Why does a child in a wagon seem to fall backward when you give the wagon a a ;vvpq7 6. sxb-bicq0sharp pull qia .qc-b s7xvp6bv;0 forward?

A box rests on the (frictionless) bed of a trueo e5bcz)6 x*:hq.ym hck. The truck driver starts the truck and accelerates forward. The box im mb:c)5ezo*.6hxeyh qmediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an4cwe d8set.w5 object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Cb5u.lb 1b 2/(mjknxru+ :rf5 -lqfbbqan the object have zero acceleration? Can it hb( xb5 rnbujlk.5-/2: +fruqq1mbbf lave zero velocity? Explain.

When a golf ball is dropped to 4(ol6zkznj jg2vcc18/wnq6 q the pavement, it bounces back up. (a) Is a force needed to make no8lc4nckqg wj1q6/jz 2 v6z (it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lxa6oh v cq4u q1se*++rm tc.4aake, why does the log move in the opposite direcvo+x*6.ama4 qc c qu te+1hsr4tion?

Why might your foot hurt if you kick a heavy desk or a tksehvzj9gz6hgx* b :g-/8e0j i, da+wall?

  When you are running and want to stop quickly, you must decee a1;gxmjwg9xf ;ds,.lerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experie;1 wsgx9 agf; d.,mxjence) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the same threajgtgx/tg+mt z1 7ba jz ;;9bz8d dangles from the bottom of the stone (Fig. 4–36). If a person giv98jj;+17xtgzm bt/zb ; gag ztes 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-kgqrwt6 y:ql;.qazkfoq:6 h24b ae p5 9:jif5uo rock. Why then doesn’t the heavier rock fallq4; z26fhalu5q tfi a5.::eoo :jkyqwpbr69q faster?

Would a spring scale carried to the Moon give accurate resul9jgy0 p: x9uvpts if the scale had been calibrated (a) in pounds, or (b) in kilograpj:9vy9 pg0x ums?

You pull a box with a constant force across a frictionless table using ankt.al-h/y0 i7e bo-w -g2v4,iispte u attached rope held horizontally. og0iyt27 e hkw-ie/ua- sb-4p tl ,iv.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 influence of gravity there is a netj s,gd3e++gw lrpm9a(r) j,nf force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal anjg 3r(+lgm es ,frwdn)p, +ja9d opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are on the1t)vqqxo xkpn y7oc jx *45(f5 Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horit)5v ok*fnoxc(5qxxpq4 1jy 7zontally with a given speed on the Moon and on Earth.

According to Newton’s third la6zi* (n s6yt)nvmnjtj*.-pg ow, each team in a tug of war (Fig. 4–37) pulls with equal force on the*nn vz jj 6sm6).tot-*pin( gy other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a b(;v g2re:m/;sqy dwb tag 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 tvm(yb dg2/qs rew:;; object it is exerted.

When you stand still on theutx 25 .tl*cvcbfr g6py(1yr/ ground, how large a force does the ground exert on you? Whyl. f y/tbxr5y6gpuv c1t*r(c2 doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when tpxj( p/;jbl:w 4f8ukche victim’s car is struck violently from the rear. Explain why ;lu(fbkpjcx 8w /:pj4 the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck xrw+7ksm l1cqcx* 0u :so-lj; accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the c1lxmwcso cjq ;+:l*7s xurk-0rate to accelerate?

A block is given a push so that it dx).o7d uo9m)pzvz+fmflb: 7z8 /uhpslides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Whyov)lmfu.hou 8xz f9b /d)z+7dp :pz7 m?

What would your bathroom scale read if you weighed yourself up; 9c)yxmri(hkni0, ;yv . noon an inclined planeoui. rcm0(nyvhi9xk;), np;y ? Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1.25m/q j )awttk17g3s$^2$?   

