Why does a child in a wagon seem bpewa7f-c s35l ehj7, n8y.bm(f hv*kto fall backward when you give the wagon a sharp pull forwa5cmshp 3-be*ylh 8bf a,wk.7jn e (vf7rd?

A box rests on the (frictionless) bed/ rd3:uqtcd ti 0,bwy1 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 on the ground beside the truck yicdubdt 01tw /:3r, qand (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces actingxte y9j(09vx w* 8eg 5xax5rr: j0ncop on it? Explain.

Only one force acts on an object. Can the object have zeri k 0pr87t b+revbjj18hk /8 ss+8j ml1:rfdhfo acceleration? Can it have zero velocity? Expk8btj s ++0kfrir f1d8bl1v p/jsmeh8h :r8j7lain.

When a golf ball is dropped to them so*vb 8s+-ll pavement, it bounces back up. (a) Is a force needed to make it bounm8sb+-l l svo*ce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log moa9saj.h*)9cfad w1+anf g, h.f pbir2ve in the opposite direcf rf,*cs+w a99 hhp2idaajb.g 1)an.ftion?

Why might your foot hurt if you kick a heavy r1 b8ifcf 6ftni); ao1desk or a wall?

  When you are running and want to stop quickly, you must decelerate quicg;t;7mjxei/vui+ t3 ogc/+ pi kly. (a) Wha3 ;t+7picxoigtm;j uve// gi+t 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/ 9twc3 fnuoq: a section 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 af oc3qw9n :ut/ slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is l/u)r/q fdolas:m7c 9twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall faster?c/us a9) rofq:/7llmd

Would a spring scale carried to the Moon give accurate results wu7vre9cb r*/ ea v;t9if the scale had been calibrated (a) in pounds, or (b) in kilogra;eb / te c7*v99rauwvrms?

You pull a box with a constant force acpr/ e7g +ty)jdross a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on tjp)y+d 7rg /ethe table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freel7d9d :dn afsilz o1m81y under the influence of gravity there is a net force mg 18oddid: 1zf9s 7a nmlexerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kgx/p *)60 ycgu wq(budu object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon andxyup /b dqw*)ucgu 06( on Earth.

According to Newton’s third law, each tea eug+gz+u/m+n/ + cv9raqc :oym in a tug of war (Fig. 4–37) pulls with equal force on the m c crg eu+/9+qna+:voguzy+/ other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe the5)0:frq0g qp/1ltcm8*pqnf i u, l bzk “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.f n0kqt:5qqppcb g l,1ifl/*8zum)r 0

When you stand still on ecymgg r;f( /.p1jr/gthe ground, how large a force does the ground exert on you? Why doesn’t this force make you rise up into thefr g;(/mgcj/1 gp.rye air?

Whiplash sometimes resusu( -zmhq 4 2iwx(ghhgz l97.plts from an automobile accident when the victim’s car is struck violently from the rear. Explain whyz pl7whsu-x 94qmh gi(z g2h(. 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 flatbe ufsbo m;b6v1jx) +x3ad truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, ac x+;3a6jvubofmx 1b)scelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches91pn - eli-cub3 6q5i ibypd*q its highest point, it slides back down but the magnitude of ic6il5i*3b- 9ybe 1ipqn-updq ts acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclin;d:vjc6: v2qb0hrgto jua) +/ dtxggmd6*m,r ed plane? Assume the mechanism func+ /jvmgbqm6 v0;:hgtx 6*j2r,tcdaod rdu):gtions properly, even at an angle.

  What force is needed to accelerate a child on a sl7 qs8*)dhq. p.dfrkzfcr/f, t ed at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.30is zqwxx4 i23e mt )nuo-6,*gd$ \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 96trnj 3bd1r 5 t)s: wyoby04sg*0$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of ap;g7d xmfc fx;t .:vroen6;c* $76-\mathrm{kg}$ 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 i mfnt6e+i m7/ps required to stop an 1100-kg car in 8.0 s if the car is traveli7 +m6/emtn pifng at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet frh7xg3 7-utza i15tl++ swep(; mx mzxpom rest to 125m/s over a distance of 0.800 m along the barrel oam( zx-h5;xx7 +wz1ttms7ple3 +iupgf a rifle?   

