124 CHAPTER 4 Forces and Newton 's Laws of Motion

SUMMARY The goal of Chapter 4 has been to establish a connection between force and motion,

GENERAL PRINCIPLES

Newton's First Law Consider an object with no force acting on it. If it is at rest, it witi remain at rest. If it is in motion , then it will continue to move in a straight line at a constant speed.

f =o

• • Ii • • • Ii • Ii • , , , , " li= 0

The first law tells us that no "cause" is needed for motion. Uniform motion is the ;'natural state" of an object.

IMPORTANT CONCEPTS

Force is a push or pull on an object.

Force is a vector, with a magnitude and a direction.

A force requires an agen t.

A force is either a contact force or a long-range force.

The SI unit of force is the newton (N). A I N force will cause a I kg mass to accelerate at 1 m/s2.

APPLICATIONS

Identifying Forces Forces are identified by locating the points where other objects touch the object of interest. These are points where contact forces are exerted. In add ition, objects feel a long-range weight force.

Newton's Second Law An object with mass m will undergo acceleration

_ Fnci a=-­

III

where the net force F nel = F I + F 2 + F3 + ... is the vector sum of all the individual forces acting on the object.

F"", Ii

The second law tells us that a net force causes an object to accelerate. This is the connection between force and motion. The acceleration points in the direction of F nel'

Net force is the vector sum of all the forces acting on an object.

¥> = !F, "'\

F "'" = f] + F! + FJ

Newton's Third Law Every force occurs as one member of an action/reaction pair of forces. The two members of an action/react ion pair:

act on two differelll objec ts.

point in opposite direct ions and are equal in magnitude:

... :,....,-_, --+m--,.A---.,~_B_~ Action/reaction pair

A \ B F ,-

~.

Mass is the property of an object that determines its resistance to acceleration.

If the same force is applied to objects A and B, (hen the ratio of the ir acce lera­tions is related to (he ratio of their masses as

The mass of objects can be dete rmined in terms of the ir accelerations.

."-Q Free-Body Diagrams )'

Weight if Normal force ii

A free-body diagram represents the object as a particle at the origin of a coordinate system. Force vectors are drawn with their tai Is on the partic le. The net force vector is drawn beside the diagram.

ii·

r--~T1oI For homework assigned on MasteringPhysics. go to IMP ..

www.mastenngphyslcs.com

Problem diff icu lty is labeled as I (straightforward) to 11111 (challenging).

QUESTIONS

Conceptual Questions

I. A hockey puck slides along the surface of the icc. Iffriction and air resistance are negligible, what force is required to keep the puck moving?

2. If an object is not moving, does that mean that there are no forces acting on it ? Explain.

3. An object moves in a slmight li ne at a constant speed. Is it true that there must be no forces of any kind acting on thi s object? Explain.

4. A ba ll sits ncar the front of a chi ld's wagon. As she pulls on the wagon and it begins to move forward, the ba ll roll s toward the back of the wagon. Explain why the ball rolls in thi s direction.

5. If you know all of the forces acting on a moving object, can you tell in which direction the object is moving? If the answer is Yes, explain how. If the answer is No, give an example.

6. Three arrows arc shot horizontally. They have left the bow and are trave ling parallel to the ground as shown in Figure Q4.6. Air res istance is negligible. Rank in order, from largest to smallest, the magnitudes of the horizon/ol forces Fl' F2, and F3 acting on the arrows. Some may be equal. State your reasoning,

10 m/s 2 9 m/s 3 9 Ill /s

-F-:D~-2> e"D~-2> ~D~-2> 80. 80.

FIGURE 04.6

7. A carpenter wishes to tighten the heavy head of hi s hammer onto its light handle. Which method shown in Figure Q4.7 wil.! better tighten the head? Explain.

S. In ternal injuries in vehicular acci­BID dents may be due to what is

called the "third coll ision." The first collision is the vehicle hit­ting the ex ternal object. The sec-

FIGURE 04.7 ond coll ision is the person hitting

90.

something on the inside of the car. such as the dashboard or windshield. This may cause ex ternal lacerations. The thi rd colli ­sion. possibly the most damaging to the body, is when organs. such as the heart or brain, hit the ribcage, skull , or other confines of the body, bruising the tissues on the Icading edge and tearing the organ from its supporting stmctures on the tra il ing edge. a. Why is there a third collision? In other words. why arc the

organs st ill moving after the second collis ion? b. If the vchicle was traveling at 60 mph before the first co lli ­

sion, would the organs be travel ing more than , equal to, or less than 60 mph just before the third col li sion?

