Why does a child in 8a h q yg,c2 uptss01g3m)hvv/a wagon seem to fall backward when you give the wagon a sharp hua gt1)sghq8 pymc0s2,v3/vpull forward?

A box rests on the (frictionless) bed of a trw0ket9ibx h7d02)qb q 0ozmb *uck. 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 terms of Newton’s laws, as seeh0qe*x md tz)9kbb2bi007 q won (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 no forces mnu4r kc1n ) z7o6dzm4o6 /hvwacting on it? Explain.

Only one force acts on1pe8e(yp9cu h an object. Can the object have zero acceleration? Can it have zero vu1y9 ep8p( hceelocity? Explain.

When a golf ball is dropped to the pavement, it bounces 8n8a 2awmn9byfhz 08a.jms,eback up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts the forcn.a2emh8z 8f 0m89nb, wsy aaje?

If you walk along a log floating o j-ikxlc l38xsod+ g2).h/m zon a lake, why does the log move in the opposite sgklz i+c8ldh o2 /m-)x3jx.odirection?

Why might your foot hurt if y,ijt 00k-;bw.uv s+6 dfklteeg2 o x-sou kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quicklyne1skt6y 2nx5 ad2x/r. (a) What is the origin of te xn1ta6 sky/nr52xd2 he force that 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 efr,h93ww;rt of the same thread dangles from the bottom 93w thre;rw,fof 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 above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great ascopp61h6/ o una3 f9*gcmyi:w that on a 1-kg rock. Why then uiofh3g6m /pac6ny1p9* ow: c doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moo a +lt u25muuhl g+gw5um5q,,nn give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilq5u 5 5w +agln,uh2m lu,mgut+ograms?

You pull a box with a constant forcecyggf0o sce;h od++ 7, 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) decreasc0+ge;co fy+dgsh,7o e? Explain.

When an object falls freely under the influence of gravity there is. ssju:dxpj c8 0 :x0lo/o0tfy -wl1po:f ds*m a net force mg exerted on it by the Earth. Yet by Newton’s third lw1l*s :uxx0poj/o s f m8:0 t0- fod.pcljd:syaw the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or forcun*t*tyycotp:7lw9b) 2g; rqe) 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 throwut n*py7:r; *)oqtc 2glwt 9by a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls ws;slf q* zf3c( 0ich(fith equal force on the other team. What, then, det fcq(fz0(slf;hs3 *ciermines which team will win?

A person exerts an upward force of/d-o:g9g9-*6 mqf y n6phzjllpl1h ua 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitmp:/9dohnq6 l-*6 lal9fy hz1-u gpj gude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on t 6x8g mek.rnj n4)amg2he ground, how large a force does the ground exert on you? Why doesn m)ang64n kmr28 xeg.j’t this force make you rise up into the air?

Whiplash sometimes resul3/lz6q v:t(j3 :mrekbt vi-sdzhd+q -ts from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this svr 6l3bjdszq :/ thti-(qmvk+3d-z: eituation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the tltp/at 0 ohux+t., a,bruck accelerates, the cra.+0ta,lha tuop, xb/tte remains where it 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 2 mkp-j90hvvs, j*n;b q-fxleup a ramp. After the block reaches its highest point, it slides bac jhnvj0m x*,q9kl -fv2e b;p-sk down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bath+dvf v0gucp6.5a f /cjbc/s 6 nji6l6droom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an alcvv/dc6j0f.ig ps bn+66 5 jd/uc6afngle.

  What force is needed to accelerate a child on a sleg3zk0rqb wg 0 d3;0opud at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at dr3+s eyi l+g( jfd+-c2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rop rv:dpg:hh3 lr-i;0 hae withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a 5m4fa* za5gj d$76-\mathrm{kg}$ 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 car is tra sbs(/*6dg v 7qh/ghgcvels gs (/ /gqd*hvchb6g7ing at 95km/h? -  

