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.71: (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish. 2.3 Time, Velocity, and Speed 5. (a) Calculate Earth's average speed relative to the Sun. (b) What is its average velocity over a period of one year? 6. A helicopter blade spins at exac... |
south of east, what was her average velocity? (c) If she returned home by the same path 7 h 30 min after she left, what were her average speed and velocity for the entire trip? 12. The speed of propagation of the action potential (an electrical signal) in a nerve cell depends (inversely) on the diameter of the axon (n... |
rode a rocket sled, accelerating from rest to a top speed of 282 m/s (1015 km/h) in 5.00 s, and was brought jarringly back to rest in only 1.40 s! Calculate his (a) acceleration and (b) deceleration. Express each in multiples of (9.80 m/s2) by taking its ratio to the acceleration of gravity. 18. A commuter backs her c... |
the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.30 s. What is its emergency deceleration in m/s2? 24. While entering a freeway, a car accelerates from rest at a rate of 2.40 m/s2 for 12.0 s. (a) Draw a sketch of the situation. (b) List the knowns in this problem. (c) How far does the car trav... |
a) What is the final velocity of a freight train that accelerates at a rate of 0.0500 m/s2 for 8.00 min, starting with an initial velocity of 4.00 m/s? (b) If the train can slow down at a rate of 0.550 m/s2, how long will it take to come to a stop from this velocity? (c) How far will it travel in each case? 30. A firew... |
ation to be relatively small. If we assume that a pilot's speed upon impact was 123 mph (54 m/s), then what was his deceleration? Assume that the trees and snow stopped him over a distance of 3.0 m. 35. Consider a grey squirrel falling out of a tree to the ground. (a) If we ignore air resistance in this case (only for ... |
race to clinch a victory. The racer has an initial velocity of 11.5 m/s and accelerates at the rate of 0.500 m/s2 for 7.00 s. (a) What is his final velocity? (b) The racer continues at this velocity to the finish line. If he was 300 m from the finish line when he started to accelerate, how much time did he save? (c) O... |
2.00, and (e) 2.50 s for a rock thrown straight down with an initial velocity of 14.0 m/s from the Verrazano Narrows Bridge in New York City. The roadway of this bridge is 70.0 m above the water. 43. A basketball referee tosses the ball straight up for the starting tip-off. At what velocity must a basketball player le... |
, and he is 1.80 m tall? 49. You throw a ball straight up with an initial velocity of 15.0 m/s. It passes a tree branch on the way up at a height of 7.00 m. How much additional time will pass before the ball passes the tree branch on the way back down? 50. A kangaroo can jump over an object 2.50 m high. (a) Calculate i... |
to travel up the well. The speed of sound is 332.00 m/s in this well. 56. A steel ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.45 m. (a) Calculate its velocity just before it strikes the floor. (b) Calculate its velocity just after it leaves the floor on its way back up. (c) ... |
in Figure 2.75, verify that the acceleration is 3.2 m/s2 at = 10 s. Figure 2.72 Figure 2.75 63. Construct the displacement graph for the subway shuttle train as shown in Figure 2.30(a). Your graph should show the position of the train, in kilometers, from t = 0 to 20 s. You will need to use the information on accelera... |
acceleration of a feather as she drops it to the ground. If the student is looking to achieve a positive velocity and positive acceleration, what is the most sensible way to set up her coordinate system? a. Her hand should be a coordinate of zero and the upward direction should be considered positive. b. Her hand shou... |
2.5 Motion Equations for Constant Acceleration in One Dimension 6. A group of students is attempting to determine the average acceleration of a marble released from the top of a long ramp. Below is a set of data representing the marble's position with respect to time. Position (cm) Time (s) 0.0 0.3 1.25 2.8 5.0 7.75 1... |
3.5. Addition of Velocities Connection for AP® Courses Most instances of motion in everyday life involve changes in displacement and velocity that occur in more than one direction. For example, when you take a long road trip, you drive on different roads in different directions for different amounts of time at differe... |
