Why does a child in a wagon seem to fall backward when you give the wagon a sharw-33y:hnz y)2f fg6,qoc wmx dp pulldn -3,qz6)y3cg2ox m yfwf w:h forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts z;2rx+ -s*3hr dougrgthe 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 or+srgh ;drzx u- *32gground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zerod4b0f.pym5lg zi) t4l er,k)1tj+ a kc, are no forces acting on it? Explain.

Only one force acts on an object. Can t-gc j7 2zok+mq6ljho w(jw6 8rhe object have zero acceleration? Can it have zero6hrkj qj7w8 mzw-6(+oc ljo2g velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back u1g/qv:r y.ward 6dbm.mj0 o3crjs0( k p. (a) Is a force needed to ma03 :kj (v 6womr/. dgbm0ya1js.dcqrrke it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does vsc3fr(2k m( qthe log move in the opposite dirf(vr c2qsk3( mection?

Why might your foot hurtrz r5 bffqs9za-/8:q.sa1 futv fy 9d) if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you musyb(ird1a:iqi 84*n lmuk +n. ct decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top s+maq1i*nu.nrid:( y ikl84bc peed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the same thr+m hbd+74 a,bs7js qtgead dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain yasqb+gb htmj,74s+d 7our answers.

The force of gravity on a 2-kg rock is tzf*pvn/ +pf0sn) xx7fwice as great as that on a 1-kg rock. Why then doe)0pzxfpfns+x f*/7 nv sn’t the heavier rock fall faster?

Would a spring scale carri ehvmx0g fnn0l-+gxbeo55 a,2ed to the Moon give accurate results if the scale had b0gex2bvn,glfno+ -xh55am e0 een calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a fr7fr(g 4 : pcgr/0uoke tgi+c*3zq+teqictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an tr/ ++c(rpefcqzq*74u:ggoke it03gangle 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 undez-bo+ ( a7qcickl8l mmsl.,5br the influence 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 7b5k lzlc m,- q(.sclom8aib+on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object *mcu2vk2zb(gwq:)iowhen you are on the Moon with the f:* zmw2bqv)k2g i(uc oorce 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.qt2 )vog4yz i; 9h8/u uvan.uu 4–37) pulls with eg9 2z8;u n) . iat4vouuvhuqy/qual 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. Describe t-sjo xyo ) k1rw2no5-dhe “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object ixo152y o js d)-nowk-rt is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does ercn 5z;hvo87m1f 0zr)/za)ju e:qqi6bz3 ll the ground exert on you? Why doesn’t this force ma;vqrlz1 c :)5 uiezmn07eo/ zq) f3bj68zlrha ke you rise up into the air?

Whiplash sometimes results from an automobile accident when the victipotc9r ; w9g2dm’s car is struck violently from the rear. Explain why the head of the vicgo p9wdtr ;c29tim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When ths tubr:7 e nelbv40b+l4zw3q 2e truck accelerates, the crate remains where it is on the truck, so it, too, ae0br4 l:lu bwvz23s tb4+enq7 ccelerates. What force causes the crate to accelerate?

A block is given a push so that yhq dx:1k 2r/fvc-gx: it slides up a ramp. After the block reaches its highest pyh : k1:2v- x/cfxgrqdoint, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined plaercyh80 rcjmcykjp:8fr 9vl: p*;s0:ne? Assume tp0: 88hysjr:e ;jm9c:rrfp *0kvcy c lhe mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sle jc1 (ba:w 55jcyhnow+ j4d/vod at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider atl/2auji. h x.,xpjg( z 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 9t/qnugbu-ikugx u) i +x5v58360$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight oj -mof mk:r 1xmry.5*sf 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 11-s; ty;u5hde v00-kg car in 8.0 s if the car is traveling at 95km/h? h;stu5 e-vdy; -  

