scene_type large_stringclasses 10
values | data_source large_stringclasses 1
value | prompt listlengths 1 1 | ability large_stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|---|
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown vertically upward. The ball is launched from an initial height of 1.06 m from the ground and it has an initial speed of 2.49 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball an... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 565,
"json_index": null,
"split": "test"
} |
BasicCollision | math_p_numeric | [
{
"content": "In a system called 'twodcollisionplane_0', a smooth table (XY plane) has 3 spheres on it with the following properties (position and velocity are relative to the table): | Sphere | Mass (kg) | Initial Position (m) | Initial Velocity (m/s) | Radius (m) | |----------|-------------|------------------... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 567,
"json_index": null,
"split": "test"
} |
DifficultSpringMass | math_p_numeric | [
{
"content": "In a SpringMass system, 2 blocks are placed at -1.33 and 1.3 m on the table. They have masses 2.56 and 2.07 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 188.05 N/m respectively. The natural length of these springs ar... | math | {
"ground_truth": "3.621253563653946e-11",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 568,
"json_index": null,
"split": "test"
} |
BasicInclinedPlaneFriction | math_p_numeric | [
{
"content": "In a system called 'twosidemassplane_0', a block of mass 1.0 kg rests on a plane inclined at an angle of 0 degrees. A string connected to the left side of the block in 'twosidemassplane_0' runs parallel to the plane to wrap around a pulley on the left side of the plane, and extends outward to conn... | math | {
"ground_truth": "1.8933504419665432",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 569,
"json_index": null,
"split": "test"
} |
BasicInclinedPlaneFriction | math_p_numeric | [
{
"content": "In a system called 'twosidemassplane_0', a block of mass 1.0 kg rests on a plane inclined at an angle of 0 degrees. A string connected to the left side of the block in 'twosidemassplane_0' runs parallel to the plane to wrap around a pulley on the left side of the plane, and extends outward to conn... | math | {
"ground_truth": "6.867000000027773",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 570,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_0', a block of mass 1.5 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_0' extends outward to connect to the block in 'masswithfixedpulley_1'... | math | {
"ground_truth": "8.55909223069305",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 571,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_0', a block of mass 0.7 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_0' extends outward to connect to the block in 'masswithfixedpulley_1'... | math | {
"ground_truth": "9.142235979590899",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 572,
"json_index": null,
"split": "test"
} |
DifficultOrbitalMotion | math_p_numeric | [
{
"content": "In a planetary system, a star with mass 3.34 M and radius 0.88 R is at the center. 1 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------... | math | {
"ground_truth": "-0.024240593701219462",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 573,
"json_index": null,
"split": "test"
} |
DifficultElectroMagnetic | math_p_numeric | [
{
"content": "A charged particle with charge 2.23 C and mass 1.08 kg is initially launched from origin in the space. It has an initial velocity of 0.92 m/s in the x-direction and -1.32 m/s in the y-direction. There is a uniform magnetic field of strength 0.17 along the +Z axis. The field is effective in a recta... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 574,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown vertically downward. The ball is launched from an initial height of 1.17 m from the ground and it has an initial speed of 2.31 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball ... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 575,
"json_index": null,
"split": "test"
} |
BasicCollision | math_p_numeric | [
{
"content": "A smooth table is inclined at an angle 2.93 degrees with the horizontal. There are multiple systems on this table. A spring (initially relaxed) fixed on its right end, extends to the left to -4.04 m on the table. It has a stiffness of 69.11 N/m, and a natural length of 0.12 m. A block of mass 1.0 ... | math | {
"ground_truth": "1.6267233207419383",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 576,
"json_index": null,
"split": "test"
} |
DifficultSpringMass | math_p_numeric | [
{
"content": "In a SpringMass system, 3 blocks are placed at -1.54, 0.48 and 1.42 m on the table. They have masses 1.61, 2.95 and 1.7 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 160.72 and 56.45 N/m respectively. The natural leng... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 578,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown horizontaly. The ball is launched from an initial height of 1.67 m from the ground and it has an initial speed of 1.77 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball and the ... | math | {
