Why does a child in a wagon seem to fall backward whenrs l8;xkz/ z9m you give the wagon a shar lr;z8/mx9z skp pull forward?

A box rests on the (frictionless)q wko+o8r1v 9;lxajr 25wc-w) dou,vu bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truc5w uwq) 1kvcj9x l8;o,ao+-ur dovw2rk bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces(ee)n hn 1xfda4, pdv:xpk1:h acting on it? Explain.

Only one force acts on an object. Can the obu6; aj 2akn2h6ifrws+ject have zero acceleration? Can it have zero velocits2jn6f;a iu rkha w62+y? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forc83kk tsw5 s r,9zspq;re needed to make it bounce back up? (b) If so, whtsqz3p 9, wk 5ks8r;rsat exerts the force?

If you walk along a log floating on a lake, why does the log move in the sno 6zs+ipmd*nf(jr/y wq370opposite6zdi y+( p/*073srownsn jmfq direction?

Why might your foot hurt if yo3t gykgzf;m88a a4+2/lu hm cnu kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must 8wnm dh:s5itje1c:3jdecelerate 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 i:83wjcm5dej: s1n h tperson running at top speed to come to rest.    m/s$^2$

A stone hangs by a fiq(mu0 4g:u xjl 2eat zgl45;tpne thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Figte 054jz g2ptl ux:mlag (q;4u. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg ruf2s rg3 h:b)kock. Why then doesn’t the h2f bhg 3)rsk:ueavier rock fall faster?

Would a spring scale carrsz ,foga7;,je k6hd0yied to the Moon give accurate results if the scale had bee,,07jok6g;h y edzsfan calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless t : /w5yo)bsdvz ku4t*-h 5estdable using an attached rope held horizontalled5s)4u *hd-yt :b v s5/wozkty. 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 iny-7/1u+y.w-f gwv hc etkl6htfluence 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 opposit -7t-wlhg6+hy/1kuwyfv te c.e force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you , 4xf:a qvvh) qu*(rz lw;w6cuare on the Moon with tau qhq) vv f4w(, czwl:6;*rxuhe 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 and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls wirblhp m/ icp ;1nu31j2th equa3bc1l2 j 1mp;/inhr pul force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describ wsjo*32nk6f ae the “reaction” force (Newton’s thi2fs n*o 3wakj6rd 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 groun0,iza(g0 j3 j4ux dnqrz(9 gkjd, how large a force does the ground exert on you? Why doesn’t this force make you rise up ind0uq z a(i,grxg9 n3jjz40(jk to the air?

Whiplash sometimes results frgk syr5g0t . 7+iq.zraom an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seemqzg.yi+5gsr 7r t. 0aks to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed tru9tuwloo k:c1r;1l;orozu )pc 8a 5;ohck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the cratetrc ol1kal;9)ow;o :5o;r pzoucuh18 to accelerate?

A block is given a push so that it slides up a ramp. After the block rea(k7qil 8t qvi5ches its highest point, it slides back down bl5kv(iqqt7i8 ut the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yo 1;dsdm)5tqr curself on an inclined plane? Assume theq5dcd; s)mt1 r mechanism functions properly, even at an angle.

  What force is needed to a;x7ldwc d4fwji8: d0cccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider. jckc12z6+3lf cyoq 3odnxt f* 6gj1q at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withkaw/3 ty /*ctbstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of6dx3/k bxc 6+r9af tje a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s if hgc r-av2e r6m/ g6s3fjd: e5ithe car is traveling at 95km/h? rsefej6g3 mv 5 irg6a:/cd2h--  

  What average force is needed to accelerate a 7.00-gram pelletv*boc2/ja4ybyyf 8 3c from rest to 125m/s over a distance of 0.800 m along the barrel of a rifle?yaj* o/bcv f3y4cyb28   

