Why does a child in a wagon seem to fall backward when you give the wagon a s mb buyvo+)p 5thf2lh4.9v 8csharp pull forward 5ohp).42v+fuhs9b8 bc vlytm ?

A box rests on the (frictionless) bed of a truck. The truck driver starts thezi(efn:v vd rw/; 5k6o4 ix+yb truck and accelerates forward. The box immediately starts to slide toward the rear of the truc:rvwi fzkb 4o ( 65nd/;xeyiv+k bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no4 z gh7tmqf 2up4q86ck forces acting on it? Explain.

Only one force acts on an object. Can the object have zerofuy8k ihex;p:+ycs 2;;kjxo6 acceleration? Can it have zero velocity? Explaip;;yje2su;ohk :c+6 x yixfk8n.

When a golf ball is dropped to the pavement, it bounces back 1zbqeexw ux;;n1h x28up. (a) Is a force needed to make it bounce back up? (b) If so, what exert q8hx;uew1e bx12nxz;s the force?

If you walk along a log floating on a lake, why does the log movvljvo5ag- 8;ke in the opposite direct- kg8vl5 oj;avion?

Why might your foot hurt if you kick a hel,y2i +5zomkp avy desk or a wall?

  When you are running and want to stop quickly, you muk(b e,wc9* y1v (zzakust decelerate quickly. (a) What is the origin of wy,vc ( *kz1kzb(uae9 the 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 sectcg0-gqn waa 5-ion of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if th-g a-0 5qgnawce person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2ehp4 at3+x8agkq5 j l4-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall fql+ phkae4 3a 4t5jx8gaster?

Would a spring scale carried to the Moon give accurate results if b z1v0-k4rhzuthe scale had been calibrated (a) in pounds, oz huv01zrk- b4r (b) in kilograms?

You pull a box with a constant force across a fricosj;wh i, re4pf/ cd0in+p:. /z:tjritionless 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, (,/.:sejf rop/ zi c+4ti;prhwj0i dn:b) increase, or (c) decrease? Explain.

When an object falls freely under the influenchvfk 2;c0 -ulqf8xi 6ce of gravity there is a net force 2fi8cv-qh 0k; lx6cf umg 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 Earth move?

Compare the effort (or force) needed to lift bteesjvyo q++)r , 0q4a 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 speeds ++t,)oy rq4qvj0ebe on the Moon and on Earth.

According to Newton’s third law, each team in a tug of/ q pn.j (tpgh73tsr+d war (Fig. 4–37) pulls with equal force on the other team. What, then, determines whi/ pr(t.td7 qs+hpg 3njch team will win?

A person exerts an upwa7c uk4rghyk. +rd force of 40 N to hold a bag of groceries. Describe the “reaction” fkkchr g7.4u+y orce (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 exerted.

When you stand still on the 22a)u knj q)fl*ut4na dzmfp+ k7-r5hq)*xud ground, how large a force does the ground exert on you? Why doesn’t this fomq pn)z+-) kxadf 2j)lta r fdku2q7u n5h*u4*rce make you rise up into the air?

Whiplash sometimes results from an automobile accident (q 2os(ds1r miwhen the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it real1(rs(d mo sqi2ly?

A heavy crate rests on the bed of a flatbed tru os h*v,j1* 8lkgudh1vck. When the truck accelerates, the crate remains w 8lhvv*dg*o,hj1uks 1 here 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 up a ramp. After the block reao7gdkgckh s3l2/xt)*ljk:tat:*5 h i (tq0r kches its highest point, it slides back down but the magnitude of its acceleration is ltk5l/o):qrc*ht7i0thlj 2( a 3 kd* ggk:xsk tess on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed ./j0hhex y.xjyourself on an inclined plane? Assume the mechhh/y .xj e.0xjanism functions properly, even at an angle.

