Why does a child in a wagon seem to fall backward when you give the wagon a shaw;9eqix(jxn7v.8 1i nmjc w9 vv*8dccn* us.qr*cvecim sxu* q..8 9w(j dvc8n7n;vwn1xq i9j p pull forward?

A box rests on the (frictionless) bedsjcx5h2eh+ vk+5qv: i of a truck. The truck driver starts the truck and accelerates forward. Thshj5 qhx: +i5v+eck 2ve 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 nou-3p,a3j;e: 6gnwxx 5e bq4qsg ui3 vg forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Casmq (mk5 wat)dq3-b;w n it have zero velocitwmw q)-m3a;( kb5st dqy? Explain.

When a golf ball is dropped to the pavementq jszd5o.-y-yz z7 0bq, it bounces back up. (a) Is a force needed to make itqqzy.o-57y dzb -jz0s bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a -pzd)hcwmre+ g2a;1 flake, why does the log move in the opposite direcewh -fr2dp)mz; a+ c1gtion?

Why might your foot hurt if you kick9,hz(wnka( ud a heavy desk or a wall?

  When you are running and want to stop quickly, you must dechmw+,:zm(aaq1 l( *wvrqhx-d -xe1 zv elerate quickly. (a) What is the origin of the force thatdql +-vr:awh ,1 1q(mhazxez(mwx *v- 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 rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of tw:oq8 v0yc;uetvsf 9 zd7d;c-he 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 the thread likely to break: below tq0ytvvud: f 9 -w8c;ed;soc7zhe 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 g pt d u0o:ft/qt0q;wph w/- /;)nglqrjreat as that on a 1-kg rock. Why then doesn’t the heavier rock fall fasteghd ww)00: //pq;qltqurnt ;-fop/tjr?

Would a spring scale t t1c(2 rujez5carried to the Moon give accurate results if the scale had been calibra1(rze tuc2 jt5ted (a) in pounds, or (b) in kilograms?

You pull a box with a constant forceg2(mc usx;4au-dzx u. across 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 remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) duu gus(-x 2ac m4;x.dzecrease? Explain.

When an object fallsdeo5 n-3*wjehy:spx 2 freely under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal an:dew-oshxp j 5e y3n*2d opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when youe5 ke3,opk3tc)o9g gk(zn9du are on the Moon with the force needed to lift it on Earth. Compare the force needek p9 ck (5d3gtk 9zo,egen)ou3d to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, jmank p+w5y7k-,,8qu rme-,u-wf p ezeach team in a tug of war (Fig. 4–37) pulls with equal force oz,7u eajn yw ,-emp5 mr+u8kfkw ,p--qn the other team. What, then, determines which team will win?

A person exerts an upwxj xej24 v2rd,ard force of 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) on wr 2x4d,jvx2ej hat object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how lay t7s:g m .4lrp-lai6drge a force does the ground exert on yagri tp.l-6ymsd74 l: ou? Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s car : srq c.ssfl2t (ork,h/4 .xjyis struck violently from the rear. Explain why the head of the victim seems to f jh(x:.qssk,cs4.lr2o rty/ be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck acceleratf/xohl( *yry ,es, the crate remains where it is on the truck, so it, too, accelhf lr,*/oy xy(erates. What force causes the crate to accelerate?

A block is given a push so nxxz6.,3hr :athqhhi88 kc38hnb3 w ethat it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. W e:h83xnqnwtc8. 3 azk6r8ih hx3h,bhhy?

What would your bathroom scale read if you weighed yourself on an inclined plalq-s 0j 1j v5lbd(j iw.:7p-e.athiftne? Assume the mecalw 5-q:j (tif - 0p7tleihjd. sb1vj.hanism functions properly, even at an angle.

  What force is needed to accelerate a child on an )gqot k:1p(f sled at 1.25m/s$^2$?   

