Why does a child in a wagon seem to fall backward when you gizopg,ts l)4 +hve the wagon a sharp pultsz ), p4+hglol forward?

A box rests on the (frictionless) bed of a truck.esce3e./ g(r6ziv- -eprlj 6q The truck driver starts the truck and accelerates forward. The box iqg e-pe-irsvce rj/3e6(lz6.mmediately 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 of3 pre/)cxa 14us y6zyk an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can d ,:wh;miw.h0 6ajkd 5iya.hhthe object have zero acceleration? Can it have zeroyd,6k;a: h jmaw.h 0h.dihi5w velocity? Explain.

When a golf ball is droppoydc//me4yx d(von2*t5nz/,tud gp 1 ed to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the force? dx/5, o yeny /ctzn/2p* md1ot4d(vgu

If you walk along a log floating on a lake, why does the log move in the opjtl f51wk67a u)b+ks oposite6a+bj7k f 5tl1 ok)usw direction?

Why might your foot hurt if you kick a heavy desk or a walx.*wln* u8n.gfo /oaml.c.ftl?

  When you are running and want to stop quickly, you must decel.rs/zxj.b3*3va:kvn kdxw, n ha.:eserate 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 exn3.w:da3:kv*jknrz /xh sv ,bs a..of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the kdtpp8y(n9/f g 3 op7 de2)kmxsame thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely)p9xfdk( km/2 n8t dygeppo73 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 rock is twice as great zeedk,4hm*l 9as that on a 1-kg rock. Why then doesn’t the heavier rock fall hkl d, 4zm9ee*faster?

Would a spring scale carried to the Moon give accurate results if the scale hcn59j)+rc1y x4 jpginad been c4jc1cr95+jy gnn)xi p alibrated (a) in pounds, or (b) in kilograms?

You pull a box with a consth,kx eoa vd:/+ant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with thoh xvk+/e,a: de same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net fomb0d)mi,q*kqqu m8 y 2rce mg exerted on 2dk),8*m muq q0miqbyit by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you 2m 1hulrnxp yb00*:ch are on the Moon with the force needed to lift it on Earth. Compr1 hyum0hl:c0b *2nx pare 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 g)-6zb (ykvcd in a tug of war (Fig. 4–37) pulls with equal force ok6c)-gv dybz( n the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N1l 1g+3 lec8f:h rfqgn to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its di8g3 f:crlh +ef1n gql1rection, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force d9mne/c,d-f0jv. 4fp 7 s.pln0xu xbvaoes the ground exert on you? Why doxmjued9.x acf 0s0nv7p4-p ,lfvnb/. esn’t this force make you rise up into the air?

Whiplash sometimes results from an autoy*fvnv3e(3 tsmobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be tfe(svn3tv3* y hrown backward in this situation. Is it really?

A heavy crate rests on th+;cx b jd8x nkgeh 9h 7(h+nufg5u9kb,e bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the97xhuuf8+5+xgk(bc ;bg j,9nehn d hk truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Aftevz s-a2kym07juq,/v; x o3niur the block reaches its highest poinyuaz/ 7n2 qo;-0,vkxsj3imvut, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale fx s+ 7fxz.cy7ahxn6wq3uy 4/read if you weighed yourself on an inclined plane? Assume the mechanism functionz.wy7f7 fa c3xn+4hu x6/yxqs s properly, even at an angle.

  What force is needed to -xmk ):r1 t/b2dcajp pa/vg9 qaccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and r2kuqz1o3oo e3h0p ch3ider 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 if it is used to acceler77nog9p2- yrpv qhl3 wate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of g+fy ts9.q5 tna $76-\mathrm{kg}$ 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 thenr+;r9eqp n5d vu gq,4 car is traveling vuqrq ; 9+, 5d4pngenrat 95km/h? -  

  What average force is needed to acce;5oudn e25b gxlerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alonu52 xg;do5 ebng the barrel of a rifle?   