Questions 125

Problems labeled M integrate significant material f rom ear lier

chapters; BNJ are of biological or medical interest.

9. a. Give an example of the motion of an object in which the fric­tional force on the object is directed opposite to the motion.

b. Give an example of the motion of an object in which the fric­tional force on the object is in the same direction as the motion.

10. Suppose you arc an astronau t in deep space, far from any source of grav ilY. You have two objects that look identical, but one has a large mass and the other a small mass. How can you te ll the difference between the two?

11 . Jonathan acce lerates away from a stop sign. I-li s eight-year-old daughter sits in the passenger seat. On whom does the back of the scat exert a greater force?

12. The weight of a box sitting on the floor points directly down. The normal force of the floor on the box points directly up. Need these two forces have the same magnitude? Explain.

13. A ball weighs 2.0 N when placed on a scale. It is then thrown straigbt up. What is it s we ight at the very top of its motion? Explain.

14. Josh and Taylor, standing face-la-face on frictionless ice, push off each other, causing each to slide backward. Josh is much bigger than Taylor. After the push. which of the two is moving faster?

15. A person si ts on a sloped hill side. Is it ever poss ible to have the stat ic friction force on th is person point down the hil.l ? Explain.

16. Walking without slipping requ ires a static friction force BIO between your feet (or fool wear) and the floor. As descri bed in

thi s chapter, the force on your foot as you push off the floor is forward while the force exerted by your foot on the floor is backward. BlIt what about your OllieI' foot , the one moved dur­ing a stride? What is the direction of the force on that foot as it comes into contact wi th the fl oor? Explain.

17. Figure 4.31 b showed a situation in which the force of tbe road on the car's tire points forward. In other situations, the force points backward. Give an example of such a situation.

18. Alyssa pushes 10 the right on a filin g cabinet; the friction force from the floor pushes on it to the left. Because the cabinet doesn' t move, these forces have the same magnitude. Do they form an action/reaction pair? Explain.

19. A very smart three-year-old child is given a wagon for her birth­day. She refuses to usc it. "After all," she says, "Newton's third law says that no matter how hard I pull, the wagon will exert an equal but opposite force on me. So I will never be able to get it to move forward'- ' What would you say to her in reply?

20. Wil.l hanging a magnet in front of an iron cart, as shown in Figure Q4.20, make it go? Explain why or why not.

FIGURE 04.20

126 CHAPTER 4 Forces and Newton 's Laws of Motion

Multiple-Choice Questions

21. I Figure Q4.21 shows the view looking down onto a frictionless sheet of ice. A puck, ti ed with a string to po int P, s lides on the surface of the ice in the circular path shown. If the string sud­denly snaps when the puck is in the position shown, which path best represents the puck's subsequent motion?

22.

B c D A

String E .--:.;;~+-----+ P ~ Puck

String snaps otT here

FIGURE 04.21

I A block has acceleration a when pulled by a string. If two ident ical blocks are glued together and pulled with twice the original force, their acceleration wiU be A. ( 1/4)a B. (1/2)0

c. 0

E. 4a D. 2a

23. I A 5.0 kg block has an accelerat ion of 0.20 mlS" when a force is exerted on it. A second block has an acceleration of 0.1 0 m/s2

when subjec t to the same force. What is the mass of the second block? A. 10 kg B. 5.0 kg C. 2.5 kg D. 7.5 kg

24. I Tenni s baUs experi ence a large drag force. A tennis ball is hit so that it goes straight up and then comes back down. The direc­tion of the drag force is A. Always up. B. Up and then down. e. Always down. D. Down and then up.

25. I A person gives a box a shove so that it slides up a ramp, then reverses its motion and s lides down. The direction of the force

of friction is A. Always down the ramp. B. Up the ramp and then down the ramp. e. Always down the ramp. D. Down the ramp and then up the ramp.

PROBLEMS

Section 4.1 What Causes Motion?

I. I Whiplash injuries during an automobile accident are caused BIO by the inerti a of the head. If someone is wearing a seatbelt, her

body will tend to move with the car seat. However, her head is free to move until the neck restrains it, caus ing damage to the neck. Brain damage can also occur.

Figure P4.1 shows two sequences of head and neck motion for a passenger in an auto accident. One corresponds to a head­on colli s ion, the other to a rear-end collision. Which is which? Explain.