"ground_truth": "2.2566385547503027",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 579,
"json_index": null,
"split": "test"
} |
DifficultElectroMagnetic | math_p_numeric | [
{
"content": "A charged particle with charge -2.39 C and mass 1.25 kg is initially launched from origin in the space. It has an initial velocity of 0.58 m/s in the x-direction and 0.17 m/s in the y-direction. There is a uniform magnetic field of strength 1.0 along the +Z axis. The field is effective in an annul... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 580,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A bar called 'bar_0' has a mass of 2.28 kg. It has a length of 0.7, width of 0.13, and height... | math | {
"ground_truth": "5.0497114925363755",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 581,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown vertically upward. The ball is launched from an initial height of 1.08 m from the ground and it has an initial speed of 2.91 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball an... | math | {
"ground_truth": "1.2313101720105903",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 582,
"json_index": null,
"split": "test"
} |
DifficultOrbitalMotion | math_p_numeric | [
{
"content": "In a planetary system, a star with mass 3.34 M and radius 0.88 R is at the center. 1 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------... | math | {
"ground_truth": "4.189870954170266",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 583,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown vertically upward. The ball is launched from an initial height of 1.33 m from the ground and it has an initial speed of 1.89 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball an... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 584,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A cylinder called 'cylinder_0' has a mass of 1.63 kg. It has a radius of 0.19 and a height of... | math | {
"ground_truth": "5.204267866746365",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 585,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 2 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A cylinder called 'cylinder_1' has a mass of 3.94 kg. It has a radius of 0.23 and a height of... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 586,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithreversedmovablepulley_1', a movable pulley of mass 1.37 kg supports two blocks of masses 1.94 kg and 6.05 kg hanging on its left and right sides respectively, pulling the pulley down. The string that connects the movable pulley in 'masswithreversedmovablepulley_1' to an... | math | {
"ground_truth": "1.7428272134789258",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 587,
"json_index": null,
"split": "test"
} |
DifficultOrbitalMotion | math_p_numeric | [
{
"content": "In a planetary system, a star with mass 3.34 M and radius 0.91 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------... | math | {
"ground_truth": "4.136791110071576",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 588,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_1', a block of mass 2.0 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_1' extends outward to wrap around the movable pulley in 'masswithmova... | math | {
"ground_truth": "6.554322800929026",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 589,
"json_index": null,
"split": "test"
} |
DifficultSpringMass | math_p_numeric | [
{
"content": "In a SpringMass system, 2 blocks are placed at -1.33 and 1.3 m on the table. They have masses 2.56 and 2.07 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 188.05 N/m respectively. The natural length of these springs ar... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 591,
"json_index": null,
"split": "test"
} |
BasicCollision | math_p_numeric | [
{
"content": "In a system called 'twodcollisionplane_0', a smooth table (XY plane) has 2 spheres on it with the following properties (position and velocity are relative to the table): | Sphere | Mass (kg) | Initial Position (m) | Initial Velocity (m/s) | Radius (m) | |----------|-------------|------------------... | math | {
"ground_truth": "1.0566651879217954",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 593,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown horizontaly. The ball is launched from an initial height of 1.13 m from the ground and it has an initial speed of 2.92 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball and the ... | math | {
"ground_truth": "2.995555399275406",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 594,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_1', a block of mass 2.0 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_1' extends outward to wrap around the movable pulley in 'masswithmova... | math | {
