Physics Assignment Answers

Chapter 6 - Newton's 3rd Law


Chapter 6 Review Answers:

  1. In an interaction between a hammer and a nail, there is a force exerted on both the hammer and the nail. Newton's Third Law says that every interaction involves two forces - in this case (1) hammer pushes nail, and (2) nail pushes hammer.
  2. When a hammer hits a nail, Newton's Third Law says that the force that the hammer exerts on the nail is exactly the same size as the force the nail exerts on the hammer.
  3. In order to walk across the floor, you push backwards on the floor with your foot. Newton's Third Law says that the reaction force to this action force is "floor pushes you forward" (Action: You push floor (backwards). Reaction: floor pushes you (forward).) So, when you walk, it is the floor that pushes you along!
  4. If "you push water backward" is the action force, the reaction force must be "water pushes you forward." So, when you swim, the water exerts the force that pushes you along!
  5. If the action force is "bowstring pushes arrow", then the reaction force is "arrow pushes bowstring."
  6. When you jump, you push downward on the Earth. Call this the action force, and notice that this force pushes the Earth - not you! According to Newton's Third Law, the reaction force in this interaction must be "Earth pushes you upward," and this is the force that causes you to accelerate into the air. Newton's Third Law also says that these forces are exactly the same size.

    Why doesn't the Earth appear to accelerate? Well, remember that Newton's Second Law says that the acceleration of an object depends on two things: (1) the net force on the object, and (2) the object's mass (inertia). The Earth has a huge mass (about 6 x 1024 kg!), so the force that you exert on it produces only an extremely tiny acceleration - hardly noticeable. (For instance, suppose that the force that you exert on the Earth is 600 N = 6 x 102 N. The Earth's acceleration, a = Fnet/m = (6 x 102 N)/(6 x 1024 kg) = 10-22 m/s2 = 0.0000000000000000000001 m/s2!)
  7. When a cannon is fired, the force that the cannon exerts on the cannonball ("action" force) is exactly the same size as the force the cannonball exerts on the cannon ("reaction" force). The acceleration of the cannonball, however, is MUCH larger than the acceleration of the cannon!

    Newton's Second Law (a = Fnet/m) says that the acceleration of an object depends on the net force pushing on the object and the object's mass (inertia). Since the cannonball has a small mass, it gets a large acceleration (Acannonball = Fcannonball/mcannonball). Since the mass of the cannon is (relatively) large, the cannon gets a small acceleration (acannon = Fcannon/Mcannon).
  8. Rockets don't "push against the air!!!" Rockets are designed so that their engines force the exhaust gasses out the back of the rocket at extremely high speed. This is the action force - "rocket pushes exhaust gasses." The Newton's Third Law reaction force in this interaction must be "exhaust gasses push rocket." This is the force that accelerates the rocket!

    Note that a rocket is a completely self-contained system - no "air" is necessary. In fact, all air does is provide air resistance (drag) to slow the rocket down. Rockets are much more efficient where there is no air!
  9. (Refer to figure 6.10 on p. 79 of the text.)

    In the interaction between the apple and the orange, there is one force exerted on the apple. It is the force "orange pulls apple."

    In the interaction between the apple and the orange, there is one force exerted on the orange. It is the force "apple pulls orange."

    Yes, these forces are equal in size and opposite in direction, since they constitute a Newton's Third Law action-reaction force pair.

    Note that these forces do not cancel! The "action" force "orange pulls apple" acts to accelerate the apple, and the "reaction" force "apple pulls orange" acts to accelerate the orange. Note that this question treats the apple and orange as separate objects, so the Newton's Third Law action/reaction force pair do not cancel.
  10. (Refer to figure 6.10 on p. 79 of the text.)

    First, "Consider the orange system." means "look at what's happening to the orange, and ignore all other objects." In this system, action and reaction forces do not cancel! First of all, there is only one force acting on the orange - the force that the apple is exerting on it. This is the only force that affects the motion of the orange. The force "orange pulls apple" does not affect the motion of the orange - it accelerates the apple (what it is pulling on).

    Yes, the orange accelerates - because there is a net force acting on it. (The force is "apple pulls orange.")
  11. (Refer to figure 6.10 on p. 79 of the text.)

    First, "Consider the orange-apple system." means "Count the apple + rope + orange to be a single object (after all, they're connected)." In this situation, the forces "apple pulls orange" and "orange pulls apple" do cancel, since they act on different parts of the same object.

    No, the apple and orange don't accelerate away from each other (why would they?). The apple and orange accelerate toward each other, but the apple-orange system, as a whole, remains at rest. After all, the net force on it is zero!
  12. (Refer to figure 6.13 on p. 80 of the text. Click here for a complete discussion of the horse/cart problem.)

