what time $t$ does the plane strike the ground?Please direct... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Predictive Reasoning'] | [
0.020263671875,
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732 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIKBG4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows part of a street where traffic flow is to be controlled to allow a platoon of cars to move smoothly along the street. Suppose that the platoon leaders have just reached intersection 2, where the green appeared when they were distance $d$ from the intersection. They continue to travel at a certain speed $v_... | C | Mechanics | Kinematics | ['Multi-Formula Reasoning', 'Predictive Reasoning'] | [
0.01361083984375,
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733 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFmAfwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a heavy piece of machinery is raised by sliding it a distance $d = 12.5\ m$ along a plank oriented at angle $\theta = 20.0^\circ$ to the horizontal. How far is it moved vertically?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 2.42 m B: 3.81 m C: ... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning'] | [
0.0201416015625,
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734 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAK8Az4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Typical backyard ants often create a network of chemical trails for guidance. Extending outward from the nest, a trail branches (bifurcates) repeatedly, with $60^\circ$ between the branches. If a roaming ant chances upon a trail, it can tell the way to the nest at any branch point: If it is moving away from the nest, i... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.021484375,
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735 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHGAugDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Rock faults are ruptures along which opposite faces of rock have slid past each other. In figure, points $A$ and $B$ coincided before the rock in the foreground slid down to the right. The net displacement $\vec{AB}$ is along the plane of the fault. The horizontal component of $\vec{AB}$ is the strike-slip $AC$. The co... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.0244140625,
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736 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIGAuADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A wheel with a radius of $45.0\ cm$ rolls without slipping along a horizontal floor. What is the angle (relative to the floor) of the displacement of $P$?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: $25.5^\circ$ B: $27.5^\circ$ C: $32.5^\circ$ D: $34.5^\ci... | C | Mechanics | Rotational Motion | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
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737 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAI2AhYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure gives the path of a squirrel moving about on level ground, from point $A$ (at time $t = 0$), to points $B$ (at $t = 5.00\ min$), $C$ (at $t = 10.0\ min$), and finally $D$ (at $t = 15.0\ min$). Consider the average velocities of the squirrel from point $A$ to each of the other three points. Of them, what is the m... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.025634765625,
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0.0150146484375,
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738 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAJuAnoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A certain airplane has a speed of $290.0\ km/h$ and is diving at an angle of $\theta = 30.0^\circ$ below the horizontal when the pilot releases a radar decoy. The horizontal distance between the release point and the point where the decoy strikes the ground is $d = 700\ m$. How high was the release point?Please directl... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0299072265625,
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... |
739 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHgBOoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a stone is projected at a cliff with an initial speed of $42.0\ m/s$ directed at angle $\theta_0 = 60.0^\circ$ above the horizontal. The stone strikes at $A$, $5.50\ s$ after launching. Find the maximum height $H$ reached above the ground.Please directly answer the question and provide the correct OPTION LET... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
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0.005157470703125,
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740 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAG2ArADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | You throw a ball toward a wall at speed $25.0\ m/s$ and at angle $\theta_0 = 40.0^\circ$ above the horizontal. The wall is distance $d = 22.0\ m$ from the release point of the ball. How far above the release point does the ball hit the wall?Please directly answer the question and provide the correct OPTION LETTER ONLY,... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
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741 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGUAxgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a ball is thrown leftward from the left edge of the roof. The ball hits the ground $1.50\ s$ later, at distance $d = 25.0\ m$ from the building and at angle $\theta = 60.0^\circ$ with the horizontal. What is the angle relative to the horizontal of the velocity at which the ball is thrown?Please directly answ... | C | Mechanics | Kinematics | ['Multi-Formula Reasoning', 'Spatial Relation Reasoning'] | [
0.00836181640625,
0.01141357421875,
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0.001129150390625,
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742 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIyAoADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Upon spotting an insect on a twig overhanging water, an archer fish squirts water drops at the insect to knock it into the water. Although the fish sees the insect along a straight-line path, a drop must be launched at a different angle $\theta_0$ if its parabolic path is to intersect the insect. If $\phi = 36.0^\circ$... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0137939453125,