3.A.1.1 The student is able to express the motion of an object using narrative, mathematical, and graphical representations. (S.P. 1.5, 2.1, 2.2) • 3.A.1.2 The student is able to design an experimental investigation of the motion of an object. (S.P. 4.2) • 3.A.1.3 The student is able to analyze experimental data descr... |
you walked. (Note that we are using three significant figures in the answer. Although it appears that “9” and “5” have only one significant digit, they are discrete numbers. In this case “9 blocks” is the same as “9.0 or 9.00 blocks.” We have decided to use three significant figures in the answer in order to show the ... |
north (two perpendicular directions). How far he or she walks east is only affected by his or her motion eastward. Similarly, how far he or she walks north is only affected by his or her motion northward. Independence of Motion The horizontal and vertical components of two-dimensional motion are independent of each ot... |
experiment, consider the following questions: • How will you measure the maximum height reached by your object? • How can you take advantage of the symmetry of an object in ballistic motion launched from ground level, reaching maximum height, and returning to ground level? • Will it make a difference if your object ha... |
playback the motion to analyze the behavior. Figure 3.7 Ladybug Motion 2D (http://cnx.org/content/m54779/1.2/ladybug-motion-2d_en.jar) 3.2 Vector Addition and Subtraction: Graphical Methods By the end of this section, you will be able to: Learning Objectives • Understand the rules of vector addition, subtraction, and ... |
represent a vector with a boldface variable. For example, we will represent the quantity force with the vector F, which has both magnitude and direction. The magnitude of the vector will be represented by a variable in italics, such as, and the direction of the variable will be given by an angle. Figure 3.9 A person w... |
12 Step 2. Now draw an arrow to represent the second vector (5 blocks to the north). Place the tail of the second vector at the head of the first vector. Figure 3.13 Step 3. If there are more than two vectors, continue this process for each vector to be added. Note that in our example, we have only two vectors, so we h... |
resultant vector, R. Figure 3.17 (4) Use a ruler to measure the magnitude of R, and a protractor to measure the direction of R. While the direction of the vector can be specified in many ways, the easiest way is to measure the angle between the vector and the nearest horizontal or vertical axis. Since the resultant ve... |
from vector A is then simply defined to be the addition of –B to A. Note that vector subtraction is the addition of a negative vector. The order of subtraction does not affect the results. A – B = A + (–B). (3.2) This is analogous to the subtraction of scalars (where, for example, 5 – 2 = 5 + (–2) ). Again, the result... |
In this case, = 23.0 m and = 7.5° south of east. 106 Chapter 3 | Two-Dimensional Kinematics (5) To determine the location of the dock, we repeat this method to add vectors A and B. We obtain the resultant vector R': Figure 3.24 In this case = 52.9 m and = 90.1° north of east. We can see that the woman will end up a si... |
we may know that the total displacement of a person walking in a city is 10.3 blocks in a direction 29.0° north of east and want to find out how many blocks east and north had to be walked. This method is called finding the components (or parts) of the displacement in the east and north directions, and it is the inver... |
be made. Analytical methods are limited only by the accuracy and precision with which physical quantities are known. Resolving a Vector into Perpendicular Components Analytical techniques and right triangles go hand-in-hand in physics because (among other things) motions along perpendicular directions are independent.... |
29.1º, so that = cos = = sin = 10.3 blocks cos 29.1º sin 29.1º 10.3 blocks = 9.0 blocks = 5.0 blocks. (3.8) (3.9) Calculating a Resultant Vector If the perpendicular components A and A of a vector A are known, then A can also be found analytically. To find the magnitude and direction of a vector from its perpendicular... |
direction. Those paths are the x- and y-components of the resultant, R and R. If we know R 2 and = tan–1( / ). When you use the analytical and R, we can find and using the equations = method of vector addition, you can determine the components or the magnitude and direction of a vector. 2 + Step 1. Identify the x- and ... |
/col11844/1.13 Chapter 3 | Two-Dimensional Kinematics 111 Example 3.3 Adding Vectors Using Analytical Methods Add the vector A to the vector B shown in Figure 3.33, using perpendicular components along the x- and y-axes. The xand y-axes are along the east–west and north–south directions, respectively. Vector A represen... |
