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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
Newton's Second Law
Newton's Third 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.
An object with mass m will undergo
acceleration
Every force occurs as one member of an
action/reaction pair of forces. The two
members of an acti on/react ion pair:
f =o
, •• , , •• ,
Ii •
li=
Ii •
0
Ii •
"
_
Fnci
a= - -
act o n two differelll objec ts.
III
where the net force Fnel = FI + F2 +
F3 + ... is the vector sum of all the
indi vid ual forces acting on the object.
F"",
point in opposite direct ions and are
equal in magnitude:
.:,.,-_
. . ,--+m
--,.A---.,~_B_~
Ii
The first law tells us that no "cause" is
needed for motio n. Uniform motion is
the ;' natural state" of an object.
The second law tells us that a net force
causes an object to accelerate. Thi s is
the connection between force and
moti on. The acceleration points in the
direction of Fnel'
Action/reaction pair
\B
A
F,-
~.
IMPORTANT CONCEPTS
Force is a pu sh or pull on an object.
Force is a vector, with a magnitude
and a direction.
A force requires an agen t.
A fo rce is either a co ntact force or a
long-range force.
Net force is the vector sum of all the
forces acting on an object.
"'\
¥>
=
!F,
F"'"
The SI unit of force is the newton (N).
A I N force will cause a I kg mass to
accelerate at 1 m/s 2.
APPLICATIONS
Identifying Forces
Forces are identifi ed by locating the
points where other objects touch
the object of interest. These are
points where co ntact forces are
exerted. In add ition , objects feel a
long-range weight force.
=
f]
+ F! + FJ
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
Weight if
Normal force ii
Free-Body Diagrams
A free-body diagram represents
the object as a particle at the
origin of a coordinate syste m.
Force vectors are drawn with
their tai Is on the partic le. The
net force vector is drawn beside
the diagram.
)'
ii·
Questions
r-~T1oI For homework assigned on MasteringPhysics. go to
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..
www.mastenngphyslcs.com
Problems labeled
chapters;
M
125
integrate significant material f rom ea r lier
BNJ are of biological or medical interest.
Problem difficu lty is labeled as I (straightforward) to 11111(challenging).
QUESTIONS
Conceptual Questions
I. A hoc key puck slides along the surface of the icc. Iffriction and
air resistance are negligibl e, 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 mov ing object, can you
tell in whi ch 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. Th ey 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 magn itudes of the horizon/ol forces Fl' F2, an d F3 acting on
the arrows. Some may be equal. State your reaso ning,
10 m/s
2
9 m/s
3
9 Ill/s
-F-:D~-2>
e"D~-2>
~D~-2>
80.
80.
90.
FIGURE 04 .6
7. A carpen ter wis hes to tighten the
heavy head of hi s hammer onto
its li ght handle. Which method
show n in Figure Q4.7 wil.! better
tighten the head? Explain.
S. In ternal injuri es in vehicular acciBID dents may be due to what is
called the "third coll ision." The
first colli sion is the vehi cle hitting the ex ternal object. The secFIGURE 04 .7
ond coll ision is the person hitting
something on the in side of the car. such as the dashboard or
windshield. Thi s may cause ex tern al 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 colli sion? In other words. why arc th e
organs st ill moving after the second collis ion?
b. If the vchicle was traveling at 60 mph before the first co lli sion, wo uld the organs be travel in g more than , equal to, or
less than 60 mph just before the third col li sion?
9. a. Give an exampl e 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 othe r 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 passe nger seat. On whom does the back of
the scat exert a greater force?
12. The weight of a box sittin g 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 weigh s 2.0 N whe n placed on a sca le. 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 withou t slipping requ ires a static fri ction 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 pu sh 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 whi ch the force of tbe road
on the car's tire points forward. In ot her situ ation s, the force
points backward. Give an example of such a situation.
18. Alyssa pu shes 10 the right on a filin g cab inet; 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 ch ild 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 th e 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 subseq uent motion?
B
c
D
A
String
E
.--:.;;~+-----+
P
~ Puck
String snaps otT here
FIGURE 04.21
22. I A bl ock has acceleration a when pulled by a strin g. If two
ident ical blocks are glu ed together and pulled with twice the
original force, their acceleration wiU be
A. ( 1/4)a
B. (1/2)0
c. 0
D. 2a
E. 4a
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/s 2
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 Ten ni s baUs experi ence a large drag force. A tennis ball is hit
so that it goes strai ght 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.
26. I A perso n is pushing horizontally on a box with a constant
force , ca us in g it to sl ide ac ross the fl oor with a co nstant
speed . If the person s udd e nly s top s pus hing on the box, the
box will
A. Immed iately come to a stop.
S. Continue movi ng at a constant speed for a while, then gradually slow down to a Slap.
e. Immediately change to a slower but constant speed.