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743 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHmA8QDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In 1939 or 1940, Emanuel Zacchini took his humancannonball act to an extreme: After being shot from a cannon, he soared over three Ferris wheels and into a net. Assume that he is launched with a speed of $26.5\ m/s$ and at an angle of $53.0^\circ$. How far from the cannon should the net's center have been positioned (n... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.049072265625,
0.00946044921875,
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0.010498046875,
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744 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEcAowDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a ball is launched with a velocity of magnitude $10.0\ m/s$, at an angle of $50.0^\circ$ to the horizontal. The launch point is at the base of a ramp of horizontal length $d_1 = 6.00\ m$ and height $d_2 = 3.60\ m$. A plateau is located at the top of the ramp. When it lands, what is the angle of its displacem... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
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745 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIuApoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a ball is thrown up onto a roof, landing $4.00\ s$ later at height $h = 20.0\ m$. The ball's path just before landing is angled at $\theta = 60.0^\circ$ with the roof. What is the magnitude of the ball's initial velocity?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A,... | C | Mechanics | Kinematics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.02099609375,
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746 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADmBBgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A skilled skier knows to jump upward before reaching a downward slope. Consider a jump in which the launch speed is $v_0 = 10\ m/s$, the launch angle is $\theta_0 = 11.3^\circ$, the initial course is approximately flat, and the steeper track has a slope of $9.0^\circ$. How far below the launch level does the skier land... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.030029296875,
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-0... |
747 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGeBSQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a baseball is hit at a height $h = 1.00\ m$ and then caught at the same height. It travels alongside a wall, moving up past the top of the wall $1.00\ s$ after it is hit and then down past the top of the wall $4.00\ s$ later, at distance $D = 50.0\ m$ farther along the wall. How high is the wall?Please direc... | C | Mechanics | Kinematics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.01129150390625,
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... |
748 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCALqA0gDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | At the instant shown, a police car $P$ is distance $d_P = 800\ m$ from the intersection and moving at speed $v_P = 80\ km/h$. Motorist $M$ is distance $d_M = 600\ m$ from the intersection and moving at speed $v_M = 60\ km/h$. In unit-vector notation, what is the velocity of the motorist with respect to the police car?P... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.0294189453125,
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0.0218505859375,
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... |
749 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHkA/gDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a sled moves at constant speed $v_s$ while a ball of ice is shot from the sled with a velocity $\vec{v}_0 = v_{0x}\hat{i} + v_{0y}\hat{j}$ relative to the sled. When the ball lands, its horizontal displacement $\Delta x_{bg}$ relative to the ground (from its launch position to its landing position) is measur... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.02734375,
0.00604248046875,
-0.0103759765625,
0.0172119140625,
-0.0089111328125,
0.0133056640625,
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0.00445556640625,
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750 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGGA7gDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A radar station detects an airplane approaching. At first observation, the airplane is at distance $d_1 = 360\ m$ from the station and at angle $\theta_1 = 40^\circ$ above the horizon. The airplane is tracked through an angular change $\Delta\theta = 123^\circ$ in the vertical east$-$west plane; its distance is then $d... | C | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0302734375,
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0.042236328125,
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0.017578125,
0.0218505859375,
-0.0... |
751 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHoAlADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The horizontal distances are $d_1 = 1.0\ ft$ and $d_2 = 14\ ft$, and the heights are $h_1 = 7.0\ ft$ and $h_2 = 10\ ft$. At what initial speed must the basketball player in figure throw the ball, at angle $\theta_0 = 55^\circ$ above the horizontal, to make the foul shot?Please directly answer the question and provide t... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.010986328125,
0.004058837890625,
0.0022125244140625,
0.0019989013671875,
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0.00726318359375,
... |
752 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGaA8YDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | During volcanic eruptions, chunks of solid rock can be blasted out of the volcano; these projectiles are called volcanic bombs. Figure shows a cross section of Mt. Fuji, in Japan. At what initial speed would a bomb have to be ejected, at angle $\theta_0 = 35^\circ$ to the horizontal, from the vent at $A$ in order to fa... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00092315673828125,
0.0091552734375,
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0.03271484375,
