Why does a child in a wagon seem to fall bap-ot pivrnpg cxf 9)*va625 2vckward when you give the wagon a sharp ppgfcpr5n*x av29t v2o i)- v6pull forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts the6l;jz)ep8co n truck and accelerates forward. The box immediately starts to slide toward the reez; cjn6o8p l)ar 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 an object is zero, are no forces acting on it? Explain.-vmot(i:m9yz 02mj/qto wbo* k 0ebw;

Only one force acts on an object. Canv mw;m rphi94li4d*( n the object have zero acceleration? Can it have zero vem9(h p 4 viwnm*;idl4rlocity? Explain.

When a golf ball is drez*pr3- xv7 b9jkd y k(amev.+0ju v5oopped to the pavement, it bounces back up. (a) Is a force neede3m +veja( vpojzkx0.kev9 yd-u *r 57bd to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a la*+rje4pgl tl o gnm40su3urnty 42w5wm34 nd,ke, why does the log move in the opposite y 4gnwlgw,5s244+lpr nn0 m3m *udo 3tjute4r direction?

Why might your foot hurt if you kick a heavy desk or a waxme)5o9 )pluso o: .* kvxamp+ll?

  When you are running and want to stop quickly, you must decelerate quicklyk(nc.i/v v/ xv. (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 atix v /n/.vc(kv 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 th02aiuzfeu b4vn5 xoh d-lpq21sy3b o96j7av7read dangles from the bottom of the stone (Fieqy9 f2jop o75bavu7z03 n-a h 1diul6xvs42b g. 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 rockpp 2,jv/rh gdvr4 5i4g is twice as great as that on a 1-kg rock. Why therij p4r5 vhgd g2,p/v4n doesn’t the heavier rock fall faster?

Would a spring scale carried to the 9)dspm2c-xd k(scf;/bv 1n epyp4h8aMoon give accurate results if the scale had been calibratep9xd2mey () 8- psnvc4cdhb;pka/1fs d (a) in pounds, or (b) in kilograms?

You pull a box with a constant force acrossla+mr3nf 8y y4 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 box (a) remain the same, (b) 3n +m48ly rfyaincrease, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a nxc e4r) .mtcem/m) b4let force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth mov et.xcrmme4/)cbml)4e?

Compare the effort (or adnptslp8 * jq*s. ct-1j(ev - 5u3trlforce) needed to lift 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 o8sqjv. *ltet*rj- 3ldtsap( up1-5 cn bject horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (9:g8xwvb33vik jtw thc,v;8kFig. 4–37) pulls with equal force on the other team. What, then, determine ;tkv,3i8: 398cjgw thwv kbvxs which team will win?

A person exerts an upward force of 40qm0v 8 st/8qcj N to hold a bag of groceries. Describe the “reaction” for 80jqs8 c/qmvtce (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the grot og6a1 4 660,;jtb(z:rxyz hmhnjua zund exert on you? Wh01ur6; y66:4bg(xnzz tjjt hzo ,ama hy doesn’t this force make you rise up into the air?

Whiplash sometimes resuo),ypr.zw mt:qz52hx lts 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. Is it rep5: hro. t2zyxm )zqw,ally?

A heavy crate rests on the bed of a flatbed truck. When the truck ahdz8b ;9wlr+1 wbfqjc* 96 bdaccelerates, the crate remains where it is on the truck, so it, too, 9hwf bj;bcbd1qdra 6w 9*+l8z accelerates. What force causes the crate to accelerate?

A block is given a push so thm v6:1pdzdwzi 4l (v.jat it slides up a ramp. After the block reaches its highest jv 4lzwd(i:6z.d1mvp point, 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 youn5p79:2w lydkys 0ho w weighed yourself on an inclined plane? Assume the mechanism func w9k:oywy2dsphl n750 tions properly, even at an angle.