D. Immed iately begin slowing down and eventuall y stop.
27. I Rachel is pu shing a box across the noor while Jo n, at the
same time, is hopin g to stop the box by pushing in the opposite
direction. There is friction between the box and floor. If the box
is moving at consta nt speed, then the magnitude of Rachel's
pu shing force is
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.
28. II Dave pushes hi s four-year-old son Thomas across th e 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 pu shes on Thomas.
29. I Fi gure Q4.29 shows block A siltin g 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 fri c tion force o n b lock A, directed to the
left.
B. Block B exerts a fri ct 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
PROBLEMS
Section 4.1 What Causes Motion?
I. I Whiplash injuries during an automobile accident are caused
BIO by the in erti a of the head. If someo ne 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 in g damage to the
neck. Brain damage can also occur.
Fi gure P4.1 show s two seque nces of head and nec k motion
for a passe nger in an auto accident. One corresponds to a headon colli s ion, the other to a rear-end collision. Which is which?
Explain.
Ti m e _
"O"....
:'~
);}
AD
Problems
2. I An automobile has a head-on
BID colli sion. A passe nger in the car
experiences a co mpress ion injury
to the bra in. Is thi s injury mos t
likely to be in the front or rear
portion of the brain? Ex plain.
3. j In a head-on colli sio n, an infant
is much safer in a child safet y seat
when the scat is in sta ll ed facing
the rear of the car. Explain.
Section 4.2 Force
Prob lems 4 through 6 show rwo forces ac ting o n an object at rest.
Redraw the di agram , then add a third force that wi ll allow the object
to remain at rest. Label the new force Fl'
4.
5. II
6. II
r >
_-1"
1',
F,
F,
FIGURE P4 .4
FIGURE P4 .5
FIGURE P4 .6
Section 4.3 A Short Catalog of Forces
Section 4.4 Identifying Forces
7. II A mo untain clim ber is hanging from a rope in the middle of a
crevasse. T he rope is vertica l. Ide ntify the fo rces on the mountain cl im ber.
8. III A circus cl ow n hangs from one e nd of a large sprin g. T he
other end is anchored to the ceilin g. Ide ntify the forces on the
clown .
9. 1111 A basebaLl player is slidin g into second base. Identi fy the
forces on the baseball player.
10. 11111 Ajet plane is speed ing down the run way during takeoff. Air
res istance is not neg li gible. Ident ify the forces on the jet.
II . ! A skier is slidin g down a 150 slope. Frict ion is not negli gible.
Identify the forces on the skier.
12. II A ten ni s ball is n ying horizo ntally ac ross the net. Ai r resistance is not negligible. Identify the forces on the ba ll .
127
14. I A constant forc e applied to object A causes it to acce lerate at
5 m/s 2 • The same force appli ed 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. Wh at is the ratio of mass A to mass B (m AIm B)?
15.
Two rubber ba nds pulli ng on an object cause it to accelerate
at 1.2 m/s 2 .
a. What will be th e obj ect's accelerat ion if it is pull ed by four
ru bber band s?
b. What wi ll be the acce leration of two of these objec ts glued
together if they are pulled by two rubber band s?
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 obj ect to
acce lerate a18.0 m/s 2 • Wh at will the accelerat ion be if
a. The force is doubled?
b. T he object's mass is doubled?
c. The force and the obj ect's mass are both doubled ?
d. The force is doubl ed and the object's mass is halved?
18. III A man pulling an e mpty wagon causes it to accelerate at
1.4 n:lfs 2 . What will the acceleration be if he pulls with the same
force whe n th e wago n 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 • Wh at will the
max imum acceleration be if the car is low ing another car of lhe
same mass?
Section 4.6 Newton 's Second Law
20. II Figure P4.20 shows an accelerat io n-versus-force graph For a
500 g object. Redraw thi s graph and add appropriate accelerati on val ues o n the verti cal scale.
Section 4.5 What Do Forces Do?
13. Jill Figure P4 .1 3 shows an accelerat io n-versus-force graph for
three objects pull ed 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 .20
o -IL--~-~-~-~ F (N)
0
2
2 1. I Fi gure P4. 2 1 shows an objec t's acceleration -versus- force
graph. What is the object's mass?
(/ (m/s2)
2
5
4
3
3
2
2
2
FIGURE P4 .13
3
4
5
6
Force (number of rubber bands)
FIGURE P4 .21
o -IL--~-~-~-~ F(N)
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
pull s to the right with a 15 N force and the 20 kg girl puB s to the
left with a 17 N force. Ignore all other forces on the bear (s uch
as its we ight).
a. At thi s in stant , can you say what the velocity of th e bear is?