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0.0150146484375,
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0.0233154296875,
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0.006500244140625,
0.0220947265625,
0.0033416748046875,
-0.04345... |
753 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGOAlgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a lump of wet putty moves in uniform circular motion as it rides at a radius of $20.0\ cm$ on the rim of a wheel rotating counterclockwise with a period of $5.00\ ms$. The lump then happens to fly off the rim at the 5 o'clock position (as if on a clock face). It leaves the rim at a height of $h = 1.20\ m$ fr... | C | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0322265625,
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0.003814697265625,
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0.030517578125,
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0.005340576171875,
-0.02502441... |
754 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE6AjIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a ball is shot with an initial speed of $v_0 = 7.00\ m/s$. Simultaneously, a construction elevator cab begins to move with a constant speed of $v_c = 3.00\ m/s$. At what rate does the speed of the ball change relative to the cab floor?Please directly answer the question and provide the correct OPTION LETTER ... | C | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.04541015625,
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0.00543212890625,
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0.0050048828125,
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0.01080322265625,
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0.0113525390625,
0.041748046875,
0.002105712890... |
755 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAISAkIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Astronauts, propelled by jet backpacks, push and guide a $120\ kg$ asteroid toward a processing dock, exerting the forces shown in figure, with $F_1 = 32\ N$, $F_2 = 55\ N$, $F_3 = 41\ N$, $\theta_1 = 30^\circ$, and $\theta_3 = 60^\circ$. What is the asteroid's acceleration as a magnitude relative to the positive direc... | C | Mechanics | Dynamics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.021240234375,
0.017822265625,
-0.0245361328125,
0.006195068359375,
-0.006500244140625,
0.010986328125,
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0.010009765625,
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0.00677490234375,
0.03369140625,
0.00360107421875,
-0.02526855468... |
756 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCALGAlYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of figure. The tire remains stationary in spite of the three pulls. Alex pulls with force $\vec{F}_A$ of magnitude $220\ N$, and Charles pulls with force $\vec{F}_C$ of magnitude $1... | C | Mechanics | Statics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.001617431640625,
0.011474609375,
0.0186767578125,
-0.00640869140625,
-0.02001953125,
0.017578125,
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0.005157470703125,
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0.004913330078125,
0.00124359130859375,
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0.0103759765625,
0.00430297851562... |
757 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAK4AYYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Figure shows an arrangement in which four disks are suspended by cords. The longer, top cord loops over a frictionless pulley and pulls with a force of magnitude $98\ N$ on the wall to which it is attached. The tensions in the three shorter cords are $T_1 = 58.8\ N$, $T_2 = 49.0\ N$, and $T_3 = 9.8\ N$. What is the mas... | C | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.022705078125,
0.004608154296875,
-0.00494384765625,
0.0035552978515625,
-0.010009765625,
0.028076171875,
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0.01409912109375,
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... |
758 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGEApQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Some insects can walk below a thin rod (such as a twig) by hanging from it. Suppose that such an insect has mass $m$ and hangs from a horizontal rod as shown in figure, with angle $\theta = 40^\circ$. Its legs are all under the same tension, and the leg sections nearest the body are horizontal. What is the ratio of the... | C | Mechanics | Statics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.01806640625,
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-0.00494384765625,
-0.00927734375,
0.01336669921875,
0.01495361328125,
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0.00848388671875,
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0.0167236328125,
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0.006622314453125,
-0.005859375,
-0.0227... |
759 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGkAnADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a crate of mass $m = 100\ kg$ is pushed at constant speed up a frictionless ramp ($\theta = 30.0^\circ$) by a horizontal force $\vec{F}$. What is the magnitude of the force on the crate from the ramp?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: ... | C | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.0186767578125,
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0.00958251953125,
0.0128173828125,
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0.02734375,
-0.0258789... |
760 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE0BLgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In earlier days, horses pulled barges down canals in the manner shown in figure. Suppose the horse pulls on the rope with a force of $7900\ N$ at an angle of $\theta = 18^\circ$ to the direction of motion of the barge, which is headed straight along the positive direction of an $x$ axis. The mass of the barge is $9500\... | C | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
-0.01953125,
