Exercises from Chapter 4

1. Why do you lunge forward when your car suddenly comes to a halt? Why are youpressed backward against the seat when your car rapidly accelerates? In your explanation,refer to the most appropriate one of Newton’s three laws of motion.

Newton’s first law applies. When the car is slowing, you tend to continue moving with the

velocity you had before the car slowed.

2. A bird feeder of large mass is hung from a tree limb, as the drawing shows. A cordattached to the bottom of the feeder has been left dangling free. Curiosity gets the bestof a child, who pulls on the dangling cord in an attempt to see what’s in the feeder. Thedangling cord is cut from the same source as the cord attached to the limb. Is the cordbetween the feeder and the limb more likely to snap with a slow continuous pull or asudden downward pull? Give your reasoning.

The cord between the feeder and the limb is more likely to snap with a slow continuous pull.

With a sudden downward pull that ends quickly, the feeder will largely resist being accelerated

(an object at rest tends to stay at rest).

3. The net external force acting on an object is zero. Is it possible for the object tobe traveling with a velocity that is not zero? If your answer is yes, state whether anyconditions must be placed on the magnitude and direction of the velocity. If your answeris no, provide a reason for your answer.

The object may move at a non-zero velocity provided the velocity does not change. There are

no restrictions on direction.

4. Is a net force being applied to an object when the object is moving downward (a) witha constant acceleration of 9.80 m/s2 and (b) with a constant velocity of 9.80 m/s? Explain.

If an object is moving downward with a constant acceleration, then a net force is acting. If

an object is moving downward with a constant velocity, then there is no net force. This is a

consequence of Newton’s second law: An object is accelerating if and only if a net force acts on

it.

5. Newton’s second law indicates that when a net force acts on an object, it must accelerate.Does this mean that when two or more forces are applied to an object simultaneously, itmust accelerate? Explain.

It is possible to apply two or more forces so that they cancel. If this is the case, then the

acceleration is zero.

6. A father and his seven-year-old daughter are facing each other on ice skates. With theirhands, they push off against one another. (a) Compare the magnitudes of the pushingforces that they experience. (b) Which one, if either, experiences the larger acceleration?Account for your answers.

The pushing forces on the father and daughter are of equal magnitude. The person with the

smaller mass (daughter) experiences the greater acceleration since F = ma.

7. A gymnast is bouncing on a trampoline. After a high bounce the gymnast comes downand hits the elastic surface of the trampoline. In so doing the gymnast applies a forceto the trampoline. (a) Describe the effect this force has on the elastic surface. (b) Thesurface applies a reaction force to the gymnast. Describe the effect that this reaction forcehas on the gymnast.

The force of the gymnast on the trampoline stretches the surface of the trampoline. The force

of the trampoline on the gymnast slows down the fall of the gymnast.

8. According to Newton’s third law, when you push on an object, the object pushes backon you with an oppositely directed force of equal magnitude. If the object is a massivecrate resting on the floor, it will probably not move. Some people think that the reasonthe crate does not move is that the two oppositely directed pushing forces cancel. Explainwhy this logic is faulty and why the crate does not move.

The reasoning is faulty because the action and reaction forces apply to different objects. There-

fore, they will not cancel. The reason the crate does not move is that the frictional force between

the crate and floor is canceling the pushing force.

9. Three particles have identical masses. Each particle experiences only the gravitationalforces due to the other two particles. How should the particles be arranged so each oneexperiences a net gravitational force that has the same magnitude? Give your reasoning.

Place the particles at the vertices of an equilateral triangle. By symmetry, the size of the

gravitational force will be the same for all three.

10. When a body is moved from sea level to the top of a mountain, what changes—thebody’s mass, its weight, or both? Explain.

From Newton’s law of gravitation F = Gm1m2/r2, we see that gravitational force F decreases

as distance r increases. Therefore, the weight of the body is less on the mountain than it is at

sea level. The mass of the body stays the same.

11. The force of air resistance acts to oppose the motion of an object moving through theair. A ball is thrown upward and eventually returns to the ground. (a) As the ball movesupward, is the net force that acts on the ball greater than, less than, or equal to its weight?Justify your answer. (b) Repeat part (a) for the down-ward motion of the ball.

When the ball is moving upward, gravity and air resistance are in the same direction. Therefore,

the net force is greater than the weight. As the ball moves downward, gravity and air resistance

are in opposite directions. Therefore, the net force is less than the weight.

12. Object A weighs twice as much as object B at the same spot on the earth. Would thesame be true at a given spot on Mars? Account for your answer.

Object A will always have twice the weight of object B provided the two are experiencing the

same acceleration of gravity.

13. Does the acceleration of a freely falling object depend to any extent on the location,i.e., whether the object is on top of Mt. Everest or in Death Valley, California? Explain.

There will be a small difference. We take g = 9.80 m/s2, but its true value is location dependent.

In the two examples given, there is a difference of several miles when measuring the distance

between the falling object and the center of the earth. We expect a small difference in g.

14. A “bottle rocket” is a type of fireworks that has a long thin tail that you insert intoan empty bottle, to provide a launch platform. One of these rockets is fired with thebottle pointing vertically upward. An identical rocket is fired with the bottle lying on itsside, pointing horizontally. In which case does the rocket leave the bottle with the greateracceleration? Explain, ignoring air resistance and friction.