If so, what are the magnitude and direction of the velocity?
b. At this in stant, 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 in g 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 actin g on the car during thi s ti me?
24. II Very small forces can have tremendous effects on the motion
of very small obj ects. Consider a sin gle electron, with a mass of
9.1 X 10- 31 kg, subject to a sin gle force equal to the weight of a
penny, 2.5 X 10- 2 N. What is the acceleratio n of the electron?
25. II The motio n of a very mass ive objec t is hardly affected by
what wou ld seem to be a substantial force. Co nsider 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 throu gh 2R show a free-body diag ram. For each, (a)
Redraw the free-body di agram 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 descriptio n should be like.
26. I
"
27. 1
y
F,IJru~
tFx ..
--+ - -<
D
F..." = 0
FIGURE P4.26
28.
w
Section 4.8 Newton's Third Law
36. II A we ightl ift er stands up from a squatting pos ition while
hold in g a heavy barbell across hi s shoulders. Identify all the
act ionlreact io n pairs of forces between the we ight lifter and the
barbell.
37. II Three ice skaters, nu mbered 1, 2, and 3, stand in a line , eac h
with he r hands on the shoul ders of the skater in front. Skate r
3, at the rear, pu shes o n skater 2. Identiry all the ac ti onl
reaction pairs of forces betwee n the th ree skaters. Draw a freebody diagram for skater 2, in the middl e. Ass um e th e ice is
frictio nl ess.
38. I A girl stand s 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 in g.
40. I Red raw the moti on diagram
INT shown in Figu re P4.40, then
draw a vector beside it to show
the direction of the net force
actin g on the object. Explain
your reason in g.
v
4 1. I Redraw the mot io n diagram
FIGURE P4 .39 FIGURE P4.40
INT shown in Figure P4.41 , then
draw a vecto r bes ide it to show the direction of the net force
acting on the objec t. Ex pla in your reasonin g.
i
t
FIGURE P4 .27
,I f"
"
_-.__~J."--+_____x
/
/
v
FIGURE P4 .41
iI'
FtGURE P4.42
FIGURE P4 .28
Prob le ms 29 through 35 describe a situat io n. For each, identify all
forces acting on the object and draw a free-body diagram of the object.
29. II Your car is sittin g in the parking lot.
30. II Your car is acceleratin g from a stop.
3 1.
Your car is slow ing to a stop from a high speed.
32.
Your physics textbook is sliding across the
table.
33. II An ascendin g e levator, hang ing from a cab le,
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 ion less aga inst a wall
FIGURE
by press ing o n it, as shown in Figure P4.35.
42. I Redraw the motio n diagram show n in Figure P4.42, then
INT draw a vector beside it to show the direction of the net force actin g on the objec t. Ex pl ain your reasoning.
Problems 43 through 49 show a free-body diagram. For each:
a. Redraw the diagram.
b. Ide ntify th e direction of the acce lerati o n vector a and show it
as a vector next to your diagram. Or, if appropriate, write
a= O.
P4 .35
c. Write a short descripti on of a real object for whi c h thi s is the
co rrec l free-body diagram. Use Ex ampl es 4 .7, 4 .R, and 4.9 as
mode ls of what a description should be like.
Problem s
43. I
44. I
)"
"
1.
C
f
-
iii
.l'
X
Foct
FIGURE P4 .43
45. I
"1.
F
"
X
II'
~
,..-"",
FIGURE P4 .4S
47.
y
FIGURE P4 .47
49.
.l'
FIGURE P4 .49
50. HIli A st udent draws the flawed free~body d iagram show n in
Figure P4.50 to represen t the forces acting on a car travel ing at
co nstan t speed on a leve l road. Identify the errors in the d iagram, then draw a correc t free- body d iagram for thi s situat ion.
Incorrect
diagram!
"
"
. / -+--=+--x
Action! Car
1,.,.,\
re~ction~
p;m
Incorrect
diagr;Jm!
."
jj
iv
ii·
FIGURE P4.50
FIGURE P4.51
5 1. III A stude nt draws the flawed free-body d iagram s hown in
Figure P4.S I to represent the forces actin g on a gol f ball that is
travel in g 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 situatio n.
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, suspe nded by a single cable, has j ust left the tenth
fl oor and is speed ing up as it descends toward the grou nd floor.
III A roc ket is being launc hed straig ht up. Air res istance is not
negl ig ible.
III A jet p lane is speed in g down the runway d urin g takeoff. A ir
resistance is not negl igible.
