PROBLEMS

130 CWAPTER 4 Newton's Laws of Motion
Key Terms
dynamich. If17
Newton's lawa ol motion, 107
classical (Newlnnian) ~nwhanics, 107
force. 108
contact force, 108
r~ortnal force, 108
f~,ic.tion force, 108
tctlsiot~ €orce, 108
long-rancz rurces, 108
weight. I08
superposition nf forces, IUY
net force, IIO
Newton's first law oCmc)tion, Ill
inerria. 112
eyuilibrii~t~i, 112
inertial frame of reference, 113
tIMS5, lib
kilogratl~. 116
~IP.W[OII, I16
Newtuu'r s.e~.ond Ii~rv of molicln, 117
Newton's third law of motion, 123
action-reactiot~ pair. 123
tension, 126
free-body diagram, 127
Answer to Chapter Opening Question 7
Newton's lhird law wlla u> that the seated child (who we'll call
Ryder) pushes a1 the btantling cllild (who we'll call Slan) just as
hard as Stan pushrh on Kydzr. but In the opposite direction. This is
tme whether Rydrr pu\he\ I)n Sun "actively" (for instance, if
Ry&r pushed his hand again.;[ Stan's) w "passively" (if Ryder's
back does the puching, ~LS in the photograph that opens the chaptco.
The force niagniludes would he gr-cater in the "active" case
than in the "passive" case, hul either way Ryder's push otl St,m is
iuat as strot12 as Stan's puqh on Kyder.
Answers to Test Your
Understanding Questions
4.1 Answcr: (iv) The gr~vitatiunill force on the crate poinrs
straight downward. In Fig. 4.6 thc x-axis points up and to the
right, and the y-axih pr~ints up and to the left. Hence the gravila
tianal force has both 21) ~-cornponcqit and a y-component, anci
both arc negative.
4.2 Answer: (i), (ii), a ~ (ir) ~ d 111 (i). (~i!. ar~d (iv) the body is out
accelerating, so the net force on Ihr huJy ih zero. [In (iv), the box
rema~ns stationary as seen in the iner~ial rcfircncc frame of the
ground as the truck actcceleraies forward, likc the skater in
Fig. 4. I la.] In (iii), the hawk is moving in a ~,ircle: hcncc it is
accelwati~ip and ri tlor in equilibrium.
4.3 Answer: (iii), (i) and (iv) (tie), (ii) The accelrra~ion is zqir~l to
the net ftirlrcc divided by the mass. Hence the ~nagn~~udt of thr
accrleratiilrl UI each situation is
0) Q = (2.0 ~)](2.0 kg) = 1.0 m/s2:
(ii) u = (x.0 N j /(2.0 N ) = 4.0 rnls2:
(iil) a = (2.0 N)I{XII
kg) = 0.25 1111s-.
(ib) n = (8.0 N ) l(8.0 kg ) = 1.0 1111s'.
4.4 It would Lake twice the effort tot thc iiSU'OWdUt to walk WUUII~
because her weight un the planrt wculrl bc twice as much as on the
earth. Bul ir would he just a< easy 11, catct~ a ball moving hosizontally.
The ball's ?nun is the Fame ah nn carth, so thc horizontd
force the astronaut woulcl have to exert tc~ bring it tc) a stop he.. tu
give it the same acceleration) would also he lhe same as on earth
4.5 Uq' Newton's third law, the two forces have equal magnitudes
Because the car has much greater mass than (he mohquito. it under-
FDCS only a tiny. itnpercepiible acceleration in rebptmsr to the
tnrcc of the uupact By contrast, the mosquito, with 11s mlnuccult
rndss. undergoes a catastrophically large acceleration.
4.6 Answer: (i\) Thc buoyancy force is an uptpwurrl force that the
wntir exznc on thc nrmrmnaPP: By Newton's third law, the other half
of the ;c~ioii-rza~tiun p~irs a dowawnrd fo~cc that the slt.immer
rxt'rth on the wat~r and has the same magnitildr: ns the buoyancy
force. ll's (rut: that tbc wcight of the sw~nutlet is aIso downward
and has (he sanic magnitude ss tl~c b~oy~ltlcy force: however, the
weight acls un the 5amc borlv (TIIF bwillunet) as the buoyancy
force, and so Ihe5e force'; aren't an act~nn-rfiic'tio~i pair.
