Why does a child in a wagon seem to fall backward when you giv51.6 me1/vt:9xvog 3waabi rm uunfh0ngpu 0:e the wagon a sharp pull fanrtnvm 15uh ig o3:p16/ e9mfu.0u axvb:gw0orward?

A box rests on the (frictionless) bed of a truck. The truck driver starts thq6+(r-t p8.ap jlvij te truck and accelerates forward. The box immediately starts ttp68qlij(.a vpr+ j-to slide toward the rear of the truck 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 w6)n vzi7i- v6sxdx6nobject is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accelq:tb(ggq. k ;oeration? Can it have zegb:; g qt.o(qkro velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is y1zd6 pw9 mlw.a force needed to make m zwyd6l.19wpit bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the)0mcs bs7adnsv(/ )np opposite danv7 )sdmc( nb/0sp )sirection?

Why might your foot hurui ,r g78ayp-at if you kick a heavy desk or a wall?

  When you are running arzwy5w(14 dc -aodvrm z49-:u w.b synnd want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a pz bw(4o-w1.:m5yuv-ddzy4rn a s cwr9erson running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a sec xz;i 6cmdwa:l7 r3d(ntion 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 the person gives a slow and steady pull? riwa:7 z3mxd(6 ld;n cExplain your answers.

The force of gravity on a 2-kg rock is twice5o) lhzg6c +yy as great as that on a 1-kg rock. Why then doesn’t the heavier rlohcg 5+6 )zyyock fall faster?

Would a spring scale carr;d-l9 bc amrk7ied to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilogramsk; 7c9mlr abd-?

You pull a box with a constant force acros, frd;1fqw lu8s a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an anu,fr wf;l1 8qdgle 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) decrease? Explain.

When an object falls freely under the influencek : lji*b1fx,:wa pe1d of gravity there is a net force mg exerted on it by the Earth. Yet by :f*kx,pjl 1db1a e:iw 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 tzj+kwco9 0ja -)yry+ bo lift a 10-kg object when you are on the Moon with the force needed tca+ jz +j ry)9by-wko0o lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a ako.f74 r l kria,.xd;z du6q+tug of war (Fig. 4–37) pulls with equal force on the other team.aq.6d,4ld xk ori7.r u+ kfaz; What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of grocerig+ 3k* .whnpooes. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object io+wgk*n . p3hot is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the g(j juxa6(o r, v 9vp;)nu5grtground exert on you? Why doesn’t this for u(jva o6rggnp;t)xu 5,jv r(9ce make you rise up into the air?

Whiplash sometimes results from an automobl -t5 iz ixj0h6zkd(/( j3iiyvile accident when the victim’s car is struck violently from the rear. E hyizjj x0 i(d3l/kv(i6i5t -zxplain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the trucrdv(ask 83tm h15soy p/ txhz9r02 r;mk accelerates, the crate remains where it is on the truck, so it, too, accelerates.m(5r1yh 3mk h2;v/tod8 t xaszspr9 r0 What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reachf6yj4ds* q04 iwvzbz6es its highest point,s 06id fz* 46zq4ywbvj 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 if you weighed yourself o0 jgw -bst/y+an an inclined plane? Assume the mechanism functions properly, even/aty-g+b sw0j at an angle.

  What force is needed to acceleratek2-g xpm1ji4 py y7ofplcw2;,5wg og; a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.oagz p9y0 p4 8jel2;vh30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a5sew4+z d1gdsk s*:np 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a u;ycb t +ny*nd0e.u;ae;xos ( $76-\mathrm{kg}$ 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 rf q2kxrk n3hs0 ,d,u3vyb tm923pq2m to stop an 1100-kg car in 8.0 s if the car is traveling aq3 y9qkm,f2tb m svr rh x0,du3p32nk2t 95km/h? -  

  What average force ifga f-1*o pk2rs needed to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rifog prfkf-1* a2le?   