26. I A person is pushing horizontally on a box with a constant force, caus ing it to sl ide ac ross the fl oor with a constant speed . If the person sudde nly s tops pushing on the box, the box will A. Immediately come to a stop. S. Continue movi ng at a constant speed for a while, then grad­

ually slow down to a Slap. e. Immediately change to a slower but constant speed. D. Immediately begin slowing down and eventuall y stop.

27. I Rachel is pushing a box across the noor while Jo n, at the same time, is hoping to stop the box by pushing in the opposite direction. There is friction between the box and floor. If the box is moving at constant speed, then the magnitude of Rachel's pushing force is

28.

29.

A. Greater than the magnitude of Jon's force. S. Equal to the magn itude of Jon 's force. C. Less than the magn itude of Jon's force. D. The question can't be answered without knowing how large

the friction force is. II Dave pushes hi s four-year-old son Thomas across the snow on a s led. As Dave pushes, Thomas speeds up. Which statement is true? A. The force o f Dave on Thomas is larger than the force of

Thomas on Dave. B. The force o f Tho mas on Dave is larger than the force of

Dave on Thomas. C. Both forces have the same magnitude. D. It depends on how hard Dave pushes on Thomas. I Figure Q4.29 shows block A silting on top of block B. A con­stant force F is exerted on block. S, causing b lock S to acceler­ate to the righl. Block A rides o n block B without s lipping. Which statement is true? A. Block B exerts a fric tion force o n b lock A, directed to the

left. B. Block B exerts a frict ion force o n block A, directed to the

right. C. Block B does not exert a friction force on block A.

A

B

FIGURE 04.29

Time_

"O" .... :'~ );} AD

2. I An automobile has a head-on BID colli sion. A passenger in the car

experiences a compress ion injury to the bra in. Is thi s injury mos t likely to be in the front or rear portion of the brain? Explain.

3. j In a head-on colli sion, an infant is much safer in a child safety seat when the scat is insta ll ed facing the rear of the car. Explain .

Section 4.2 Force

Problems 4 through 6 show rwo forces ac ting on an object at rest. Redraw the diagram, then add a third force that wi ll allow the object to remain at rest. Label the new force Fl'

4. 5. II

r _-1" 1',

F,

FIGURE P4.4 FIGURE P4.5

Section 4.3 A Short Catalog of Forces

Section 4.4 Identifying Forces

6. II

> F,

FIGURE P4.6

7. II A mountain climber is hanging from a rope in the middle of a crevasse. The rope is vertica l. Identify the fo rces on the moun­tain cl imber.

8. III A circus clown hangs from one end of a large spring. T he other end is anchored to the ceiling. Identify the forces on the clown .

9. 1111 A basebaLl player is sliding into second base. Identi fy the forces on the baseball player.

10. 11111 Ajet plane is speeding down the run way during takeoff. Air res istance is not neg ligible. Ident ify the forces on the jet.

II . ! A skier is sliding down a 150 slope. Frict ion is not negligible. Identify the forces on the skier.

12. II A ten nis ball is n ying horizontally ac ross the net. Ai r resis­tance is not negligible. Identify the forces on the ba ll .

Section 4.5 What Do Forces Do?

13. Jill Figure P4 .1 3 shows an accelerat ion-versus-force graph for three objects pulled by rubber bands. The mass of object 2 is 0.20 kg. What are the masses of objec ts 1 and 3? Ex pla in yo ur reason ing.

FIGURE P4.13

(/ (m/s2)

5

4

3

2

2

2 3 4 5 6 Force (number of rubber bands)

Problems 127

14. I A constant force applied to object A causes it to acce lerate at 5 m/s 2

• The same force applied to object B causes an accelerati on of 3 m/s 2. Applied to object C, it causes an acceleration of 8 m/s 2.

a. Which object has the largest mass? b. Which object has the smallest mass? c. What is the ratio of mass A to mass B (m AIm B)?

15. Two rubber bands pulli ng on an object cause it to accelerate at 1.2 m/s 2

.

a. What will be the object's accelerat ion if it is pulled by four ru bber bands?

b. What wi ll be the acce leration of two of these objec ts glued together if they are pulled by two rubber bands?

16. A constant force is appl ied to an object, caus ing the object to accelerate at 10 m/s 2. What will the acceleration be if a. The force is halved? b. The object ' s mass is halved? c . The force and the object's mass are both halved? d. The force is halved and the object's mass is doubled?