"ground_truth": "6.586826735277706",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 595,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown vertically downward. The ball is launched from an initial height of 1.09 m from the ground and it has an initial speed of 1.13 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball ... | math | {
"ground_truth": "1.8884422769269373",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 596,
"json_index": null,
"split": "test"
} |
DifficultElectroMagnetic | math_p_numeric | [
{
"content": "A charged particle with charge 2.23 C and mass 1.08 kg is initially launched from origin in the space. It has an initial velocity of 0.92 m/s in the x-direction and -1.32 m/s in the y-direction. There is a uniform magnetic field of strength 0.17 along the +Z axis. The field is effective in a recta... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 597,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithreversedmovablepulley_0', a movable pulley of mass 0.6 kg supports two blocks of masses 5.67 kg and 8.28 kg hanging on its left and right sides respectively, pulling the pulley down. The string that connects the movable pulley in 'masswithreversedmovablepulley_0' to an ... | math | {
"ground_truth": "9.09444784773415",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 598,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A bar called 'bar_0' has a mass of 2.66 kg. It has a length of 0.73, width of 0.1, and height... | math | {
"ground_truth": "4.4286073103899355",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 599,
"json_index": null,
"split": "test"
} |
Rotation | math_p_numeric | [
{
"content": "A pendulum with a rope length of 1.55 m is attached to a fixed point in the ceiling on one end and a bob of mass 6.98 kg on the other end. The bob has an initial velocity of (0.79, -0.73) m/s in the horizontal plane, and the rope initially makes an angle of 15.66 degrees with the vertical. What is... | math | {
"ground_truth": "2.6440668797749693",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 600,
"json_index": null,
"split": "test"
} |
DifficultSpringMass | math_p_numeric | [
{
"content": "In a SpringMass system, 4 blocks are placed at -0.96, -0.0, 0.32 and 1.59 m on the table. They have masses 1.22, 1.93, 1.33 and 2.7 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 56.0, 187.73 and 194.17 N/m respectivel... | math | {
"ground_truth": "5.960462102345492e-11",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 602,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown vertically downward. The ball is launched from an initial height of 1.09 m from the ground and it has an initial speed of 1.13 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball ... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 603,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A bar called 'bar_0' has a mass of 2.28 kg. It has a length of 0.7, width of 0.13, and height... | math | {
"ground_truth": "6.407023068522799",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 604,
"json_index": null,
"split": "test"
} |
DifficultElectroMagnetic | math_p_numeric | [
{
"content": "A charged particle with charge -1.99 C and mass 1.08 kg is initially launched from origin in the space. It has an initial velocity of -0.52 m/s in the x-direction and -0.66 m/s in the y-direction. There is a uniform magnetic field of strength 0.83 along the +Z axis. The field is effective in an an... | math | {
"ground_truth": "1.2933977522792004",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 605,
"json_index": null,
"split": "test"
} |
Rotation | math_p_numeric | [
{
"content": "A pendulum with a rope length of 1.64 m is attached to a fixed point in the ceiling on one end and a bob of mass 5.91 kg on the other end. The bob has an initial velocity of (-0.76, -0.0) m/s in the horizontal plane, and the rope initially makes an angle of 86.23 degrees with the vertical. What is... | math | {
"ground_truth": "3.6326281887125833",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 606,
"json_index": null,
"split": "test"
} |
BasicCollision | math_p_numeric | [
{
"content": "A smooth table is inclined at an angle 34.27 degrees with the horizontal. There are multiple systems on this table. In a system called 'complexcollisionplane_0.mass-0', a block of mass 1.45 kg is placed at -7.49 m on the table. It is initially moving with a velocity of 0.92 m/s. In a system called... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 607,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A bar called 'bar_0' has a mass of 2.95 kg. It has a length of 0.82, width of 0.14, and heigh... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 608,
"json_index": null,
"split": "test"
} |
DifficultPulley | math_p_numeric | [
{
