Why does a child in a wago0ejdalev .b h:l 2;wu)n seem to fall backward when you give the wagon a sharp p2.)hee:a 0j dulv;w lbull forward?

A box rests on the (frictionless) bed of a truck. The truck 32mq g+kt yj;udriver starts the truck and acceleraty 32m qj;gk+utes 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,bxfb/i*dm 7r , are no forces acting on it? Explain.

Only one force acts on an object. Can the object have ze 6z by*8h9qsss96gb pwro acceleration? Can it have zp wb6*sgs sh6 89q9ybzero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) wva / h)m1geo5ngk p8cby4/lw i.a6 516uz sbiIs a force needed to make it l5)b 4hevagc 5ynw6/ 81sz6ub1 ki.i/mawopgbounce back up? (b) If so, what exerts the force?

If you walk along a log floq ,ymb /7se,/l jy( vqeyu)gg.ating on a lake, why does the log move in the opposite dir,/vqm(qs l) y/7bgeu yy, ejg.ection?

Why might your foot hurt if you kick a heavy desk or a wa m yhnkbm0m6f43:g )tycbu 3f8ll?

  When you are running and want to,gj w+.p qdds1 stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (u dd1s,g jw+qp.sing your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fin2f6s+s nd1bma y/e;av e thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36dsm+2fn6/;v1 eay bas). If a person gives a sharp pull on the dangling thread, where is the 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 aem2 d0yoj6 72ondqmlx d), vh9 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock 6oydd2ohvjeql )92d ,mm0x7 nfall faster?

Would a spring scale carried to the Moon/k 9+f dgooq.q give accurate results if the scale had been calibrated (a) in+qqo f .og/kd9 pounds, or (b) in kilograms?

You pull a box with a constant force acrose;2sag e7 jz7ss a frictionless table 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 remainingse gsze7j a2;7 flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls fa3e qlh 5q 6j2:ojir0,za-g*aafi7myreely under the influence of gravity there is a net force mg hjfz:yqi7a-eqm 53o,alj a gr*20 i a6exerted on it 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 (zko8pd3 9h,r2jull s +or force) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it onl3 h,s9 pd+rkzjlo 2u8 Earth. 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 a tug of war f mzg3r4:mgsde2a2w njd4 9b0 (Fig. 4–37) pulls with equal force on the other team. What, then, 2e3d m4wr2am0szbgj: n49fgddetermines which team will win?

A person exerts an upward force ofgvx(q;/ zf 5wwd ug)z7/i voe; 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c;zuqg5i;/ef vvod /w x7wg( z)) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on tl+yebau5i p( iq+f h)2he ground, how large a force does the ground exert on you? Why doesn’t this force maey5 (uh p l)aq+iifb2+ke you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’sn xnr/ys fkebl:vu+ 0 pm6m+/: car is struck violently from tel/+y6us p 0f:v:/n bmmxk+nrhe rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accele;9g :e*zair nhrates, the crate remains where it is on the truck, so it9 eah:r;gi n*z, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ram ad06 4g5ox1pn(tp ppqp. After the block reaches its highest point, it slid 5(p0xt1p46 pqpndag oes back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourwhr) c(x;j.9zq0mg djedi+6rp,d0enself on an inclined plane? Assume the mechanism functions properly, even at d6i +zgxrp;)j0qmc .dnr j0 e9 ew,hd(an angle.

  What force is needed k9c3cszu )xe3 st ;1fkto accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N as ygqw 6s+9nv;-i /hnxccelerates a bike and rider 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 acceleratxd+yev +f306-e4ku/ikkuuws e a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of091s a/ nw/(u+01uv 1ndld +gqe,xhqheql ted a $76-\mathrm{kg}$ 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 i2sp,xhs m 3y2p nb; *0s6w ,rnqeg9ndzf the car is traveling at 95km/h?nzg q s ndynm0h*rws3x6,2;ps be9, 2p -  

  What average force is needed r69hnu dqw;+oto accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alongn 6;u hoqdw9+r the barrel of a rifle?   