PROBLEMS
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Discussion Questions
m.1. Can :I body he in equ~ljbriu~li when 0111 one force acts on it?
Explain.
Q4.2. A hall thrown straighr up hns zert? velocity at its highcst
point. Is lhe ball in equilibrium at thiq point? Why or why nut'!
44.3. A helium balloon ROYCIS In mirl:~ir, ne11h.e:- ascending nor
descending. Is it in equilibrium? What foxes acl on iit?
44.7. WRrn a r.31 \tops suii~lcnly, the passengers tend to make forward
rela11te t ~ tlxit- ) seat>. Why'! When a car inakes a sharp turn,
the passengers rend ro slid< to une side of thc car. Why?
44.8. Same people say that thc "force of inertia" (or -'force of
momenlum") throws the passevgers forward whcn n car brakes
sharply. Whai is wrong with this explanation'!
44.9. 4 passenger in 3 moving bus 1l:irh Ilo WIII~~WL
notizcs that a
ball ttl~t has been at xsl in the aisle xuddenl? stam ttj tnove toward
the rwr of the bus. Think of two dilTerenl p>hsthle ekplwations,
iilid devise a way to decide which is crlrrecl.
44.10. Suppose you chose the fundanjental SI units 10 he rorcrce,
le11gt11. atid time instead of mass, length, hnd time. What would he
Q4.4. When you fly in ail airplane at night in smooth air. there i<
no sensation of mtrlicrn, ecen though the plane rnay be rnovin~ at
800 hnlh ( 50(1 n11/ h ) . Why is this:'
Q4.5. If the twr end5 r)f a rope in equilibrium are pulled ~.iih
forces of elpal magnltucle and opposite direction: why is rhr torah the ullits of mass iri terms of lhose r~nda~nental ~mits?
tcnsion in lhe rup no1 /~I-O.!
Q4.11. Some of the ancient Greeks thought that the "nat~~ral stale"
Q4.6. You tie :I bn~k II? the end uf a rope and whirl rht brick uf an object was to be at rest. so objects would seek their natural
muund you in a horjzonral iir~le. Describc thc path ol the brick stale by cuining tu rclt lt left alotle. Explain why this view can
after you suddenly let go of the ]-ope.
actwilly heem qulle plau\ihlc iti t 1 eve~yday ~ world.

Exercises 1 31
44.12. Why is Lhe earth o~ily approximately an inertial reference
frame?
04.13. Does Newton's second law hold rnle for an observer in a
van as it speeds up, slows down, or rounds a corner? Explain.
44.14. Sorne students refer to the quantity naz as "the force of acceleration."
Is it correct to refer to this quantity as a force? If so, what
exerts this force? If not. what is n better description of this quantity9
44.15. The acceleration of a falling body is measured in an elevator
traveling upward at a constant speed of 9.8 m/s. What result is
obtained?
Q4.16. Yuu can play catch w~tb a suttbdl in a bus moving wrth
cunstant spccd un a straight road. just as though thc bus wcrc at
rest. Is this still po~siblc whca thc bus is mnking 21 turn at ct>nstant
speed 011 a level ruad'! Why or why notr!
44.17. Students sumetimes say that the tcjrce uf gravrty

132 CHAPTER 4 Newton s Laws of Motion
4.3. A warehou>c wurker pushes a crate alot~g the floor, as shown
in El:. 4.3 I . with a for a ptihul~ ulth
mass 60 kg who is resting on the edge 01' 3 h\r imminp pool, whar
hori~c~ntal ilccclcration is produced9
4.8. What rriagnit~lrle OF net fforce is rcquned tcr pve a 135-kg
refrigerator an accclcration of magnitude 1.40 mls"~
4.9. A box rests on a frozen pond, n,l~ich scrvcs ;is a frictionless
horizontal surrace. If a fishcrmm applies a horizontal force ivilh
niagn~rudc 413.0 N to the box and p~nduces an accelcrahon of magnitude
3.110 mls', what 15 rhc mlus of the box?