  What average force is needed to accelerate a 7.00-gram pellet fro*ce4 7-* p;4pxrvfd9n.gf m4 bgozmunm rest to 125m/s over a distance p 4nmmzx dc eff*;b. -7 v9gun4org4*pof 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelerati9toqi -gp s:m5l95 fjn4rd-cton of 2.5 9 dmqft9gtor--spl 4 5cn5 :ij$\mathrm{~m} / \mathrm{s}^{2}$ 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 quarterjb/r7mnd7 d,iq h57r h-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 thatn9fy + tey2uognfm1. / the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the .f y2tmen +guof19y/nmotor 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,u h nzvy-e5nu2t0of+w: n5m v a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the nu h:mut,+w v 5yz n5fv-02neoacceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. x:*vjwn fs); 4z/bol qWhat maximum u)vo l jq:w;4b zf/nsx*pward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fal-tz0e1av70doet0kiehd ) d o1 ling sky divers (mass 132 kg including parachute)o0i0dda e0 ho11kezet -7tv )d 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 ho(t6xts)ke43ib lh 3owuse 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excotlt()3bxsi4 h6 e3k wluding 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 box runs s4c *ft)etvm 4vertically upward over a pulley and a weight is hung from the othfv44 mtes)*ct er end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball player ebtv 2;2 ppcj+
(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 moment it is hit by el9.1 r;pew tn-ed1h3l-s;wbz5vo nethe bat-;;ew1rwz bhlt3-senl9en.o 15dpv e , and again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second xr vf.p7j6)ms650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer6jsvx fr.m7)p with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two bui l3sss07mk6apm tcm.2ldings 10.0 m apart. The sag in the rope stk m26a73sm.mcspl0 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 massless cord from anot ,;jtd 7imtcd;her 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 14.05,9q eg -gibqfs5ikv( $-\mathrm{kg}$ 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 aolpuyg ht-o ::o ) .znmohz0.: new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum o:gh 0.: p:-n.ohzumylo zo)to f the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4i j;xsp k2*k;mzyj51 tsas:j6-47 . Determine the ratio of the tension in the coupling between the locomotive and the firstjkj p:z5ks1mst ij6;*xa2y s; 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 hers tnovn*;i)veqf0 :zp2 elf upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant s:ov)0fv* nzpnite; 2qpeed?   
(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;+ 6n:claqvk(e3dva ddl)gf 9sy1.gy began, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a bloc/ri-;qy mqxu 9k (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 contaztro yk.ye(0t*u . c8gct with each other, as shown in Fig. 4-51g*t u8y0.ez or k(ty.c. 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 in6roq/0e yez32+ vptyvitially 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 oyo z6vv/y3qe0t 2er +pf 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 a heavy cord oq -5);/fewd hr 9ytehaf mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. -ret95ahh )eyqd;/w f 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 fric i xb vys)nu:;58+nbgikp.yb8tion 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 require)a1rk0m74 i vrglr5. sbhhlya m*3b *ed 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 mik8r 8znr7jv; i64-/ fjdz1ltw3kqpwjnimum coefficient of sj4;qj l/wjrzw d v3k8 1i zknrp6-8tf7tatic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum accelerata idj1. ud+s4nion a car can undergo if the coefficient of static friction between the tires and the ground ii4 .uanjsdd1+s 0.80?   