A fisherman yanks a fish vertically out of th ,/ grynn176va ;dihfwe water with an acceleration of 2.5 wf1ryvdih /7ng6;a ,n $\mathrm{~m} / \mathrm{s}^{2}$ 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(l*j4:eu apeh y2vw-r-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 the hwdivu-x m+)p vx(p()maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the dx uxip))hwm+( -v p(vsupporting 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 scale in a motionless elevator.j c7hshfpi./o0 *gi( c When the elevator begins to move, the scale briefly reads only 0.75 of the pers .i*hchfpo0(7cjg/ s ion’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 strength of 21,7) y4xvh:*zladgd1etxw8 e,3 n50 N. What maximum uywtzgdhv38x ed 1),*le nx:a4pward 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 p0lz iy+v.z4m7so:zxy arachute) when the upward force zimzz y4 .v:+l07sxyoof 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 6vb0f9t hmj gr(6i *oez yll;,of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If gllbh me6y,f v0zr9;t i j*o(6the 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 tabi 3 fz*cjtp :5u;yz6bale. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). *i;c:6z 5 jb3aytzpf uDetermine the force that the 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 diagra5qfupf ; q1zp2(hzl*hm for a basketball 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 ba1 i,h*p2dz arrhi;5e y8snm/useball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flyin,/1mpu;r e5y *2n rhhiidz8s ag toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force /t 5f4lnb-ndugn3pg3lh9 *,6untupm must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answerp4n , fut6gug n59n hmnb3-3*p/uldtl with a vector diagram.

  Arlene is to walk across a "high wire" s lj/:;thbdl mno0;t6hf:ya:b trung horizontally between two buildings 10.0 m apart. The :/nh0:lamttbbjy; ;6h o: d lfsag 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 cot),v1kqzd -yjx53ki x rd from 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 14of dn ae0:,21pl,v+uwhzp3 ma.0$-\mathrm{kg}$ 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 housin0ab/cj h(j9+njkr u1b g unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4jabkuh( +9nb /10jcj r-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 tcr/5jskktqk/oj , a 5:wo cars of the same mass behind it, Fig. 4-47 . tr 5j,skck/a5 j/qko:Determine the ratio of the tension 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 ym*ohet8b/f- lf upward using the bucket-pulley apparatus shown in Fig. 4-4 ehyt8fm/ob-*8. (a) How hard must she pull downward to raise 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, b-*bi 4kezngfp5- uz28s * smua 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 blocnq i:3s,c:pkw eg9//f dmq2v ik (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 horizontal survd tacme*)jop;r ) *w4face are in contact with each other, as shown in*v ;pr)c4e*a w jdmot) 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 initiac ql;vvd6 )shh(dj*+tlly 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 dd6(sq+lh hjv*;d) ct vetermine the acceleration of the lighter mass and then its velocity at the moment the heavier 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 heavy c0m; -/m.q f+s. +sd/taedh+ayzsx eqtord of mass 1.0 kg . Calculate the accelerx-.sf+ es0 z/qha qmme+tt /. d+ads;yation of each box 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 kinetic friction betwe*nj,i ./eens /9iunz2de71ixteri; v en 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 isb+2v.tqgdd kq.o:qy,j 3besk n y kx1:,ec 33s required 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 standirt vq4v3rhl+u wj 6c0kx.lu4lspr0 78ng on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you atu 4c 8 0+6uv0.wpr3rqrxhlvl7 4ljksre not to slide?   

  What is the maximum acceleration a car can undergo if the 49it2kof m+e u-/flrh coefficient of static friction between the tires a9fmolrk/ eh 2+tu 4fi-nd the ground is 0.80?   

  The coefficient of static frictiazwz9u *ppg. 4on between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a c 4wz*aup pz.g9ar 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 d1,i n:lwb zn36kfzd.d q m9,z-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 c8hw0xdnl/4h.u +z *go iu /peon a rough 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 asphq3il3zs-n +:lw6t ) vuydfex3alt surface have a very high coefficient of zf q3 3wyi-vn :l+tx6u es3)ldstatic friction.