4.10. .4 dockwtrrker iipplic\ a cotisant horizontal force or 80.0 N
ro a block (rf ice trn a smrwth Iltwizontal floor. The frictionul force
is neplieiblc. The hlwk 5t~t-t~ from rest and moves 11.0 m in
5 00 s. (a) What is the mass of the block of ice? (b) If the worker

4.18. A bowling ball weighs 71.2 N (16.0 Ib). The bowler :~pplieh a
hurizont~~ force of 160 N (36.0 Ib) to the ball. What is the magnitude
of the hori7c)ntal accclcration of the ball?
4.19. A1 the surface of Jupiter's moon Icr, the acceleration due to
tty is g = 1.81 in/s2. A watermelon weighs 44.0 N at the surf;~~?
or' ihe earth. (a) What js the watcrrnelon's mass on the earth's
surr'acr" (b) Whal are its lnass and wcight on the surface of Io?
4.20. An asironaul's pack weighs 17.5 N whcil she is on earth but
only 3.24 N when she is :it the surface of an asteroid. (a) What is
tile acceleration due to graviiy on this asteroid? (h) What is hc
t11;lsu of the pack on the asteroid'!
(R) What is the reaction to eaih force; ih~t
by which body is the reaction exertzcl?
4.24. Thc upward ~larrnal torce exerted bj the floor is h20 N un an
elevahr passenger who weigh> 650 N. Wh21t are the reaction
tnrcc~ to these two forces? Is rlw p,~s~enger :~ccelerating? If su,
what arc the 111agnitude and dirwrior~ of thz acceleration?
4.25. A >tudcnt wth mass 45 kg jur~ps off a high diving huard.
hing 6.0 /: 10" !q fc~r thc tn:~ss of the earth, what is the acceleration
t)f the earlh toward hst 15: shc ~ccrlerates toward the earth
wilh an accrleration ol q.8 III/~':' Ass~itlle that the net force on the
enrlh is the f~~rcr uf gravity shc cxct-ts otl it.
Sectron 4.6 Free-Body Diagrams
4.26. hn athlete throws a ball of 11m.5 ~ I I dmctl upaard, and II
feels no apprzciahlz air reslstancc. Dr~a n tter-body diagram of
~hjs ball wh~lr 11 i< lrrz ot the athlctc's hm~i atid (a) moving
upward. Ib) ilt itc highr\~ point; (c) movlng doivnw:ird. (d) Repeat
parts (a), (b). nnd (c) if the athlete throws rht. h~ll at .J ho" li~igls
abuvc thc horizo~lral instead of rlllrctl) ilpwitrd.
4.27. Two cratcs, ,-I snd B. it st rest side by side 011 ,I hi'rictionlzrr
h- the earth equal 'ind
opposite to the force exerted on the earth 1y thr book? (k) Is the
force exerted on the hook by yuur hand qua1 snd opposirt ro the
force exerted on your hand by the buok'l Finally, suppose you
constwt s ~ed by a tow rope that is pwallcl to the gmund. The
snatch your hand away while the book is moving upu'ard. (1) Horv
guund sl.Ur 3bo1 c thc hnrimany
forces then act on the btak? (m) Is thc book in equilibrium?
zntal, and you ran ignore friction. (a) Draw a clciuly lal~clcd frcc-
4.23. A bottle is given a push alung a tliblctop and slides off the
hdy diagriim fur the skier. (h) Calculate the tensiun In Ihe tna rope
edge of the table. Do nor ignurc air resibtsncc. (a) What forces are
4.33. A truck is pulling u car un a hurixuntal hrghwuy using a hariexerted
on the bottle while it is call in^ from the table to thc floor?
zontal rope. The car is in neutral gem, so we can mumt thal Ihrrr.
is, on which budy and
is no appreciable friction between its tires and the high\\,ay. .As thr
truck is accelerating to highway speeds, draw a free-body dinpam
of !a) the car and (b) the truck. (c) What force accelemlrs this systern
forward? Explain how this force originates.
Problems
4.34. A 22 siflc bullct, travclmg at 350 xnls, strikcs a luge net,
which it peiietrdtes tu a depth of 0.130 m. The mfis c)f the bullet i\
1.80 g. Assume a constant retarding furce. (a) Ho~v much tline 1s
required fc)s the bullet to stop'! (b) What forcc, in ilcu7tuns. does the
tree exert un the bulletr!
