Why does a child in a wagwi8sk/ -gk :y..sql alxpnn3:on seem to fall backward when you give the wagon a sharp pull forwg/a: nlks .q:n isp y8kw3-.lxard?

A box rests on the (frictionless) bed of a truck. The truckww8(of jlnw.0 ee +o7 jjqh;g7+5avsq driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion w0 +jqnw5.hovj +q(j wfoe la7e7gs8; 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, nd gtd 6us14k.1xa6gdare no forces acting on it? Explain.

Only one force acts on an object. Can the object have zej+q2(v:wfv-; a tr;:ryig+qw hij 1p lro acceleration? Can it have zero velocity? Expla fr :(vj :l+ gjyw;+1-2rhtwvpaiqi q;in.

When a golf ball is dropped omcaywm yr*fq nl-f(yhs l-;/f1-c15to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If sfcml1h;-* y crslm ywy -5q a1nfof-/(o, what exerts the force?

If you walk along a log y(4k/i :4tkbp e *0gc;z1 rihqtxpn b;floating on a lake, why does the log move in the opposite dkbt1 0q/x;*4yeb(izt h :n;4ppgrc kiirection?

Why might your foot xg4a :i u .89tso9ictr9vrgx .0)db sghurt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (a 4wis1u bud4:e) What is the origin of the force that i1bsudewu:44 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 thread6cxfy-a*dz 6j from the ceiling, and a section of the same thread dangles from the bottom of the stone (6*fycjxdaz6 -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 gr- 4(ls)yo hzxmbl4i )a :bj2gzeat as that on a 1-kg rock. Why then doesn’t the heavier rock fal - molhiby4bj4gsa)2 l)zz(x:l faster?

Would a spring scale carried to the Moon givej1(ilf m;d.-o v muenw /)c qh2qv,7bn accurate results if the scale had been calibratem2vjnwq;obe7iuvn. (- f dcm/l1 h)q,d (a) in pounds, or (b) in kilograms?

You pull a box with a cons5h, tvfu /b,ma7*z4cljrhrp)hrg.) f tant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle toft) rp,. clhr5/)h 4juvr zf,7*m bgah the horizontal (with the box remaining flat 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 b*g 6f7.mf/o sevobitw;t0 l 7of gravity there is a net force mg exe/t ;7 bob m. *esg67fiwv0ltforted 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 yf g(pq4xvd(5qn ;:toto 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-kgxp((5:fq o ;vdgqn4 yt object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third lex ;9*lr45d qki z:a8u:tjqeyo h1ha;aw, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. Whade:xeu 1hqqoa;i8;z*kjta 94hr 5l: y t, then, determines which team will win?

A person exerts an upward forcl4tjggaaqw hu,u2 (uj8: 4r7ce of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) itsg,ru(4 ju c2t hja7luw:qg a48 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 ground, how large a force does the ground exer ben,onib)k(:df 0)bff t9 y6jt on you? Why doesn’t this force make you r tfj(9f0:b6 b,y)fdn obeik )nise up into the air?

Whiplash sometimes results from an iixdcgy93p t (tro2:2automobile accident when the victim’s car is struck violently fi9(r 2tp ix2gdct3: yorom the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a xxa - /tqb.ao )(,ektar r3zt5pxiat;y 5x(m.flatbed truck. When the truck accelerates, the crate remains where ra.a- tk5;i,atra xo e)p 3/(qzxy t (xbt5.xmit is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it sl7)geb hackz s9:0yab1ides up a ramp. After the block reaches its highest kb197cahz 0a :)yegsbpoint, 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 iz9 g e ssa7veef+;r5a;f you weighed yourself on an inclined plane? Assume the mechanism function ras e;5eeas; gv79f+zs properly, even at an angle.

  What force is needed to accelerate a child on a sled at yl)yftr(4)a sr ylf.r3n wdzj() by5- 1.25m/s$^2$?   