  What force is needed to accelerate a c*rj0 ym7 5p 4ea m5ylph rox12w1bbhedf2gr +0hild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a biaw dq c me9;up,yf3i7,st(/sl ke 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 use0+bkn kmoxsf5 ,dr8ma 6 d6r8ed to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ofim 4c q4 j-fjfq.-t7s*oirh)z 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 in89ip y+ u b3t72;ls-vex iuetm 8.0 s if the car is traveling at 95km8t uu-ili3s xy;+7veb2me9t p/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125d:e z )o iilm,xp(pl4gtjm (s y-6;hj.m/s over a distancmdjl )pxt;zi4:sp mel g6y-o,. jih((e of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelerati8)p1r/c flpfmon of 2.5 fcr1lf/)8mp p $\mathrm{~m} / \mathrm{s}^{2}$ 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-md;e3 dd rnmcgj46v,f,ile 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 design 3 pc/v24.ue4z ltrvqhed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable3h l4vv ztcqp 4e.2r/u? 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 motionle9d4my;xkp bl x+p4j lco ))z(mss elevator. When the elevator begins to move, the scale briefly reads onb jkx )9m +4dx lypl4)z(o;pcmly 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 strength of 21,75h f0wy ziv5 f7dm*w34z,use5k0 N. What maximum upward acceleration can i m73su e *dz5wvfhy5w 0fz4i,kt give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky diversyae fdp; ;s-g2 (mass 132 kg including parachute) when the upward forcfe ;g2-dy s;pae of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strr7fx *an3 l4fnikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.f 7nfxn4a *3rl70 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 ro 1kev 4n:wcycd+s:i/qpe tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the othecvk+:4n iw:1s/qdye cr 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 playq.xr;w7)3xaypq /kh zer
(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 the 0yu+grp6b5jx4y + nwibat, annyg6+iurp j+xy45wb 0 d again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a1w9e8kh,u9 umuno +qj northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagra9 jwu mouq98+h,u 1knem.

  Arlene is to walk across a "high wire" s gcbe9 -j67xdztrung horizontally between two buildings 10.0 m apart. The sag in the rope when shg-dbjzec6 x79e 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 another 3 i805 hl)whh* sjxswtmo3(plo, o2im.9kw;mu .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 1,un(kh5ep-c no uw q68wc:( uu4.0$-\mathrm{kg}$ 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 housi 7tp9-mg.ktk:cwz ck7 u:6bbnng unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum kcb:bgkp:m t67u wkc9z-nt7.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 ca8)gbk1aeh,twj j e 6u5rs of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the,6hga jwej bue)k815 t 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 upwar3brppja uxj t *n+ )n,q0lk2u1d using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slutjnn12 u3kxp pb0 ),r*+qjalowly 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, a j;mfmlgn5,3zm+ gl1i *q; plywv:4si 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 (mas 4utlbo(eza, )lo9ke53mz- cys $ 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 frictionlse1(7g zc 6wrfk 1vf.sess horizontal surface are in contact with each otherz(1k.1 6ssrf7 v efcwg, 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 ground, 7 j1n;2 3cnzyy:icxdoand 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 of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it dyj i3 7c 12:ycznodxn;oesn't hit the pulley.]   

Suppose two boxes on a fatn rmk:m/2j0c 4e0zrbjr:a)rictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the c abz0r ja 20tc/rnr :em)4jk:mord, 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 friction betweenmzjx5o +z6-hqoo(bqe t(: yd7 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 requiredpsq *c; e5a)prd/yup 6p-zuq 5 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 a1w,w kl)4 6el:mpafbstanding on a train accelerating at 0.20g. What minimum coefficient of static ,)b:l lep6awfk1 a4mwfriction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if )ym trpptv *uxvl),72*t/tei the coefficient of static friction between the tires and th/xtr*lv*)em itu ,2pvtp 7y)te ground is 0.80?   

  The coefficient of static friction between hard rubber cp4r :zlm-;4v3i,l ufz0f0 zuiidq +vand normal street pavement i4liu+qz4mdcfi pz0fl: z,r vv;u03i -s about 0.8. On how steep a hill (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.q vry6 t2rq gz 5c6uk6olx9*.kzh*- v k*gd6uw80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 res fwfxf8xbc. 9whz5tb k10yhxgg) 95 z3t 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 have a veryv.au2na : *iv32 kslzlmm:4ot high coefficient of static frictio:ov vk *lt3l a2ms:4i2.maznu n.