  A net force of 265 N accegqb 7ji jkzfc9. 8y8tlx7++x-u at( oslerates 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 accelerate a 3v klm9anys wr :-(4s7axt,vq 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a3h6bda4ly q2 t $76-\mathrm{kg}$ 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 senb 0v*t/ e qzb9wve1+ if the car is traveling at 95km/h?1bvzn btee ew +*/09vq -  

  What average force is needed to accelerate a 7.00-gram pellet fromrh-t9o alywj)2pcy:q (,xr .q rest to 125m/s over a distance of 0.800 m along the barrel of a rifle?:(wcjx.-y,2 r9l qpyhta orq)   

A fisherman yanks a fish vertically out of the water with 6eq 5n bxp1t7g3 q;-ehwbwz8dan acceleration of 2.;18gw -q3e b bnxdq wz576tpeh5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 quartkbm 4kds*z 56xer-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 maxi9eujsvic *)6amt lkb 8e.h:x5 mum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supportin9t cke8u*m.ie b)xavsl6:h 5 jg 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 ba(mr1g+ 4pcjq is7(f: ,l u4dgu 4he /ubj5ibcythroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of t4i5glrj /fb:1 duc q4,s yjg7u4mu(bei(c +hp he person’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 amm0k 2 c/5q,g7nkbimr maximum strength of 21,750 N. What maximum upward acceleration can it givemkb0 / qimr2c5,mgnk 7 the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration ofp tb:q keaypfk,58-4m two falling sky divers (mass 132 kg including parachute) when tf, a84mk:-ye p5tkbqp he upward 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 housp i /ogjp1*+ple 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approol*gijp pp 1/+ximate 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 tabhy7-je),zp ui.bjc w:le. A rope tied to the box runs vertically upward over a pulley and a weight is hung frob.-c j)h7eyzuwpi,j :m the other end (Fig. 4-40). Determine 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 diagram for a basketbs,v(62y,hl-hihp(1 nz qktu eall 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 is hit *u0hy5k33y.mf b7ccwx)po iv by the bat, and again (b) after it has left the bat axy3kw c7i.0bmp c5f oyu3v* h)nd is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must be es hsz-(bpj:r xe0f0k t:*2 koixerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagramext2 0p s *(ihzk-j 0frk:o:sb.

  Arlene is to walk across a "high wire" s,mctc:r,x (xw2b dn0h trung horizontally between two buildings 10.0 m apart. The sag in t(w cc,nrm2 hxd0 bxt:,he 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 massles9a+y9nz4 nfs ts cord 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 14.xv7r9zr *pus: k cl1b(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 housing unit to a new lpj9 5kh(okpyd f i-v,3 (d.bypocation at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum op dk.ihyppj v5 (9ykf -db(,o3f 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 s, .y5+nrpp3w8o q daicame mass behind it, Fig. 4-47 . Determine the ratio of the tension in the couplingpr83q, p.5in+y daoc w 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 herseltftv8z( vk 7q2c:) qa q-y1 huudy:fl7f upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant ska 8c2qh yt7)-:y:v7dfqfqz (t1uul v peed?   
(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 6wgqzn,6*, .bu6k eug un+w6 -x rfvi.k5$-\mathrm{kg}$ 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 blw3,5qty*hfmcbhn 1e 6 ock (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 surface are in1y lkx5nl1xf * contact with each other, as shown in Fig. 4-51. A forxl*15yk1 xf nlce $\overrightarrow{\mathbf{F}}$ 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 iniqel dvf j.vrb; 3bog35/(rxu8tially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum he3 /8efjlbx5( qr o3v.dvbg;ru ight 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 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 byenf0 w13vo51vwrg/ olset(:lo5a u9l a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using theu ov151lwsr3 otwvl(:05 e/afeonl9g 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 kii4maqlg/ctaleta,t0v4of6/um5 ) x3netic 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 start 2wd l mspp8vp907:2:vmfs lz/d tctm-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 .+l95nn4 vinf+t ; t8n:rrqf 0jiencoaccelerating at 0.20g. What minimum coefficient of strn ntin iqn: ; o enfr5+v894fc.t+l0jatic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceledi gp:-q(j9ca ration a car can undergo if the coefficient of static frict:cpqi(da -j9gion between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and no *bvj7z /;rmxf(n gztlw jk,-(rmal street pavement is about 0.8. On how steep a hill (max tlzx, (7vn(jg; rkb*fw-zm/jimum 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.y2r78pgno5 os jlfo1 )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 hexpi3 3om 06ion 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 asphalt surface have a very high coeffici4 zxsa24gaix 3 3:7oc5nwvgnjr6h sl -ent of static f wa6gjns4- lx3o4rzi ncxh:735s2 agvriction.