    (a) There are two horizontal forces pushing/pulling on the cart, labeled "P" and "f." The force "P" is the force "horse pulls cart," and the force "f" is the friction force "ground pushes cart."

    (b) The net force on the cart is the difference in the two forces pushing/pulling on it: P - f. Therefore, if the horse pulls harder on the wagon than the friction force pulls it back, the wagon accelerates. If the two forces cancel (balance) exactly, it doesn't.
  13. (Refer to figure 6.13 on p. 80 of the text.)

    (a) Looking at the diagram, there are two horizontal forces on the horse, labeled "F" and "P." The force "F" is the force "ground pushes horse," and "P" is the force "wagon pulls horse."

    (b) The net force on the horse must be the difference in the two forces pushing/pulling on it: F - P. If the ground pushes forward on the horse harder than the wagon pulls backward on it, the horse accelerates. If the two forces cancel (balance) exactly, it doesn't.

    (c) Since there are two forces exerted on the horse, the horse must be exerting two forces (Newton's Third Law). The force "horse pulls wagon" is the Newton's Third Law action/reaction partner of the force "wagon pulls horse." The force "horse pushes ground" is the action/reaction partner of the force "ground pushes horse."
  14. (Refer to figure 6.13 on p. 80 of the text.)

    (a) First, remember that "horse-cart system" means "consider the horse and cart to be one object," With this in mind, there are two forces acting on the horse-cart system, labeled "F" and "f." The force "F" is "ground pushes horse + cart forward," and the force "f" is a friction force "ground pushes horse + cart backward."

    (b) Since there are two forces acting on the horse + cart system, the net force on it is F - f. As long as the ground pushes forward on the horse + cart harder than the friction force pushes backward on it, the horse + cart accelerates forward. If the forces balance (cancel), the horse + cart doesn't accelerate.
  15. In order for the horse to increase its speed, it must accelerate. In order for the horse to accelerate, there must be a non-zero net force on the horse. Looking back at question #13b, there are 2 forces on the horse - the wagon pulls backward on the horse (force "P"), and the ground pushes forward on the horse (force "F"). Therefore, the net force on the horse is F - P, the difference in the ground's force and the wagon's force. If both forces are equal (F = P) the net force on the horse will be zero, and the horse won't accelerate. We don't want that.

    In order for the horse to accelerate, the force that the ground exerts on the horse must be greater than the force that the cart exerts. How can the horse arrange for the ground to push harder on him/her? Easy! Newton's Third Law says that the forces "horse pushes ground backward" and "ground pushes horse forward" are an action/reaction pair, which means that they are always equal in size. If the horse pushes harder on the ground, then the ground automatically pushes harder on the horse. Voila! A net force on the horse, and the horse accelerates!
  16. If you hit a wall with a force of 200 N, the wall hits you with a force of 200 N (Ouch!). The forces "you hit wall" and "wall hits you" are a Newton's Third Law action/reaction force pair, so they are always equal and opposite.
  17. You can't hit a feather in midair with a force of 200 N because the feather is not capable of exerting a 200 N force on you. The forces "you hit feather" and "feather hits you" are a Newton's Third Law action/reaction force pair, so they must always be exactly equal in size. If an object isn't strong enough to exert a certain amount of force on you, then you can't exert that amount of force on it.


Chapter 6 Think & Explain Answers:

  1. Your weight is the force "Earth pulls you downward," so the reaction force in this interaction is "You pull Earth upward."
  2. When you pull upward on the handlebars, the handlebars push downward on you with an equal and opposite force. This force is transmitted through you to the pedals, in addition to the force you exert on the pedals with your legs.
  3. (a) Yes, the forces are equal and opposite - otherwise, there would be a net force on you and you would be accelerating vertically!
    (b) No, the forces are NOT an action-reaction pair. The reaction force to "the downward pull of gravity" (= Earth pulls you downward) is "you pull the Earth upward." The reaction force to "the upward support force of the floor" (= floor pushes you upward) is "you push the floor downward." Just because two forces are equal and opposite does NOT make them an action-reaction force pair. In this case, a give-away clue is the fact that both forces mentioned in the problem act on the same object - you.
  4. (You may not have much experience walking on floating logs, but walking on a wagon or skateboard is practically the same thing.) So, why does the log move backward? Because you push it backward, that's why!

    In order to walk on the log, your foot must exert a force backward on the log. The reaction force in this interaction is "log pushes you forward," and this is the force that accelerates you forward. The force that you exert on the log accelerates the log backward.
  5. In order to walk on a floor (or any other surface), your foot must push backward on the floor (action force), so that the floor pushes you forward (reaction force). The force that your foot (and the floor) exert on each other is a friction force (between the sole of your shoe and the floor). So, more friction between your foot and the floor means more force available to push you forward, which means easier walking. Since there is generally more friction force between a carpet and your foot than between a smooth floor and your foot, it is easier to walk on a carpeted floor.