  What force is needed to accm i6rzb. yqai hzt1.7uct0+/8tm9awi + a-gybelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike a(:qh.8rg a-w;ig+u2lb ehbms nd 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 wg+yvs;5nb1g* aon n e2ithstand 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 slxpc a),1jx-l l2;px /x3 tqv $76-\mathrm{kg}$ 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 i ;za6v.rx p7n)pud0 ;cdtzh11tt w4b required to stop an 1100-kg car in 8.0 s if the car is traveling atcrdbnzuvt ;azh1px pwd6.0) ;1tt74 i 95km/h? -  

  What average force is needed to agd f q:i+uku)ec.of*5ruf239a 3jlwx ccelerate a 7.00-gram pellet from rest to 125m/s over a distance of .u fe k2cqjo*dulwfi5uxr ):g af339+0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accec7yv7z bbx:fj0)x 2g bleration of 2.5 c0gz:vb j)2 7 bxxbf7y$\mathrm{~m} / \mathrm{s}^{2}$ 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 0c wgol( yx.l,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 48nug1 l96lo )cx50 kg ) is to 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? max n 9l)g6o1cux l=    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 .x,kirmyv1: s 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.s1yi vmkxr, :, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg )ci u.eq2g 7mkx3-jeb elevator has a maximum strength of 21,750 N. What maximum upward acceleration .3 kgiemj) 2bqu c7ex-can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fallingbkvhm+-uw/s1-ly6a4 tx d a:v sky divers (mass 132 kg including parachute) when the upward force of air resistance is elsd-vhba41-t/vyu x k +w a6m:qual 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 b, t3 7g :f c,afvcqbw(h0woa7yelow, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torsf,vy7 0wwca,c3tabq:g 7h(f oo (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 dakmi9o e88l4z(; wop on a table. A rope tied to the 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 thlok88awed4omp(z9 i; e other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball pdncz)pi6v hc*w t: ,9player
(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 baseball6ar r55 kb1*xy0eyoo w nft6m- (a) at the moment it is hit by the bat, and agaan5-ekr56* rx yywmo1 fo b06tin (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N forcep(8asm,g (w/d*l sy2 qob u4ve must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vdwy ,a(u/ sp2mvs*ol ge qb4(8ector diagram.

  Arlene is to walk across a "high wire c/o 2nbi-t(xm" strung horizontally between two buildings 10.0 m apart. The sag in the rope whe -tm/ix(no2cb n she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a mass*uf4k4o n; whjless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.e2fhq*k n5,b7y z- pi;xxo;df 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, Ant ;afigrq.h f(22vpp )rxi1al9b+p6 sfarctica, as shown in Fig. 4-46. The sumlbf .1p2ri+( 9grvfi qa)fa phs26 xp; 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 i 8u/dmrhfk)g;jwkk9 .s pulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the/dmh;k8j .k9r )f guwk 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 using the bucket-pulley apparatus zllz/, 4o9kgjw *9p ) hxg0pitshown in Fig. 4-48. (a) How hard must she puppxw hg/99il 4jgo,k t )zl*z0ll downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 61szpt s26+137nkae1xf hrcj j5$-\mathrm{kg}$ 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 (maa x7ys01o s+egope2 0nss $ 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 contact :)bc3d6wq-dqe d wyo8with each other, as shown in Fig. 4-51.:qwdq3-d o 8cd b6wye) 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 abovb*) ;v- mip: c .0pkdh5io bgofxa-s6ie 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 ground. This is oi :hpx-5kob sia;06 -bim)v*gc f. dpits "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on+rx-lbzft c.,t o f:q1 a frictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagramc.bl-txzo1r q+ :,f tfs 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 a 35h(s7m;x bjz -s$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to startx/;cuedp3wcc0osw/ dqr 4 ,1j 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 vgrg.ps 2h90n3o c4ag a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not tngg. oh r ca4sp09g23vo slide?   

  What is the maximum accelerat2ixl lp2,b0k4f*ajo.qc/ni42 do j miion a car can undergo if the coefficient of static friction between thid2 lj io0k.jm2 4n*, l2opxqaif b/4ce tires and the ground is 0.80?   