4.35. 'Tiw horses pull hc~i~onntally
lopes attached to a wimp
->
The iwo forces P, and k: that they apply tu the stump are such that
the net (resultant) force 3 h? a magnitude equal to that of z1 and
makes an angle of 90" aith c,. Let F, = t3W N &mJ H = h300 N
also. Find the magnih~de of F, and its direction r relarive to F,)

134 C HAP T E R 4 Nebvtcln's Ldws of Motion
4.36. You hht2 ~U\I Isndeil on Pktnct X. You take out a 100-g ball. hare u mass of 55.0 kg, a~ld air resistatice rwrts a ttrlill upwarrl
release ~t fro111 rest Cram ;1 height OF 10.0 m, and n1easurt that it rcrrce c~f h20 N on hcr and her parachute. (a) \I'hnt is thr &eight tjt
takes 2.2 s ro reach ihe ~ ~ound. You c~~i ignnrc any force on the the paraciiuiist'! (b) Draw a free-body diagram fur ihr p;lrachuti.;i
bdl frij~n the amlosphere of the planet. Ho\r much duel thc 100-p
b;tlI weigh on the surface of Plane[ X?
(see Section 4.6). Use that diagram to calculate ihe nrt force on the
parxhutisl. Is the net force upward or downwx-d7 tc) What 1s the
4.JT TWO adults and n child want Figure 4-36 ~ ~ 4.37. ~ t ,
L~czlen~tion
\ ~ ~
(magnitude ar~d~rectionj of the paraslx~t~sl?
to push a wheeled cart in the
4.43. Tcvu crates, one with mass 4.00 kg and the otbttr w~ih mars
rl11,cciion nrarked x in Fig. 4.36.
6.09 kg, sit on the frictionless surface uf a frozen pond, connecwd
b@f
The two ;~dults push with-hori-
by a light rope (Fig. 4.38). A wuinan wcasing golf shoes (so she
,ont:il forces ?, and F2 as
cml get traction on the ice) pulls horizontally nn the 6.00-kg crate
sh~)wn in the figure. (a) Find the
with a force F that gives the crate an accceleratiuii uf 2-50 mls2.
'
rt~~~giilude and direction of the
(ii) What 1s the acceleration of the 4.00-kg ct-ale'! (b) Draw a frccsnl~~llc.~t
force that the child
body diiigran~ for the 4.00-kg crate. Use that diagram aiid Ncw-
\ha~llcl cxefl. Yuu can ignore the
ton's second law tcr firid the tensicrn Tin lhc n)pe that connects thc
cffer.!.; or friction. (b) If thc
two cratcs. (c) Dm\\- a free-body diagram I;)r lhe 6.00-kg crate.
ch~ld txeris ihe minimum forcc
What is thc direcdon of the net force on [he b 00-kg crate'? Which
found in part (a). the cart
ix larger in magnitudc. fwrr T or force b"l id) Use part (c) and
accelerates at 2.0 mla' in the
+x-direction. I+'hat IS the weight tlf the iiut'.'
4.38. An oil tankrl.'~ rnginea have hrnbtl down, and the wind is
blowing the tanker s~r.lighl tuward 3 ~ ct' ;kt a constallt speed of
Newton's second law tn c~lcilliiie the t~~agturudt: of the force F.
4.44. An aqlmna~rt is trtherzd by a strong cable to n spacecraft.
The ahtronaut and hcr spaccsujt hve a tod nuas of 105 kg, while
the masx of the cable IS ncpligjble. The Inass of the spacecraft is
1.5 ni/s (Fig. 4.37). Whrn thr tanker IS 5C)U 111 from the reef, the
wind dies down jusi as Ihr: enginerr gets thc cnpines going again.