  A net force of 265 N accelezdkxkowkrcz tm5) :1j2yf x6 t(cu .k6ms/- i3rates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if itk0vj:+ crua lkywauz8r -sb30:g1 xf3 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(n+2ta.js mn)4bw pfm $76-\mathrm{kg}$ 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 th4o z)hfuz8*ute sg0+raveling z*8htzs+he u0 4u)ogf at 95km/h? -  

  What average force is needed to accelerazonjphil5 g 00+c:b0rte a 7.00-gram pellet from rest to 125m/h5rb0l0o gi0n+z :pcj s over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically,a- ygz .0bllg out of the water with an acceleration of 2.5 zagl0,-y.l gb$\mathrm{~m} / \mathrm{s}^{2}$ 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 quart6vrh wf)qr0z7 er-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that4kqkzf+ j- m2:pvpzs; the maximum acceleration is 0.0680 g . What are the maximm2 k zs-q:pfjzk+;4 vpum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathrvc enzb29 cpp54h m5b/oom scale 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 el29p bp55c/ m vnzcb4heevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator hes; *.r /d xx2hyln8kfas a maximum strength of 21,750 N. What maximum upway8/nk*x d2 xer.l;hfs rd acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fallvc: okddj -g mp*lhngret0 +7)7tal,,ing sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourr gatd govd07)+tlm -j7*hl:cpe ,,nkth 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 rooft0ibvt1qmpncj ebw*7b*vih/52 2 mq: of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass *vb qni/*t b20c5qp emwm thv:b1ji72of 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 t5z9 axar chmtm4. l t ,ye2asf/d.ny-5able. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40)f m ./a,5shet.rxtyadc9 24z-a nmyl5 . Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a bask si cta7s +8qx:l7:oa+go3ow metball 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 ofppl/. .p qhj(gx y3.cr a baseball (a) at the moment it is hit by the bat, and again (b) after it has left th/( .h.ry j ppx.lcqp3ge bat and is flying toward the outfield.

A 650-N force acts in a northwesterly dir28+rop z v-fj2eh i;ark50krfection. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? jfier8ko022 a;rpf+k5 v-r hz Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betweemf-ljwn*1:s i:9k2r y *d bywzn two buildings 10.0 m apart. The sag in the rope whe :fr1 9byk*s*:zl2dwmnw-y j in 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 bucketqxbgu186kmaan)lml )+8f v(q is hanging by a massless 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 14.0c( ryam;x,ux9 $-\mathrm{kg}$ 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, An3/zog/n5 s1bbu * cvhdtarctica, as shown in Fds1 zug5b/*vc 3/hno big. 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 pulz sb6f91db 8wnling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension wb8nz 6b1 9fdsin the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bw1ul5y;7-b* kf z9f wsv w .9kckoy+u3lc+rl iucket-pulley apparatus shown in Fig. 4-f+91us.cwiwlzk ykw ylc u; 7-b*9o3r+vfk l548. (a) How hard must she pull 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,nt dy ;/av);,ohsb ija9a e+*t 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 bb2hp, 6m joap*lock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with eacnab p/zi85o-fh other, aap nb 5zi/-of8s shown in 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 m above :r l lwr: )80juzahdu8the 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 tl::w8ua rj 0)u8lhzd rhen its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are1rgm0xs gtgp)t3z7(t /ow6g q connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the g1)0gzot /swxg6 tr 7qmtgp3(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 betyh)3xcmj 8t y8zzt5.rween a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start. l:sati d(ot1 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 viztd/ ppg:r m5r8*d u-c1o7 jstanding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between pjd* /1gr oum:pv5zi7td cr8- your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo z9klz3e p )pd*if the coefficient of static friction between the tires and the ground i9pzldz e*3pk )s 0.80?   

  The coefficient of static friction between hard ru al/ lp;vn+,di5vsd r4bber and normal street pavement is about 0.8. On how steep a hill (maximdrnli5val,ds ;v/ 4+pum 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 )vjf)ww) z2 hktm543b9csy9 e:lchu sat -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a roug v41tqjm2/f nbwobjx yl1*jzpj+:1ns)m75 kjh 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 p1dnhu ;,d9zeasphalt surface have a very high coefficient of static fricti;,nzpu d91ehd on.