resultant by using the Pythagorean theorem: = 2 + 2 = (65.2)2 + (48.4)2 m so that = 81.2 m. (3.16) (3.17) (3.18) (3.19) (3.20) (3.21) (3.22) (3.23) 112 Chapter 3 | Two-Dimensional Kinematics Finally, we find the direction of the resultant: Thus, = tan−1( / )=+tan−1(48.4 / 65.2). = tan−1(0.742) = 36.6 º. (3.24) (3.25) ... |
. Figure 3.36 Vector Addition (http://cnx.org/content/m54783/1.2/vector-addition_en.jar) 3.4 Projectile Motion By the end of this section, you will be able to: Learning Objectives • Identify and explain the properties of a projectile, such as acceleration due to gravity, range, maximum height, and trajectory. • Determi... |
, x, and y. (Note that in the last section we used the notation A to represent a vector with components A and A. If we continued this format, we would call displacement s with components s and s. However, to simplify the notation, we will simply represent the component vectors as x and y.) Of course, to describe motion... |
(3.34) (3.35) (3.36) (3.37) (3.38) (3.39) (3.40) Step 3. Solve for the unknowns in the two separate motions—one horizontal and one vertical. Note that the only common variable between the motions is time. The problem solving procedures here are the same as for one-dimensional kinematics and are illustrated in the solv... |
it explodes? Strategy Because air resistance is negligible for the unexploded shell, the analysis method outlined above can be used. The motion can be broken into horizontal and vertical motions in which = 0 and = –. We can then define 0 and 0 to be zero and solve for the desired quantities. Solution for (a) 116 Chapt... |
easiest method is to use = 0 + 1 (0 + ). Because 0 is zero, this equation reduces to simply 2 This content is available for free at http://cnx.org/content/col11844/1.13 Chapter 3 | Two-Dimensional Kinematics Note that the final vertical velocity,, at the highest point is zero. Thus, = 1 2 (0 + ). = 2 (0y + ) = 2(233 m... |
0. It is also important to define the positive and negative directions in the and directions. Typically, we define the positive vertical direction as upwards, and the positive horizontal direction is usually the direction of the object's motion. When this is the case, the vertical acceleration,, takes a negative value... |
m/s )( sin 35.0° ) = 14.3 m/s. Substituting known values yields Rearranging terms gives a quadratic equation in : −20.0 m = (14.3 m/s) − 4.90 m/s2 2. 4.90 m/s2 2 − (14.3 m/s) − (20.0 m) = 0. (3.58) (3.59) This expression is a quadratic equation of the form 2 + + = 0, where the constants are = 4.90, = – 14.3, and = – 2... |
its perpendicular components, using the following equation: = 2 + 2 = (20.5 m/s)2 + ( − 24.5 m/s)2, which gives The direction is found from the equation: = 31.9 m/s. = tan−1( / ) so that Thus, Discussion for (b) = tan−1( − 24.5 / 20.5) = tan−1( − 1.19). = −50.1 °. (3.64) (3.65) (3.66) (3.67) (3.68) (3.69) (3.70) The n... |
every initial angle except 45°, there are two angles that give the same range—the sum of those angles is 90°. The range also depends on the value of the acceleration of gravity. The lunar astronaut Alan Shepherd was able to drive a golf ball a great distance on the Moon because gravity is weaker there. The range of a ... |
3.43 Projectile Motion (http://cnx.org/content/m54787/1.2/projectile-motion_en.jar) This content is available for free at http://cnx.org/content/col11844/1.13 Chapter 3 | Two-Dimensional Kinematics 121 3.5 Addition of Velocities Learning Objectives By the end of this section, you will be able to: • Apply principles of... |
has a velocity relative to an observer on solid ground. The velocity of the object relative to the observer is the sum of these velocity vectors, as indicated in Figure 3.44 and Figure 3.45. These situations are only two of many in which it is useful to add velocities. In this module, we first re-examine how to add ve... |
the tub to the other and perpendicular to the flow of water. Which way do you need to push the boat so that it ends up immediately opposite? Compare the directions of the flow of water, heading of the boat, and actual velocity of the boat. Example 3.6 Adding Velocities: A Boat on a River Figure 3.47 A boat attempts to... |
the total velocity has relative to the riverbank. Example 3.7 Calculating Velocity: Wind Velocity Causes an Airplane to Drift Calculate the wind velocity for the situation shown in Figure 3.48. The plane is known to be moving at 45.0 m/s due north relative to the air mass, while its velocity relative to the ground (it... |