"content": "In a system called 'massprismpulleyplane_0', a large movable prism of mass 12.44 kg rests on a plane inclined at 0.0 degrees. The prism is inclined at an angle of 73.59 degrees on the left side and 67.18 degrees on the right side. Two blocks of mass 4.56 kg and 3.34 kg are resting on the left and ... | math | {
"ground_truth": "140.0608836837024",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 609,
"json_index": null,
"split": "test"
} |
DifficultSpringMass | math_p_numeric | [
{
"content": "In a SpringMass system, 4 blocks are placed at -1.02, -0.83, 0.29 and 1.62 m on the table. They have masses 0.9, 0.94, 1.73 and 2.03 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 139.82, 112.3 and 78.2 N/m respectivel... | math | {
"ground_truth": "8.689807069241954e-08",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 611,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown vertically upward. The ball is launched from an initial height of 1.89 m from the ground and it has an initial speed of 1.65 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball an... | math | {
"ground_truth": "12.2195855802973",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 612,
"json_index": null,
"split": "test"
} |
DifficultSpringMass | math_p_numeric | [
{
"content": "In a SpringMass system, 4 blocks are placed at -1.14, -0.35, 0.92 and 1.12 m on the table. They have masses 0.89, 0.68, 1.26 and 1.28 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 152.62, 144.27 and 128.4 N/m respecti... | math | {
"ground_truth": "1.0450875990943969e-05",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 613,
"json_index": null,
"split": "test"
} |
Rotation | math_p_numeric | [
{
"content": "A pendulum with a rope length of 0.79 m is attached to a fixed point in the ceiling on one end and a bob of mass 5.47 kg on the other end. The bob has an initial velocity of (0.81, -0.97) m/s in the horizontal plane, and the rope initially makes an angle of 33.65 degrees with the vertical. What is... | math | {
"ground_truth": "1.8243306321266373e-16",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 614,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_0', a block of mass 0.7 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_0' extends outward to connect to the block in 'masswithfixedpulley_1'... | math | {
"ground_truth": "3.2672364477819826",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 615,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown horizontaly. The ball is launched from an initial height of 1.13 m from the ground and it has an initial speed of 2.92 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball and the ... | math | {
"ground_truth": "6.9559513813404195",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 616,
"json_index": null,
"split": "test"
} |
BasicCollision | math_p_numeric | [
{
"content": "In a system called 'twodcollisionplane_0', a smooth table (XY plane) has 2 spheres on it with the following properties (position and velocity are relative to the table): | Sphere | Mass (kg) | Initial Position (m) | Initial Velocity (m/s) | Radius (m) | |----------|-------------|------------------... | math | {
"ground_truth": "-1.1102230246251565e-16",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 617,
"json_index": null,
"split": "test"
} |
Rotation | math_p_numeric | [
{
"content": "A pendulum with a rope length of 1.16 m is attached to a fixed point in the ceiling on one end and a bob of mass 9.86 kg on the other end. The bob has an initial velocity of (0.18, 0.1) m/s in the horizontal plane, and the rope initially makes an angle of 2.21 degrees with the vertical. What is th... | math | {
"ground_truth": "0.18852522172979608",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 618,
"json_index": null,
"split": "test"
} |
BasicInclinedPlaneFriction | math_p_numeric | [
{
"content": "In a system called 'twosidemassplane_0', a block of mass 1.0 kg rests on a plane inclined at an angle of 0 degrees. A string connected to the left side of the block in 'twosidemassplane_0' runs parallel to the plane to wrap around a pulley on the left side of the plane, and extends outward to conn... | math | {
"ground_truth": "20.742048465048622",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 620,
"json_index": null,
"split": "test"
} |
DifficultOrbitalMotion | math_p_numeric | [
{
"content": "In a planetary system, a star with mass 3.35 M and radius 0.81 R is at the center. 1 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------... | math | {
"ground_truth": "10.242300099245325",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 621,
"json_index": null,
"split": "test"
} |
BasicCollision | math_p_numeric | [
{
"content": "A smooth table is inclined at an angle 25.03 degrees with the horizontal. There are multiple systems on this table. A spring (initially relaxed) fixed on its right end, extends to the left to -5.46 m on the table. It has a stiffness of 140.78 N/m, and a natural length of 0.28 m. A block of mass 1.... | math | {