17. A constant force is appl ied to an object, causing the object to acce lerate a18.0 m/s 2

• What will the accelerat ion be if a. The force is doubled? b. T he object's mass is doubled? c. The force and the object's mass are both doubled? d. The force is doubled and the object's mass is halved?

18. III A man pulling an empty wagon causes it to accelerate at 1.4 n:lfs2

. What will the acceleration be if he pulls with the same force when the wagon contains a child whose mass is three times that of the wagon?

19. I A car has a maxi mum accelerati on of 5.0 m1s2• What will the

max imum acceleration be if the car is lowing another car of lhe same mass?

Section 4.6 Newton 's Second Law

20. II Figure P4.20 shows an accelerat ion-versus-force graph For a 500 g object. Redraw thi s graph and add appropriate accelera­ti on values on the verti cal scale.

o -IL--~-~-~-~F (N) FIGURE P4.20 0 2

2 1. I Figure P4.2 1 shows an objec t's acceleration-versus- force graph. What is the object's mass?

3

2

o -IL--~-~-~-~ F(N) FIGURE P4.21 0.0 0.5 1.0

128 CHAPTER 4 Forces and Newton 's Laws of Motion

22. II Two children fight over a 200 g stuffed bear. The 25 kg boy pulls to the right with a 15 N force and the 20 kg girl puBs to the left with a 17 N force. Ignore all other forces on the bear (such as its we ight). a. At thi s instant , can you say what the velocity of the bear is?

If so, what are the magnitude and direction of the velocity? b. At this instant, can you say what the accele rati on of the bear

is? Lf so, what are the magn itude and direction of the accel­eration?

23. II A 1500 kg car is travel ing along a straight road at 20 m/s . INT Two seconds later its speed is 21 m/s. What is the magnitude of

the net force acting on the car during thi s ti me? 24. II Very small forces can have tremendous effects on the motion

of very small objects. Consider a single electron, with a mass of 9.1 X 10- 31 kg, subject to a single force equal to the weight of a penny, 2.5 X 10- 2 N. What is the acceleration of the electron?

25. II The motion of a very mass ive objec t is hardly affected by what would seem to be a substantial force. Consider a super­tanker, with a mass of 3.0 X 10K kg. If it is pushed by a rocket mOlOr (see Table 4.2) and is subject to no other forces, what will be the magn itude of its acce leration?

Section 4.7 Free-Body Diagrams

Problems 26 through 2R show a free-body diag ram. For each, (a) Redraw the free-body diagram and (b) Write a short description of a real object for which this is the correct free-body diagram. Use Exam­ples 4.3, 4.4, and 4.5 as models of what a description should be like.

26. I " 27. 1 y

F,IJru~

--+--< tF .. x

D w

F..." = 0 FIGURE P4.26 FIGURE P4 .27

28. "

_-. __ ~J."--+ ____ _ x

iI'

FIGURE P4 .28

Problems 29 through 35 describe a situat ion. For each, identify all forces acting on the object and draw a free-body diagram of the object.

29. II Your car is sitting in the parking lot. 30. II Your car is accelerating from a stop. 3 1. Your car is slowing to a stop from a high speed. 32. Your physics textbook is sliding across the

table. 33. II An ascending e levator, hang ing from a cable,

is comi ng to a stop. 34. II A skier sl ides down a slope at a constant speed. 35. III You hold a picture mot ionless aga inst a wall

by press ing on it, as shown in Figure P4.35. FIGURE P4 .35

Section 4.8 Newton's Third Law

36. II A weightl ifter stands up from a squatting pos ition while hold ing a heavy barbell across hi s shoulders. Identify all the act ionlreact ion pairs of forces between the we ight lifter and the barbell.

37. II Three ice skaters, numbered 1, 2, and 3, stand in a line , each with he r hands on the shoulders of the skater in front. Skater 3, at the rear, pushes on skater 2. Identiry all the ac tionl reaction pairs of forces between the th ree skaters. Draw a free­body diagram for skater 2, in the middle. Assume the ice is frictionless.

38. I A girl stands on a so ra. Ident ify alllhe actionlreaction pairs of forces between the girl and the sofa.

General Problems

39. I Redraw the mot ion diagram INT shown in Figure P4.39, then

draw a vector beside it to show the direction of the net force acting on the object. Ex plain your reason ing.