west which is consistent with the diagram. Now, to find w we note that tot = w + p Here tot = totsin 110º ; thus, w = (38.0 m/s)(0.940) − 45.0 m/s = −9.29 m/s. (3.84) (3.85) (3.86) (3.87) (3.88) This minus sign indicates motion south which is consistent with the diagram. Now that the perpendicular components of the wi... |
20th century. Einstein revolutionized our view of nature with his modern theory of relativity, which we shall study in later chapters. The relative velocities in this section are actually aspects of classical relativity, first discussed correctly by Galileo and Isaac Newton. Classical relativity is limited to situatio... |
when it strikes the floor 1.50 m below its point of release: (a) Measured relative to the plane? (b) Measured relative to the Earth? Figure 3.50 The motion of a coin dropped inside an airplane as viewed by two different observers. (a) An observer in the plane sees the coin fall straight down. (b) An observer on the gr... |
s. The x- and y-components of velocity can be combined to find the magnitude of the final velocity: Thus, yielding The direction is given by: so that Discussion = 2 + 2. = (260 m/s)2 + ( − 5.42 m/s)2 = 260.06 m/s. = tan−1( / ) = tan−1( − 5.42 / 260) = tan−1( − 0.0208) = −1.19º. (3.96) (3.97) (3.98) (3.99) (3.100) In pa... |
PhET Explorations: Motion in 2D Try the new "Ladybug Motion 2D" simulation for the latest updated version. Learn about position, velocity, and acceleration vectors. Move the ball with the mouse or let the simulation move the ball in four types of motion (2 types of linear, simple harmonic, circle). Figure 3.51 Motion ... |
; opposite to the head or tip of the arrow trajectory: the path of a projectile through the air vector: a quantity that has both magnitude and direction; an arrow used to represent quantities with both magnitude and direction vector addition: the rules that apply to adding vectors together velocity: speed in a given di... |
: Determine the coordinate system for the vectors. Then, determine the horizontal and vertical components of each vector using the equations and = cos = cos = sin = sin. Step 2: Add the horizontal and vertical components of each vector to determine the components and of the resultant vector, R : and = + = +. Step 3: Us... |
, particularly when the observers move relative to one another. Classical relativity is limited to situations where speed is less than about 1% of the speed of light (3000 km/s). Conceptual Questions 3.2 Vector Addition and Subtraction: Graphical Methods 1. Which of the following is a vector: a person's height, the alt... |
Explain why a vector cannot have a component greater than its own magnitude. 12. If the vectors A and B are perpendicular, what is the component of A along the direction of B? What is the component of B along the direction of A? 3.4 Projectile Motion 13. Answer the following questions for projectile motion on level gr... |
the side of the road? Under what condition would this occur? How would the motion of the ball appear to the person who threw it? 20. The hat of a jogger running at constant velocity falls off the back of his head. Draw a sketch showing the path of the hat in the jogger's frame of reference. Draw its path as viewed by ... |
+ B = B + A.) 7. (a) Repeat the problem two problems prior, but for the second leg you walk 20.0 m in a direction 40.0° north of east (which is equivalent to subtracting B from A —that is, to finding R′ = A − B ). (b) Repeat the problem two problems prior, but now you first walk 20.0 m in a direction 40.0° south of we... |
the total distance traveled and (b) the magnitude and direction of the displacement from start to finish. In this part of the problem, explicitly show how you follow the steps of the analytical method of vector addition. Figure 3.58 The various lines represent paths taken by different people walking in a city. All blo... |
25.0 m straight south. (This is equivalent to subtracting B from A —that is, finding R′ = A – B ) (b) Repeat again, but now you first walk 25.0 m north and then 18.0 m east. (This is equivalent to subtract A from B —that is, to find A = B + C. Is that consistent with your result?) 20. A new landowner has a triangular ... |
and then flies 30.0 km in a direction 15º north of east as shown in Figure 3.63. Find her total distance from the starting point and the direction of the straight-line path to the final position. Discuss qualitatively how this flight would be altered by a wind from the north and how the effect of the wind would depend... |