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 kinetic fric b 0f)7muxmgyo9a+f/xtion 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 (Examj cr9qjg505wn6c 3hbaple 4-20) how large a mass would box A have to have to p95ag5b w6 c3ch0q jrjnrevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How q9 )j+ o:ei-q8(jcy.sz8ktm3bn q fu hfar will it go, given that the coefficient of kinetic fric(qtekb 3)qni u8+c qf.8j :szo-yh9jmtion 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 , are in contact and at rest on a horizv2wv6cu (uve 2ontal surface (Ficu u(2e6v2wvvg. 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 friction bex/ncb wky l /j;slqg2hra19 2s5v;d/9n yeju7tween the crate and the bed of the truck is 0.75. What is the maximum rate at whicl29d9 en yrbu;2wqs g/vn sj17 y/hl; aj5kx/ch the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry abou-tmbja6e n01o vu(v*tt parking your car in your driveway, which has an inclinb am (e6-*v ot0vjutn1e 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 sli onrpv+9v)r1 kde 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-nso 4mv *)5w(bgx ,9fc 8yxcwl55 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 8/q (gt6 7o4fz n1rjji-*m emxdts;ntof 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 steepest hio5v*+ aaz2olh.uog4j gau 4 9ell 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 wall by sv ;ccc- 7kmlu*omeone pushing on it with a l-v u*c7mk;ccforce 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 slip x1 :n91dhuyum1q rd8apery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the rrh8q u1xay:1 9dmd1nu idge 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 travellu/bn0blm ouhg ;;0yr.j gu13ing at speed v is equal t3br0/lg1 0jgmyun;boul. u ;ho $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 cab ,wd 5g.bldi:r slides forward on the dash when the driver decelerates from 45i ,lg: wddb.b5 $\mathrm{~km} / \mathrm{h}$ 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 inio6ad)ur3*:h*ow n ;. hwxfl myg2 (pgcj/bxf-tial 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 where7xwb8dhb/:ylzv +:x1u8lh ltr1 bwr4 they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The mosrhtd1y: r7lubx4+8 h8lb wl1w vz/b:xt 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 kineti xh/q/tme11z.hh1wq-kay06x c ;e rzhc friction 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 65 kg (includin3c:0plgd: spp lqz.af j4)g; tg 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 mammalian heart, at each pul87*tsscwry kbb7s:o8 se approximately 20 g of blood is accerys t*88s 7o7:ksbwcblerated 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 fwk*g p * *ki2f x;s),ysqjx,k33xuyxsurviving an automobile crash if the deceleration is no more than 30 " g 's." Ca3)*s wig qy;2x*3,xxx,f kk *fkpuy sjlculate 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 an.h7pmcng 1jn*zly *(d earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of sthg.(zlpm7*ynn * 1jdcatic 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 the scene of an accident involvi et8bwaonr/ (er1+x2ltp.t a, ng two cars, measure 72-m-long s1t/+nolatbee,xp 2a(rtr8w .kid 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 eachwadb5lq7 vk,34 dw6l v 4 m traveled along the road, the elevation change is 1 m). How fast is it goi3 w 7 qd,abv5vlk4d6lwng 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 drog9* lqbni,o 0 y(e1loxpped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was0g q ,nl*bei(1oo9lxy the average force of air resistance?   

  A cyclist is coasting at a stealv;j)k3 9t, )xkuvwzidy speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from th) u3v)k,i;lwzj9xvt ke 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 redesign of a hilly portion of a cz9u0di 7np gzu;2f5kaity. An important cons z n0k5zpdi9 uufa27;gideration 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 , 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 physics experiments, danga 26dno,j iaa 5),bzmsles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport ( sdj2i) a5zba6 ,ao,nmFig. 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, t ,myb -k+0nun0n,dkdu here are to be several ramps connecting different- nnudb k+k nuym0,d,0 parts 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 Fr90- kmk t* jqhfjt+,w is needed to lift the piano (mass M ) using the pulley apparatus strw+ f*jkkqm0j ,th -9hown 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 at 3.n9u0+ w u08o)xcfzfdt5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 che,el v/ +owdnpf( g8g0air, an engineer considers the following set of co8gve w(pde0no,gfl+/nditions:
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 mass of 6 2fb:tmg 3cr2c60 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 Kar q r(lgn;9 lj.*bytv;n;zp*qlen, use safety ropes of similar length. 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 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; l**zbj.nqpyq v ;gln (r;l9t 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 us5l+d fxz rqm3+ing 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 is allg -i 3e2wztf9)imv42oc5 t 3swmmuxy; owed 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 b h k9ufuol d .38kj+3 9-pc 5y45mzwge2liigvtogether are ascending an ice field inclinelf u9+4k.m3y gl 3hbi9evcg p-jkdwi5258uo zd at 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.