Why does a child in a wagon seem to fall backward when you give the wagontil0s /bdvk9 d66bhu6f *uhf7 a sharp puf66 k*fub i70l6d v9/bhtshdu ll forward?

A box rests on the (frictionless) bedd) lrl4t 43v gcxq-ad5 of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing -vl3l4q5) r gt4xddacon the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces actingn :g5vb2myd) g on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can iso2+ +w+5t2 ide xzogdt have zere zsgo++2xd2d5+iw ot o velocity? Explain.

When a golf ball is droinaq-n t oz+ .p, .ci9a+0rs ugw(kbt4pped to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If s+ (c..u i tb9aso wari -n4k,z0pqntg+o, what exerts the force?

If you walk along a log floatingrqy u+/,dmpf n)b/g;0s(djns on a lake, why does the log move in the opposite direction?/s(,nbpn/fj0g)d q rd musy;+

Why might your foot hurt 1qcf96a9 gh pk15/0.jn/ majqfebq kaif you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (pu2;ukqw li68 a) pu68lk q2u ;iwWhat is the origin of 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 g.pewa7wlkvt11 g 8r colari/j7 5:s7a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person ggrk7risglo1w :lwv /a.e cp 77jta5 18ives 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 23;b:ef7/m83hcfw or.fyrtv:fg pim n: z :rutwice as great as that on a 1-kg rock. Why then doesn’t the heavier rockmev3gf inyc23 w7r hp;:u.: fzb:/r:f tfo r8m fall faster?

Would a spring scale carried to teob2g/) sv )* ler.mithe Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in 2sgl)tiro*/e em) v b.kilograms?

You pull a box with a constant force across a frictionless 6qkz s cp;0ij3)arc hys:.+l) rgpx;m table using an attached rope held horizon c.ms;alr)gz p;+x)yr jp6qhk0 is:3ctally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influencehn (y sk*o 7;1ro;chwqxw ,klsf6s09i of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth.s1y l9, swq6kh*wx io(nksohrc0;7;f Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg vt4 moo8hh+ :jobject when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg objojv:t +h8ho4 mect horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pul8 fewxsb/cvari7.0 6r-k vanc;:s c9hls with ev :ac-68awrs9vx f7 ;hs0/.rieccn bkqual force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N ts7fmb 8uxy m/:lm3fo9 o hold a bag of groceries. Describe the “reaction” force (Newtoml fm8yu /omb9s37f: xn’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 ground, how large a force d. gakgi smg huud,2n7yxr*1)4hw a.t5oes the ground exert on you? W 7 1aa2 u gg.hwndi,).m*4rhsgukx5yt hy doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident ig(fs4)v y;7 (nzjswmwhen the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown bg4j (w(sz f)vymni;7sackward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. 6wsvu d9sw2w7 cdv4j:When the truck accelerates, the crate remains where it is on the truck, s7v2js9u wd6c dws4:vw o it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so 5x ;as4fgkr2i5y o8fhthat it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than onxga5s5y h 28of;rk4if the ascent. Why?

What would your bathroom scale read if you weighed yourself on an incl e( j5k8ze6he3czag3uined plane? Assume the mechanism functions properly, even at an agk uz(e8z56ee3 hja3cngle.

  What force is needed to accelerate a child on a sled at 1-y pwau mji.z8goz. ,).25m/s$^2$?   

  A net force of 265 N a v)s3 09yiigen-9uhfu;ab nkbf vhm6-m/m0(accelerates 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 it is used to accelerate a 96l tj yebq w-ce+c. l*+i/t6i/f0$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a0nykh d1g/5uc $76-\mathrm{kg}$ 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 1qy(4w+ig/tc l 100-kg car in 8.0 s if the car is travelii4 ywq( g/t+lcng at 95km/h? -  

  What average force is needed to accefqp:x2g8 (qr blerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rifle? g(fb28qxr:p q  