's-eye if its initial speed is 35.0 m/s? In this part of the problem, explicitly show how you follow the steps involved in solving projectile motion problems. (b) There is a large tree halfway between the archer and the target with an overhanging horizontal branch 3.50 m above the release height of the arrow. Will the ... |
the legs to see how far one can jump. Suppose the extension of the legs from the crouch position is 0.600 m and the acceleration achieved from this position is 1.25 times the acceleration due to gravity,. How far can they jump? State your assumptions. (Increased range can be achieved by swinging the arms in the direct... |
and 12.0 m above the center of the 30.0 cm diameter nest. The owl is flying east at 3.50 m/s at an angle 30.0° below the horizontal when it accidentally drops the mouse. Is the owl lucky enough to have the mouse hit the nest? To answer this question, calculate the horizontal position of the mouse when it has fallen 12... |
basket (measured in the horizontal direction) must he start his jump to reach his maximum height at the same time as he reaches the basket? 47. A football player punts the ball at a 45.0° angle. Without an effect from the wind, the ball would travel 60.0 m horizontally. (a) What is the initial speed of the ball? (b) W... |
) He flew for 169 min at an average velocity of 3.53 m/s in a direction 45º south of east. What was his total displacement? (b) Allen encountered a headwind averaging 2.00 m/s almost precisely in the opposite direction of his motion relative to the Earth. What was his average velocity relative to the air? (c) What was ... |
is in the jet stream, which is blowing at 35.0 m/s in a direction 15º south of east. What is the velocity of the airplane relative to the Earth? (b) Discuss whether your answers are consistent with your expectations for the effect of the wind on the plane's path. 59. (a) In what direction would the ship in Exercise 3.... |
results mean that observers on all galaxies will see themselves at the center of the expanding universe, and they would likely be aware of relative velocities, concluding that it is not possible to locate the center of expansion with the given information. Figure 3.64 Five galaxies on a straight line, showing their di... |
backward to give the puck a velocity toward the goal. 68. Unreasonable Results Suppose you wish to shoot supplies straight up to astronauts in an orbit 36,000 km above the surface of the Earth. (a) At what velocity must the supplies be launched? (b) What is unreasonable about this velocity? (c) Is there a problem with... |
it hits the ground. Which of the following accurately describes the graph of the ball's vertical acceleration versus time (taking the downward direction to be negative)? a. A negative value that does not change with time b. A gradually increasing negative value (straight line) This content is available for free at htt... |
4 Projectile Motion 6. In an experiment, a student launches a ball with an initial horizontal velocity of 5.00 meters/sec at an elevation 2.00 meters above ground. Draw and clearly label with appropriate values and units a graph of the ball's horizontal velocity vs. time and the ball's vertical velocity vs. time. The g... |
many centuries natural philosophers had debated the nature of the universe based largely on certain rules of logic, with great weight given to the thoughts of earlier 142 Chapter 4 | Dynamics: Force and Newton's Laws of Motion classical philosophers such as Aristotle (384–322 BC). Among the many great thinkers who con... |
). These interactions between any two objects are described by Newton's third law, stating that the forces exerted on these objects are equal in magnitude and opposite in direction to each other (Essential Knowledge 3.A.4). We will discover that there is an empirical cause-effect relationship between the net force exer... |
Big Idea 2. For example, any object that has mass creates a gravitational field in space (Enduring Understanding 2.B). Any material object (one that has mass) placed in the gravitational field will experience gravitational force (Essential Knowledge 2.B.1). This content is available for free at http://cnx.org/content/... |
useful for describing interactions that occur at a distance (long-range forces) as well as a variety of other physical phenomena. Essential Knowledge 2.A.1 A vector field gives, as a function of position (and perhaps time), the value of a physical quantity that is described by a vector. Essential Knowledge 2.A.2 A sca... |