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761 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCALKATgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, a chain consisting of links, each of mass $0.100\ kg$, is lifted with constant acceleration of magnitude $a = 2.50\ m/s^2$. Find the magnitude of the force on link 4 from link 5.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 3.38 N B: 3.69 N C: 4.... | C | Mechanics | Dynamics | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.02294921875,
0.0067138671875,
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762 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAKcAQoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In figure, elevator cabs are connected by a short cable and can be pulled upward or lowered by the cable above cab $A$. Cab $A$ has mass $1700\ kg$; cab $B$ has mass $1300\ kg$. A $12.0\ kg$ box of catnip lies on the floor of cab $A$. The tension in the cable connecting the cabs is $1.91 \times 10^4\ N$. What is the ma... | C | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.03369140625,
0.007537841796875,
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0.0108642578125,
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0.01513671875,
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763 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAB/Ab4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A block is attached to a very light horizontal spring of force constant 500.0 N/m and is resting on a frictionless horizontal table as shown in figure. Suddenly it is struck by a stone traveling horizontally to the right, whereupon the stone rebounds at 2.00 m/s horizontally to the left. Find the maximum distance that ... | B | Mechanics | Momentum and Collisions | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0277099609375,
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0.0177001953125,
0.0230712890625,
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0.010498046875,
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0.04248046875,
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0.01251220703125,
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764 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACHAi0DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A chunk of ice is sliding on the floor of an ice-covered valley when it collides with and sticks to another chunk of ice that is initially at rest as shown in figure. Since the valley is icy, there is no friction. After the collision, how high above the valley floor will the combined chunks go?Please directly answer th... | B | Mechanics | Momentum and Collisions | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.04736328125,
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0.016357421875,
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0.004974365234375,
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0.03857421875,
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765 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFYAOUDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A 0.150 kg frame, when suspended from a coil spring, stretches the spring 0.0400 m. A 0.200 kg lump of putty is dropped from rest onto the frame as shown in figure. Find the maximum distance the frame moves downward from its initial equilibrium position.Please directly answer the question and provide the correct OPTION... | B | Mechanics | Dynamics | ['Multi-Formula Reasoning', 'Predictive Reasoning'] | [
0.0189208984375,
-0.0137939453125,
0.007232666015625,
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0.00154876708984375,
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766 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEjATcDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A movie stuntman stands on a window ledge above the floor as shown in figure. Grabbing a rope attached to a chandelier, he swings down to grapple with the movie's villain, who is standing directly under the chandelier. (Assume that the stuntman's center of mass moves downward 5.0 m. He releases the rope just as he reac... | B | Mechanics | Work and Energy | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.0274658203125,
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-0.002105712890625,
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0.001556396484375,
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0.0169677734375,
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0.0010833740234375,
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0.0341796875,
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0.024658203125,
0.0033416748046875... |
767 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACiARwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two identical masses are released from rest in a smooth bowl from the positions shown in figure. Ignore friction between the masses and the surface of the bowl. If the masses stick together when they collide, how high above the bottom of the bowl will they go after colliding?Please directly answer the question and prov... | B | Mechanics | Momentum and Collisions | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.02197265625,
0.000522613525390625,
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0.006011962890625,
0.003936767578125,
0.0208740234375,
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0.015625,
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0.01361083984375,
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0.01019287109375,
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768 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEfAVADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | In a shipping company distribution center, an open cart of mass 50.0 kg is rolling to the left at a speed of 5.00 m/s as shown in figure. Ignore friction between the cart and the floor. A 15.0 kg package slides down a chute and leaves the end of the chute with a speed of 3.00 m/s. The package lands in the cart and they... | B | Mechanics | Momentum and Collisions | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.024169921875,
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0.015380859375,
0.0198974609375,
0.007354736328125,
0.01611328125,
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0.00848388671875,
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0.038818359375,
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0.0017242431640625,