A fisherman yanks a fish vertically out of the water with an acccqwv gb 6*bq:5fdxpxxi 9, d*drb1 fxv)t:t:5eleration of 2. 5b9) f* 6dftbv pcvw*gqxrx,:qb1: 5xxiddt:5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quart;k2hm rk f0w :n1x3ybker-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 bev1ms )ihwmsme7i6j2w 56l3c 0btlp ;o designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supportt;p l6i3 jh 51s7oc v6m2wis)memwb0l ing 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 *xxq:l sne0csx n; (gh9r+tu0b(+fpx. When the elevator begins s+e9n0snu0x g lxqprc; t*+bx(:(f hxto move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a x*l5yu3lget du2; x5l2125-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator ly5x*dutx5e3u g; l l2without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg 4e in ej;:pmg,including parachute) when the upward forj ;4 eg:p,minece of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes u(208a o,2n- e7xv w qaqavzpuylr/2.md)kgc the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mas)ru.aav/ 2aclk08x2e, wqmvu(z 2opq 7gdny-s 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 ya yzgs,v4 u58table. 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 forcev5s gyuy4az ,8 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 pv vd,dbx; 7etbe2,q+ dlayer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at tht+ qnk5jwe r*bp*bj+)e moment it is hit by the bat, and again (b) after it has left)*treqb j b*+k+ 5wjpn the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A sea36;jv0xnm3tpo4/dlb nb5 iqn)1 wsv cond 650-N force must be exerted in what direction so that the resultant of the two forces points westward? wbxd;m0vn 1nptbs5 )v lq 4jo/63ia3nIllustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between twmyg1zb sf5i mw y-2803auk0xko buildings 10.0 m apart. The sag in the rope when s0amfwy zx sg1u-k3 052yb km8ihe 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 masu6n0 )j ag tr8i8ot)6nfkd6pz sless 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 17p gk8wz fh,us2y+h4r 4.0$-\mathrm{kg}$ 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 teuz9li(w-*, l2rhlssr 2x*t k o a new location at McMurdo Base, Antarctica, as shown in Fig. 4-4*2 il2rx9z ke*h-srs u (l,wtl6. 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,kbq+i5p.5qpu suw 30b Fig. 4-47 . Determine the ratio of the tension in the couplbpukp.3u+s iqb 0qw55 ing 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 bucket-pulley ajqnh*i ;2bbe 9f x(3kkpparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at 9 fk (jqhen3*;k bbxi2constant 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 5lphd,2 orq ;xbegan, 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 rf:auj8 r.t6( z qm *vugq+k6hblock (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 eap:;obhze; db-e3-* 8xx emnj jch other, as shown ;-; d b3-h*xbpoje 8j:e mxznein 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/xk927s hr6/c1g7ke m s1xn1hsjph py . 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. Th//1ens 7xr 7js92h kchkmgp x116pyshis is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by axtpvg3g sl jc a1/ 11-jyaee9mo-b7. v heavy cord of mass 1.0 kg . Calculate the acceleration of each box and. e7avyjs19t gljbcgex/ov1 mp3a- 1- 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 fso1a)ibiut +86yko30 kx wlu4riction 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 a4;w0q)y-un 1ep5ye ;zw (filllro 4zt 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 d: cyftn7lxh.-cn 1.c a train accelerating at 0.20g. What minimum coefficient of static frf :l -x 7ccch.dy.tnn1iction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the cok m;a4 zgy9ji65y 0/v 5pntmntefficient of static f56 mgk;m t/9 5tayzpv0njiyn 4riction between the tires and the ground is 0.80?   