"ground_truth": "402.0180618192892",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 622,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 2 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A sphere called 'sphere_1' has a mass of 3.19 kg. It has a radius of 0.14.It is positioned at... | math | {
"ground_truth": "4.286494761004728",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 623,
"json_index": null,
"split": "test"
} |
DifficultSpringMass | math_p_numeric | [
{
"content": "In a SpringMass system, 3 blocks are placed at -1.54, 0.48 and 1.42 m on the table. They have masses 1.61, 2.95 and 1.7 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 160.72 and 56.45 N/m respectively. The natural leng... | math | {
"ground_truth": "0.001127646557514581",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 624,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A bar called 'bar_0' has a mass of 2.41 kg. It has a length of 0.76, width of 0.12, and heigh... | math | {
"ground_truth": "0.17779691596054906",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 625,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_0', a block of mass 1.5 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_0' extends outward to connect to the block in 'masswithfixedpulley_1'... | math | {
"ground_truth": "17.812894736845077",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 626,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_0', a block of mass 2.5 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_0' extends outward to connect to the block in 'masswithfixedpulley_1'... | math | {
"ground_truth": "3.9318350655516947",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 627,
"json_index": null,
"split": "test"
} |
DifficultElectroMagnetic | math_p_numeric | [
{
"content": "A charged particle with charge -2.16 C and mass 1.05 kg is initially launched from origin in the space. It has an initial velocity of 0.95 m/s in the x-direction and 0.27 m/s in the y-direction. There is a uniform electric field of strength 1.36 along the XY plane, making an angle of 244.43 degree... | math | {
"ground_truth": "1.3047023414303707e-12",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 628,
"json_index": null,
"split": "test"
} |
Rotation | math_p_numeric | [
{
"content": "A pendulum with a rope length of 0.79 m is attached to a fixed point in the ceiling on one end and a bob of mass 2.09 kg on the other end. The bob has an initial velocity of (-0.14, 0.94) m/s in the horizontal plane, and the rope initially makes an angle of 24.05 degrees with the vertical. What is... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 629,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A cylinder called 'cylinder_0' has a mass of 2.01 kg. It has a radius of 0.21 and a height of... | math | {
"ground_truth": "0.008627254669528678",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 630,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_1', a block of mass 3.2 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_1' extends outward to wrap around the movable pulley in 'masswithmova... | math | {
"ground_truth": "42.315299018659275",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 631,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A bar called 'bar_0' has a mass of 2.66 kg. It has a length of 0.73, width of 0.1, and height... | math | {
"ground_truth": "5.285603900051962",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 632,
"json_index": null,
"split": "test"
} |
BasicInclinedPlaneFriction | math_p_numeric | [
{
"content": "In a system called massprismplaneentity_0, a block of mass 1.1 kg rests on the left side a movable prism of mass 1.8 Kg. The prism makes an angle 30 degrees with the plane, which in turn makes an angle 0.0 degrees with horizontal. A string connected to the left side of the prism in 'massprismplane... | math | {
"ground_truth": "0.01490274843062255",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 633,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_1', a block of mass 2.0 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_1' extends outward to wrap around the movable pulley in 'masswithmova... | math | {
"ground_truth": "17.79078497319417",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 635,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 2 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A sphere called 'sphere_1' has a mass of 3.19 kg. It has a radius of 0.14.It is positioned at... | math | {
"ground_truth": "6.633378257269206",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 636,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_0', a block of mass 1.0 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_0' extends outward to connect to the block in 'masswithfixedpulley_1'... | math | {
"ground_truth": "9.810000000001327",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 637,
"json_index": null,
"split": "test"
} |
BasicCollision | math_p_numeric | [
{