A fisherman yanks a fish vertically out of the water with an acceleration j- qpdo01h +xvof 2.+-0 oxpjh1vqd5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-mipeg0yri;n30ic7iew24// jni gv yw7fle 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 that the m u )j h kj3om3y9vv8a,s*l-bypaximum acceleration is 0.0680youhb3vj jk* 8p) 9,vl m3-say g . What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When t;b:csyd (nuo ;he elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevc:( yuo;s dbn;ator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125p0t4bb7 y hd4n-kg elevator has a maximum strength of 21,750 N. What maximum upward achd07ynb t44pb celeration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inclf7)hskvz k (c28pek 7onapn/4 uding parachute) when the upward force of air resistance is equal to one-f7ohf4 (7zp ek/nskc8)v a2npkourth 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. ;e3id*lr m*k bd1y7yjWhen he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distancddrby1j mk7ile y;* 3*e 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 tablt3x3gdt.b w/cz :zr*u5ahqb2e. A rope tied to the box runs vertically upward over z5t:x*2b3bqu3 a/.c tzhgr dwa pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball playe2rdymn z904,lk dqd c1m8byv9r
(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 base n dbx lk,-4lftfxr:1c8lv:9zball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and i :tkzv4l, -1fn:lc8xb9 xflr ds flying toward the outfield.

A 650-N force acts in a northwesterly diref x7g4a0xw nh( b;si.3q s/cpyction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westwardi agpxb30sqy(w f/ ;h.4c7 xsn? Illustrate your answer with a vector diagram.

  Arlene is to walk across 6(ug r 6i yltj9m,a1nqn.ar:i a "high wire" strung horizontally between two buildings 10. tm a6(iylir.rjnu g69q:,na10 m apart. The sag in the rope when 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 hangw bhl7:,v*n y2xr sa,ging 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 1yi ifi*.8zltta85 o dz er0as, -)wrf14.0$-\mathrm{kg}$ 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 hes7afqjgd 84n y0+ y1at McMurdo Base, Antarctica, as shown esgq8 f+0n7y1 hjy ad4in 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. 4-4l3 i*l(ey:oq q7 . Dete:qo3yq(li l*ermine the ratio of the tension in 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 herse9 swoqd.yv 8so*wg65p lf upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise hersowv* 95gdysw8 op 6.qself 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 raccexoh+b aa(0z k7q q:6e began, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block2cn)2a :hwaaxt ab8m3 (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,-p5up9e/ys hqgsqt 9 horizontal surface are in contact with each other, as shown in Fig. 4-51. A forc,sy-p /g shet p9qq95ue $\overrightarrow{\mathbf{F}}$ 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 the ground, i8 b 4wow2yix e()n5dcand 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 its "launch" speed. Assume it doesn't hit the p4(i8wny5 idc2 b)eox wulley.]   

Suppose two boxes on a frictionless table are connected by a h(rygv f,f6 w- fns/h q bmh(jo*-hy2d6eavy cord of mass 1.0 kg . Calculate the accel6r/jvdhm6h*qyfn -yf-shgw( f 2o b( ,eration 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 fricvrmcwb 4ne 5hro;e/ *;tion between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a 5.0nyb;i20yh e- c$-\mathrm{kg}$ 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 arehb4iz:si 0 smoz:w9 ke.8dfg9 standing on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between yozs 8k mef ws0 :4i:gbzi.do9h9ur feet and the floor if you are not to slide?   

  What is the maximum acceleration a caq45i6(mkca/xh(q18m;it i4h px v xv er can undergo if the coefficient of static friction between the tires and the gr6(ii q(xhi/;4q mapcm45vkxx8t1hv e ound is 0.80?   

  The coefficient of static friction between hard rubber and normal street f)n0 lrt9px zi7h/kesn6tih ah, 187mpavement is about 0.8. On how steep a h m701tipz6i/k8e rxn,snft) ahlh79hill (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 a2uew em6m:)8jp vjq 1pt -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 os9t 3cixm:,ercd z lr*i y07s,n a 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 surface have-d*yepq v-ynmncctw /g8 vt7*1(z, z l a very high coefficient of static frictionc*l /gvte yt dpm7 (y1cz,q -nvn-z8*w.