0.04248046875,
0.028564453125,
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769 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD2Aj0DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A 45.0 kg woman stands up in a 60.0 kg canoe 5.00 m long. She walks from a point from one end to a point from the other end as shown in figure. If you ignore resistance to motion of the canoe in the water, how far does the canoe move during this process?Please directly answer the question and provide the correct OPTION... | B | Mechanics | Momentum and Collisions | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.036376953125,
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0.00148773193359375,
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0.0152587890625,
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0.0255126953125,
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... |
770 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFUARsDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A pulley on a friction-less axle has the shape of a uniform solid disk and ra-dius 20.0 cm. A stone is attached to a very light wire that is wrapped around the rim of the pul-ley as shown in figure, and the system is released from rest. How far must the stone fall so that the pulley has 4.50 J of kinetic energy?Please... | B | Mechanics | Work and Energy | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.00811767578125,
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0.00171661376953125,
0.0033721923828125,
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0.00107574462890625,
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0.040771484375,
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0.0267333984375,
0.015136... |
771 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEPAOMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A thin, light wire is wrapped around the rim of a wheel as shown in figure. The wheel rotates without friction about a station-ary horizontal axis that passes through the cen-ter of the wheel. The wheel is a uniform disk with radius \(R = 0.280\text{ m}\). An object of mass \(m = 4.20\text{ kg}\) is suspended from the ... | B | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.03369140625,
0.0048828125,
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0.003143310546875,
0.00372314453125,
0.0224609375,
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0.0031585693359375,
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0.0017852783203125,
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0.02490234375,
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0.00433349609375,
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772 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADsAakDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A disk of radius 25.0 cm is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim as shown in figure. The pull increases in magnitude and produces an acceleration of the ball that obeys the equa-tion \(a(t) = At\), where \(t\) is in seconds and \(A\... | B | Mechanics | Rotational Motion | ['Multi-Formula Reasoning', 'Numerical Reasoning'] | [
0.010986328125,
0.01263427734375,
0.004638671875,
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0.01953125,
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0.022705078125,
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0.03173828125,
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0.00482177734375,
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0.01025390625,
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0.03173... |
773 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFrAQsDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Engineers are designing a sys-tem by which a falling imparts kinetic energy to a rotating uniform drum to which it is attached by thin, very light wire wrapped around the rim of the drum as shown in figure. There is no appreciable friction in the axle of the drum, and everything starts from rest. This system is being t... | B | Mechanics | Rotational Motion | ['Multi-Formula Reasoning', 'Predictive Reasoning'] | [
0.032958984375,
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0.000728607177734375,
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0.016845703125,
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0.0091552734375,
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0.029052734375,
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0.0034942626953125,
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... |
774 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFOAVMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The pulley in figure has radius \(0.160\text{ m}\) and moment of inertia \(0.380\text{ kg}\cdot\text{m}^2\). The rope does not slip on the pulley rim. calculate the speed of the \(4.00\text{ kg}\) block just before it strikes the floor.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g.... | B | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01416015625,
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0.0098876953125,
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0.0284423828125,
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0.01470947265625,
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0.00072479248046875,
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0.0198974609375,
0.0159912109375,
... |
775 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAF9AMkDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Two metal disks, one with radius \(R_1 = 2.50\text{ cm}\) and mass \(M_1 =0.80\text{ kg}\) and the other with radius \(R_2 = 5.00\text{ cm}\) and mass \(M_2 = 1.60\text{ kg}\), are welded together and mounted on a frictionless axis through their common center as shown in figure. A light string is wrapped around the edg... | B | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.020263671875,
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0.000774383544921875,