"content": "A smooth table is inclined at an angle 8.12 degrees with the horizontal. There are multiple systems on this table. A spring (initially relaxed) fixed on its right end, extends to the left to -5.83 m on the table. It has a stiffness of 74.11 N/m, and a natural length of 0.23 m. A block of mass 1.0 ... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 638,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown horizontaly. The ball is launched from an initial height of 1.66 m from the ground and it has an initial speed of 1.31 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball and the ... | math | {
"ground_truth": "2.2536528202923845",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 639,
"json_index": null,
"split": "test"
} |
BasicInclinedPlaneFriction | math_p_numeric | [
{
"content": "In a system called 'twosidemassplane_0', a block of mass 1.0 kg rests on a plane inclined at an angle of 0 degrees. A string connected to the left side of the block in 'twosidemassplane_0' runs parallel to the plane to wrap around a pulley on the left side of the plane, and extends outward to conn... | math | {
"ground_truth": "3.62580634950243",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 640,
"json_index": null,
"split": "test"
} |
DifficultOrbitalMotion | math_p_numeric | [
{
"content": "In a planetary system, a star with mass 4.4 M and radius 0.78 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|-----------... | math | {
"ground_truth": "4.044403735048718",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 641,
"json_index": null,
"split": "test"
} |
BasicCollision | math_p_numeric | [
{
"content": "In a system called 'twodcollisionplane_0', a smooth table (XY plane) has 3 spheres on it with the following properties (position and velocity are relative to the table): | Sphere | Mass (kg) | Initial Position (m) | Initial Velocity (m/s) | Radius (m) | |----------|-------------|------------------... | math | {
"ground_truth": "1.2900766074388228",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 642,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 2 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A cylinder called 'cylinder_1' has a mass of 1.27 kg. It has a radius of 0.28 and a height of... | math | {
"ground_truth": "3.8294771711103404",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 643,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown horizontaly. The ball is launched from an initial height of 1.49 m from the ground and it has an initial speed of 2.01 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball and the ... | math | {
"ground_truth": "10.20486276832922",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 644,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown horizontaly. The ball is launched from an initial height of 1.99 m from the ground and it has an initial speed of 1.07 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball and the ... | math | {
"ground_truth": "14.581092759836201",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 645,
"json_index": null,
"split": "test"
} |
Rotation | math_p_numeric | [
{
"content": "A pendulum with a rope length of 1.06 m is attached to a fixed point in the ceiling on one end and a bob of mass 0.62 kg on the other end. The bob has an initial velocity of (-0.67, -0.37) m/s in the horizontal plane, and the rope initially makes an angle of 47.52 degrees with the vertical. What i... | math | {
"ground_truth": "3.673261420006965e-30",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 646,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_1', a block of mass 2.0 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_1' extends outward to wrap around the movable pulley in 'masswithmova... | math | {
"ground_truth": "24.6857142857044",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 647,
"json_index": null,
"split": "test"
} |
DifficultOrbitalMotion | math_p_numeric | [
{
"content": "In a planetary system, a star with mass 3.34 M and radius 0.91 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------... | math | {
"ground_truth": "0.0013349129822509615",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 649,
"json_index": null,
"split": "test"
} |
DifficultOrbitalMotion | math_p_numeric | [
{
"content": "In a planetary system, a star with mass 3.34 M and radius 0.91 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------... | math | {
"ground_truth": "11.795335852923317",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 650,
"json_index": null,
"split": "test"
} |
DifficultSpringMass | math_p_numeric | [
{
"content": "In a SpringMass system, 4 blocks are placed at -1.25, -0.56, 0.24 and 1.58 m on the table. They have masses 0.7, 2.66, 1.4 and 1.14 Kg respectively. These blocks are connected in series by springs (which may be initially stretched or compressed) of stiffness 120.44, 113.96 and 197.89 N/m respectiv... | math | {