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 kinetu-.gdxu. 3fcy8k d-bxic 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-xoz8; +prfn4qr;w .rb 20) how large a mass would box A have to have to prevent any motion from occurring? of;4rbxp.nq8zw ; + rrAssume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How g7bd3h0sgf9 d6lw, zkfar will it go, given that the coefficient of kinetic friction is 0.20 and the push impargddf0h3g7 bl 9sk6w z,ts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horizo yp u68jp1091 iyz n5)xzpg*my p2qvpbntal surface (Fig. 4myz1 yz*yn p1 5p26u8i90)pvxppgqjb-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of sta azgv4f)m 49hqjrd+4 htic friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerah hv rm4qfz)dag44+j9te and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about z ulcuzb4b29lt7p7: n parking your car in your driveway, which has an incline7pu2u 9:bzn4b tl lc7z 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 slide 21 3j1uhg9uqjgtx a1iwith 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 1pn+e2(zxn 7zha e-vetilted 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 aqarb+c l* :u0a/ig1gff+u ;o 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 th:el ;c*-0 : g;gzufkzozp)xbee top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rough wall by someone u yab-03ma+q(g in va3pushing on it with a force direct0auy 3+v- nqbig3m(aa ed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles j21 . uqb hx0pkq,oi k4e..pghas they melt. Consider a ikxboh 0hgq4,j1ke . .u 2.ppqchunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for a:/m ak /gx.f)plg/klp-bym 2rn automobile traveling at speed v is :m./ymbp r2l/a fg-)/x kglkpequal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forwiwn*iubs( 8 ,zard on the dash when the driver decelerates from 45 ,z w(ibs*ni8u$\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial mm99ye o5 r*m9ah)ylu speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to the packo5t * 5v1 2uf-7of;hk0y:+smodtf jxmo ce-n qing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The meoyf* -kt h-q:fmsvdfj0;+xo7u 15t2mon 5o cost 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 oh8t a;j:rf.ztf 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 thktnjm-l*69jnricg w8 xd5+7be bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian hw+ 1 cnv5hq2vxeart, at each pulse approximately 20 g of bloodn2wvv+c hx1q5 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 am kww3i*yx/j .n automobile crash if the deceleration is no more than 30*w/jxwimy 3k. " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , q,;tb,y9lh (,ac c xnband if an object is going to "hold 9ahcxc ylb,qnt; ,,(bits place" on the ground, show 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, 9ubev1 9 cflch9)fk(ecaf6g;92cpw kmeasure 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 initi99cf6h(c;bg9v1ck lp c efu)2wf9 ake al speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that f*yu kfk/)9r7rct3 ykhxds85 k or each 4 m traveled along the road, the elevation y d*)3 rr/ckkk hty87 k9u5sxfchange 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 Leaning tsp sj4yj4du:4)4d6qpj gy( xTower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistan6s (us4d pxytgd4q ypj44j) :jce?   

  A cyclist is coasting at a steady speed 8 )y1d5 3c-kxzrd pfdaof 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Wixpk cz a3rd1d f-58y)dll 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 :)7g1o te*,a wshpxjm hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , h* 1),px 7aj:smtowegcan 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, 8cz*k 4y9vkul ,t/fvndangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport vu48y l9c, zn*kf/kv t(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 supermarj(.w syfx(mc -ket, there are to be several ramps connecting different parts of the storesmc- jfxw (.(y.
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 xh eg+ .dy8eng) 8)zlhis needed to lift the piano (mass M ) using the pulleyeg nxyg8) ezlh.)hd8+ apparatus 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 acdk.vnhb(8 vx-p0h 1 nydq 7eg+celerating 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 q+p-a e9d o k:ci7cyp4engineer considers the following set of conditipq9dai47:yoe+ ccp-k ons:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 660 metf mu +u7zq;sj h)2*tihric 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 ropesto/c6a z 1q+1z dq7xzt of similar length. Karen's rope is mocd6aq+ t 17zqzt1xz/ore 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 " 2git*icc, 2 om10-1 $\mathrm{~b}$ 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 talpfa+4,m c8st :c x nrk8)9wzval building 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 4-:lo.ts x pobinclined at 2 loxst:. 4pb-o1.0$^{\circ}$ 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.