A fisherman yanks a fish vertically out of the water with an accel:8(jg ax1p gdhel-z3 leration of 2.5zd-g (ph3e:gxl1j la 8 $\mathrm{~m} / \mathrm{s}^{2}$ 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 .2bxve3iaw6x *4y vhwuzjs: 7-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 w-f;j2h 4avt(zxzse+ ) is to be designed so that the maximum acceleration is 0.0680 g . What aj z- 42wsxaf;tveh+(z re 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 the elcr3uifdwmx his uq07.w 41x(2evator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration3wx1(sh4f 20xci .muiduwr7q.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Wha rn,j .o,jpu+mt mj.ru o, +mjp,naximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mas(e/vrgwn;l r+ja,8qm -q zl/h s 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their weight?hr q+ 8nl/(regwl -zqjvm/a;,   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the ground b otp ;7rnd,9lzelow, he bends his knees so that his torso decelerates over a p7lrndt ;,o9zn approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the b*h93pz yus.z mox runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts 3yp*sh z9zm.uon 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 basketbll2ky,4kk5 kh-is3 mqall player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) d m tutuphix2ek65y:/xm ,6-z px-jz2at the moment it is hit by the bat, and again (b) after it has lefx e zpizj:xy-u -td,tu5 p 2x62khm/6mt the bat and is flying toward the outfield.

A 650-N force acts in a north81nf ; (o27t;sgfp5dwezxmr;0vhdhswesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your 5n;f0m7edx(8 swg ph1vz ht2o;r s fd;answer with a vector diagram.

  Arlene is to walk across a "hiu tm(y-*earj/gh wire" strung horizontally between two buildings 10.0 m apart. The sag in the ropematju y (/er-* 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 hanging by a masslemdj0uz7-+xs a ss 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.qpr k 2(pgk*kyq l *:i ;e0ah7c1xr4xp0$-\mathrm{kg}$ 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, Antar+wxbc irt60*f1vsa9 e ctica, as shown in Fig. 4-46. The sum of the forces *+i 1f609r weastv xbc $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 i 5z/9dovdyvkqgkb)p9:c i3*cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in thckdbz9 p d*i9g 3ov:ivqk)y/5 e 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 hersefym5 wz1y kq8vew o 9 +pb*zdjt,i3f1.lf upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowm t zfyfw185wdpqze 3. k,b*1 vjoy9i+ly 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 bn*+y+q h q b)az,mwz)fegan, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (maewqgyc7*3p:pb6 c yi.xu * r3ass $ 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 horizonta m8hip8qg73szl d; n4jl surface are in contact with each other, as shown inn4p83sgid;lmq8z7 h j 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 t:xl(59 9(g0ut wqo-vtkcr pgkhe ground, and the massless frictionless pulley is 4.8 m above k(9 r9tk:uw clvo0gt5-(qxgp 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 pulley.]   

Suppose two boxes on a tj( ,m.g)mqwffrictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cordq)mg f, .(wjtm, 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 kin/k69f szwzug6 etic friction 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 requ.:smz cynh1e* ired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What minimum ss k( lz-k+qh3coefficient of static friction must exist betwe +q-3kslsz(hken your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coe s*l1nzwjb) 5cfficient of static friction bet)*nlsjwb15z c ween the tires and the ground is 0.80?   

  The coefficient of static friction between har;)i+m8xoh a -hkbpj-c d rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle 8p-c mbkxahjoi ;+-h)) 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 -4.80i1rj 3gzxw-y3 5gpvn- $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough f hmp/a4yor o*d g;gja8/ij0/zylg e,2 cfz9. 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 anw wy+2+0f7e 5kb/r0yjqkh omsphalt surface have a very high coefficient of sta/req0wobhkf0+n57kyy2 + jm wtic 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 kinew +7ikvvu6 c 3x2dio)ntic 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 largjh0* q *7k. zgc1eesple a mass would box A have to have to prevent any motiong.e*shklq70 epz1j *c from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the ,e;fo ux;c*eab o0w /efloor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initi x; wboauf; *eeoe/0c,al speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in4dp- /rjjqrszz q67/r contact and at rest on a horizontal 4qrz/j/ 6q 7zjr-sp drsurface (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 carrying a heavy cracjp 2xvhu5 5oj:t:/ bbvh;h)ki;mi 1wte. 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 having the crate slide against the cab of k):xhjc 5iiu ;th5 p bjv; :b12vwhom/the truck?   