The acceleration of the vertical rocket is reduce by gravity. The acceleration of the horizontal

rocket is increased by gravity. Therefore, the horizontal rocket has greater acceleration.

15. A 10-kg suitcase is placed on a scale that is in an elevator. Is the elevator acceleratingup or down when the scale reads (a) 75 N and (b) 120 N? Justify your answers.

In a non-accelerating system, the scale would read 98 N. Therefore, the elevator is accelerating

downward in part (a) and upward in part (b).

16. A stack of books whose true weight is 165 N is placed on a scale in an elevator. Thescale reads 165 N. Can you tell from this information whether the elevator is moving witha constant velocity of 2 m/s upward or 2m/s downward or whether the elevator is at rest?Explain.

All we can tell is that the elevator is not accelerating. It could be moving up, moving down, or

at rest.

17. Suppose you are in an elevator that is moving upward with a constant velocity. Ascale inside the elevator shows your weight to be 600 N. (a) Does the scale register a valuethat is greater than, less than, or equal to 600 N during the time when the elevator slowsdown as it comes to a stop? (b) What is the reading when the elevator is stopped? (c)How does the value registered on the scale compare to 600 N during the time when the

elevator picks up speed again on its way back down? Give your reasoning in each case.

As the elevator slows, the acceleration is downward. Therefore, the scale shows a smaller reading.

When the elevator has stopped, the acceleration is zero and so the scale is back to 600 N. As

the elevator picks up speed on the way down, the acceleration is downward and so the scale

registers a smaller value.

18. A person has a choice of either pushing or pulling a sled at a constant velocity, as thedrawing illustrates. Friction is present. If the angle θ is the same in both cases, does itrequire less force to push or to pull? Account for your answer.

Pulling applies an upward that decreases the normal force. Thus, friction is decreased and so

the applied force can be less.

19. Suppose that the coefficients of static and kinetic friction have values such that µs =2.0µk for a crate in contact with a cement floor. Does this mean that the magnitude ofthe static frictional force acting on the crate at rest would always be twice the magnitudeof the kinetic frictional force acting on the moving crate? Give your reasoning.

The static frictional force is variable and depends on how hard the crate is pushed. Only the

maximum static frictional force is twice the kinetic frictional force.

20. A box rests on the floor of an elevator. Because of static friction, a force is required tostart the box sliding across the floor when the elevator is (a) stationary, (b) acceleratingupward, and (c) accelerating downward. Rank the forces required in these three situationsin ascending order, i.e., smallest first. Explain.

(c) < (a) < (b)

When the elevator is accelerating downward, the normal force is decreased. When the elevator

is accelerating upward, the normal force is increased.

21. A rope is used in a tug-of-war between two teams of five people each. Both teams areequally strong, so neither team wins. An identical rope is tied to a tree, and the same tenpeople pull just as hard on the loose end as they did in the contest. In both cases, thepeople pull steadily with no jerking. Which rope, if either, is more likely to break? Justifyyour answer.

Twice as much force is being applied to the rope when it is tied to a tree. It is more likely to

break in this case.

22. A stone is thrown from the top of a cliff. As the stone falls, is it in equilibrium?Explain, ignoring air resistance.

Ignoring air resistance, the stone is accelerating and therefore, is not in equilibrium.

23. Can an object ever be in equilibrium if the object is acted on by only (a) a singlenonzero force, (b) two forces that point in mutually perpendicular directions, and (c) twoforces that point in directions that are not perpendicular? Account for your answers.

If a single nonzero force is acting, the object must be accelerating and thus, is not in equilibrium.

If two perpendicular forces act, then their sum is not zero. So, again, the object is not in

equilibrium. If two forces act in opposite directions with equal magnitude, then the object will

be in equilibrium.

24. A circus performer hangs stationary from a rope. She then begins to climb upward bypulling herself up, hand-over-hand. When she starts climbing, is the tension in the ropeless than, equal to, or greater than it is when she hangs stationary? Explain.

Since there is a small acceleration when she first starts climbing, there will be a small increase

in tension.

25. During the final stages of descent, a sky diver with an open parachute approaches theground with a constant velocity. The wind does not blow him from side to side. Is the skydiver in equilibrium and, if so, what forces are responsible for the equilibrium?

At a constant velocity, the diver is in equilibrium. The main forces acting on the diver are gravity

and air resistance. These two forces cancel.

26. A weight hangs from a ring at the middle of a rope, as the drawing illustrates. Can theperson who is pulling on the right end of the rope ever make the rope perfectly horizontal?Explain your answer in terms of the forces that act on the ring.

A horizontal rope can only apply horizontal forces. The weight of the object on the string,

however, is a vertical force. Thus, a horizontal rope cannot support the weight.

27. A freight train is accelerating on a level track. Other things being equal, would thetension in the coupling between the engine and the first car change if some of the cargo inthe last car were transferred to any one of the other cars? Account for your answer.

The tension would remain the same. There are two pieces to the system: the engine and the

rest of the train. As the cargo is moved around, both parts of the system maintain the same

mass.