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776 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAE3ARsDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The cone has mass \(M\). Calculate the moment of inertia of a uniform solid cone about an axis through its center as shown in figure.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \(\frac{3}{8} MR^2\) B: \(\frac{3}{10} MR^2\) C: \(\frac{7}{10} MR^2\) D: \(\f... | B | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Numerical Reasoning'] | [
0.032470703125,
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0.01324462890625,
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777 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEvAOQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A square metal plate is pivoted about an axis through point \(O\) at its center and perpendicular to the plate as shown in figure. Calculate the net torque about this axis due to the three forces shown in the figure if the magnitudes of the forces are \(F_1 = 18.0\text{ N}\), \(F_2 = 26.0\text{ N}\), and \(F_3 = 14.0\t... | B | Mechanics | Rotational Motion | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.02490234375,
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778 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADHAPEDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A box resting on a horizontal, frictionless surface is attached to a weight by a thin, light wire that passes over a frictionless pulley as shown in figure. The pulley has the shape of a uniform solid disk of mass \(2.00\text{ kg}\) and diameter \(0.500\text{ m}\). After the system is released. Find the acceleration of... | B | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.02734375,
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0.00152587890625,
0.0107421875,
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0.01220703125,
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... |
779 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAD7AQQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A string is wrapped several times around the rim of a small hoop and mass \(0.180\text{ kg}\). The free end of the string is held in place and the hoop is released from rest as shown in figure. After the hoop has descended \(75.0\text{ cm}\). calculate the speed of its center.Please directly answer the question and pr... | B | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.02001953125,
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0.00921630859375,
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0.00653076171875,
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... |
780 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFLAScDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A thin, light string is wrapped around the outer rim of a uniform hollow cylinder of mass \(4.75\text{ kg}\) having inner and outer radii as shown in figure. The cylinder is then released from rest. How far must the cylinder fall before its center is moving at \(6.66\text{ m/s}\)?Please directly answer the question and... | B | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.023681640625,
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0.01953125,
0.0037841796875,
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0.03076171875,
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-0.04296875... |
781 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAFtAecDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A grindstone is a solid disk \(0.520\text{ m}\) in diameter. You press an ax down on the rim with a normal force as shown in figure. The coefficient of kinetic friction between the blade and the stone is \(0.60\), and there is a constant friction torque of \(6.50\text{ N}\cdot\text{m}\) between the axle of the stone an... | B | Mechanics | Rotational Motion | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.018798828125,
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0.01312255859375,
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0... |
782 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCABfASYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A thin, uniform, \(3.80\text{ kg}\) bar, \(80.0\text{ cm}\) long, has very small balls glued on at either end as shown in figure, It is supported horizontally by a thin, horizontal, frictionless axle passing through its center and perpendicular to the bar. Suddenly the right-hand ball becomes detached and falls off, bu... | B | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.020263671875,
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-0.03100... |
783 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGKANMDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | figure illustrates an Atwood's machine. if there is no slipping between the cord and the surface of the wheel. Let the masses of blocks \(A\) and \(B\) be \(4.00\text{ kg}\) and \(2.00\text{ kg}\), respectively, the moment of inertia of the wheel about its axis be \(0.220\text{ kg}\cdot\text{m}^2\), and the radius of t... | B | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0296630859375,
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0.006561279296875,
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-... |
784 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADEASgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The mechanism shown in figure is used to raise a crate of supplies from a ship's hold. The crate has total mass \(50\text{ kg}\). A rope is wrapped around a wooden cylinder that turns on a metal axle. The cylinder has radius \(0.25\text{ m}\) and moment of inertia \(I = 2.9\text{ kg}\cdot\text{m}^2\) about the axle. Th... | B | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0101318359375,
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0.00836181640625,
0.0023040771484375,
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0.0045166015625,
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0.0037384033203125,
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0.01263427734375,
0.0068359375,
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0.01080322265625,
0.01538085... |
785 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADTAPIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A block slides down a surface to the horizontal as shown in figure. The coefficient of kinetic friction is \(0.25\). A string attached to the block is wrapped around a flywheel on a fixed axis at \(O\). The flywheel has mass \(25.0\text{ kg}\) and moment of inertia \(0.500\text{ kg}\cdot\text{m}^2\) with respect to the... | B | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0205078125,
