Why does a child in a wagon seem to fall backward when you give the wagon a (so( yq11yeow sharp pull foeq(s 11wyoo y(rward?

A box rests on the (frictionless) bed of a truck. The truck drxrvgm-p5gx4 () cn* 2cyyp vu+)sq.msiver starts the truck and ap4yr+.xx uss- gm )ccvgv5()qn p*my2 ccelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it?w6 f p)roy60px Explain.

Only one force acts on an object. Can the object have zkyi7pa8ortl) 27kt cd5k:6qu ero acceleration? Can it have zero velocity? a6 tupkl5c2qr8dyiok ) :7k7tExplain.

When a golf ball is droppen, b9k8y wxc1(-sq qcad to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) Ifn(-sx9wq a,yqb 1 c8ck so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the opposd/ h5(yqc:nn7m pt8a8atjs2fite direc: pj( 8578q2 /mcahnyt nasfdttion?

Why might your foot hurt if ,xom)edy;st * sy-lj8you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must dec),sd avz6r3m helerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to re s6 d,zra)3vhmst.    m/s$^2$

A stone hangs by a fine thread from n 7)cjrsc3k/j the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is tc)s jnrc 7k3j/he thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rou0k/ 5 ;6psscpfgffbki5 7(g ick is twice as great as that on a 1-kg rock. Why theg5 c5i p kf/ s0isugfb(p;k6f7n doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon8 lgj9ln 7:xw q-qa s5l,fexm7 give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilogr9nlflqg 87aw,jx :7 q-xe5s mlams?

You pull a box with a constant force across a frictionless taty o s7jsq 3lvboxo+/6 .sgl:g9nz84ible using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleratiogyls8tsg/s o673o xinql9 b:o4j. vz+ n of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under thusp-0e aln baf z fuop*4pma2 n (j54446l8nude influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third nms 45-zl (uo4n*04p6ulb8nad42pefpaj f ualaw the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needxuuf5w;b n93sb r((k*;umow led to lift a 10-kg object when you are on the Moon with the force needed to lift it on Esu wm39;*u xub; o5 bfnwk(l(rarth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in nwyau45 s:g,o rgp)9 ya tug of war (Fig. 4–37) pulls with equal force on the other team. What, thenw uy5o,g)g sa9n4:p yr, determines which team will win?

A person exerts an upward force of czqb okzz9nm5+,fu0ra3 h1d 640 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d)6k13fcuq dz0,z9mbh n aoz+5r by what object it is exerted.

When you stand still on t9( l-p9dp0 l mol3x hfb4izu9rhe ground, how large a force does the ground exert on you? Why doesn’t this force make you ris rlxoi 34u ml0(9d9pf-lz9bphe up into the air?

Whiplash sometimes results:9(fh8mrb0(obgpbov :9ds ab from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in th 9b:8rsv((b 9op0g faobm hdb:is situation. Is it really?

A heavy crate rests vonqe+z(dx + o6oz;a 8:2eeboon the bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, (qnb x+a 8+ doz o:ez;v2eoo6eaccelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Aftgge7hv0 / hm 0du;o,espf j e0.jh:o3qer the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on tj eqm es oeuhg307 g:d 0hov,j.f0ph;/he ascent. Why?

What would your bathroom scale read if you weighed yourself oz9.qfehfnj-slj:4 ifawv (e x7 n293un an inclined plane? Assume the mech97efehfw:zx2(q uv s fi n-a9l3jn.j4anism functions properly, even at an angle.

  What force is needed to accelerate a 8yee6kgee)8z child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ridek4 q:kf;qe/qjr at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand 2. goux 7qnyn;jf+ cj08saf;v if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a a /f:812b lue7ejn+q-bp pkkmcvp3+ c $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s if the car is tr7kbpsl n rlz g *2,4z2dnf5im:aveling at i5m7r2 4:*ks2dznpbl lgf,z n95km/h? -  

  What average force is needed to accelerate a 7.00-gram pelle( so as:k p)05jxrbxi(t from rest to 125m/s over a distance of 0.800 m along the barrel of a rifl()k0 bx r(s:oajpxsi5 e?   