9.05 x I# kg. The hp;icecr;ift is far from any large astruncrmical
TRc rudder is stuck. 50 the only choice 1% ttj try to accelerate
straight backward awa? from rhe red. The makh of the tankcr ;md
Figure 4.38 Problern 4.43
cargo is 3.h X 10' kg. and the engines produce a nrt horii..ontul
force uf 8.0 X 10% on the tanker. Will Lhe ship hit the rat:' [L it
does, will thc nil be safe? The kuIl can withstand an ilnpact ;it a
sped of 0.2 in/\ or less. You can ignore the recarding for~,e nf ~hc
waler on the ~ulkcr's hull.
Flgure 4.37 Problem 4.38.
hodith, ho *t. cat1 lgnorc thc gravitational forces on it and the
aclrr,n;irlt. We ;11w assume that both the spacecraft and ttw astmnaut
are initially at rcst in an inertial reference frame. The nstronaut
then pulls on the cable \\ith a force of 80.0 N. (n) What force
does the cable exert on the ast~-oneut? (hj Slnce LF = trd, how
can a "mas~less" (nr = 0) cublc exert ;l force'? (2) WLut is the
4.39. -4 Standing Vcrtical Jump. Baskethall playct Darrell aslronaul's acceleratic)nr! (d) What forcc docs the cable ~ W Lon K the
Ciriftith is on record as attuning a standing vert~cal iu111p ot' 1.2 111 spacecraft? (e) Whal is the ;lccelsratil~n c,f the sp~c!c.cir~ft'.'
(4 ft). (Thismeans that he mnwd upward hy I .2 m aftc't. his feet left 4.45. To srudy damage aircraft that cullldc wlth luge birds.
the Row) Grif3ith weighed 890 N (:MI Ih). (a) What is his speed as you design a Lest gun that will accelerutc chickcn-sized objects so
he leaves the floor? (b) If the tilnr nf rhc plirt c ~ the t ii1111p bctbre his that their displacemenl almg the gun barrel 1s givcn by A =
led left thc floor was 0.300 s, wha~ x.a$ his arerJgc. wcclerdtion (9.0 X lo3 rnls2)t2 - (8.0 X l(Y] rn/l;')l3. The ubjcct lcavcs the
(magnitutic and direction) while hr pt~shing agntlst the tloor? end of the barrel ai t = 0.025 s. (a) How lung must hc gun barrel
(c) maw his free-bdy bgram (scr Sr~,tion 4.h). In ktni~ c~f the be? fi) What will be the speed of the objecu as they leave the eiid
forces nn the diagram, wh;it is the net force un h~m? Use Nrkbtc~n's of the barrel? (c) What net force must be exeried on a I 30-kg
laws and the results of part (h) tu s~lculnre the average l'orcz he objcct at (i) t = 0 and (iil I - 0.025 s'?
applied io the ground.
4.40. An arlvertiseirlent chiins that a particular ;~u~olnobile can
"stop on a dime." What nct force would actually he necesxmy tu
stop a 850-kg autoi~lobile t~ avslinp initially at 15.0 ktnlh in a distance
equal to the dran~ete~ ot i dirnc, which is 1.8 cm?
4.41. A 4 8Wkg bucket or wilier i~ accclcrated lipwacd by ;I curd of
negligible mass whose breaking strength is 75.0 N. (a) Draw the
trce-bod>- force d~agrarii Ikr the bucket. In terms of the forces on
your dinglam, whar is the twi [iircc on thc bucket'! (b) Apply Newton'~
sccond law lo t ! hucket ~ and find thc maximurn upward accelwatioii
that can be given to ihc bucket without breaking the cord.
4.42. A pa~acbut~st rzlles on alr I-esixtance (mainly on her pnrachute)
111 decrcasc hcr downward veloci~y. She and her parachute
4.46, A spxczcraft descends vertically near the surrace of Aanet X
,411 upward thrust of 25.0 kt4 from its engines slows it down al a
rntr of 1.20 n~lsl, but it speeds up at a rate of 0.80 m/s2 with an
upru-d 11lrut.t ot 10.0 I;N. (,I) LI each case: what is the direclinn of
the rlccclcratipn of the spac.ecr.~ft? (b) Draw a free-body rliagdm
Tor rhz spa~,tcraft In e ~ct~~~~;c, speeding up or slowiiing down, what
i~ the dilrc~ir>ii ot ihe net fi~rcc a11 thc spacecraft? (c) Apply New-
:on'$ ~;t'c