    On the other hand, less friction means less force available to push you forward, which means more difficult walking. This, of course, is why it can be so difficult to walk on ice or a slick, wet floor.
  6. If you step off a ledge, both you and the Earth accelerate!

    You accelerate downward because the net force on you is your weight (the force "Earth pulls you"), so, by Newton's Second Law your acceleration is:
    a = g

    You are in free fall, of course. Less abstractly, suppose you have a mass of 60 kg and a weight (= mg) of about 600 Newtons, which is the net force on you. Your acceleration when you step off a ledge, a = Fnet/m = (600 N)/(60 kg) = 10 m/s2.

    The Earth accelerates upward because the net force on the Earth (assuming that you are the only object interacting with the Earth at this moment) is the Newton's Third Law reaction force "you pull Earth," which equals your weight also (since Newton's Third Law action/reaction forces are always exactly the same size). The acceleration of the Earth, then is:

    acceleration of the Earth

    The Earth has a mass of about 6 x 1024 kg. If you have a mass of 60 kg, this gives an acceleration for the Earth of about:
    acceleration of earth - numerical
    No wonder you don't notice it!

  7. you and the sink diagramWhen you are standing on the bathroom scale and pushing on the sink, there are several interactions taking place at the same time - between you and the Earth, between you and the scale, between you and the sink, etc. It takes clear and methodical thinking to sort all of this out. The way to do it is to consider each object separately, and clearly indicate what forces push/pull on which object.

    You push sink down(a) The situation in which you push down on the sink is diagrammed at the right. In the interaction between you and the Earth, there are two forces. The forces (red arrows in the diagram) "Earth pulls you down" (your weight) and "You pull Earth up" are a Newton's Third Law action/reaction force pair. The force "Earth pulls you down" is attached to you, since it affects your motion. The force "You pull Earth up" is attached to the Earth, since it affects the Earth's motion.

    In the interaction between you and the scale, there are two forces. The forces (blue arrows in the diagram) "you push scale down" and "scale pushes you up" are also a Newton's Third Law action/reaction force pair. The force "scale pushes you up" is attached to you in the diagram since it affects your motion. The force "you push scale down" is attached to the scale in the diagram since it affects the scale's motion.

    In the interaction between you and the sink, there are two forces. The forces (green arrows in the diagram) "you push sink down" and "sink pushes you up" are also a Newton's Third Law action/reaction force pair. The force "sink pushes you up" is attached to you in the diagram since it affects your motion. The force "you push sink down" is attached to the sink in the diagram since it affects the sink's motion.

    In this problem, we are only interested in your motion. Since you are in equilibrium, the upward and downward forces on you have to balance (cancel) exactly. This means that Fearth = Fscale + Fsink or Fscale = Fearth - Fsink. So, if your weight is 500 N and you push down on the sink with a force of 50 N, the scale must supply a force of only 450 N to support you, and the scale will read 450 N.

    you pull sink up diagram (b) The situation in which you are pulling up on the sink is shown at right. Here, you pull the sink upward, so the sink pulls you downward. Again, since you are in equilibrium, the upward and downward forces must balance (cancel) exactly, so Fscale = Fearth + Fsink. So, if you weigh 500 N and you pull up on the sink with a force of 50 N, the scale must supply an upward force of 550 N, and the scale reads 550 N.
  8. When the high jumper begins her jump, she pushes downward against the ground. Newton's Third Law says that if "she pushes ground downward" then "ground pushes her upward" must be the reaction force. This force ("ground pushes her") is responsible for her upward acceleration. Actually, there are two forces on her - the ground pushes up (the reaction force to her push) and the Earth pulls down (her weight). The net force on her is the difference: Fnet = Fground - Fearth. So, if she weighs 500 N, she must push downward on the ground with a force greater than 500 N in order to jump (accelerate) upward.

    After she leaves the ground it can no longer push her, so the only force acting on her is her weight ("Earth pulls her" = mg). So she is a projectile!
  9. The forces "Earth pulls satellite" and "satellite pulls Earth" are a Newton's Third Law action/reaction force pair, which means that they must be exactly the same size at all times. Therefore, if "Earth pulls satellite with a force of 1000 N", the "satellite pulls Earth with a force of 1000 N" is the reaction force.
  10. The Earth IS accelerated by the satellite's force! However, Newton's Second Law says that the acceleration of an object depends on both the net force on the object and the object's mass. The mass of the Earth is so enormous that this force only causes an extremely tiny acceleration for the Earth. See the answer to problem 24 for some typical numbers.
  11. The forces "truck pushes bicycle" and "bicycle pushes truck" are a Newton's Third Law action/reaction force pair, which means that they must be exactly the same size at all times.

