Why does a child in a wagon seem to fall backward when yo3wucl9t :gmh *u give the wagon a sharp pull forwtm*:l9wuc3g h ard?

A box rests on the (frictionless) bed of a truck. The truck driver sta xb.q4mrxm-o b;m)4qbj z.f0l rts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of t) x0f- zjm4b4m.r ;oqbq.xlbmhe 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, fq t jl+akvt78 ke82-qare no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can it8uerx1( ; you v8yb:et have zero velocity? rtu 8(;x 8:ebe yuo1yvExplain.

When a golf ball is dropped to tze*d2 v v sv88o9mw*mghe pavement, it bounces back up. (a) Is a force needed to m*mve8vsm8*v2d9oz gw ake it bounce back up? (b) If so, what exerts the force?

If you walk along a log flocr 5q,,e(4ig*zb w lsx8nvs 2(l/xktwating on a lake, why does the log move in the opposite di*,n (x ixzslg5w8tqs /b4c,rwe2v(lkrection?

Why might your foot hurt if you kick a heavy desj,td 9+t (axbzk or a wall?

  When you are running and want to shpt*tnk 9h)ja ,x:zu2top quickly, you must decelerate quickly. (a) What is the ot*ak xuh2,j9)z: n phtrigin 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 thpnxs(:s*,.x tkjee :c44 ,zqskfw n*ye ceiling, and a section of the same threaw, (4*s p:yz:eqkx tksx4 cns.n, *fejd 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 your answers.

The force of gravity on a 2-kg rock is twice as greatge57xj 6 vy4w 4m :uxaxm3qjz4 as that on a 1-kg rock. Why then doesn’t the heavier rock fall fast64qe x7 a54u g3:jmxj4xmzwvyer?

Would a spring scale carried to the M) b7m-2une6zv )2e ybv*xqmbxoon give accurate results if the scale had been calibrm evby2 6u)bzbmvne*) qxx2 -7ated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force acdj(uw:up:nf7 no9:fx) (l w ijross 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 the table), does the acceleration of the bo ((:n9wdofunjiu::p lx) fjw7x (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influim/ +x 3 rq.j/xckxz*xence of gravity there is a net force mg exerted on it by the Earth. Yet bxmxkz +.*x 3/i/xcjrqy 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 lifthyk +*70a)m3);ygeswszwl) rz)rj m n a 10-kg 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 horizontal ;wy*y h+a r zjk)egn)m3r)slz0s)7wmly with a given speed on the Moon and on Earth.

According to Newton’s third law, each team i7 xadc4/ofu*j n a tug of war (Fig. 4–37) pulls with equal force on the othe fdc/7aox*4jur team. What, then, determines which team will win?

A person exerts an upward force of 40 N to holfql leq7np7xh-3u+e)b )9pxffb sk/: d a bag of groceries. Describe the “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 objefphsl7f )qbe ulx/7k+n:pqbx 39e)f- ct it is exerted.

When you stand still o7qnkr6on;61tt kxq 4syp1yi(n the ground, how large a force does the ground exert on you? Why doesn’t this force makp6t yr1i 7xkqsk41n ;(yt6qo ne you rise up into the air?

Whiplash sometimes results qenc49whny. *n9soz)kh b6 k)i1m c8r from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. y1wqh869hc)iobn*nz4s9mkn )e rk . cIs it really?

A heavy crate rests on the bed of a flatbed truck. When the trucoqiy6bc *8ce:z8tu5ck accelerates, the crate remains where it is on the truck, so it, toozqcec yiub58 t86co :*, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the b0mlv;jl 1k+mg w+js58z q(jtolock reaches its highest point, it slides back down wt(8qgl0k+ sjjl;5vmomz+j1but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathrobmzw 6f6/go8b) tg m6gom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even66mwg fz6gg/b ombt8 ) at an angle.

  What force is needed to accelerate a chiz5 z6bi+f:lsg ld on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates ai56c /kojoy8 p bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is uo. 3(z vdjnm: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 oc8g w7.l;tgv2p dj+gef 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 8sujef6gl0, .c o27q2u pwptxi/ m3z s4.0 s if the car is traveling t2zicpl07qu6j ss/m 2wg.xf p,3oe u4at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from res.ysv nnno:+zu0ih+ s38u+d aat to 125m/s over a distance of 0.800 m along the barrel ou+uin .3znhya +a s:8sdvn+0o f a rifle?   