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0.00836181640625,
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0.01495361328125,
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0.00640869140625,
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0.0240478515625,
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0.00885009765625,
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786 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADFATsDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A thin-walled, hollow spherical shell of mass \(m\) and radius \(r\) starts from rest and rolls without slipping down a track as shown in figure. Points \(A\) and \(B\) are on a circular part of the track, and the work done by rolling friction is negligible. How hard does the track push on the shell at point \(B\), whi... | B | Mechanics | Rotational Motion | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.014404296875,
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0.00927734375,
0.0026702880859375,
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0.0242919921875,
0.00775146484375,
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0.01422119140625,
0.01300048828125,... |
787 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADAAjYDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A basketball (which can be closely modeled as a hollow spherical shell) rolls down a mountainside into a valley and then up the opposite side, starting from rest above the bottom. In figure, the rough part of the terrain prevents slipping while the smooth part has no friction. Neglect rolling friction and assume the sy... | B | Mechanics | Work and Energy | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0230712890625,
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-0.0361328125,
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0.00634765625,
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0.0003032684326171875,
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0.0234375,
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0.003265380859375,
0.006011962890625,
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788 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCACQAQ8DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A solid uniform ball rolls without slipping up a hill as shown in figure. At the top of the hill, it is moving horizontally, and then it goes over the vertical cliff. Neglect rolling friction and assume the system’s total mechanical energy is conserved. How fast is it moving just before it lands?Please directly answer ... | B | Mechanics | Work and Energy | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.01434326171875,
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0.0135498046875,
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0.017333984375,
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0.025146484375,
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0.030517578125,
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0.00396728515625,
0.0281982421875,
0.0286865234375,
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789 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADaARoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A solid, uniform, spherical boulder starts from rest and rolls down a hill, as shown in as shown in figure. The top half of the hill is rough enough to cause the boulder to roll without slipping, but the lower half is covered with ice and there is no friction. What is the translational speed of the boulder when it reac... | B | Mechanics | Work and Energy | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0198974609375,
0.00160980224609375,
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0.000926971435546875,
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0.0186767578125,
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0.00244140625,
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0.0303955078125,
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0.000919342041015625,
0.0341796875,
0.0191650390625,... |
790 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADqAQQDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A 500.0 g bird is flying horizontally at 2.25 m/s, not paying much attention, when it suddenly flies into a stationary vertical bar as shown in figure. The bar is uniform, 0.750 m long, has a mass of 1.50 kg, and is hinged at its base. What is the angular velocity of the bar just as it reaches the ground?Please directl... | B | Mechanics | Rotational Motion | ['Multi-Formula Reasoning', 'Physical Model Grounding Reasoning'] | [
0.025634765625,
-0.00537109375,
-0.01507568359375,
0.0042724609375,
0.0150146484375,
0.017822265625,
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-0.035888671875,
0.028076171875,
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0.03173828125,
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... |
791 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGoAy4DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | The magnitudes of the vectors are \( A = 4.00 \) and \( B = 5.00 \). Find the scalar product \( \vec{A} \cdot \vec{B} \) of the two vectors in figure.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 2.40 B: 4.50 C: 8.30 D: 7.20 | B | Mechanics | Dynamics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.02734375,
0.0023193359375,
0.000640869140625,
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-0.0203857421875,
0.00830078125,
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0.0032806396484375,
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0.0306396484375,
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0.01495361328125,
0.0089111328125,
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792 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAGsAlwDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | Vector \( \vec{A} \) has magnitude 6 units and is in the direction of the \( +x \)-axis. Vector \( \vec{B} \) has magnitude 4 units and lies in the xy-plane. Find the vector product \( \vec{C} = \vec{A} \times \vec{B} \).Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. O... | B | Mechanics | Dynamics | ['Spatial Relation Reasoning', 'Physical Model Grounding Reasoning'] | [