40. I Red raw the motion diagram INT shown in Figu re P4.40, then

draw a vector beside it to show the direction of the net force acting on the object. Explain

i t

your reasoning. v 4 1. I Redraw the mot ion diagram FIGURE P4 .39 FIGURE P4.40

INT shown in Figure P4.41 , then draw a vector bes ide it to show the direction of the net force acting on the objec t. Expla in your reasoning.

FIGURE P4 .41

v

,If" /

/ FtGURE P4.42

42. I Redraw the motion diagram shown in Figure P4.42, then INT draw a vector beside it to show the direction of the net force act-

ing on the objec t. Ex plain your reasoning.

Problems 43 through 49 show a free-body diagram. For each:

a. Redraw the diagram. b. Identify the direction of the acce leration vector a and show it

as a vector next to your diagram. Or, if appropriate, write a= O.

c. Write a short description of a real object for which thi s is the correc l free-body diagram. Use Examples 4 .7, 4 .R, and 4.9 as models of what a description should be like.

C

43. I )" 44. I .l'

" 1. f X

iii -Foct

FIGURE P4.43

45. I

" F " 1.

X

II' ~

,..-"",

FIGURE P4.4S

47. y

FIGURE P4.47

49. .l'

FIGURE P4 .49

50. HIli A student draws the flawed free~body diagram shown in Figure P4.50 to represen t the forces acting on a car travel ing at constan t speed on a leve l road. Identify the errors in the dia­gram, then draw a correc t free-body d iagram for thi s situat ion.

Incorrect diagram!

" "

. /-+--=+--x Action! Car 1,.,.,\ re~ction~ p;m

ii·

FIGURE P4.50

." Incorrect diagr;Jm!

jj

iv

FIGURE P4.51

5 1. III A stude nt draws the flawed free-body d iagram shown in Figure P4.S I to represent the forces acting on a gol f ball that is travel ing upward and to the right a very short time afte r be ing hit o ff the lee . Air res istance is assumed to be relevant. Ide nti fy the errors in the diagram, then draw a correct free-body diagram for thi s s ituation.

Problems 129

Problems 52 through 63 describe a situation. For each, draw a motion d iagram, a force identification diagram, and a free-body diagram.

II An elevator, suspended by a s ingle cable, has j ust left the tenth fl oor and is speeding up as it descends toward the grou nd floor. III A rocket is being launc hed straight up. Air res istance is not negl ig ible. III A jet p lane is speed ing down the runway during takeoff. Air resistance is not negl igible. II Yo u've slammed on the brakes and yo ur car is skidd ing to a stop while going down a 20° hi ll. II A skier is go ing down a 20° s lo pe. A horizontal headwind is blowing in the skier's face. Friction is smaU, but not zero. II A bale of hay s its on the bed of a trailer. The trailer is starting to accelerate fo rward, and the ba le is s li pping toward the back of the tra iler. II A Styrofoam ball has just been shot straight up. Air resistance is not neglig ible. III A spring- loaded gun shoots a plastic ball. The tr igger has just been pulled and the ball is starting to move down the barre l. The barrel is horizon tal. II A person on a bridge throws a rock straight down toward the water. The rock has just been released. III A gymnast has j ust landed on a trampo line. She's sti B mov­ing downward as the trampol ine stretches. ll! A heavy box is in the back of a truck. T he truck is accelerat­ing to the right. Apply your anal ysis to the box. II A bag of groceries is on the back seat o f your car as you stop for a stop li ght. The bag does not slide. Apply yo ur analys is to the bag. II A rubber ball bounces. We'd like to understand how the ba ll bounces. a. A rubber ball has been dropped and is bouncing off the floor.

Draw a mot ion diagram of the ball during the brie f time interval that it is in con tact with the fl oor. Show 4 or 5 frames as the ball compresses . then another 4 or 5 frames as it expands. What is the directi on of {j duri ng each of these parts of the motion?

b. Draw a picture of the ball in con tact with the fl oor and iden­tify all forces acti ng on the ball .

c. Draw a free-body d iagram of the ball duri ng its contact with the gro und. Is there a net force act ing on the ball ? .If so, in which d irection?

d. During contact, is the fo rce of the ground on the ba ll larger, smaller, or equal to the weight of the ball? Use your answers to parts a-c to exp lain your reasoning.