A fisherman yanks a fish vertically out o pfh*6:.dc zdy-inin .n mo)f6f the water with an acceleration of 2.5o-zm6 fpn .d hync6*.in:)id f $\mathrm{~m} / \mathrm{s}^{2}$ 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 quarte,nm2ht*6lb c 11 jtfu-0cjqu.c :vfqtr-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 q,ny4rqn ,t l+k*ni;b be designed so that the maximum acceleration is 0.0680 g . What art kb q,q,nl+nri 4yn;*e 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 motionle;bpv9 4nso:sz ss elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, an p9s:4;zos vnbd find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a ma y be1g,nb2ty)cuc 53n5pxt 7mximum strength of 21,750 N. What maximum upward acceleration can it give the elevator mcu,t ey)g752y5xnntcb p 1b3without breaking?    ( two decimal places)

  (a) What is the acceleration of two fallc5e8jb,j( a wiing sky divers (mass 132 kg including parachute) when the upward force of air resistance is,e5bw8( ijcja 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. Wh7ih-j7nd wk 9/6kx wzqen he strikes the ground below, he bends his kni6/ qk7h7jw -nwdz k9xees so that his torso decelerates over an 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 ti gu 3wu pm7vda6,f/p*he box runs vertically upward over a pulley and a weight is hung from the gapv 7p*6 /wmufui3,dother 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 diagra68yraavg cr qhg+ r6(g:os;- dn5xh9bm for a 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 (abb)8 unuyh:i 2) at the moment it is hit by the bat, and again (b) after it has left the bat ai)b:h2 yb8uu nnd is flying toward the outfield.