A fisherman yanks a fish vertically out of the water with an 5 b(/l;wcwwevx h-6pbacceleration of 2.5 pb bv(/e 56x-wclwh w;$\mathrm{~m} / \mathrm{s}^{2}$ 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 coverrx kk-sbhwu835ss9zy.lw; s 6 a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum acceleratiotiw9 e pb- s(05d4oubqn is 0.0680 g . What 4o(p u -sb9b5iteq dw0are 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. W5ww* c/)j (,yo6ohhin de;wv) 6ksb sshen the elevator begins to move, the scale briefly reads only 0.75 of the person’s reo,oivsejdyw s;h*n6)5) kb swc6w/h(gular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a qfvk2ec wt597j )ew 4rmaximum strength of 21,750 N. What maximum upward acceleration can it give tqcw)e5te2k w 47rj f9vhe elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky dive0j bzn *-aa k3jdgr)s,rs (mass 132 kg including parachute)nrj0z,3-)ga*d k s jab when the upward force 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. W3rkjb-1f w 0dgmca( *f okkg p9+(3xn98twmhihen he strikes the ground below, he bends his knees so that his torso decelerates over a9+w( ftmw of(-dg33rn jac1hb08pkx *kkim9g n 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 rh55+san l8hdp zg6pf c3 5zq0a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determcf+shpqd5zhrp n5lz36g0 58aine 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 apfst6 ykc,)/i0isl t*mi1q k) basketball 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) at the momg1 sx;g.1rkum cu6e8lent it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfr 8mu1.su1lx;gk ec6gield.

A 650-N force acts in a northwesterlyhkmb +)cm*qzd6j v5n+ nqt h++ direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate yourh56t k)hn+ zqcdbmn v+j+ +*mq answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two bur gu9,vg: -fesildings 10.0 m apart. The sag ig fv-: r,g9uesn 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 hanging by a mas4zzos8 5ikcw( 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 14.1nd8 qbw;s,i a7c icrv38 cl7b0$-\mathrm{kg}$ 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 neb;x)a6miu2**k k 0:jxom*bb m/ lu bxow location at McMurdo Base, Antarctica, as m j6bam;/o *mkb *xx 02ub kloui*)b:xshown in 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 tb+y9n l4qon mypcs, /;he same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locom/n9bs cym ,l+pq o;4nyotive 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 apy x4,h f).wmgnparatus shown in Fig. 4-48. (a) How hard must she pugwm.h, xny 4f)ll downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, hg )x +,2awtmga 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 blk4x(yg wsq+/2w 52uz0esmlmjq48 ijn ock (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 contjl1+,h*6mfzf a1q i ebih,.kl act with each other,+.* jh1,,kbz6fameii 1fhl ql as shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above the gc8oimte:x- 3 nround, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the syst8t-e cmion :3xem 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 frictionless table are connected by aler m+2b8u t*zc2z j)l heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at ear* emj lz cz8b2u)2+ltch 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 frb1u2,xohk u))d wvn ;-i2xw2llom ut :iction 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 requir s3fqrp:wf) os6 4r3 ndg*p77hkbfb6yed 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. a.d u1xr (0w2fd ymm/m5(ppnhWhat minimum coefficient of static friction must exist between yoy mda12pwhxm.n5 p(d/ ( 0rmfuur feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergz9hjid y-3ja, o if the coefficient of static friction bz-hid ,y aj3j9etween the tires and the ground is 0.80?   

  The coefficient of static frictionxt ahm-h 15lv1 between hard rubber and normal street pavement is about 0.8. On how steep a hilhv1ahl5 m-t x1l (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 -4.80 6 rt-u4qjotu+.bg 8tt$\mathrm{~m} / \mathrm{s}^{2}$ 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 oncrs(:.nmke8rz g m k fd*;8q4i 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 6x2:ef r - eul9go1iiwhave a very high coefficient o er-uoe6 g:wli9i x12ff static 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 a 3yx7f;:xarqvxj5 gp *pa/jwf 1f 0c98 jhv2sy $ 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-z ( qpi4baem8 large a mass would box A have to have to prevent any motion from occurring? Assume 4imb aq(-pz 8e $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. Hob s m,f6v-vjonm1j,)g4i5ioxw far will it go, given that the coefficient of kinetic friction jmogs b,xf 6)m5n,ji4oivv-1 is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at xoapv;;( hu8dnt pm4q7.q :iirest on a horizontal surface (:otiauq(i.xp vqn;87d4p ;mh 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 crf1.hqd/ dy9 hzate. 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 .hqd d1/z9hyf cab of the truck?   