A fisherman yanks a fish vertf upcde/9 49m lrki0ipx;+;z2hj s9rzically out of the water with an acceleration of 2.zxuze/ppr;s2 l 0fr4d 9i9h9i+k j;cm5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 cover a quarter-mile zk 0w,;6oujewpudu 7 3rc8*xltrack (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 the maximum acceler63gc l: bz.vllation is 0.0680 g . What are the maximum and minimum fzvg6 l b:3cll.orces 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 z/eff/4yvc ggr+hni.+0; v a ;y;nm hjbathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s g0;f j /.h znv a;rg;/4y+mih+yefnvcregular 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 strength of 21,750 N. Wha1tlk72qywqs( 3bmyw: t maximum upward acceleration can it give the elevator wimy bs:lww1qty7 2(3 qkthout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers2ppdn,c:j 8-fvro a i) (mass 132 kg including parachute) when the upward )pp, 8 ro2:jf c-nivadforce 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 str9)s uchdpz uz19doxl.,vsl) .ikes the ground below, he bends his knees so that his torso decelerates over an approximate disulc.z zvl s .d,9)9 s1houd)pxtance 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 i -btd -sr7xo2k (k,xs naz70ohhyl97on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that thho2ysix 7k-0onl(dr7k9zs a7 ,-h bxt 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 bas 0,h lz8dnis, *hbm1p x(;jchaketball player
(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 e :4j/*ia ovsh+ z(hqris hit by the bat, and again (b) after it h er4( hv*hszjo:i+aq/as left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A sek58nw )-)gide o05kl1u vvjd/t wgu(mcond 650-N force must be exerted in what direction so that the resultant of the two for0klo)-1v m )(5/jtwni g5duvd8u wegk ces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizqd qif9t e)73sontally between two buildings 10.0 m apart. The sag in es3qiq)7 dt9f 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 from anotherri ,r8hz:zr ,s 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.l-jx 0u qoj75y0$-\mathrm{kg}$ 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, Antarctwoe imm8k 4zi1;/qic;ica, as shown in Fig. 4-46. The sum of the c / ziq;i mwme1;ki4o8forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 hjav+pxtx/*;s8 3np emo* kk;(e bmv0pulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the firsa+m;xxems*3 (btkpo8h0pev ;j vn*k/ t 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 herself upward using the bucket-pulley apoy gx1 t7bqe,8paratus shown in Fig. 4-48. (a) How hard must she pull downward to raiseeo7t1bgyq8, x 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 65 pxnhx 5m2tomt7+o:p;o:z ynb1o.fi/$-\mathrm{kg}$ 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 bejzy/s t x41-ulock (mass $ 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 -8jgi9pnefqm 0 iyal(/0nme4 horizontal surface are in contact with each other, as shown in Fig. 4-m0 9ymqe nfj4 p(ai0-elnig /851. 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 Fa( (gtk1*)eqihd)plh (ue 7vtig. 4-52 are each initially 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 moment1t()g(7 aqi* tv( h d)lepuekh the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionlew-owj o*+4a*hi7 iqg+ fm8,1jhe sizpss table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each boxhojz+ ag, 1iw*q fms8*h7oji-ip+w e4 and the tension at each end of the cord, using the free-body diagrams shown in Fig. 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 kinej(nr tzp;.z*q tic friction 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 to st q,l83pn nyxdu/1h 0rzart 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 standing on a train accelerating at 0.20g. What minimbe5- izptu0+leib;7 pum coefficient of static friction must exist between your feet and the floor if you are not+5ulbtpz-e p bi i07e; to slide?   

  What is the maximum acceleration a ca, qr y/fu:ta34flb2p do z/vk8r can undergo if the coefficient of static friction between the tires and the g lzp/vu48f 2k ,/dqfr3tyabo:round is 0.80?   

  The coefficient of static friction between hard rubber and normal2 ;8e(q1rx,yqgpuh om street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked?ro;q1e8h p,xg(m uy2q   $^{/circ}$

  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 atv/ eoo3(op 6 y-plxkfkq 8e.)y -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rd 6hbn 9q-ej+qough 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 asphalt surface have a vekiw 69f vhjl+y se66k;ry high coefficient of static fyevk 69fj;hlw ks6 6i+riction.