  A net force of 265 N aczyd vs (ce1ks*:mp6 :ccelerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstanpxskb/s n z,p 7327l(pn2xk sad 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 of x5v 7i( me;g r vsuefd;i,x/t893prwma $76-\mathrm{kg}$ 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 iwsl nt8z; +j)ds required to stop an 1100-kg car in 8.0 s if the car is travetnwj ;)8szl d+ling at 95km/h? -  

  What average force is needed to accelerate a 7.0:)u2tshcg z 6a3m6zph0-gram pellet from rest to 125m/s over a distance of 0.800 m alacs hzu:) thzg pm6326ong the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleratio,fu pq9gm3i s2n of 2.2u9pmg f3i s,q5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mi/erz7,ufc; t rle 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 bee564n8 / nyeh pqfii.p designed so that the maximum acceleration is 0.06806ny i 8q/epp54f.i hne g . What are 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 motionh) :qxmwb yfin+pv;:c;+38 5u(fqrvbrf 5mjyless elevator. When the elevator begins to move, tbi5c; (u; nr+fpj)yxfbqw:m:vvmh+f8 qy5 3rhe scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum stren8bnzs o)wm*q1zw e+s3gth of 21,750 N. What maximum upward acceleration can it give the elevator without breakiz )s sqn m8+e*z3bww1ong?    ( two decimal places)

  (a) What is the acceleration of twoi4 ws*ui8jsio o r,gqwg11 /7r falling sky divers (mass 132 kg including parachute) when the upward force of air resistanceg,/qoww*is ir ugrs471 io81j 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 ro,*b/ksm:vm6 whgz:h idynd6 znh;e- )of of a house 3.9-m high. When he strikes the ground below, henkv 6-w )dg/sh e:y,d6mn :h *;ihbzzm bends his knees 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 re rw8;,c xm2zkk 1x /briqh0t.ksts on a table. A rope tied to the box runs vertically upward over a pulley 0m xtz.c,r2khwqkr 8ib / x;k1and a weight is hung from the other 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 pc.5ka1e f b.+hubcfy 3ba)ihn 9jc *z6layer
(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)fs)v1.gu(yfc b2pvl 5bhw (l, at the moment it is hit by the bat, and again (b) afbh1yfb 2v,w(. 5ugvf c()lplster it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A seconm.+yci x 6 7rvzl0o+mhd 650-N force must be exerted in what direction so that the o .v 7h0yzxmir6c+ml +resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally bet9na 1z6ddm1gn yvad5 )ween two buildings 10.01)v6mdz1a5 na 9ddny g m apart. The sag in 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 massless cord from a)r*whji,5p k rnother 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 1pmh :e)0nr 9hs4.0$-\mathrm{kg}$ 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 locat (kk kqriiezlf+y0y.m: 3)k(bion at McMurdo Base, Antarctica, as shown in Figqlby:f3.( rk k e(ziy0ik+ mk). 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 the same mass behind it jp;e (tb)egd-, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first p ej)e- ;(btdgcar $\left(F_{\mathrm{T} 1}\right)$ , 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 apparatus showtappoh4 vv8y d9i+l91;,k;m9w hj d+.vqol nb n in Fig. 4-48. (a) H h+; wtpm94;a dlbdqno.+vp1h,yjoi99k v8 lvow hard must she pull 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 u),k/fwobkua221xbt 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 block ( fuv0/w1mn:fcmass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with eac-0wmxuw7ka.m tj +g*ch otherukmcj.mta7 w0*- w+x g, 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 gros7zpl r/q 8dt8k)s7efund, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter st/k8 8re)s lp qf7z7dobject 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 corvb 1h:tu)tev v9/ineb9 :x76, o zlmyvd of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, usinbve1vt/e 6 9:xz 9 ibo,n7hytuv mvl):g 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 friction between fzm:s :u ;5qa8a kw9lna 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 ism3xw4 r-vd14kqs)z ey required 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 t6cg7 3vb;j* eo *xe*amxx)feo rain accelerating at 0.20g. What minimum coefficient of static a;gb )cxooe6* * x7m xe*3jevffriction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of e+h4 .g7 qknxrstatic friction between the tires and t knqexg rh7+4.he ground is 0.80?   

  The coefficient of static friction between hard rubber waytj:5jk .2l d xq-(fand normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leafjdaxtj:( wy52. lkq- ve 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 -4.83kllsh66u.. iycdelow3kr91u y /hj 60 $\mathrm{~m} / \mathrm{s}^{2}$ 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 roc;h6/ rag i;kc lo-pl-ugh 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 5hqlscag 31qyj v +qp32h:i8whave a very high coefficient of static frichyswl8q+c3 g3:ji1q 5vqap2 h tion.

