Why does a child in a wagon seem to fall backward when : 3x-kwlpl (qfv*i *)pz vy7gxvwi*)gyou give the wagon a sharp pull forgl gp:-* izlw3)pxf)y(v kq*vix*w7v ward?

A box rests on the (frictionless) bed of a truck. b5ug ;o/xmm p)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 o)ugb m/pm5x; 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, *4a. ox guum)lare no forces acting on it? Explain.

Only one force acts on an object. Can the object havz0cq)xz , cwv.8jn4n 2bvtg,c e zero acceleration? Can it have zero velocity? Explc2tc nqg)x .8,v zbjcv0,4zn wain.

When a golf ball is dropped to the p hf0:u/owo8edavement, it bounces back up. (a) Is a force newo ehd0/ 8fu:oeded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the lolh::1j( n)i z-pk ljlhl l3*mxg move in the oppositelj):h(pnjh* :lx 1kliz- llm3 direction?

Why might your foot hurt if ya(c yvj3upz*n5f w:5sou kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (a) 47fy-dk/dpg2nj q b/av4bmf+ls ra)0 What is the origin of the force tq7rfdaa2f m40bby/g)/p+kdjv4 sn -lhat 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,ampr -e*dh;l v ei3q( the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the danglihv( m,pe-d*i;r3alq eng 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 a 2-kg rock is twice a8 r mxzu65: ;yu2fwtc9fr0za ss great as that on a 1-kg rock. Why then m uu62r9zc0astxfw 8zyr:;f5 doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scale hhau6w o5 nzpd4/,fuwwl- ks8,ad been cazf,-a 5sw u46uh8ownwkd/ lp,librated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force acrosvj3/z*q1v lfl s 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 1 lqlv vfjz3/*on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net force ez9clef0a:c/mg exerted 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 Eart9 c0afc/l:e zeh move?

Compare the effort (or force) d 2/-vd; hw bgpww0wb+needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon anvp0dwbgww2hd b-w +/;d on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) p jua o,, -ob,j00jya 7u;pmojiulls with equal force on0 uu ojiam,,yjo 70;ob,j-paj the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceri5 sm-tm-;bk o04crg/*jo,zyorwo2 b ves. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exertemogw5br/zrbtoomykcs o , v ;-*-420j d.

When you stand stillrjyfv j+f(9r:p *uno 4 on the ground, how large a force does the ground exert on you? opr:+v9n*jfyjfu4 ( rWhy doesn’t this force make you rise up into the air?

Whiplash sometimes results fromwd 94zsxnf nu;1n :,uw an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seux9,nn f; :ndsw14uwz ems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of8+r zru7j.hmy a flatbed truck. When the truck accelerates, the crate remains where h+.7 zmrj8r yuit is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After thpa1 pepz njz(k.q/v m.n7 +8xce block reaches its highest point,m(p pcajz1e. nxq. /p8vnz7+k it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read i 66dtwevh7 l)div48y2 )k bevwrh:6p htqd2 1af you weighed yourself on an inclined plane? Assume the mechanism functions prok 6 d)h4pteielw qy1t7r2bd:68 da 2v hvhwv)6perly, even at an angle.

  What force is needed to accelerate a child on a sled ksqye ;;gil0j2kex;( at 1.25m/s$^2$?   

  A net force of 265 N accelerates a)lhv b.fl luz- 0:cp q6nzy1;h 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 accelerm5dc.3pq jl p 5,.rbfvk:cx ,qate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ofco c- . puu1cs1a3eh/il6w; jo 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 r2ol82 )w*dsai3fu u sfiwo. v,equired to stop an 1100-kg car in 8.0 s if the car is trave)ds fu, ouwsi2a3 o*2vlw 8.filing at 95km/h? -  