On an icy day, you worry about parking your car in your driveway,1*yojj 18tojvsya6x0 which has an incline yo s1 *yj 860jjxv1toaof 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a 6 0-vappq/nlv 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 v1 l)g/d h;7ok2z mxixgk)2 iwplane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 8rfmwkdd20laue84f w kt 9w )bo)qc*as- s-- h 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 spel 7glpxle9o4 6ed 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 y3nfd4ewm w 0;a rough wall by someone pushing on it with a force directed updf0emww 4n3y; ward 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 bec) sud+8yv/ zo/8 mcoayzp/1 hhome dangerous projectiles as they melt. Consider a chunk of smy//ahzdv+ coz/s hy) 81op u8now 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 an automobile tra)ip+iow9 y)i,5 ,avs 8flavrqveling at speed v isarw )a5i y+oifp vv ,9i8q)sl, 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 4rps/ quo+u b*c3w lcssp tu/q*a*6w6a car slides forward on the dash when the driver decelu spc/s*s *a cuo+4wl3wr*qt6/q6 puberates 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 masr kvl sy q+:0qh+:5hpms m is 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 arwbt61 6r4 :q4+ n)oe mozkdkime filled to the packing station 11.0 m away. The belt is initially stab:m w r 644mtz6)kdkienoqo1+tionary 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 is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic friction betwig5tt lid35b( een $m_{1}$ 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 bicyq vi:on:rx8x st5/ kp7npw2d (cle) 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 heart, at eacrzsq9h n/io3 n-opk-ics5l ):9ja/knjijs65 h pulse approximately 20 g of bli-jk/l5hcr3zq:o -o ii9n6s5nn pj)a9sj ks /ood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crashpizq rkgs 9+m u0ip5s5+hw-3 n if the deceleratiok0n +iqp +5s-mw5 ih3ruzg9psn is no more 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 an earthquake5q a2-h evyth/ is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the groun/hyqh 2ta5e v-d 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 acdrm4 ovr9 2ns+cident involving 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 aboudn9ovrr m4 s+2t 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling dormyq7yv 3 ,aj/wn a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it3vq,ay7/ my jr 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 Tower of Pisw ),j1 +nj x,9nfyfksoa and falls 55 m before reaching the ground with a speed of What was the average force of n9sjfn ,kw+fyo)1j, xair resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretqugxdc 8 gr 6.zu:p lk467jbm.ch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy sgl.xj6bd: m 4upq.cu678rg zktretch 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 hilly portion of a city. An im 3zq,dff2-5to , knzox:bvkb8zwt7q 2 portant 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 , can accelerate o2tk7nx5:kvb- fw , tqf3zzoz bdq8o2 ,n 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 experim8jth93/rherivlp z w-.* ixk5ents, dangles her watch from a thin piece of string while the jetliner she iwkvp3.-zr9/e hli*h xr jit85s in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are t sx7 zl-ryb/*zk 7zfy*o be several ramps connecting different **/f 7yl z7x skrz-bzyparts 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 the piano m4vv2 knyh4us0a6re/( d5pap (mass M ) using the pulley0 e5has r adnuvpy2k4 v/6pm4( 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 accelera (n (f,v.grgxuting 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 processl8zl4,lo n3ew for a child-restraint chair, an engineer considers the following set of zlelnow3l4, 8 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-carzofh* l.ri0s5v-1 b9 r3e cheo Italian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, ussznj kqtz9yw;b06kt 0r+95mp e safety 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 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 hik6k9jz t0btq+ y5z90pw; nmrsm? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 1041j; rdp1xkwh.ttcv4 8e c-ri-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 spptz/i 3egrd.)i4zk h *eed 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 as y;g*y5v)bf iqcending an ice field inclinev* fyb;igy)5 qd 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.