Why does a child in a wagon seem to fall backward when you g9buyaw -(u3mz ive the wagon a sharp pull for muu(3a -bzw9yward?

A box rests on the (frictionless) bed of a tru w-z kbvph0/ bmzkd,4jro4a k8rd.9r4 ck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in topz4d-4k.zkbk9r,v8 0jrah r4w/bdm erms 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 n(+lef8o j: vgho forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? ngiv5( crj7l1of 2kt r/ck7 l+Can it have zero velocity? Expc15r/ klklgr7oc(7inv+ jt 2f lain.

When a golf ball is dropped to the pavement, itwl0-9k lf 6 ,x q,tcdlo.su(ui bounces back up. (a) Is a force needed to make it(cltuo .096 kd-, lsifqw xl,u bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the logt+*cn*phvww .n5i ; uh move in the opposite direction? vwnt*hhi; 5.nupc+* w

Why might your foot hurt if you+o 8ldaio5bx7 - ek ra+,d8ljf kick a heavy desk or a wall?

  When you are running and want to stop quickly,:lp0je,re g:b you must decelerate 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 or:gbe,e: 0 jplf 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 same threae9vm tn7dus7 t8-f nj-d 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 the stone or t s- -v7ntmdfej7un9 8above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-k7ww xtrf++ k*rzt;cm, g rock is twice as great as that on a 1-kg rock. Why thwz; ft7 ,m* xtk+wc+rren doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale h:/ ,xm caa ml-)c4ojmlad been caliblmm m-aj: ,4)ac/lx ocrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an att/pdn 7vx /(qqwq zb l/0mj14jlached 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 acce/qlv1q d07 4(jlmx/wz bpnj/ qleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gr.v(pyidl pc5+ax 8k-lavity there is a net force mg exerted on it by the Earth. Yet by N5 yplxpv dl-ca8i(k+.ewton’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 yoc r2m i(-1yv- qy5rmcfu are on the Moon with the force needed to lift it on y2q yccv5fr-m(m1-ir 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 off2+;yug mij k7 war (Fig. 4–37) pulls with equal force on the other team. What, then, deterj 7+;m2iyfkgumines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. De yks:c ap.ey+.scribe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) onky:ps e+ ay.c. what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force doeft5 ng b6lcv), n*v8zws the ground exert on you? Why doesn’t this force make you rwcn8*gbl t,vzn)5fv6ise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s car a +kjyb427 yz pysz3v0is struck violently from the rear. Explaizyavp 3kzybs0 2+jy47n 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 i3 m ;k/kmav b:nul,u wrskkdy6w6 /9(truck accelerates, the crate remains where it is on the truck, s /6 nk /wmk,(6v3kubm riay;:ud l9kwso it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the blol ws9:awz -)ykb4uzkrvz14r+ ck reaches its highest point, it slides back down but the magnitude of its acceb):4skl1-ka rzw vz9yz4r+ wu leration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yohyh )uq ;. h9p7aa9v fkcsri17urself on an inclined plane? Assume the mechanism functions p7hp)ra1;fy9v7hu9 c aks q. hiroperly, even at an angle.

  What force is needed to jf6i,w4) j h -(hh5qsht(lh9vevci2o accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates an f+frn1( od; xz6ask) 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 5b2.o/oynnoqm dfs( *960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a :ui 7drchfc+c+j j5x6d97 tny $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 s if the ;+ 3zx8qndlab car is traveling at 95km/q8+x 3;bd zlanh? -  