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 kinetinn i vn39y4ysqs80w/ om4a xti2x9( mvc 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 e6 *rn*p 2,r,rpkcc yylarge a mass would box A have to have to prevent2r r6yyp,k* cen,cpr * any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How faertm dt, j)66fg,.vewr will it go, given that the coefficient of kinetic fri.w ,m e6 )j,rfvg6ettdction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , aradf)x s :5dhi-wx2t+ xe in contact and at rest on a horizontal surh wits+-)fx2x: xd 5adface (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.e3um3, aenw 9f The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the dr wnua,93ee fm3iver 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 y4 coxmy ccwr:h*by/;8 our driveway, which has an incline of 1:*c;xb/ cco hy8wr4ym2$^{\circ}$ . 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 fxlts+ig- ftx d a 22*sb1uc:0slide 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 Fig. 4-55 lies on .*ft m8s ,fa6+uzkr ji m(.pvi f3rnu.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 on8otd8n. +7 ptw:wvy awqfqkw;0- bv)f 3.0 $\mathrm{~m} / \mathrm{s}$ 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 steepestwdeuy1bfr(.. i ( j0nn 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 ro-h9q(qg) r,ygk 0sr )sby.hyuugh wall by someone pushing on it with a b(qkrgh ).s 0-ghy) ys ,ur9qyforce directed upward 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 *7/q 8nzr ddklbecome dangerous projectiles as they melt. Consider a chunk of snow at the 8* r/dqdnlkz7ridge 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 -yr+dnash62 y an automobile traveling at speed v syh +2n y-6rda is equal 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 car slides forward on the dash when the drivp .r4; qcewn*w.+haii er decel;+ .chiw wn.eir* 4qpaerates from 45 $\mathrm{~km} / \mathrm{h}$ 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)2 .pc6bzfj0(ix th pk 7p,:+:h ml hxngvl.gl 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 are fixcmy4ui;a ayt4p; z34 gt cx7;lled to the packing station 11.0 m away. The belt is initially stationary and mus 3p ict 4 y;4x4;xc;gmu7aztyat 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 the 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 fric a ltrl;ke3q ,tr36f+stion between $m_{1}$ 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 /gu ku0 :c/hko98zhxj65 kg (including the bicycle) can 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 mammali/md izpzz +9k-an heart, at each pulse approximately 20 g 9zz / d+-kimpzof blood is accelerated 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 autofv.e eq.dzj:0 mobile crash if the deceleration is no more than 30 " g 's." Cqf:e0jev. dz .alculate the force on 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 acceleration produced by ccs100i45f ckgyogp) an earthquake is a , and if an object is going to "hold its place" on the ground, show that tcok) i gp f450yc1gsc0he coefficient of static friction 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 th(/(c ojds1ngt7;-n7gr ax dade scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between 7(7 /ngrgdt-xd1d n(jco sa;a 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-inua+03l-lv;ft z+yy 2q(/ra1 mtpfzeo-4 means that for each 4 m traveled along the road, the el-laf+;of3t +2e0myav1 /ytz rzl( uqpevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa g8iwh,-myqrf:6s.m4t(ijhh*9 nii/ ma , hhw and falls 55 m before reaching the ground with a speed of What was ta8/, ( rfmgww,mmj-9q4n.*hiih htiy6 ihh s:he average force of air resistance?   

  A cyclist is coasting at a steady. 8 3uxs;edmwy speed of 12m/s but enters a muddy stretch where the ef83.e w;suymdx fective 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 speed upon emerging?   

  A city planner is working on the riebmh.j scd9t4,w 0h *edesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , eic0mh4b, w9h * t.jdscan 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 physicqrue96o- cek w0kt )*z-0tnkys experiments, dangles her watch from a thin piece of string while the jetl-u-kz0coq)9 0 nr6eky te *kwtiner she is in takes off from JFK Airport (Fig. 4-58). She notices that the 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 fl/ .qg *j;6ca4jyzrgonnecting different parts of f4q6*jla z; . crgjgy/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 F isgnc1b6.mk 32 6onc 4xyvxzbi 7 needed to lift the piano (mass M ) using the pulley apparatux.6c1nbc6yx nvb ozk3 img2 74s 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 acceleratinrqs xnsrd47e *6sv**ng at 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-r7o:;t,g;oz e 75 xfexla(nvc7-zccvq estraint chair, an engineer considers the following set of condit(en 77f;z7 z:xagxoccv5vqt c,;oe- l ions:
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 mas)j0si /rpu -mk/uy5n js 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 length. Kare h;.u9 n;gcrmurvg ,2wn'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 freely 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 gm2;hur, nwvg9.cu ;rcm 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 using ap tn, foh,8i.tw4j ff7pj*l2 g " 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 is a fmp pey4,xh3dt(2x *1n.mkxallowed 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 ic 8vjg3qkeesx3x 3vlk3w ja8-9e5 i e;ye field inclined at 2x3 lke sx3ee yjae- g3wi9;3j 5vk88vq1.0$^{\circ}$ 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.