    However, Newton's Second Law says that the acceleration of an object depends on both the net force on the object and the object's mass. Since the truck has a very large mass (compared to the bicycle's) it gets a relatively small acceleration from this force. The bicycle has a relatively small mass, so the force gives it a relatively large acceleration.
    The smaller acceleration of the truck will cause a smaller change in the truck's motion (velocity), and the larger acceleration of the bicycle will cause a larger change in the bicycle's motion (velocity).
  12. In the interaction between the bus and the bug, we can call the force "bus pushes bug" the action force. Then the force "bug pushes bus" is the reaction force. Since these forces are a Newton's Third Law action/reaction force pair, they are exactly the same size.

    The accelerations of the bus and the bug are definitely not equal, however. Newton's Second Law says that the acceleration of an object depends on both the net force on it and the mass (inertia) of the object. Since the mass of the bus is ENORMOUS compared to the mass of the bug, the same force will accelerate the bus MUCH, MUCH less than it will accelerate the bug.
  13. Rockets don't "push against the air!!!" Rockets are designed so that their engines force the exhaust gasses out the back of the rocket at extremely high speed. This is the action force - "rocket pushes exhaust gasses." The Newton's Third Law reaction force in this interaction must be "exhaust gasses push rocket." This is the force that accelerates the rocket!

    Note that a rocket is a completely self-contained system - no "air" is necessary. In fact, all air does is provide air resistance (drag) to slow the rocket down. Rockets are much more efficient where there is no air! (This is the same as Ch 6 Review Question #8.)
  14. Since the forces "cannon pushes cannonball" and "cannonball pushes cannon" are a Newton's Third Law action/reaction force pair, it is true that they are exactly equal and opposite. However, they do not cancel to produce a zero net force!

    The force "cannon pushes cannonball" affects the motion of the cannonball. The force "cannonball pushes cannon " affects the motion of the cannon. The forces do not cancel because they act on different objects. Only forces that act on the same object can cancel!
  15. If the refrigerator is moving at constant velocity, its acceleration is zero. If its acceleration is zero, then the net force on the refrigerator is zero (Newton's First Law), which means that all of the forces pushing and pulling on the refrigerator must cancel exactly. Therefore, if you push with a force of 200 N on the refrigerator, there must be a 200 N friction force acting on the refrigerator which cancels your force.

    Yes, the forces are equal (both 200 N) and opposite (in direction).

    No, the friction force is not the Newton's Third Law reaction force to your force. Your force is "you push refrigerator," so the Newton's Third Law reaction force must be "refrigerator pushes you." The friction force is "floor pushes refrigerator." so the Newton's Third Law reaction force for it must be "refrigerator pushes floor."

    Notice that the forces that cancel ("you push refrigerator" and "floor pushes refrigerator") both act on the refrigerator.
  16. No, it can't be done. Newton's Third Law says that the two forces "You pull friend" and "Friend pulls you" must be equal in size and opposite in direction. One end of the rope can't be under a greater tension than the other end.
  17. The spring scale reads 50 N. Scales read the tension in the spring - not the net force on it - not the total force on it. (We set up a similar situation in class, remember?)
  18. (a) The tension in the strong man's arms is the same when one rope is tied to the tree. Since the net force on the man is zero (since he is in equilibrium), and the same force is exerted to the right (by the horse), the force exerted by the tree must be the same as the force exerted by the horse in the upper diagram. (Suppose a horse can pull with a force of 500 N. What is the tension in the man's arms? 500 N. See Ch 6 Review #13)

    (b) In the lower diagram, two horses pull to the right. It is reasonable to assume that two horses can pull with twice the force of one horse, so the force pulling to the right on the man is twice what it was before. Therefore, the tension in the man's arms will be twice what it was in the upper two diagrams. (Yes, the tree is exerting twice as much force to the left, too.)
  19. In order to climb upward, the balloonist pulls downward on the rope, so as the balloonist moves upward, the balloon moves downward.
  20. When you get up from a sitting position, your feet must push downward against the floor with a force greater than your weight. Since you are accelerating upward, there must be an upward net force on you. Therefore, the floor must push upward on you with a force greater than your weight. How does the floor "know" to do that? Newton's Third Law! You push downward on the floor with a force greater than your weight, so the floor automatically pushes upward on you with a force greater than your weight.
  21. When a weightlifter jerks a barbell over his head, the force he exerts on the barbell must be greater than the barbell's weight. Since the barbell is accelerating upward, there must be an upward net force on the barbell. This means that the force that you exert upward must be greater than the weight of the barbell (Earth pulls barbell downward).