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 frictio1 (h7ae 8f9jgbeg(sakn 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 large a mass would box A i;:emv x:v6jehave to have to prevent any motion from occurring? Ae6 mvx;e i:v:jssume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the flo4uanbp o ;s/)oor. How far will it go, given / 4ounopb;as)that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 k))ei6njeai - yg and 110 kg , are in contact and at rest on a horizontal surface (Finj6a)i)y eie- g. 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 crd ifyfb-h90dtd hu0*hb ;)v a5ate. 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 driver can decelerate hbby ) dt*haf9- di0vf5;d0u hand still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your cw,7y *pnly2kn ar in your driveway, which has an incline o,n ky2y7n pl*wf 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 slide with/dj wtc ;7bki8 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 lies4s1 8ssg2g yux1cv)qs 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 5g/ tcfsf;w) toouu00speed of 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 steep4dn u)2wdp9e mv:* vhqest 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 agepghw*:b 6t 0e7t+-ka /kkyv vainst a rough wall by someone pushing on it with a fo t:/+ae v6 h pywb-7e*0gktkkvrce 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 become d-2gij ),ksj obangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch of-gs2j,)b jiok $ 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 at vr yo *ww;v ;lssncz .0yp:e,hc6q5a9speed v is equal too v, 0w:5cas;c. ls*e;pw9zvyqhny r 6 $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 36;ts -dvpgxq slides forward on the dash when the driver decelerates v3dqpxts;6-gfrom 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 h.2+y/xatwb 0 gt+ji;rrg1tj is given an 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 fillr)r:.vo hv rs2ed 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 thers r.ov2r h)v: 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 coefficienoq a5c zujd.6f, vc38 (b1lgudt of kinetic 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 (including the bicycle) can e /pnpk;kjw+hk v7uh ne9/ru,9*rfa: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 mame3l fd41ee( y6qz vndt/2qg*b malian heart, at each pulse approximately 20 g of bl n1d3dfel*veb6g4t2 zy qe/(qood 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 automobile crash if the b7a2e2zpja53mc: 5cv /b tftk deceleration is no more than 30 " g '3 mka2tzcjp 5e :5bbf7a c/2tvs." Calculate 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 eart/ n6 :xrsz*obd6 9xuucz lyio*g6-2iqhquake is a , and if an object is going to "hold its place" on t qrlc* uxi-6zx9o 6/*n:gysdo6zui b2he ground, show that the 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 the sc ozsw4mja; /-hpz yy kvgv/n9+wv/:o*ene of an accident involving two cars, measure 72-m-long skid marks of one/:zonvp9ho aymg*y kw- 4w; z/vv/sj+ 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 fore y5kxhr/(ir 4 each 4 m traveled along e x irrky(/45hthe road, the elevation 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 Pwmrz:rjw5;wv 7l2tx,tkd*enpe9aaqt +25 5visa and falls 55 m before reaching the ground9rtvl 2apn2,a7 xq5*zkt5ej:tv wd5 ewrm ;w + with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch wher r)j.u ;kc knzzq+f6j/e the effective coefficient of friction is 0.60. Will the cyclist emerge from z. n;f/r6+kjjckz) q uthe 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 city. An ig p;hpn/3mp+v l ueoi7 3sl2,amportant consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing do3+; m ,sogp27pnheauip 3lvl/ wn. 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, dangles her watq *s+5m*2 qhvqlr5ia96loyejq ,2 yil ch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an anlie2l,*6 myql5h oqy9svjq25+*ai rq gle 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 sutn*3ls; ;av-k 8ev(vonqps j0permarket, there are to be several ramps connecting different parts of thjlosnqa 3p*- ;ev8n(;vtv0 kse 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 is needed to lift the piano (mass M ) u wn,2l//vycsesing the pulley apparatlsvwn,c/y e/2 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 if r9vgjo,rqx9i,5 n5at 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 engineer considers the folyvb4 dy en,7rt h/7s2vlowing se,vb2n7s h4t/vr yy ed7t of conditions:
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 tn+o t4jh2z 8rhv(vth8rain has a mass 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 sa7 oht4 kyul;u,3vz*y lls+ws)fety 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 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 mant) hus*l3lso+ wlzuy 7y4; v,ky times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boau* ((h9 mruuv1j;s +)di fizs+(jppk bt is using 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 allowed to reach awfjz7 ul+ fu3hdk 76 b/ezu24s 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 ascendi-dzy 5 pvnk/m*ng an ice field inclin- knydzmp5 */ved 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.