  The coefficient of statxabd-:5ha uni5at)q. ic friction between hard rubber and normal street pavement is about 0.8. On how s qntd)h5aa- iax b.u:5teep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.+)tn ygrf4mm 280 $\mathrm{~m} / \mathrm{s}^{2}$ 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 n(ei ldwe 6,xord1uh f +uvhfr-.192con 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 wi m*;b:y6cu ofeth an asphalt surface have a very high coefficient of static:fcmuey6 *;ob 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 friction for k3;j1qvmb o0ga $ 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) ho .99erbidmw7agl1:t sw large a mass would box A have to have to prevent any motion fromagbe tm1lr:99i sd7.w occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides ai0jlnvtk.bl) ; omu,e6lah;1ml ue( 7 cross the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push impart av;l buj i)lm(.o1et06llkmnu,h;7 es 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 horvy-d x 4;g .gnctv.c8mizontal surface (Fig. 4-54)- c.ggcy;4 vvnm.8tdx. 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 cai , hzk78x8or zsu7j9wrrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid havinh987zr o8i kju z,ws7xg the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car k 3+-o z -hhoi;d5ojgjyq2zr 9in your driveway, which has an incli-rqzh j-i9jo +d;o52 gkhoyz3ne 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 slioqvu/x;(j*0h (3f, ch9fhnwvae g*. q uskpq+de with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane ti/2h;m *)z4 np.p fkewxxyb*zilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.lmba qj*r0:h;eor3 y5 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 reachf h1:vhq/eb;k2is zvb85 4gynes the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wa5gx -k.6h+d /guv)um0 ilr pyrll by someone pushing on it with a force)gv+ruhl0 gk upd5yi/ xr.6m- directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs caqku/yd:7jt:oywmlvmb.s ;o9 :4x5 w3m ddg7on become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pit yk4bdd:s.ojx t/m vm uy9 7o5:wm: qowld3g7;ch 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 autom0o/4.g a bovw9hei,stobile traveling at speed/ 0,.ei9h avob4to gsw v is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when tnx . 7o0/ heo cloq0y/0u+lduvhe driver deceleratev07x0helod//. o0+uy qcol uns 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 ipg ;*f dltp58xs given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are fii c,pahihd58 yj1j9m4lled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most raj ph,5ahm849jii dy1c pid 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 kinetic1k44 dqw klhf6z2vy2k friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a 6.c,rfr: m yaqp(5es (o;0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, a7u.x8u awne. kx+z(p jt each pulse approximately 20 g of blood is acceleeaxzp nkj8(uu.7+ x .wrated 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 autobr,wa3hx u/myy6.we(bzlno6+ um 4/fmobile crash if the deceleration is no more than 30 " g 's." Calculate the forc6/uo6aex.yr flm b whb/y+(z,3m4n uw e 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 acceleratrcl.:cpl u)v-y.- ocmion produced by an earthquake is a , and if an object is going cy rlmp u-lo ):.vc.-cto "hold its 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 infhqz v(tksleax3,awza41i00,u m;9hvolving two cars, 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. Estima qzaahatk4vz0m3x;shu9,, fil 1e w0(te the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1kug hy:.is6 b11o2a(rm/ :s 0 asbcikc-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reache:b ic h1s61a:ki2.s0 b/ursoc gkmy(as the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and r 0;c((6z 0sofite;) w 3rgsmty vmf7f6 gsy:ofalls 55 m before reaching the ground with a speed of What was the average force of air remos0;y3tim(f6:rgrtfss( fow7y )v z ;6g e0csistance?   

  A cyclist is coasting at a st+)/* n 2gs o hjec6idfobe)jw)eady speed of 12m/s but enters a muddy stretch where the effective coseo)ngf / w*)o2i e6c+h)bjjdefficient 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 working on the redesign of a h30 cfbco/w t yxz3dp30illy portion of a city. An important consideration is how steep the roads can be so that even low-powered c0c33pxtwc3zdb/0 fy o ars 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 mt fv(s vnuy5 i*:0ez/ l3rth8physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the strin0i yu:f5mtsv3zrl(t nv8e*/h g 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 are90bt3anbnbqrn-(r, /f2f7. o8 yraioqdt +uq to be several ramps connecting different parts+uqdb 0829 rtn/fr, frn ant q(3ba-.oyib7q o of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the8s xtw9 +:km(/m:ei qhkic;m o piano (mass M ) using the pulley apparatus shown in hc :s89t w i(xo:/qmkm;mkei+

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 acceleratkd ,d50 03ghl i2pqreqing 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+y9. tcg-7xu 2,ddfruc4qy9jl (cca x-restraint chair, an engineer considers the follt,xu9g+ 2a( d xc.c4ryuc-dqf lj7c9y owing set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric tons (cg9o 2 sez.1 pxcc):nx660,000 $\mathrm{~kg}$) . 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 simh(1vgy rd;*vw6 cxf9bi);xk mmfw 9s2ilar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a stat9;yxwc*12vbik fm 6wxr f m v9g)s;dh(ic 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 usit k+d a.4feh;ing 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 buim tis.myxmq; :u10*mg is9w5j lding 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 cnqm(. /au7lwgm/fi0-cd9i u inclined.f-9dc7mgu l/i wc0nmqa( ui/ at 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.