On an icy day, you worry about parking your car in your driveway, which has mo/30rd1 p+ eqp7vimlan i/qp +1 em op0milv7dr3ncline 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 wit*;-l t7enmw1ul eu3k dh 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 tilted at an ab7y:mme /7wly4y n s,d 6s(zymngle $\theta=22.0^{\circ}$ 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 av(l*+cak4 lk 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 with a hv z2/q2zq/ vgspeed 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 wa72 py mlzw g931rhz5i yulw o,p017dbhll by someone pushing on it with a force directed upward z53p y wug, 7bwl0i1m7ydh1 z9hl2orpat 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 pr 00 mkvcpog7an6ijipi 756s //ds;rhcojectiles as they melt. Consider a chunk of snow at the ridge of a roof wits76jni/h/0krc0ps v gaicp7;6 oim 5dh a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling 7 jv-a 3n)u kwqjd2j-/p2qzzn at speed v is equa-w23vu q jnjnqj-kp7zz2 da /)l 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 dasb *c:+-cexj wihboard of a car slides forward on the dash when the driver decelerates from 45 *xejciw :c b-+$\mathrm{~km} / \mathrm{h}$ 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 )4zpe+5y9;zm2t :j il (mav2ibmvy jzgiven 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 filled7*ijk7ipkg( c/ t2rjr to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what iskk7riip 72(cj*t r/ jg 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 between z-(aexsj9 f/d* o e8av$m_{1}$ 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 a0 i; +dw/wug )amsb,hu 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, xfh6drdi l53s20v-jrpc6rraf 70p 1kat each pulse approximately 20 g of blood is acceleratrrr5ij6 20 f7clrh063v - ax1s kdpdpfed 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 aw g opd2f 2qsa54csa77utomobile crash if the deceleration is no more2spq4d 5af2w7aog cs 7 than 30 " 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 anz,y(z opcwjmuish+1 +sz zq,8j( ( qww wh9*r. earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at lea(s.h(homq+yp,c8+uzw i r zj(z zj1*,wsww9qst $\mu_{\mathrm{s}}=a / g$ . (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 involvin,v9vc) to (xdg2gf6 p+v rlic8rf3+jug two cars, measure 72l fcvg9x, )(uo6r+r2+tjdg3 ivcpf8v-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m travele4yl:da oegxmc:9zizn 0 nvoeg7291j fq5 d*k/ d along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after trg*xdv:9e7:5mqjc9ni ka 2 y ozfg/ zl 14endo0aveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropp l mg/*5fnysski+id 5w4a-b i0ed from the top of the Leaning Tower of Pisa and falls 55 m before reias0 id4f 5by niw- 5lg*s/+kmaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a stdf cx luk;r:56eady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emer5 ku ;lx6d:cfrge 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 hiqdv,0jv wp 1c-xxskx 2r :x0w -kyl3,qlly portion of a city. An important consideration ix,kvqjs,1 ql2 x- :cdywx x30-kvw0rps how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physf1i l tsn6)o1zics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airpor) tsoi1n f1lz6t (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, tiz b4 wuomg15mc9+ja*;au.j chere are to be several ramps connecting different pamg.za1 j+4 oau 5; *bicwm9cjurts 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 tczl68whxc7t6wo 4)m) p8is eF is needed to lift the piano (mass M ) using the pulle6c)teio wxph8t 4 lw 87cm6z)sy 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 acceo 0em7;aibzs4lerating 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-re 2gk/od -fk4rwstraint chair, an engineer considers the following 4-2k/gfw ordk 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 ha3 vw .))hnpfc8mh:p.wx h7zw ls 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, Bill and Karen, use safet;fnni lr5o ds,c;z 0lt4z:8 zyy ropes of similar length. Karen's rope is more 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 iy5n0t lo,z ;;cz n :d8lzsrf4the 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 issbjhyitmy3n2qlx 81u2*5 cs ) using 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 building is allowed to reach a maximum spee/yd5h0w j5je4)v jktjhdci. d,0u)n j4n4az kd 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 togetv3wx e; m.mkf.;rf ll)her are ascending an ice field incline;wmfxe. lf3mr );vk.ld 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.