  The coefficient of static friction between hard rubber and normal street pavuin /-*0pn: mhcf(azqo9.c cpement is about 0.8. On how steep a hill (maximum angle) can yo0i*fn/nq. u po ahp9cc-(cmz:u 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 addo g)k8n-b ntxm4 *.*hukktz y h4(g0t -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest:0qaz4m/ ( mmcp5ocbp on 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 2y+fh8g 30yrl, b ulfqhave a very high coefficient of yq30+uf8l fr,hbg 2 lystatic 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 frias76a j4ct;txktsn7 ;qas pfd - y+(.jction 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 larg2gghtk/h1:j y a c oik2d1ps25)qe (noe a mass would box A have to have to prevent anyishopch1ak)q2 n5kg ge /o1 yt (2j2d: motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it blztj82n b8ktc *89nc slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 tb cn8*8 ct z2knbj8l9and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kfc rf(o71v hd8g , are in contact and at rest on a horizontal surface (Fig1 o7f(v8 fcdhr. 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 crate. The c6b0wr+uad :yo 5ni x2bggo 8-loefficient 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 deceleaxg:-og n0y+b5i l u28r6d obwrate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your x9j:yk t; ul (;ujaqe*driveway, which has an incline oftqx( j:ly;a ;ujeuk9 * 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 2;68 pxxx l( z;wz+feg+ke yy+o8$^{\circ}$ 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- 3lgi,t1w7ask+ 2rzkf 55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initia +qfde1rm5z)+ttf jk5l speed 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 speed of7jw+2c )k b7*f1b, r xvgx+,vgk nupd5r+ ajul 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone puuai8 4h; yjk7hshing on it with a force diruhij84 a 7;hykected upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectil+k;mygpk4i-: g o/ zqnjg0wqk+ug02u es as they melt. Consider+mk/kjo+g2 -ki :gwp;g0ny4z q uqu0g a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum skut w3l of/.8 ff+ekn-topping distance for an automobile traveling at speed - ek/f. owktf3u8l+fn 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 wheoepr*rlm sb 550m6lf 1jez44i n the driver de po5 flmi e4s0rj*5bl61zmer4celerates 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 is givenid.: 9t;(segszcq6n tr,+v0fps m.pb 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 filled to the packing stapmcle62+mw) f )k48+ih/rz;+.oktjwi oiy a ttion 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 is the f+ki4 tar) jmit+ok)8 2y w +io6cw. /;hezmplminimum 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 betwee(.mnonx 4cv4 sn $m_{1}$ 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 tcom5ba(,:nmon6;,(n as q,wlc ao7a/ugr1y(including the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approximal/6 w06dhhlqdv1+bz 4wxd()ky na, txtely 20 g of blood is accelera)h6dda14k0lwwx zltbyhqv(d/x n6, +ted 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 )ue9js.ipp hg 3;1q*wj ,vh e7+ego iscrash if the deceleratoi *ih+ sg.wh1eejp9 ugpje vs3, );7qion 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 earthquake is a , and hsnlozx3sr*- (e:33cyakpe 7if an object is going to "hold its place" on the ground, show that the coefficient of*l s-a ez(rxns3p33k 7ch :yeo 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 t 0 mndd7h4+0p qkejvf;he scene of an accident involving two cars, measure 72-m-long skid marks of one ode+nq0fm 4jkp ;vh7 0df 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 1-7fwg4si8fai (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 it going when it reaches the bottom after traveling 55 m? (a) Ignore friction fag f78w4i(si.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped fromjo- pcmy kl3ifytt/7d18 4oi) the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speedicky 4 lyt8m3td7o1)i f-/j po of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch wh5 xynk cscur u::k//l(ere the effective coefficient of friction is 0.60. Will the cyclist emerge frc:/c5( kulyx r/su:n kom 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 workingika0n e f*nhw2tjm85, on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 110 *f,58wnm iknea 0t2hj0 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dan+t p h4).omizdzkqj;0(cl i7x8l e2 tmgles her watch from a thin piece of string while the jetliner she is in takes off .;c 2thm)zqpo0jxi kl4+zl t(7m 8eidfrom 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 to be.byc12 dodwmocrf;6 0 several ramps connecting differencmo.df1 c0 byr;do2 w6t parts 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 (maf+1e:r)e n9 sni(xcsyc8bt 4ass M ) using the pulley apnist a(fy 4 :r8exbc91)nc +separatus 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 accelerating at 3. p9tl86p(nlzv.c) ey m5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rsvl ;;ln3j)h for a child-restraint chair, an engineer considers the followis; j3lvlh;rn) ng 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 mw tcn5ts3f/ ,qsq51cjass 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 andjmlx +ht3d;fv 8 c (11q0enwhe Karen, use 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 flw+ d 0;emh1ch1vt8(nex3 j qfrom 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 5. 4y6d*xdt))bxwign cd;lvp 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 ish pbc,+m b(f3* ei/gib 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 whh:ffcpq, qhl.ueq55+gxuo k2 qnq y4m2qe 80-o are roped together are ascending an ice field inclined at 2q,mhpu.4lkgf8 o2fhu x 0q-eq5 n+:qq5ye cq21.0$^{\circ}$ 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.