  What average force is needed to acb- ,bz:xtog;b celerate a 7.00-gram pellet from rest to 125m/,:- ;gozbbtx bs over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accel+rval l -bvp:d,;cmx,eration of 2.,lxvd:- ap, rm+bv;lc 5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 covzg ( wf/zty4*gy0rlw9er a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kgbtjw* * vl*8;aeep0rylzx ab14p1 +m4*kqknk ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimumvjw14m ykpl4q ne *+1razp**ek0k* bt; albx 8 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 motionless elevator. When the elevatorl 3o.maf7r5g4bxwk4y begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acce o75x4rmba.3lw 4gkyfleration 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,e8t:d ,b;t pvp750 N. What maximum upward acceleration can it give the epte, ; :ptvd8blevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divert9q9 o1t,0v t8l1cuk3k rn01 qmeat ies (mass 132 kg including parachute) when the ma1,ot1nikt l0rtv q 9u8c9ekqt30e1upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the ground 1bcubiw qu16; below, he bends his knees so that his torso decelerates over an approximatebu6b1q1 u;ci w distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs verticbj (3tncq9, ve1(raxghn:hwwp4p 2 h /ally upward over a 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 pu /,r (pgwhc ajnnte :qh1 v29p(43xbhwlley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basaefao79y w3m 5u: 4v:ycqnk jhfn9n;2 ketball 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 itpl 2m8 9 ;ayruob .w6dw5vl/nc is hit by the bat, and ag2/rmo nl.wwv;5pu 8cblyda96 ain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwh-754u b 5k k*3kchg0- qdmyyva)ayoqesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces poic574oa *kbvk-g3quyykh-)d 0ayhq 5mnts westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" stfr7vk8arpo ;vi/g5 kcd 2cn2)rung horizontally between two buildings 10.0 m apart. The sag in the rope when shrkn/kp vg2c7) fdc2 ai58vor;e is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from 9l(xwfhc4b1*hl5mh4gu k e -n 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.s.,; :ubtke2bwf/svu 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, Antarctt1,/ y.mkpz mcica, as shown in Fig. 4-46. The sum of the forcesp ,tc mz/k1y.m $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 on)xk z9jzp7tfcqq vq* n* odz)7w;7+ same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and tkoz 9;)fq*n ) 7*zdxo+jz77qvc pwqnthe 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 herself upward u83 wtacqi4 k9lsing the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant spcw q3ai8l 4t9keed?   
(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 begk0qt- qb98a3xdq8tl kan, 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 block (mass +j4 u8atdo db0$ 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 in conttpu,x 8,p3 sekact with each other, as shown ines,pu p3,x kt8 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 initially 1.80 oa:mrvf0c9 5gdo mf62m 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 heavier one hits the r9fdof g5o02mmv:ac 6 ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are conneayr*xp (.s3:e cacmb0 cted by a heavy cord of mass 1.0 kg . Calculate the acc*r(mab x:ycc30se pa .eleration 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 w(ys+ ay mct-: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 isj )1bhhwdsx3k sh5w f;j1 w6f/ 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 standing on a train z-: jzlymy (m6accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slid mlz:yj- m6zy(e?   

  What is the maximum acceleration a car can undergo if the coefficient of s 09x.xct f6wv wv*fs; 8sz/rxltatic friction between the tires and ts;. xrxfl6x9 vcw/st8 w0fv*zhe ground is 0.80?   

  The coefficient of static friction between hard rubber and normal swpqhr *a+ y+r9 /t/a bnhee)v)treet pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parkee9*rer) +h a/bv+yp a/w)nqhtd?   $^{/circ}$

  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 ;ojr 0)zmk3 nsat -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 rough 30 lhpvi,peo4k ,m )zm;xb5m76:hf.njd $^{\circ}$ 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 coefficienkan( x(/)ugm6vqidv 1t of static frict(6kdx(qu) m/ vaiv 1ngion.