0.03857421875,
0.00994873046875,
-0.018310546875,
0.00762939453125,
-0.01251220703125,
0.007293701171875,
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0.008056640625,
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0.002044677734375,
0.000827789306640625,
0.0257568359375,
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0.003204345703125,
0.018798828125,
0.00762939453125,
... |
793 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEqA2ADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A motorcyclist heading east through a small town accelerates after he leaves the city limits as shown in figure. Where is he when his speed is \( 25 \, \text{m/s} \)?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: 27m B: 55m C: 45m D: 65m | B | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.033203125,
0.0184326171875,
0.00299072265625,
-0.0018463134765625,
-0.00701904296875,
-0.00131988525390625,
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0.01806640625,
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0.01171875,
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0.02880859375,
-0.00811767578125,
-0.00787353515625,
-0.003173828125,
-0.01226806640625,
-0.0... |
794 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCADoBLgDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A motorist traveling at a constant speed passes a school crossing where the speed limit is \( 10 \, \text{m/s} \) (\( 36 \, \text{km/h} \), or about \( 22 \, \text{mi/h} \)). Just as the motorist passes the school-crossing sign, a police officer on a motorcycle stopped there starts in pursuit with constant acceleration... | B | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.02685546875,
-0.007080078125,
0.00135040283203125,
-0.00119781494140625,
-0.00396728515625,
0.0194091796875,
-0.014892578125,
0.006561279296875,
-0.0089111328125,
0.0174560546875,
-0.0186767578125,
0.006378173828125,
-0.023681640625,
0.0068359375,
-0.00225830078125,
-0.00049209594726... |
795 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAMqA0QDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A one-euro coin is dropped from the Leaning Tower of Pisa and falls freely from rest. What are its position after \( 3.0 \, \text{s} \)? Ignore air resistance.Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: -35m B: -44m C: -65m D: -51m | B | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Predictive Reasoning'] | [
0.034912109375,
0.012939453125,
-0.0003299713134765625,
0.00141143798828125,
-0.0011138916015625,
-0.002960205078125,
-0.02880859375,
0.01239013671875,
-0.02294921875,
0.01141357421875,
0.00885009765625,
0.013916015625,
-0.004913330078125,
-0.005340576171875,
0.01385498046875,
-0.00010... |
796 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAHMA1YDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | a projectile launched as shown in figure. For a given \( v_0 \), what value gives maximum horizontal range?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 30^{\circ} \) B: \( 45^{\circ} \) C: \( 60^{\circ} \) D: \( 90^{\circ} \) | B | Mechanics | Kinematics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.0181884765625,
0.0087890625,
-0.00323486328125,
-0.0005035400390625,
-0.01470947265625,
0.019287109375,
-0.033447265625,
-0.01153564453125,
-0.02392578125,
0.0140380859375,
-0.017578125,
0.03369140625,
-0.01043701171875,
-0.0002498626708984375,
0.0218505859375,
-0.015625,
0.0088500... |
797 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAK+AZIDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | An airplane's compass indicates that it is headed due north as shown in figure. If there is a wind from west to east. what is the velocity of the airplane relative to the earth?Please directly answer the question and provide the correct OPTION LETTER ONLY, e.g., A, B, C, D. OPTION: A: \( 160 \, \text{km/h} \) B: \( 26... | B | Mechanics | Kinematics | ['Spatial Relation Reasoning', 'Multi-Formula Reasoning'] | [
0.01171875,
-0.0125732421875,
0.00093841552734375,
0.00860595703125,
-0.005157470703125,
0.0263671875,
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0.012939453125,
-0.0162353515625,
0.0118408203125,
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0.0140380859375,
-0.0087890625,
-0.008544921875,
0.007080078125,
0.015869140625,
-0.0336914062... |
798 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEcAhADASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A waitress shoves a ketchup bottle with mass to her right along a smooth, level lunch counter as shown in figure. The bottle leaves her hand then slows down as it slides because of a constant horizontal friction force exerted on it by the countertop. What are the magnitude of the friction force acting on the bottle?Ple... | B | Mechanics | Dynamics | ['Physical Model Grounding Reasoning', 'Multi-Formula Reasoning'] | [
0.020263671875,
0.007110595703125,
-0.034912109375,
0.0279541015625,
-0.00732421875,
0.00078582763671875,
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-0.0458984375,
-0.00665283203125,
-0.0245361328125,
0.0238037109375,
0.000408172607421875,
-0.0213623046875,
0.0130615234375,
-0.002639770507812... |
799 | /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAEiAcoDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIh... | A car of rests on a slanted ramp attached to a trailer as shown in figure. Only a cable running from the trailer to the car prevents the car from rolling off the ramp. (The car's brakes are off and its transmission is in neutral.) Find the force that the ramp exerts on the car's tires.Please directly answer the questio... | B | Mechanics | Statics | ['Physical Model Grounding Reasoning', 'Spatial Relation Reasoning'] | [
0.00274658203125,
0.006988525390625,
-0.00628662109375,
-0.005279541015625,
-0.014404296875,
0.001708984375,
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-0.0205078125,
-0.026123046875,
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0.0294189453125,
0.01080322265625,
-0.005218505859375,
0.005767822265625,
-0.0069580078125... |
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