A fisherman yanks a ak.zqc17r,s s0d izw7fish vertically out of the water with an acceleration of 2.51 7,zs qikc7z adws0.r $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can covermxedj.;p) a0hve b:b- a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that thzk k su219xchw :0kv6 2pyt )wekvcm:4e maximum acceleration is 0.0680 g . What are the maximum and: 0v42 evp:xyhz2w ku9twm1kk)scc6k minimum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scalem5 ldydgz /w7, in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the pe z 5,mgwdyl/7drson’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strengw3mqx + ,sil7bx8p+v sth of 21,750 N. What maximum upward8 xp3 bsv+ qs+xi7mlw, acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including pgo4aan76xt q ;aw-eie4gd .7h arachute) when the upward7oew4a-;tagh6d gnqx4 .iae 7 force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the grmvhb0h hgtk+, w. f6j)ound below, whhv , 0).g6jkb t+mhfhe bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box ru f;t1 giuzq.+ab ;rxdajg b1y3:qm1-xns vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that thm3x;1iy .ax1gru -j zf+btdg;q abq1 :e table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball playknvjd+/; 5 z1kn cy6zmer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hum gjs.rx;) ;wkowa03r5 1w qkit by the bat, and again (b) after it has left th53q.go u0 w)rmwxwkja 1;srk; e bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction.6 l;t55(3zpwn jw .if;gv ejgp A second 650-N force must be exerted in what direction so that thi f t(g5jw lzep;v; n6.53jwgpe resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across q9old83yot) ba "high wire" strung horizontally between two buildings 10.0 m apdylqbt 98o )o3art. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless cord froqfg- un.vw3o/i/s8 hem another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.0xd4aqm5fl.s43 o0s d l+6hzgr$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, Antarcticam5wrn8v x,a nr+d++ th, as snnt+r5arh dv+x, w+8 mhown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the smj 7(r u0px)d -hwxvu 7cc):gcame mass behind it, Fig. 4-47 . Determine the ratio of the tensi(c :0murwxx cp)g-)77j uhcvdon in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herse;8u;lpf a cb:llf upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to cfua;p:l 8b; lraise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a v8fn7.pz.vj b 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (massss ubfb wn7d/i 6+of1+ $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surf ur;vqe e1tl95ace are in contact with each other, as showve;etql5 91run in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initiax1m+yf.a x x+doh-fx. lly 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavie-fxyx+mf+1xo.dh .a xr one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a he(+k 10-i wwwby;v tfjeavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in F kb;vw w f1-+0(twyjieig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction (n/jwjd(q)ww-o.vwx between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required m6*b mc haw4s1ex;u*bx y6l*z to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are stand n-a2)b+ohr 9evg6 4gbu-rmhaing on a train accelerating at 0.20g. What minimum coefficient of static friction must existh r4 v+ -mrb2-g)9enh6gaab uo between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of stat clpfv.1y yc:mq68ph*ic friction between cfmh *y c .:61pylq8vpthe tires and the ground is 0.80?   