exerted at all scales and can dominate at the human scale. Big Idea 4 Interactions between systems can result in changes in those systems. Enduring Understanding 4.A The acceleration of the center of mass of a system is related to the net force exerted on the system, where = ∑ /. Essential Knowledge 4.A.1 The linear m... |
objects and systems to move. To understand this, we need a working definition of force. Our intuitive definition of force—that is, a push or a pull—is a good place to start. We know that a push or pull has both magnitude and direction (therefore, it is a vector quantity) and can vary considerably in each regard. For e... |
isolated point (or free body), and only those forces acting on the body from the outside (external forces) are shown. (These forces are the only ones shown, because only external forces acting on the body affect its motion. We can ignore any internal forces within the body.) Free-body diagrams are very useful in analy... |
if the weights are also pushed to the side with a pencil? 4.2 Newton's First Law of Motion: Inertia Learning Objectives By the end of this section, you will be able to: • Define mass and inertia. • Understand Newton's first law of motion. Experience suggests that an object at rest will remain at rest if left alone, an... |
by rubbing 146 Chapter 4 | Dynamics: Force and Newton's Laws of Motion lubricating oil on it, the object slides farther yet. Extrapolating to a frictionless surface, we can imagine the object sliding in a straight line indefinitely. Friction is thus the cause of the slowing (consistent with Newton’s first law). The ob... |
the object by an external force. Roughly speaking, mass is a measure of the amount of “stuff” (or matter) in something. The quantity or amount of matter in an object is determined by the numbers of atoms and molecules of various types it contains. Unlike weight, mass does not vary with location. The mass of an object ... |
elements of the system. Again looking at Figure 4.5(a), the force the child in the wagon exerts to hang onto the wagon is an internal force between elements of the system of interest. Only external forces affect the motion of a system, according to Newton’s first law. (The internal forces actually cancel, as we shall ... |
The vector f represents the friction acting on the wagon, and it acts to the left, opposing the motion of the wagon. (b) All of the external forces acting on the system add together to produce a net force, Fnet. The free-body diagram shows all of the forces acting on the system of interest. The dot represents the cent... |
myriad of forces between atoms in the objects, but by doing so, we can easily solve some very complex problems with only minimal error due to our simplification 148 Chapter 4 | Dynamics: Force and Newton's Laws of Motion Now, it also seems reasonable that acceleration should be inversely proportional to the mass of th... |
trouble ensuring that the mass is constant? What did you learn? Newton’s Second Law of Motion The acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. In equation form, Newton’s second law of motion is Thi... |
air resistance is negligible, the net force on a falling object is the gravitational force, commonly called its weight w. Weight can be denoted as a vector w because it has a direction; down is, by definition, the direction of gravity, and hence weight is a downward force. The magnitude of weight is denoted as. Galile... |
Earth, the Moon, the Sun, and so on. This is the most common and useful definition of weight in physics. It differs dramatically, however, from the definition of weight used by NASA and the popular media in relation to space travel and exploration. When they speak of “weightlessness” and “microgravity,” they are reall... |
less, even though you do not look any skinnier. This is because the force of gravity is weaker on the Moon. In fact, when people say that they are “losing weight,” they really mean that they are losing “mass” (which in turn causes them to weigh less). Take-Home Experiment: Mass and Weight What do bathroom scales measu... |
by the person pushing the mower must be greater than the friction opposing the motion (since we know the mower moves forward), and the vertical forces must cancel if there is to be no acceleration in the vertical direction (the mower is moving only horizontally). The acceleration found is small enough to be reasonable... |
is net = 4 −. (4.12) 152 Chapter 4 | Dynamics: Force and Newton's Laws of Motion Substituting this into Newton’s second law gives net = = 4 −. Using a little algebra, we solve for the total thrust 4T: 4 = +. Substituting known values yields 4 = + = (2100 kg)(49 m/s2 ) + 650 N. So the total thrust is and the individual... |