65. If a car stops suddenl y, you feel "thrown forward." We' d like to understand what happens to the passengers as a car stops. Imag ine yoursel f sitt ing on a very slippe ry be nch ins ide a car. Thi s bench has no fricti on, no seat back, and there 's nothing for

you to ho ld on to. a. Draw a picture and identify all of the forces acti ng on you as

the car trave ls in a straight line at a perfec tl y steady speed on level ground.

b. Draw your free-body d iagram. Is there a net force on you? If so, in which di rection?

c. Repeat parts a and b with the car slowing down. d, Describe what happens to you as the car slows down. e , Use Newton 's laws to ex pla in why you seem to be " throw n

forward" as the car stops. Is there really a force pushing you forwill'd?

130 CHAPTER 4 Forces and Newton 's Laws of Motion

66. 1111 The fastes t pitched baseball was cloc ked at 46 m/s . If the BID pitcher exerted hi s force (assumed to be hori zontal and constant)

over a distance of 1.0 m, and a baseball has a mass of 145 g. a. Draw a free-body diagram of the ball during the pitch. b. What force did the pitcher exert on the ball during this

record-setting pitch? c. Estimate the force in part b as a fraction of the pitcher 's

weight. 67. Tbe froghopper, champion leaper of the insect world, can BID jump straight lip ar 4.0 m/s. The jump itsel f lasts a mere 1.0 ms

before the insect is clear of the ground. a. Draw a free-body diagram of this mi ghty leaper while the

jump is taking place. b. While the jump is taking place. is the force that the gro und

exerts on the frog hopper greater than, less than , or equal to the insect's weight? Explain.

68. A beach ball is thrown straight up, and some time later it lands on the sand. Is the magnitude of the net force on the ball greatest when it is going up or when it is on the way down? Or is it the same in both cases? Explain. Air resistance should not be neglected for a large, light object.

Passage Problems

A Simple Solution for a Stuck Car

If your car is stuck in the mud and you don ' t have a winch to pull it out, you can use a piece of rope and a tree to do the trick. First, you tie one e nd of the rope to your car and the other to a tree, then pull as hard as you can on the middle of the rope, as shown in Figure P4.69a. This technique applies a force to the car much larger than the force that you can apply directly. To see why the car experi e nces such a large force, look at the forces acting on the center point of the rope, as shown in Figure P4.69b. The sum of the forces is zero, thus the tension is much greate r than the force you apply. It is this tension force that acts on the car and, with luck, pulls it free.

Stop to Think 4.1: C. F,

F2 , -----~"-+

: FJ I} : y-component of F) _ _____ I cancel" -,, ·component of F l.

'---r---' _ (-component of F1 i, to the left and larger than the x·component of F~ .

Stop (0 Think 4.2: A, B, and D. Friction and the normal force are the only contact forces. Nothing is touching the rock to provide a "force of the kick." We 've agreed to ignore air res istance unless a problem spec ifically caUs for it.

Stop to Think 4.3: B. Acceleration is proportional to force, so dou­bling the number of rubber bands doubles the acceleration of the original object from 2 m/s2 to 4 mls2

• But acceleration is also inversely proportional to mass. Doubling the mass cuts the accelera­tion in half, back to 2 m/s2

.

(,) N

W 4 E 1 Pull rope in this direction

~ ___ s --Ji.------ro::Ol (b) 1 - -

c:: J The !'>Ul1~ of ule force --- _ vecton. !~ 7ero.

FIGURE P4 .69

69. I The sum of the three forces act ing on the center point of the rope is assumed to be zero because A. This point has a very small mass. B. Tens ion forces in a rope always cancel. C. This point is not accelerating. D. The ang le of deflection is very small.

70. I When you are pulling on the rope as shown , what is the approximate direction of the tension force on the tree? A. North B. South C. East D. West

71. I Assume that you are pulling on the rope but the car is not moving. What is the approximate direction of the force of the mud on the car? A. North B. SOllth C. East D. West

72. I Suppose your efforts work, and the car begins to move for­ward out of the mud . As it does so, the force of the car on the rope is A. Zero. B. Less than the force of the rope on the car. C. Equal to the force of the rope on the car. D. Greater than the force of the rope on the car.

Stop to Think 4.4: D

F,

F,

F,

First lIdd PI and F2·

Then add F,. This is P ,"".

ii

ii is in the slime direction as F "",.

Stop to Think 4.5: C. The acceleration vector points downward as the elevator s lows. Fne! points in the same direction as G, so FIleI also points downward. This will be true if Ihe tension is less than the weight: T < w.

Stop to Think 4.6: C. Newton 's third law says that the force of A on B is equal and opposite to the force of B on A. This is always true . The mass of the objects isn' t relevant.