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 kined5gj r1*v ia3yx50/smfhy;potic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-324;it:j ;wub md-wb 8 aaef/tt, (Example 4-20) how large a mass would box A have to have to prevent any motion from occurring? Assumet b; w4btam u:- ,/w8i;efdatj $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How farm4bhph4sipt06 y(ov84voof /3 ,e olk will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initis4t i6homvbo p4 4kv/hoeyf,(l8p3o0al speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest onkfbdc57p yj1st9.g 5+tt kgux.f- rd. a horizontal surfacedkdc jrg .ux5 ft+y p1.sb9g.kt7 t-5f (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 c6/w v;zqn-1cb jb. qvpoefficient of static friction between the crate and the bed of the truck is p w .qq/bvzb6j-c1n v;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 parkinglmm,ftjh71 i pad2u p/.,hg2p your car in your driveway, which has an incline of 12p7m/j2ufd h ,ml,pg12iaph.t$^{\circ}$ . 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 slye)qgv h )8tc:vsxbj;;s2alpbh*;( z ide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on7el7khrf /uasikbb c-cm5 76g0aws): a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.0 qe84hzqv8v(w: 1 y hum$\mathrm{~m} / \mathrm{s}$ 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 reachx+)sug,8+h6 (hmx bp shu5endes the top of the steepest 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 agains ;y7hr.tg ul2jt a rough wall by someone pushing on it with a 7yrh g2lu;tj. force 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 cu3sirh8. l 1hxan become dangerous projectiles as they melt. Consis ux1hrl.h8 i3der 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 minimasazg3 ve5v8 (ew,1pkum stopping distance for an automobile traveling at speed av1zpwvs(8ea e3kg5 ,v is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboadbeybft f(.8 (rd of a car slides forward on the dash when the driver decelerates frobbe(y t.(fdf8 m 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 z;0gyr wf1l 8q+)s sg6zpx1q cm 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 frlsa a).igw+d at3a:or,nh-r2lq q/7 b om where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip.t 3hllaw27qa + ibqrsn:ogad-)a, r./ If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic fricticeh(8 3 4qfp6gw18sconyi /fhon 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 +xhb / c.w,p4g+m l6n)nmzkdncoast 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 ozd *jb5j,cwr g.qrgcq-1/i;0kysm: mammalian heart, at each pulse approximately 20 g of blood ir q5 ,rgjmd1yci qs;0j: /wo.*gzbk-c s 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 autoy:)y 4b-t,jd4g 7u4a: xkd udg dovkz32im 5oqmobile crash if the deceleration is no moyoaxgyu5 kt4vq ,uo:3m2i4dz d g4)7d-kb d:jre than 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 acceleration produced by an ear9-z0ip,m uohckchg 9:thquake is a , and if an object is going to "hold its place" on the ground, show that the coeffici0gk:h 9coimz 9,c-hpuent 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 scene of an accident involving two cars, m, ol,c5oa+1kwhv a.vweasure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of wa,a l.ko v1+c,ho5wvkinetic 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 h0cjh7l qlor u) +) ll*kotd*d8ill (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 reaches the bottom after traulo))+ r*7 jdl 8kdllo* 0thcqveling 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 olo8 8bb- bym *i7la/rjf the Leaning Tower of Pisa and falls 55 m before reaching the grour/*8b7lla8 o-jm bybind 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 muddymf;-t)2grl1 1dfj slk stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speedkrg1 m;js1 -2fllfd )t upon emerging?   

  A city planner is working on the redesign of a hillybts8ang5 u4t; portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, wgt5usn8a ;4btith 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 watch from a thin pie 1nm0 km)wgy4 +yif/amu5po (wce of string while the jetliner she is in takes off frommo/1nyu fpma )kg+(45ym ww0i JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there ar c6wq1qx5;u xre to be several ramps connecting different parts of th5x; 1wc6uq xrqe 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 8w l 1i1vvj6s(k dm5qmo8:oji M ) using the pulley as18:d jmiv q5ovk( 8iwoj m1l6pparatus 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 at 3 (/h0nfq ktp8p)fnnm9.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 thee.9ajrgy6 r6q 2s vu3p following set of con v96q3gr2syajeu.pr 6 ditions:
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 metrsmi/58; *ww zvvak(gv3 ztns4 ic 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 rmu+bz*w 9jn-q 8xub/Karen, 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 thenwr bub-u/m *+x9nq8 zj the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using amhsv8 se l x 7+uo1iil*fef92:y41qv e " 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 reac6tzz3(uhca2, vy;ui nh 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 climb; fm75g,nb9 eru1yffs ers who are roped together are ascending an ice field inclined ay5;fmsneb 17,ff9u r gt 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.