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 f)d 2 l-gnad4(cpjpch6hnfdth 4 , df94riction 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.7*o r i87cn ovqkmj1a )(3mugb 4-32 (Example 4-20) how large a mass would box A have to have to prevent any motion from occuq7gncvbk8)1(mmuraoj3 7 *oirring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push sry)o8cl 4tuz0 o that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push ty cruz)84l0oimparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass hp6lx9wd-d9i 75 kg and 110 kg , are in contact and at rest on a horizontal surd9l- hwpi9d6x face (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 heavo .:kp5jpt) vysz. 7zfy crate. The coefficient of static friction between f) zpk y57jotpz.s v:.the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parkinttad2h c57i*p tiv m+4g your car in your driveway, which has an in2m vicpati5t*4t+h d7cline of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a qe * vzk78fn:g28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an angle )dl uipqr4,5ocws(e( $\theta=22.0^{\circ}$ 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 iy k*n6ltsrm957by1 rjqs/lh / nitial 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 steepe zp6es l-qalf3, rtu*8st hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by som3inf*) zgase/1 mok zd8nx5j-eone pushing on it with a force directed/i d zm3ajg8ek5f*n)1-s xno z 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 a jw(dt4r p0xcph9+y- can become dangerous projectiles as they melt. Consider a chunk of c0j wp4ap-(tdrh9yx+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 stopping distance for an automobile traveling at ukne-kx97ej;vt:y1aiw-;pp 6 p0f(zymf rv/ speed v k71fawvtxj;my 6-/9py0r;k z(:p vfie n ue -p is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when the drix; k9gm1- 2q/p anioolverna lox kgo-21/i;9 qmp decelerates 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 given an inii /6e)i/b,b jghsh4 ottial 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 to8xk6 tm e u4-tia2/mwa the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction betwe me/wma2t x u-t4a6i8ken 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 coeffici 24 y,g wm11meyc3msubent of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a uxe04wc-bg(gw 2 cx/m vra+v96.0$^{\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 hear okbgmz+i8p)8 jb8j17yn+a6ncf 4at 75 tjoy gt, at each pulse approximately 20 g of blood is accelotn6+ycjg 4ktzp88nj7 8 5bafimoyba17) +gj erated 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 e7+(w9c5 k3s zlqqlwyc 7.obpautomobile crash if the deceleration is no more than 30 " g 'k9c zoq. s(q+ c77w5plw3by els." 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 eare3c1hgn1c 51ku/dj+ bs 1vi pjthquake is a , and if an object is going to "hold its place" on the group13 c v15hbi+gu1kenjj 1/sdcnd, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving tw)k5*g3kj smxrv o/m1pnv)pj :o cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before m* pkr v jkp5mon3xs))v/j:g1colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-aorz) p:a*1o6 p w:le7pbqji 74 hill (1-in-4 means that for each 4 m traveled along t:paarbloio 76)1j : pzp*7weqhe road, the elevation change is 1 m). How fast is it 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 Leanwg xl2/ ( qjd8ojoq-m8ing Tower of Pisa and falls 55 m before reaching the ground with a speed of 2 /w-j q8jgmol(oqx8d What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy strelco:- umr)p8u5rfo ; ltch where the effective coefficient of :p5-ur r8uc o)fo;lmlfriction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working vh+ cqspb) k04on 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 partsvqk0bp )ch 4+icular 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 physics experiments, dangles her watch from a thin piece ofa 71x/ xdmi5,w9qc,fgaqc(kj string while the jetliner m / a(xj x95i ,wq,da7ckqgc1fshe is 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 to be several ramps connecting dift 0abt -e)sf0yferent parts of the st-tt0f )ab0eys ore.
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 needez*lfb d2eh4q)d to lift the piano (mass M ) using the pulley appe2 fqd4b*l)zharatus 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 acceleratiwp6v5exjl714 nbdhl( ng 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 chair, an engin5yd8 wolgdj21 eer considers the folwo8ddg2jl15y lowing set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 me ulj:*fd f3e3eqouo .cy*qepx4 g-4 d7tric 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, Biy .8ed lt83ty+ lpim4rll and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static ry4tld88re 3py i+.l tmope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 1js*ziws+0 k5s0-1 $\mathrm{~b}$ 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 maximul402z* dbwt ao (0n2ce6nggfcm speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice fie) tdn2r: sd+oh0)jpn ald inclined at 21.sp o2a njht)n+:0)d dr0$^{\circ}$ 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.