II Yo u've sla mmed o n th e brakes an d yo ur car is s ki dd in g to a
stop while going down a 20° hi ll.
II A skier is go ing down a 20° slo pe. A horizontal headw ind is
blowin g in the ski er's face. Friction is smaU, but not zero.
II A bale of hay s its o n the bed o f a trailer. The trailer is starting
to accelerate fo rward, and the ba le is s li ppin g toward the bac k
o f the tra iler.
II A Styrofoam ball has just been shot straight up. A ir resistance
is not negli g ible.
III A sprin g- loaded gun shoots a pl astic ball. The trigger has just
been pulled and the ball is starting to move down the barre l. The
barrel is horizon tal.
II A perso n on a bridge throws a rock straight down toward the
water. The rock has just been released.
III A gymnast has j ust lan ded o n a trampo lin e. 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 rig ht. Apply your anal ysis to the box.
II A bag of groceries is on the bac k seat o f your car as you stop
for a stop li ght. The bag does not slide. Appl y yo ur analys is to
the bag.
II A rubber ball bo unces. We'd like to understand how the ba ll
bou nces.
a. A rubber ball has been dropped and is bou ncing off the floor.
Draw a mot ion diagra m of the ball during the brie f time
interval that it is in con tact w ith the fl oor. Show 4 or 5
fra mes as the ball compresses. then another 4 or 5 frames as
it ex pands. W hat is the directi o n o f {j duri ng each o f th ese
parts of the motion?
b. Draw a picture of the ball in con tact w ith the fl oor and identify all forces acti ng o n the ball .
c. Draw a free- body d iagram o f the ball duri ng its co ntact with
the gro und. Is there a net force act in g on the ball ? .If so, in
whi ch d irection?
d. During contact, is the fo rce of the ground o n the ba ll larger,
smaller, or equal to the weight of the ball ? Use your answers
to parts a-c to exp lain your reasonin g.
65.
If a car stops suddenl y, you feel "thrown forward." We' d like
to understand w hat happens to the passengers as a car stops.
Im ag ine yoursel f sitt ing on a very slippe ry be nch ins ide a car.
Thi s benc h has no fricti on, no seat back, and there 's nothing for
you to ho ld on to.
a. Draw a pi cture 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 o n you? If
so, in whi ch di rection?
c. Repeat parts a and b w ith the car slow ing 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 pushin g you
forwill'd?
130
Forces and Newton 's Laws of Motion
CHAPTER 4
66. 1111 The fa stes t pitched baseball was cloc ked at 46 m/s . If the
BID pitcher exerted hi s force (assumed to be hori zontal and co nstant)
over a distance of 1.0 m, and a baseball has a mass of 145 g.
a. Draw a free-body diagram o f 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 in sect 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 in sect's weight? Explain.
68.
A beach ball is thrown straight up, and some time later it
lands on the sand. Is the magnitude of th e 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 s hould 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 ex peri 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 ten sion 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.
(,)
~
1Pull rope in this direction
--Ji.------ro::Ol
___
s
(b)
-
1
c::
J
--- _
-
The !'>Ul1~ of ule force
vecton. !~ 7ero.
FIGURE P4 .69
69. I The s um of the three forces act in g on the center point of the
rope is assumed to be zero because
A. Thi s 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 pullin g on the rope as shown , w hat 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
mov ing. 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.
F2
I}
F,
, ----~"-+
:
_ _ _ _ _I
y-component of F)
_
cancel" -,,·component of F l.
'---r---' _
(-component of F1 i, to
the left and larger than
the x·component of F~ .
Stop
4E
Stop to Think 4.4: D
F,
: FJ
N
W
F,
ii
F,
First lIdd
PI and F2·
Then add
F,.
This is
P,"".
ii is in the slime
direction as F"",.
(0 Think 4.2: A, B, and D. Friction and the normal force are
Stop to Think 4.5: C. The acceleration vector point s downward as
the only contact forces. Nothin g is touchin g the rock to provide a
the elevator slows. Fne! points in the same direction as G, so FIleI also
"force of the kick." We 've agreed to ignore air res istance unle ss a
points downward. This will be true if Ihe ten sio n is less than the
problem spec ifically ca Us for it.
weight: T < w.
Stop to Think 4.3: B. Acceleration is proportional to force, so douStop to Think 4.6: C. Newton 's third law says that the force of A on
bling the number of rubber bands doubles the acceleration o f the
B is equal and opposite to the force of B on A. This is always true . The
original object from 2 m/s2 to 4 mls 2• But acceleration is also
mass of the objects is n' t relevant.
inversely proportional to mass. Doublin g the mass cuts the acceleration in half, back to 2 m/s 2 .