an experiment, using a motion capture system looking down at an air hockey table to measure the motion of the 0.10-kg puck. The table was aligned with the cardinal directions, and a compressed air hose was placed in the center of each side, capable of varying levels of force output and fixed so that it was aimed at th... |
A.4.3 The student is able to analyze situations involving interactions among several objects by using free-body diagrams that include the application of Newton's third law to identify forces. (S.P. 1.4) • 3.B.2.1 The student is able to create and use free-body diagrams to analyze physical situations to solve problems w... |
is the action and the force experienced as a consequence is the reaction. Newton’s third law has practical uses in analyzing the origin of forces and understanding which forces are external to a system. We can readily see Newton’s third law at work by taking a look at how people move about. Consider a swimmer pushing ... |
person toward the Earth. As stated by Newton’s third law of motion, the person also exerts a force that is equal in magnitude, but opposite in direction, pulling the Earth up toward the person. Since the mass of the Earth is so great, however, and =, the acceleration of the Earth toward the person is not noticeable. O... |
at http://cnx.org/content/col11844/1.13 Chapter 4 | Dynamics: Force and Newton's Laws of Motion 155 Figure 4.10 A professor pushes a cart of demonstration equipment. The lengths of the arrows are proportional to the magnitudes of the forces (except for f, since it is too small to draw to scale). Different questions ar... |
) (4.19) (4.20) (4.21) 156 Chapter 4 | Dynamics: Force and Newton's Laws of Motion None of the forces between components of System 1, such as between the professor’s hands and the cart, contribute to the net external force because they are internal to System 1. Another way to look at this is to note that forces between... |
) (4.29) Discussion It is interesting that this force is significantly less than the 150-N force the professor exerted backward on the floor. Not all of that 150-N force is transmitted to the cart; some of it accelerates the professor. The choice of a system is an important analytical step both in solving problems and ... |
representation of action-reaction pairs of forces. (S.P. 1.4, 6.2) • 3.A.4.2 The student is able to use Newton's third law to make claims and predictions about the action-reaction pairs of forces when two objects interact. (S.P. 6.4, 7.2) • 3.A.4.3 The student is able to analyze situations involving interactions among... |
as the weight of the load. At this point the net external force on the load is zero. That is the situation when the load is stationary on the table. The table sags quickly, and the sag is slight so we do not notice it. But it is similar to the sagging of a trampoline when you climb onto it. 158 Chapter 4 | Dynamics: F... |
(a) What is her acceleration if friction is negligible? (b) What is her acceleration if friction is known to be 45.0 N? This content is available for free at http://cnx.org/content/col11844/1.13 Chapter 4 | Dynamics: Force and Newton's Laws of Motion 159 Figure 4.13 Since motion and friction are parallel to the slope,... |
, and the magnitude of the component of the weight perpendicular to the slope is ⊥ = cos (25º) = cos (25º). (a) Neglecting friction. Since the acceleration is parallel to the slope, we need only consider forces parallel to the slope. (Forces perpendicular to the slope add to zero, since there is no acceleration in that... |
Resolving Weight into Components Figure 4.14 An object rests on an incline that makes an angle θ with the horizontal. When an object rests on an incline that makes an angle with the horizontal, the force of gravity acting on the object is divided into two components: a force acting perpendicular to the plane, w⊥, and ... |
a flexible medium, such as a rope or cable. The word “tension” comes from a Latin word meaning “to stretch.” Not coincidentally, the flexible cords that carry muscle forces to other parts of the body are called tendons. Any flexible connector, such as a string, rope, chain, wire, or cable, can exert pulls only paralle... |
the spring would extend a length corresponding to a force of 49.0 N, providing a direct observation and measure of the tension force in the rope. Flexible connectors are often used to transmit forces around corners, such as in a hospital traction system, a finger joint, or a bicycle brake cable. If there is no frictio... |
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