  What average force is needed to accelep/x6 b:,hrs wgrate a 7.00-gram pellet from rest to 125m/s over a dis,hw xs 6/pb:rgtance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish verticallyi /66:nyvhts t out of the water with an acceleration of 2./tn:6vys it h65 $\mathrm{~m} / \mathrm{s}^{2}$ 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 lwtb9 dibn.j5: )9spxbu2v:vquarter-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 t-21( +jl3w gzcdqtrruz l-b 4lo be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? mauc( d-lzlj-wgrz+l1t r4 3qb 2x =    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 scaavw1j;0sn9 anr rj;x+v n53.yqpi (l yle in a motionless 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 of accelsxr jvwp+nn1r0 .vyl;yq9(;3ain j5a eration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator h1d0j pf7vr d06 oyq)lnas a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator wfdlp 1v nyo60jdr07 )qithout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg .dm6gq -;1 qnglz4wfv including parachute) when the upward force of air resistance is equal to one-fourth of their w1 fgmndgz 6q;wvql4 .-eight?   
(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 striyf(i 8s/ c,s6myruc*ykes the ground below, he bends his knees y i u(mcfs*,6 yr/scy8so that his torso decelerates over an approximate 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 5k*a b mhtel(p/et*e)box runs vertically 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 pulley weighs /*t5ep (h me)*ketlab
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram foruq n7is2z8g8 8(f1ny los wcd( a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit by the oc vrbx -0tazr29.f e6bat, and again (b) after it has left the bat and is fv.t 0aor-xr6b2zcf9e lying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force mus* w)vb8x +c+woeepe8qt be exerted in what direction so that the resultant of the two forces points westward? Il)qpw8ovcwx+ *be e+ e8lustrate your answer with a vector diagram.

  Arlene is to walk acrosscsy(qpaml g x3ya) vt*/z4k79 a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10 gtzk s*/3m(qxp v7ayyl 49)ca.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 ccw6oho9w+3wu 93 zyhhord 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 1)n3pj v;5jher 4i hi:g4.0$-\mathrm{kg}$ 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, Antarctica8us es0 h0ll.k, as shown inehs 0lk.u 8l0s Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-coofi2k63bg9dgw f+m3 +te a647 . Determine the ratio of the tension in the coupling between a iet 6c92o mdgf3+fbg+ko 3w6the 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 herself upward uszk54cd j3au g yga1s/1ing the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she 3kyazd1 j1ag 5s 4uc/gpull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race 8pdnag2nr+ y5vt ,a2pbegan, 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 (mar kawi 0stc.:l+0o*pmrmuo-*tsr 9 8ass $ 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 h49xha+kv7t h.9 olrhf orizontal surface are in contact with each other, as shown in Fig. 4-59vx.+f7o t9lh4a khrh1. 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 1.8by c 7k4hj*gdy)wga /-0 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the 7g)k y cabyw-* j/hgd4ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by mlyl /zkvejn+fe 1 1j1(q;t6da heavy cord of mass 1.0 kg . Calculate the acceleratqn tvjj + e1d/1lle1f6y ;mzk(ion of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between fa8m wno1l0 f7l7u6vqa 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 d-,npsux-7b oto 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 accelerating apbnamnx07m 3 d1h )u- (emh7qnt 0.20g. What minimum coefficient of static frictionumm 1xd(7 hb3annm)- 0e7hqn p must exist between your feet and the floor if you are not to slide?   

  What is the maximum ap;oh uxar6 ;a4cceleration a car can undergo if the coefficient of static friction between thr;6;o axpuh4a e tires and the ground is 0.80?   

  The coefficient of static k*n5,exk2 d1lyov m1 qn:jsau- wm,l*friction between hard rubber and normal street pavement is about 0.8. On ,:ls-1nak j5kw,1 e**2y qmxvn muoldhow steep 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 at -4.80skp*+jiae- (hzn cy,pnz*g+tz f5a+: $\mathrm{~m} / \mathrm{s}^{2}$ 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 97kf/8jc1sq: l/ z/ m:rbnum cxb1l bja 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 surfaceai(.s3rj:isgi+ o:7au9: tstgnr) rc have a very high coefficient of static frictio(s3sg9u.n: j r:oiis7r gr+) tc iaat:n.