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 kinettbz6z2 rfa -br; .u:xdic 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 box A hav 0k.-ebdif+f9zr0t f de to have to prevent any motion from occurri 0rd+bf9- f.0det kfzing? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How fl p9zj z3o(kkgo126eg ar will it go, given that the coefficient of kinetic friction is 0.20 and the push impap6 k(z913z 2kgojoge lrts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 jbh ; 72*hffgnnrt02ekg , are in contact and at rest on a horizontal surface h ;h*bg07jnt ffr 2en2(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 carryiuvopkqrns 5+0:l ewgy 8il5)-ng a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximuq5ylgep : 8w)0o lu+nvr s-ki5m rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which 7c actxml,avty+d g-q tgj --206ny vc2awq 7/has an incline of c,xygqana/vq yt -tcwgd0aj6mlt-22c- +7 7v 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a v.v*udt; il-g28$^{\circ}$ 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 2 ll)tu 2r :f sfbzk8u0i93vmna 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 c.; w9ozw odk6speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill wi/xz *h.kg war0th 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 somf.u1 r2i fz1gd eixb6(. gp(njeone pushing on it with a force directed upware j6.((21nr.g g1zip ffbdxuid at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous project d-ku65thaly(+jjb6i n o: ha.iles as they melt. Consider a chunk of snow at the ridge of a roof with a pitc d.n6-kj:5ojh (t+u yh6ial abh 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 traveling4fq1 hng*3z,q)xui )z p 6vmuq at speed v iuqz61 ) mx*fpu zgvh,i4nqq 3)s 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 dashboard of a car slidesa 5h d.c(w,sr6fq(xu.q 4jo ml forward on the dash when the driver decelerates m.6l. jaoq, 5(xsw(chu4qrdffrom 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 in-iuo 9zyurtl k70 r+5zitial 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 whct 8h9: t7jircere they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The mosct9 rh j87ti:ct rapid transit 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 of kinetic friction p6m,kp9u3ikp 2wkuh bm s3(m+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 (incqx3n/w145,g 3xwz chpqm 9trzh x0 fg 03ome3oluding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simpl a5h hbf4o*o7wified model of a mammalian heart, at each pulse approximately 20 g of bloo5w 7h* 4hboafod 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 ne.ew;-m0pkqcrash if the deceleration is no more than 30 " g 's." Calculate the force on a -m0 e;wenk.pq 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 acce52b hd8bct ev:leration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, sbc 2vh5dbet8:how that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accident involving two cars,dk:0u0aog+pp ts z/ ;y-napv1 measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficazy/: v+k0 -0g1a;to pdsnpp uient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m tr5 )igu d,+iowmaveled along the road, the eg ) id,o5uimw+levation 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 b)vig z29kp2 qtop of the Leaning Tower of Pisa and falls 552i9bq pv)gk2z m before reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed.cb4 5l:nyq fi of 12m/s but enters a muddy 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 5.cn iqyl:4f bthe speed upon emerging?   

  A city planner is working on the6m6 w )tu lhdhn9slop)vyf-p3b e:h91 redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that evenew- :3)huvm 1 9hlb6pyols9)6f d ntph 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, d j5h dns o-l/ofv)4pd0angles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notice04ojdv/l fs pn5)d-hos 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, there9b2lbke+mf/hz0 )ca zizf 6v4 are to be several ramps connecting different parts of the stoi)0k 4zfhlambz/+ vczfe b2 69re.
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 mf;: 70i8y x2td, q ui+l/d0kgpznivj m4*m igthe piano (mass M ) using the pulley apparatus shown ink,tgfpm/qdiymgvi m2:4 n7;x 8 zu0dii+l0* j

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 accelo yk 8lm(u9pu;erating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer considers themj1+oao8.kev5xe 3j(ld 0s kk following set o1a 8m0k+os. kel3odjvkx e( 5jf 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 l i,i z1crjx5xuen+nz ,f. -s;train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bils8pohuzpg i3of q,pi3f464/ a l and Karen, use safety ropes of similar length. Karen's rope is moreguziph 3asiop,qf483po f/6 4 elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 1) 8iwp 8c3*n8 bxjkvo,ygs/eb0-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum sp4/c)bec;w v fqeed 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 fieldci6zi5 e.bei3nqcm oe-1 fh 42xk hz93 inclined e23 ienhzm 5-zf.eo19c 4ix q3cbk6h iat 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.