A 650-N force acts in a northzw4 n/d w5-epbo tfc0(westerly direction. A second 650-N force must be exerted in what direction so that the resultant ed ncwpf4z(0o-5bw t/of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizonta3x g ifd.pl29wlly between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 29 dgw.flipx 310.0$^{\circ}$ 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 c 3dh*+ u1hvw/y jqzek9ord 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 1kbsqp8 :o p e.zp7/kf/4.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location/a.sjo wrc5 7b l1i)hiu5x5pl at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces ./i5xouwsih57)llra 5 bj1p c $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 pullingpkif d 1vjsp m1/lt+31 two cars of the same mass behind it, Fig. 4-47 . Detkmdl spvji1 3+/t1f1 permine the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using0fb aq j4 kb3h *qoj*hpmpaq:5noz9 *7 the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downwa79n ab3ozq0mk fapp5q*** q:hhj4jbord 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, 9usutx 6 3vl1aa 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 blocpevq af p7hja 2e+y.jarl0i, h;po/9;k (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 frictionfe6b(ghqaukhtl )06e,z 3.p cless horizontal surface are in contact with each other6chzqku),g.lh b3e(6a0ef pt, 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 z2pzv-)/un( u re 7khj*sx d03*l kskpm)fcp2the ground, and the massless frictionless pulley is 4.8 m abp*fhkk)s27/) u *epzcjvn-krp3mzslxu( 0d2 ove 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 frictionless table are connected by a heavy /lc,y jfecnf ni.3a822 q4y nqcord of mass 1.0 kg . Calculate the acceleration ylfc2 iq8qa nje2n4,fc /3.yn of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic fric9fawo- *;yx3e 3qfpdition between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required t3db u1j/f) n 5/inak3mgej8gxo 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 stanx8 0wbyv2;(w h awkgz:ie:as 3; rtx:kding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your8kr2bs g:etw3awwyix:x ;0k(z ; a vh: feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of stan. b2 /3b ab+sdf m5fok6w4qcbtic friction betww2fb3da4b m/ ok+n.bc qfb s65een the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber a+ :jxkw od p9may ;miw,hau10hn); ng)nd normal street pavement is about 0.8. On how steep a hila xd+ hywmu 1)ph;n:na gkw),0;9jomil (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 wmdmamwn5j9ymo+ ;7* .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 on a rough 3ebq ihvp rj8a8-,h- 9k0$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coeffici 7uufd laxk96u(o jg,ctlo5/ )ent od6 u/ko9cat )ju(x7 gul,olf5 f 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 c5od21ztcvy(cr3w) m$ 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 large a mass would box j( icxcrxa xyp(.jue6f,t jy(hp3 79+A have to have to prevent any motion x(,ayx( jfryc6e+ uic.7p jxph3t9(j from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it gof6 1oj.e/+ vl vl44gfcmo0fam, given that the coefficient of kineti644fgefcv0m1f o. ll+mj / avoc friction 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 ,9 zf5fz/hp1n .r,7hmi+xuvv 8ff opycontact and at rest on a horizontal surface (Fig. 4-5f7,8,fo. nh+prvhvfp5 xfmzz9i/ u1y 4). 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 cdby7b8 3s.a4 n 3ouzdaarrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can dec a bud7anz4b3.y3do8s elerate 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 dri*8cun/yut8yp); z-fr0 w yxwsveway, which has an inclinwx8c8z)wf-y/r *; pytu 0syune 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;xh3g, *jpob wq-cnk* slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted a61otzs ti c4/nt 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 spee)m hzb)1aqnv( d 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 of k w::9utt2jid1 -csad6.0$ \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 pushing on it with )0lwopcyz, (js y db7gtm31,77va lrw a force directed u 1oyz7wa (7yrjcmgslv, )lp7db0, 3wtpward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as t r3v3w joe-w9phey melt. Consider a chunk of snow at the3rw e93w-jvp o 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 travelid0nz5etd8a6v p7 dnu0 ng at speed v uea 6z578dnv00 pn dtdis 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 slid jv, ,x;+gsut) ovhtj h/9t,qyes forward on the dash when the driver decelerates t;, y9ht j/o,jvxhvs)q ,+gutfrom 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 given an p8ja0uqwd:f(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 tb/,+oq6v5ehlok.e u nthor vmd;f e889oe20 qhe 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 coeffiko. 8 h6 ,hbd2u r0fe59m+to /vq eolq;8oveencient 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 boom*- 9 zp4vl9tlugaig3 ( a(cetween $m_{1}$ 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 6:.y w**yivm kfusec0 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 4w cys8vneb;w m0 rtg(+1 *vtzpulse approximately 20 g of blood is acceezsnvtr+4m;v0w *t gy8w (c1blerated 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 su2 ppx)*r id69qn . znewsfia.ho1c57prviving an automobile crash if the deceleration is no more than 30 " 5s 7no i w2cn.i1qapp)z6fe9xrdp* h.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 if n 3adev3qwc* psbfr(j 5,vf )(an object is going to "hold its place" on the ground, show that the coefficient of static friction j(f5v*(nw) ebfpcdr3 v3q,sawith the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accident involving two cars, mehlw34vif 3 z5j ueg8*,rmozuk3vc/ ,easure 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 ab3/uv53 fo4kclj ezu *zivr,whe m8g,3out 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-mxzm, zb 9bl.- 0y)x wr/.zoqiv kj)):cxgkb34 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 mrx)bx )/,vyoqkb39gzb.ck-z:mz0 jxl)iw. 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 Pimj6fwd04 e/n,or6(b.og ic ftsa and falls 55 m before reaching the ground with a speed of What waf6n (doje b6r t40mcfwg/.,oi s the average force of air resistance?   

  A cyclist is coasting,yi5fjvwivp1hp 9f65 n m/gy + at a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be thv 59,n v +i65fwp1 /jiyhfygmpe speed upon emerging?   

  A city planner is working1u8tks9ejyq a1* ug( a on the redesign of a hilly portion of a city. An important consideration is how(tkaj8ug9 *u1 aqsy1e 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 . upc ej,ci/jo)hb4, jphysics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig.e,/cuj, oj. j4)bhp ci 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 several ramps connectirr4;+vd g 9soing different 9rdir4vgos+; 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 forceae :br)-sc)gs 37h,pewdo 3ag94 w*jjm xv4wk F is needed to lift the piano (mass M ) using the pulley 3 x*)rja7-hc)wo4b j9sd g3kw emsa,4g pewv: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 accele-ioa 0nje xi*,iqc,p -f6crd9rating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chi 9(;v2feag edair, an engineer considers the following set of conditions: 2a9idv (;fe eg
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 o6dl;wfl ibui80p u+/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, usvqn 3v 9syrxvdx6:((8j e6icde 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 tijce:8q(sv vin9(dx63x dvyr6mes his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using 4o1hj+*rt hs oa " 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 buildins-/zyt0wkjqfl 9t:4y/cv a0i. 8csme g is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together are ascending .a n,k+sat nh9an ice field inclined a . ta,+hksn9nat 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.