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 kine;ed0wq -:a4hac:m x xstic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would bot7icfn: gt914rlb jj ;x A have to have to prevent any motion from occurring? Ass:jcil t94;b1 r7ftngj ume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the f/ggv, gqj1ihg 5pzd9.o-fo o4 3c. piez k+td1loor. How far will it go, given that the coefficient of kinetic friction is ,gjpd gh51gfvdeo iootp9.zk1 -i4+cg .q/3z 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , ard2ab3(;gmomm pg*6yv p x/vs5e in contact and at rest on a horizontal surface (Fig. 4-54). Ap;ompg36vy5*2(vb xs mag /d m 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 carr,pk k2dhujrj6y 4q+i6 ying a heavy crate. 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 and still avj642p+dyqj,rhi6 kuk oid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car ibdv (.di1wnc-jrxm v)+xh27p n your driveway, which has an incl . dmh7-xpd2 vrcibjvwx+ ()1nine of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down ty4y));r afe f p7keb7a slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane 3q /h3y 5pn jbv)bjaj3tilted 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.rsug/ s ty7b6,.h1 3s 28idgdoazz;gn0 $\mathrm{~m} / \mathrm{s}$ 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 reaches8 gi8 6ys( (zjregvg2g 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 place25 0asm u*vyt: y8vkc -ta)zo;nf6fxh4 xr6 rp against a rough wall by someone pushing on it with a force dire;vr5p6fzhv04fys 2:n a xr- uoktt y6c8ax*m) cted 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 u j18px9v9hyq can become dangerous projectiles as they melt. Consider a chunk of snouhq y9xvp9j 18w 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 traveli oe d p xx4w:)b)m5tuwqe7f9oa yg2n19ng at speed v is equal to ewd459oowm)qe7 yu)x 9bxng 2 t1:fap$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 s vzhszs31)2h/df;do of a car slides forward on the dash when the driver deceleratesz;sz3 sv2fd 1 oh)/sdh 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 masihv/6r;)ttw )xu :w tss m 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 filled tgll,nyriaam+ l+ 9a)9 o the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid trans m)+ly ra9i,agnlal+9it is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient ofdv*b/twomg 7v/ur1;g0o0 wao 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 bia ij )o(.br0gdcycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulsgth4 3f*kuo srn8h :n6 8xk3z :7aoyyce approximately 20 g o oyzun4 rahn8 *ckgy :s8h67x33tofk: f blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if the deceler723v12 w:k7bo lyipp8es lnhfation is no more than 30 " g 's." Calculate 3o28l1sin w kv 27fb ylpphe:7the 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 earthquake is m(mnt0p) -r eaa , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the gron0m(t m-repa) und 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 hf49 nds/y r4.hhv natie s055of an accident involving two cars, measure 72-m-long skid marks of one of d5.4n f04es r /9shnyahi v5htthe 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-iny6m;l0ikkn6 t-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it rea0ykl6 ki6;n tmches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and ie eh uf8vot1 1qkz/:1falls 55 m before reach11u eo1ft z eq:k8v/hiing the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but gb;), x9v di.gp+rpp fenters a muddy stretch where the effective coefficient of friction is gp9vf,ib;d .)ppgx r+ 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. Aozp)df)d ; 9enn important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A p dp9)nf;odze) articular 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 hefc:xkd5b, f vjjggvh-nl55 /:wu:b2zr watch from a thin piece of string while the jetliner she5 zlkff2b xj5g:dw :gubch v:n/v-5 j, is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connecting dtp8 ucx9hquu0v76 nu)ifferent pa)pu nvchu 0qu u9x7t68rts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force xh kgt2;+k ai) F is needed to lift the piano (mass M ) using the pulley ik+a2 )x tgh;kapparatus 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.(yo b :shzox: 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 considbvpxuw,9p3 k 3ers the foll,p3xbupw 9v3k owing set 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 train has a mass ofeww n7 r42h/ev 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of sglsgke9p+ h, 8ta1/bw imilar length. Karen's rope is more elastic, called a dynamic rope by climbers/9p ,k1+g l8bewahgts. 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 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 2kmc-3/c +xq ip,f nppa " 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 reaxt2 qvhj2l 33wch a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers whoj meu5g:fg, wr iaj n.us./2y8s*0epo are roped together are ascending an ice field inclined at 21.j.* pn8uo,ssy5 .: e2gi0 j/grumeawf 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.