"ground_truth": "0.0008182083870182054",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 651,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithreversedmovablepulley_0', a movable pulley of mass 0.6 kg supports two blocks of masses 5.67 kg and 8.28 kg hanging on its left and right sides respectively, pulling the pulley down. The string that connects the movable pulley in 'masswithreversedmovablepulley_0' to an ... | math | {
"ground_truth": "9.094447847736586",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 652,
"json_index": null,
"split": "test"
} |
Rotation | math_p_numeric | [
{
"content": "A pendulum with a rope length of 1.24 m is attached to a fixed point in the ceiling on one end and a bob of mass 7.92 kg on the other end. The bob has an initial velocity of (-0.59, 0.26) m/s in the horizontal plane, and the rope initially makes an angle of 56.9 degrees with the vertical. What is ... | math | {
"ground_truth": "1.3600784973622273",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 654,
"json_index": null,
"split": "test"
} |
DifficultOrbitalMotion | math_p_numeric | [
{
"content": "In a planetary system, a star with mass 3.45 M and radius 1.14 R is at the center. 2 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------... | math | {
"ground_truth": "0.045545867570300186",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 655,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown horizontaly. The ball is launched from an initial height of 1.49 m from the ground and it has an initial speed of 2.01 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball and the ... | math | {
"ground_truth": "2.9024020049193324",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 656,
"json_index": null,
"split": "test"
} |
Rotation | math_p_numeric | [
{
"content": "A pendulum with a rope length of 1.64 m is attached to a fixed point in the ceiling on one end and a bob of mass 5.91 kg on the other end. The bob has an initial velocity of (-0.76, -0.0) m/s in the horizontal plane, and the rope initially makes an angle of 86.23 degrees with the vertical. What is... | math | {
"ground_truth": "3.0056799313032995e-13",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 657,
"json_index": null,
"split": "test"
} |
BasicInclinedPlaneFriction | math_p_numeric | [
{
"content": "In a system called massprismplaneentity_0, a block of mass 2.8 kg rests on the left side a movable prism of mass 3.4 Kg. The prism makes an angle 30 degrees with the plane, which in turn makes an angle 0.0 degrees with horizontal. A string connected to the left side of the prism in 'massprismplane... | math | {
"ground_truth": "19.566587319617554",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 659,
"json_index": null,
"split": "test"
} |
Rotation | math_p_numeric | [
{
"content": "A pendulum with a rope length of 1.64 m is attached to a fixed point in the ceiling on one end and a bob of mass 5.91 kg on the other end. The bob has an initial velocity of (-0.76, -0.0) m/s in the horizontal plane, and the rope initially makes an angle of 86.23 degrees with the vertical. What is... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 660,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 1 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A bar called 'bar_0' has a mass of 1.09 kg. It has a length of 0.87, width of 0.13, and heigh... | math | {
"ground_truth": "3.000416854386026",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 661,
"json_index": null,
"split": "test"
} |
DifficultElectroMagnetic | math_p_numeric | [
{
"content": "A charged particle with charge -2.03 C and mass 1.2 kg is initially launched from origin in the space. It has an initial velocity of 0.75 m/s in the x-direction and -0.4 m/s in the y-direction. There is a uniform magnetic field of strength 1.55 along the +Z axis. The field is effective in a rectan... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 662,
"json_index": null,
"split": "test"
} |
DifficultPulley | math_p_numeric | [
{
"content": "In a system called 'massboxplaneentity_0', a long movable box of mass 1.15 kg rests on a plane inclined at -6.66 degrees. A small block of mass 0.71 kg is placed on its top, allowing it to slide freely on the box. A pulley is fixed to the right edge of the box. A rope is attached to the right side... | math | {
"ground_truth": "0.052817523170045656",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 663,
"json_index": null,
"split": "test"
} |
BasicCollision | math_p_numeric | [
{
"content": "In a system called 'twodcollisionplane_0', a smooth table (XY plane) has 3 spheres on it with the following properties (position and velocity are relative to the table): | Sphere | Mass (kg) | Initial Position (m) | Initial Velocity (m/s) | Radius (m) | |----------|-------------|------------------... | math | {
"ground_truth": "-2.220446049250313e-16",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 664,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithreversedmovablepulley_1', a movable pulley of mass 1.37 kg supports two blocks of masses 1.94 kg and 6.05 kg hanging on its left and right sides respectively, pulling the pulley down. The string that connects the movable pulley in 'masswithreversedmovablepulley_1' to an... | math | {