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 frictinpe eng9pf7-;on 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 large a mass would box A have ,rg 0l7i8rwj xf7 gf2cto have to prevent any motiwg2fcilxr,f7j 7 r80gon from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across *;xl2xo( wo,k ws(z yithe floor. How far will it go, given that the ck; 2iz( x *swyo(x,woloefficient of kinetic 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 xnzst 6ac(r6ci;i * r9in contact and at rest on a horizontal sur6 6r*niz i(9acx ;strcface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate.9 .)vlm kvb 2+bppe70zw6 szuyqn)wy . The coefficient of static friction between the crate and the bed of the truck is 0.75. Whbz) 6e2m ulvq z wbyp wpk.yv+709n.s)at 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 pw ioi5sc.dli5g-cye/)6z9pwx+ q mt*arking your car in your driveway, which has an incli msi xd /pty*-l igeq6cw)55i.+c9zow ne 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 gvzytlj:b(c3d .ga:5 a 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 a65 aa dj nvigsjeo2/qq4x,;zg56 mp9 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 initial agb0zff84i0t 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 t hr ,oikq-(3i +ly4pwvop of the steepest 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 dylumy7h8 6p q.yy lkl:*(jmxl45*)ntkel+ z a rough wall by someone pushing on it with a forcezyq * ny4 +*ye.l)pjt: (u6lklld5h ly7mmx8k directed 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 bbsx;:zc5q/t 3gk dk 0gecome dangerous projectiles as they melt. Consider a chunk of snow at the ridge oxdz s0kbk; t3 :ggc/q5f 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 mi+uhohb-p/sjmw0q 2-* uim .h wnimum stopping distance for an automobile traveling at speed h -ho*mi20. p/sujqbm h- w+wu 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 db2x t)r7v3,z.j ;8pttlvhz0gm f e9tvash when the driver deceleratest3mt;f,v0 ljrbev7z z v8t. thx9 )g2p 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 acepa55g(;o8qu2la tpd.p:0 pitp 9sxn 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 fqbq7) uef 8-y0qt mmp:illed to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of th)mbqpt0 7:qu8 -yqem fe trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction betwee pw-p9g (s4ocalur,nt 4n;c5 mn $m_{1}$ 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 td rn12v :m9q j/)h+lfc z+ qhx0gu/bfihe 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 mob6- 2xoaw s cl0coyeo0*6prp0del of a mammalian heart, at each pulse approximately 20 g of blood is acce2 yc00sol-o0aob r6e wx* cp6plerated 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 reason;,h7hsg)su(5v jongsh u-7 giable chance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a i-hsu h5;7(j ggnhs sv,g)7ou70$-\mathrm{kg}$ 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 eaun9ql *zivj.5 gi )lt)rthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the groun)lv 5q.)u 9znigj* iltd 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 /au)9ilx2e5 dp5qd adthe scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop befoeq)ulp dad92 /ix5a5 dre colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that*ah4 -5 7vmzk(exrm(6dzw g a:f31x )uxmnirt for each 4 m traveled along the road, the elevation chaazx)7-aigz w hx1(4nt6 r x ef rd5m(u:3kmvm*nge 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 oe:8ls :mxfouo:(l8()z owjdthe Leaning Tower of Pisa and falls 55 m before reaching xo uozdjf8l(:mw o:o ls:(e8) the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretchx:,bxjt)y juw2e g+)k 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 the,wb ) u+ex)ygx k:2tjj speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. An impori(3xn rz4o( uttant consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowin(t nz(ri3ou4x g 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 physics experiments, dangles her watch from a thin vp z6qxg0;v1ver+b i3 piece of string while the jetliner she is in takes off from JFK Airport (Figz0bv gvi3r+6xpeq1 ;v. 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 diff,cim j-ayb4dlc1 h: 4gzuy33m)xi kv/erent ji,vxiac4uky y:1hm4 cl3)d/3bgm z -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 (mass M i.h, 387i15e tpfl htrtvho;j7p7a ub ) using the pulley apparatus sh3b;piht1i775t8tf7ho v rph, uj.ealown 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 acceleratinz*(goas-t: abj 7g ezfwi(8p-g 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 engineer co 6ptyvvy-l2 h4nsiders the following set of con-vpv42h 6yyl tditions:
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 mexa0 eay ccw rzj7.f3go+)ci ;/tric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ro+ w ,ez8wzexf4fd9)iq1f h,od pes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Whiw8fe,w qd xzfe)f91 ohid+4z,ch climber is more likely to be hurt?

A fisherman in a boat q 1uhk- (gi* ml*gxfzmon+nq7 ar pi77f2/ar/ is 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 buildi/vw ,mxoxyqc1* h4 3zfng 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 ;qsct0yj nw) /are ascending an ice field inclinj /)nsw0cyq;t ed at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.