  What average force is needed to accelerate a +qd62: fwfn 0 o:gmiry7.00-gram pellet from rest to 125m/s over a dn6rwfiqm0d o:y2 +g:fistance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acce1 -f +y7tv1ckb+p11x l6d u2cptlio releration of 2.5c xlcy61ue111 rl- pb+t2odv7fpk+ ti $\mathrm{~m} / \mathrm{s}^{2}$ 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 z +m ;x-hyjl/atrack (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 ) .xs) iep y,yi,is to be designed so that the maximum acceleration is 0.0680 g . What are the max s.pyeiyi ,x),imum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionldw0i-7/auz6g hm0a e2,yy xz hess elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction o wz0, g2ze6/ahmxy ui-0 ayd7hf acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,75*kux45xbsfbn 814gaqy )uw i +0 N. What maximum upward accelerat) wqxy fbb1u8+4ng4 xis5k a*uion can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including ,ds4skl l qjmw*f*x y236nf 6mt hz18bparachute) when the upward force of air resistxk tys6fb31,zlhj 2sdl8*n 4qmf m*6w ance 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 hq cg,l xhy. nsrd3/;7a 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 0x3hq,r;hn7 syl/ c.g d.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A r7 y q-1,xtjswfope tied to the box runs vertically upward over w, -tfsx1qy7 ja pulley and a weight is hung from 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 fole+lcts gwyl7 6(:b09 -twuez r 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 ovwks;32rh, it;)xmhi ho)aqe o :8 tu+f a baseball (a) at the moment it is hit by the bat, and again (b) after itaemh:3k ;2rov)ist )uiw xt8;q h o+h, has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N 59mlb dwt:igxz 7x/ 8*vikbj:force must be exerted in what direction so that the resultant of the two forces points westward? Illut9 *8li: gmw dxbivb/ 5:kzj7xstrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betw7hmf a(f3(qvddy hg8i 0ho0.heen two buildings 10.0 m apart. The sag in the rope when she igv (m fhd0 0hfha3.dih(8 yqo7s 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 massle xi igd1a1f5.3fv bz,51cyixyss 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 14d7ylj- - 0z 98 prrypd1zm w8z5zv:mat.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 location at McMurdo Base, Antarc/t71d, vhcrce tica, as shown in Fig. 4-46. The sum o/ctvrd ch1e ,7f 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 ckca cwramse)97 xfq8d 0-l+dfh28*y fars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first car sm+qxrff acd-* k a8dh9 l2we)8y0c7f $\left(F_{\mathrm{T} 1}\right)$ , 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 apparatus s4)(.x abolm.y;i ilv3bg ce e(hown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at(bc (m.;ily )ogv 3b4ialxe. e 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 racg/rste) r a-ez f-)/dbe began, a 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 blo0kgtrg*oo8 e9 82efisur- (ydck (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 surfa3;d w8mu1ux-tmc9 jsuq mc48jce are in contact with each other, as shown in Fig. 4-5w8 mdj 1 s-34tjuxcum89m u;cq1. 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 initially 1.80 m s/nq-5cjdwj;ro td */ above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavsr 5//dq *cjondt;w- jier 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 cord of mass ,gp1z)sv 5kswpdel56c5h.ya 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cor v zy5ecg65l dpa.)51ks,psh wd, 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 fr mpdi :rts98.rk( u7lziction 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 requro68:idehwf c w43 3asired 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 standing on a traaj3d .k)i4ou din accelerating at 0.20g. What minimum coefficient oojak) du.d i43f static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergos-senen96vw + if the coefficient of static friction between the tiws n6ns+- 9veeres and the ground is 0.80?   