  The coefficient of static fri9 k vc5g*)u k f+cgm6ys0.mnulction between hard rubber and normal street pavement is about 0.8. On how steep a hill (mv.gsgyclu9k 6 muk0*m5f cn+)aximum 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 atwvlrv znw+)j);8/ vrn -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 0jy-yv t.xfld /)p-jt 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 co.a q0kcgaqddhrx 4 0/ ;mbw98xntact with an asphalt surface have a very high coefficient of stat/d4rd90aq.m;bw qh8x kg0xc aic 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 fvv4r q1e3c0 dg5dfk;wv)ly, criction 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) hol/v42b k3k,lcxcwz f9w large a mass would box A have to have to prevent any motioncx z,fbl 2v/clwk4k93 from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that itvj9 euwx. u6,ce uif+cql()ggfy0,) w slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial .ug0y f)qfl, ,9e c6()+ewvucwixgj uspeed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and alab 7w-cy arn )j30ucz/h01ly t rest on a horizontal surface (Fig. 4-1rzn7jhb-ly)yalccw au0/ 3054). 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 hza bi m ;a0h17c5irg.7tvse 9ceavy crate. The coefficient of static friction between taa rb0mg5i9 i h1v7esct cz7.;he crate and the bed 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 y+cyf6u0r3k asc svu:d91jc9 wour car in your driveway, which has an inc3 s0dcycw9+6ursj c:ua1kvf9line of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a sl*qw/(os wo ek j1)t(55xzdrq qo-r7y pide 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 ldn.neah(t. :9nqp /.g,vn jjiies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an rrb zma 9/6k-vinitial 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 taj8m24 fjp lfq)))8ikfoz1xgo 94oa/k9n xz uop 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 against a rough wall by some7z05es vv v2ooone pushing on it with a force directed upward vzv 7sv0e2oo5at 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 theyndx, 1dqd8 eo)daduopu p/h -y: d0f*- melt. Consider a chunk of snow at the ridge of a rooffad 8h-1d/ upoded,n)udq:xy*-0 d po 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 minqt7naj)p 6sa yj6-;en lu16kj imum stopping distance for an automobile traveling at speed v is equal p66n6j)t-j u 1ek; aqjnal7ysto $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 slid-b.t. 46t vdb5redtn sm/tupaa1 q80bes forward on the dash when the driver.nv atd6u1ba8 qp -ebt4b/0d m. s5rtt decelerates 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 icjt9+ewk*zux v/uk 8w*0, 5 lriayh1enitial 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/wwwfls l /j g,ix )0k3w/b,pe 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. If the coe/s0b/wl k) i,ewpgj lw/f, xw3fficient 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 friction vfr,0z:fv,b-m.g gd ybetween $m_{1}$ 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 coo( d*ez c(p .ga5)zknqast 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 mode8c5er,h abd-r l of a mammalian heart, at each pulse approximately 20 g of blood is acceleratedhrr5- db 8ace, 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 crat-hn3k+yb b 1gbe7-of sh if the deceleration is no more than 30 " g 's." Calculate f-b-1o yte+hg n k7b3bthe 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 qzjf 6y hr)yt9 8ldifzz7318gis a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at ldz 9fh3jzyy)z8i7fqg68rt1 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 cah 1o -9gprq 2.,gvhskwrs, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a hh p2w1r, .sqko9g-gv level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m travgjz m7toc*;c-f0.l0c 0 xc ffbeled along thez0.b;0-og0c*m ccjfc7 flftx road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leanil:-dg ima q:j*yj+ne:ng Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistance? iqn j: a::*-jd+gyelm  

  A cyclist is coasting at a steady speed of 12a*s, ayi6ji4qj 7)qx xm/s but enters a muddy stretch where the effective coeffixj 6asji*y)q,axq 47icient 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 workin ,jt lfi3uzqm*6l2 ;iug on the redesign of a hilly portion of a city. An important considerau lliuf6 q3*t,; 2zmjition is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a th4tu x1q9* adp3ry0q ozin piece of string while the jetliner1dr0*a xo tzp49y3 qqu she 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 con(wrr a :uz8mpwz6s8eo.i0 hwx+:j+ clnecting different parts of the storew +rzezm08wjw:.s:hri+ pl (u xa68co.
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 Mcqqz hx( .j)6g ) using the pulley apparatus shown inc)6qxj (ghq .z

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 9qiacpfa 4-y8 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 cons t22, wxzc:zle wypd75iders the following set of conditionsz,w2y2 75wctl:xzde p:
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 maox *nnd35d+-xndo9y ass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length. Karevq (geh2 5+avp pfjc*uln u33+n's rope is more elastic, called a dyna52 (aup+3qv gfc+hnepjul *3v mic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is uszxnina4y5 *; bing a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall buildo7 zd82cu/ 6ps 9sl2n(bw1j :xrw ifafing is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice field incligxy4i n7o+l gt0sv-o0ned at 27o x0vlso +-t4gign0y1.0$^{\circ}$ 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.