  The coefficient of stii2 d)gw 7h1tvatic friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maxthw)2g 1i7d ivimum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.).nsv.ni/nb2e od6oe 80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a r gjk9ykw 59thfu* -c+cough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalty sl:g(2*d jgt pn ;ov(zxzw*8 surface have a very high coefficient of static frictjo s (w(t*vgyxgz 2:;p8znld*ion.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kil51-vd,so:- rma:9zpdt wp tp netic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how lac 1;kd rgez3/rrge a mass would box A have to have to prevent any motion from occurring? Assume31r g;er/zdkc $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acrossvbndb( u52kj qneqlm5(/5jl6 the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push jb6 lq(en 2m5qn/ u 5v5ljb(kdimparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horizon: i +hdl,j5tolcucz.9 tal sth5oil jc,+9:zc .ul durface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static fricti4,l 9sgthlim f3nez)2on between t3,hsllfmt)z ig4n92 e he crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your drive70cigz xqft61 way, which has an i70 61gq ficztxncline of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slideua 14 (yciqf +-u5-hy 9kpdmiu with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fbw4:nw-bg) vav* ny z,ig. 4-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3u2 cyo(hio(fx + e5nf+.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepeuu6 9qqi y+ra ozu((7wst hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rough wa8oe uc fq /p*,n 4a4ccdizc:e1ll by someone pushing on it with a force directed upwarco/ 8ieq *pdf1 ea 4:4uccc,znd at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become danaxk(f/aqb*f 3 c5sq0d gerous projectiles as they melt. Consider a chunk bf/ 0xq fa3daks5*cq(of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling atebt+xo+ t 17 e3o,2h4d9lx2hqk ucs mf speed v is equmbtf l1hu dx3hxe+o 9tse k2 q2co,+74al to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a) .eo8b(qss:s ywl2 rb car slides forward on the dash when the driver decelerates from bl8y(2bswq)e .s:s o r45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an nfi 3jxqb )h,e*jup0(initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they ares39(v*kbdtse u.kd 0 st*jba0 filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If 3a bb s*9u0 dje.kts(sk* tvd0the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic friction betweeb 2i* ms68rasb/nd ,mjn $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) . .8etnmn x63afzs6sacan coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse appe o9 up/qthk,w2j6l 6troximately 20 g of blood is accelerlktwopt/2 6,q eh6 j9uated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if the decel8rt.d bqrwk8 v *dx9gu:w;2syeration is no more than 30 " g 's." Calculate the force odqxkg .;s2*r8w tu9ry8:wdv bn a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleratihwqje:qudkh3m ,o ny(n/u:+(9sy*e)q ipi 0won produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static frictionq+qu /)*wduwiy:j0o (she 9hy 3nn(e im,pkq : with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accident invz1u6l a ra6(l3 fdmx60otm6dpr4gy )qolving two cars, measure 616m43p d(y)0tf6umqa6lad rxog z lr 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m trz76 0,cty .iyvgbix, kaveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Igk7.x ciyvytig,b60 , znore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the bp 3pfn)c;it 9uge7y3v 9ef)9wings, Leaning Tower of Pisa and falls 55 m before reaching the uy3;bns f9p )3en ,w)e97i ipcgg9vt fground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s bu226iegvfp; g f r.,bayt enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speeigpgf,2y6bfa.r e2v ;d upon emerging?   

  A city planner is working on the redesizqzy htvqw8-tkhtr2qjn)*1:8-ws+9 t p7 djngn of a hilly portion of a city. An important consideration is how steep the roads can be so tha zyt12tpt :tq*s-hq )+kq8jj9 n-h78zvwwnrdt even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes phy,sn xoo +zx78xsics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that t8noo xxs7z+, xhe string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be several ramps c-bdv z65bhlk:)rn bm t:g /)euonnecting different t)nrm/zgebl hu::-b6v5k b) dparts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force ip-f u2px d 6 3bq34awk)c8l(i(rximh F is needed to lift the piano (mass M ) using the pulley apparath(ipx 343 urp) kl(cid-6wi8q mbxf2a us shown in

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating a6d;zr;yo:r-d/8vk r+eyx k/ pqw 5ugxt 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engine-bl;mk 0ah )h2it9yf o7k 5)dlzunak1er considers the following set of cond;lh )ik2 bth)yz lo 0fk dmua7a19n5k-itions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a m+ /ai6sgs*ph bass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of similar lengt 7 2ip0n )s 6)ew 5o8z9+:un5gcqfyqn gobocaqh. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls free8q5 n cn wspfubn 7o0aq2)gygi6o+q9o: c z5e)ly about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using8jiab u4:pt,anja4kk5+w5 jq a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building ist2 bf 42o41bwnv8 ep( o5phevj allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together are ascending an ice field i5h*n wn3p(sd pnxi 5n(7 rceh8nclined w in3xr e*nh58(n ncds (7pp5hat 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.