  The coefficient of static friction between hard rubber and no: r;e x:a 4v 59mnifxv4*v g.7btuvxnzrmal street pavement is about 0.8. On how 9ztx4nixvv4 :m 5 f x:e.7v;ubrnav *gsteep a hill (maximum 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 ab0 adk+ex y5oy h6 s5yk2v/x,st -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 roug-w ; suyt0ats5g:(esj h 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-/efg 6 xbd/ugr qy*l( surface have a very high coefficient og/(/e6bfrdy qg *ulx-f static 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 fricafh 5bwb-nvu *9t.ty7 tion 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 7zj +w q *h3.fzbbjd-abox A have to have to preb+djzh37*q jz. waf- bvent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How aelbkd,4 :*5 *gd qeyrfar will it go, given that the coefficient of kinetic fr*r4e y:a5dd*qel g,bk iction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and-fmcxazpt:nl )80xx(vb4n*m 110 kg , are in contact and at rest on a horizontal surfacef:a c mp-)4nnxl0 bx* zx(mvt8 (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coeffic: ndl(x/6k/bk4 nnhwoient of static friction between the crate and the b(6 o hnn//kx kbl4dnw:ed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car ivj 0)sha yw2s.q zs.c3n your driveway, which has an incline of 1203c zqs). vy 2jswa.sh$^{\circ}$ . 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 a( .hk.mkcc4zmnsl2.ivn v6 s. 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 a pl*8xy f x/r,i;x))bgmlbqy y 6p+8ibliane 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 io/2 su:vh idd+c4ho5 knitial speed 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 steepest hi 22hx /jf bvdke6j+ -xcyz2mu9ll 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 k.:qy-a l95kw x,kmz l hfnb;(by someone pushing on it with a force dirq n5f yl.-z:kkl wxh;9(,bka mected 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 dangerous projectiles as they melt.to c9:gjr8wcq30 zn2l5v0,bc ekbg4 a Consid03tbj l5k,q gr8zbc4 wnoa9:vceg 20c er a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile trawi+t +6 iftg5dveling at speed v is equali65d+ fg+tw it 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 vt txbd)+8tg6forward on the dash when the driver decelerate8b+ t)d g6vxtts 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 initial ux0h-o+2+ njft s)fcg 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 filled to yf : 8vhczu 30q,5 9acbzjan*zthe 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 distqu cy8:0,z3c5naazzj *h9v fbance, 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 coefficiento9c v (7hu(it/znb7rt 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 (i,w)tv raz d 0b++u3lrjncluding 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, a1oriqd 7(k1jat each pulse approximately 20 g of bl1kdr qi1oj7a(ood 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 i3juu ;x1tvs i6f the deceleration is no more tha;i uj6xu s1tv3n 30 " g 's." 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 ac 2f b6ot(0:hrsgz :.ghtzrh ;pceleration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static 06.rt( tho;zrh:bzg gpsf :2hfriction 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 fp,2 lahslt*u:)yt8+s q 7bhz5g1b* 4gmz igtthe scene of an accident involving two cars, measure 72-m-long skid marks of 1+:qlmzhy**bzgtu lp)2 gsbs 5a 84tg iht,f7 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-y*m6c 3z/8orfhy cg,y 4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reac 3zr h*y m,cy/f6cgyo8hes 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 ofcb)d)e344 t(vc hrnm,r g.0kg t r7iok the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What wa7rmbetiv n kdr0))tc,4go(r43c . hg ks the average force of air resistance?   

  A cyclist is coasting at a steady speed of;8d rab9 cea4+g./nza elo6x d 12m/s but enters a muddy stretch where the effect a6xg d.danl ;8ra49bc/ez+e oive 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 wor q,no4sqy2 mi6king on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so thn 4q,qm26ioysat 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 exfj 6yl ++0rbsrq;sb(p qc;/luy9np) mperiments, dangles her watch from a thin piece of string while the jetliner she is in takebrjm69cy/q lnu 0)yrpfl (q;b sp+;+ss 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 supsk :xex+0 )bimu9iks 4n f mpz7m)(jj6ermarket, there are to be several ramps connecting different parts of the 74(j 06m )kpjnizb9 :xmuxis)mke+fs 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 vdi: x rp4-/fm,e*e/qar06h0msrmfgM ) using the pulley apparatus sqmi*/4-0s:fme x,r e rdm/pa 0v6rh fghown 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 3.5 s6, ryypcl,n ).xqa s)$\mathrm{~m} / \mathrm{s}^{2}$ 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 csudgco.fa-,fp*2 o9g hild-restraint chair, an engineer considers the following set of conditiou*ps fgo, o .a92cg-fdns:
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 660 metric tons (6y5s 4a evzn5t960,000 $\mathrm{~kg}$) . 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. Karen8sov v; gvu)k.c7p hranys +p+yhd-:3'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 thevv ;h:apcr)+ 8h k 7sod.v yy3p-sg+un rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-1 +w oz2;f,5bpugjp3y ux5dtq / $\mathrm{~b}$ 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 a maximum speed k9;kyxbu ram 57 aj7z/of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice fi abc.1p/ lawa4vr;k6keld inclined at 21.0;c1aa lw6 ak4vkp/ br.$^{\circ}$ 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.