"ground_truth": "8.90009464344307",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 665,
"json_index": null,
"split": "test"
} |
Rotation | math_p_numeric | [
{
"content": "A pendulum with a rope length of 0.97 m is attached to a fixed point in the ceiling on one end and a bob of mass 8.99 kg on the other end. The bob has an initial velocity of (0.85, -0.36) m/s in the horizontal plane, and the rope initially makes an angle of 52.48 degrees with the vertical. What is... | math | {
"ground_truth": "23.92224176590167",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 666,
"json_index": null,
"split": "test"
} |
BasicInclinedPlaneFriction | math_p_numeric | [
{
"content": "In a system called 'twosidemassplane_0', a block of mass 1.0 kg rests on a plane inclined at an angle of 0 degrees. A string connected to the left side of the block in 'twosidemassplane_0' runs parallel to the plane to wrap around a pulley on the left side of the plane, and extends outward to conn... | math | {
"ground_truth": "27.135969230688968",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 667,
"json_index": null,
"split": "test"
} |
DifficultProjectile | math_p_numeric | [
{
"content": "In a setup, a ball of mass 1.0 kg is thrown horizontaly. The ball is launched from an initial height of 1.66 m from the ground and it has an initial speed of 1.31 m/s. Assume that horizontal is +ve x axis and verticaly upwards in +ve y axis. The coefficient of restitution between the ball and the ... | math | {
"ground_truth": "0.0",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 668,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_0', a block of mass 2.5 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_0' extends outward to wrap around the movable pulley in 'masswithmova... | math | {
"ground_truth": "26.0673162090413",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 669,
"json_index": null,
"split": "test"
} |
RigidBodyRotation | math_p_numeric | [
{
"content": "In a system, there are 2 rigid bodies, that rotate around a hinge joint. These rigid bodies are welded together, meaning they will always rotate together around the hinge. The rigid bodies are as follows: A sphere called 'sphere_1' has a mass of 3.19 kg. It has a radius of 0.14.It is positioned at... | math | {
"ground_truth": "-2.2032264755172024",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 670,
"json_index": null,
"split": "test"
} |
DifficultOrbitalMotion | math_p_numeric | [
{
"content": "In a planetary system, a star with mass 3.64 M and radius 0.89 R is at the center. 1 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------... | math | {
"ground_truth": "0.00488784363222608",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 671,
"json_index": null,
"split": "test"
} |
Rotation | math_p_numeric | [
{
"content": "A pendulum with a rope length of 0.97 m is attached to a fixed point in the ceiling on one end and a bob of mass 8.99 kg on the other end. The bob has an initial velocity of (0.85, -0.36) m/s in the horizontal plane, and the rope initially makes an angle of 52.48 degrees with the vertical. What is... | math | {
"ground_truth": "4.982906508107044e-16",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 673,
"json_index": null,
"split": "test"
} |
DifficultOrbitalMotion | math_p_numeric | [
{
"content": "In a planetary system, a star with mass 3.56 M and radius 0.82 R is at the center. 1 planets orbit around the star in coplanar orbits. The planets have the following properties at a given time (lets say t=0): | Planet | Mass (M) | Radius (R) | Position (R) | Velocity (R/T) | |----------|----------... | math | {
"ground_truth": "0.00033724381181429985",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 674,
"json_index": null,
"split": "test"
} |
DifficultPulley | math_p_numeric | [
{
"content": "In a system called 'massboxplaneentity_0', a long movable box of mass 1.29 kg rests on a plane inclined at 15.04 degrees. A small block of mass 0.72 kg is placed on its top, allowing it to slide freely on the box. A pulley is fixed to the right edge of the box. A rope is attached to the right side... | math | {
"ground_truth": "0.2847183369728428",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 675,
"json_index": null,
"split": "test"
} |
BasicPulley | math_p_numeric | [
{
"content": "In a system called 'masswithfixedpulley_1', a block of mass 2.1 kg is suspended in the air with the help of a light string that goes over a pulley. The string that connects the block to an overhead pulley in 'masswithfixedpulley_1' extends outward to wrap around the movable pulley in 'masswithmova... | math | {
"ground_truth": "-4.351390875402872",
"style": "rule"
} | {
"answer_type": null,
"file_name": null,
"given_variable_mapping": null,
"index": 676,
"json_index": null,
"split": "test"
} |
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