Why does a child in a wagon seem to fall backward when you give the wag ppculwpygp 11n)t 57,on a sharp plpu pynpg pt,71w) 51cull forward?

A box rests on the (frictionless) bed ofgmlh f87 ia vem30i-t8 a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seem-v0lm e 8fi87it3ga hn (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 non:iwo8 qs9v9t forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acc8-ayzs. z p:ldeleration? Can it have zero velocl8z z-y:as.d pity? Explain.

When a golf ball is dropvp3e45q fbpxc*0fxf-ped to the pavement, it bounces back up. (a) Is a force needed to makepqx * 5p04e- bfcx3fvf it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lakeyqlbkz+l+8u /, why does the log move in the opposite di 8b+q l/luky+zrection?

Why might your foot hf 42mf 38lkq 5s2x ugfreza.swl4;0y*tjr js :urt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must deqbjg*a3n z1/d(m93 zeszefm/celerate quickly. (a) What is the j sz9am/f33q zb*n1z e(mgd/eorigin 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 finssxf(q,r48a.ozj fh )e thread from the ceiling, and a section of the same thread dangles.)af8x( 4 zfssohjr,q 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 great as that on a 1-kg rock. Whyg1j:etp8lrpl u 2s4j ws-j)1 y then doesn’t the heavier roc)p4lt j:8jgu e2yjsl p- 11srwk fall faster?

Would a spring scale carried to the Moon give accurate results ifolt x4/5mtuk. the scale had been calibrated (a) in pounds, or (b) in kilogramso4ux5l m.ktt/?

You pull a box with a constanq(; skc7y/7bo t*u tfj40ee ict force across 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) increase, or (cfic eyquo7 4/et;(jbs t0*7kc) decrease? Explain.

When an object falls freely under the influence of gravity ther45vsw3 wv d7s4md qfb oj8y t6ry:0a/fe is a net force mg exerted on it by the Earth. Yet by Newtonsyfqvm:85dodtay4s/6w0vrw4 jb 3f 7’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 jphyaxqlh69()zzvhh8k n/2) g/ v jy;to lift a 10-kg object when you are on the Moon with the force needed to lift z/g qyj/ hyn x2(h9l6a ;vj8vkphh))z it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’stzz(f.x 22 dfa third law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will ftxafz2(.z d2 win?

A person exerts an upward force of 40 N to dr1i t6u s8(wkhold 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 object ittd1k( uwir6s 8 is exerted.

When you stand still 2n zk*376nrwwe x/c lton the ground, how large a force does the ground exert on you? Why doesn’t this force make you rise up in ce6/3lxwz2*nr7t knw to the air?

Whiplash sometimes results from an automobile accident when the victim’s car3ex x; pqh3nzn,-2bc(smu clz 3..g.8w xoygp is struck violently from th(x gcpy23.q3e w .s-;b hmgoc8pu.z 3xnznx l,e rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on va-50fsju bq6b7yo ,hthe bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to acceleraf7 y0bsv,5 bauh 6oq-jte?

A block is given a push smfyh6-s /da gk/ s)2mso that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the de/d2s )mks6ma-gysh/fscent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an incl nl6v eqt9(.ds/)+x*gz)t5kz hycjb vined plane? Assume the me)vg.)*l hczs9kvxd+bnez t/5 t6 y(qjchanism functions properly, even at an angle.

  What force is needed to accelegci2o ga*0np(w4 i: cqrate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceu;eoees7d m-2 7yu fy.lerates 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 withstand if it is usubb1 yd1 tr56ned 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 a dl7 nkeveo ecfyp 5a( jm5.r;+1jd. 1u$76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 s if the car is trbg(. crj0 c51aeo sj41 f7zuyuaveling at fgjr075(.oyzu1 jue4b1cac s95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125sjlu*7dpzf s74- 5fbum/zu7fd7l5j4-p s buf*ss over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an :j1qf htk;zy d*3hxxc+14eq(2lj nei acceleration of 2.5k1 l (:h*e ;qf+jt3 41xzjiheyncq2xd $\mathrm{~m} / \mathrm{s}^{2}$ 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-mile track (402 czo 4:h2 j6bpyfyfibe .n.0n, $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that a ,6ss+ ck783aaokafb the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting as6+,3o8c baaa skk7fcable? 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 scas/s/zt *yg-jv/x4 snmle in a motionless elevator. When the elevator begins to move, the scns ygj /-tss/mz *v/4xale 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 strength of 8y.3/ken l 4ghsj pd42e56do*r itc ti21,750 N. What maximum upward acceleration can it give the elevatog ok62s 3/irtlhyn.45 eic8de4*tpjd r without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass8 c/gohc 8ofc,;o8hc5tb)so x 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their weic5/gsfx)ho8 8,oboh tco 8;c cght?   
(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 hthwcvbep4 c 1l,41h8*ykrkd5e strikes the ground below, he bends his knees so that his torso decelerates over an approximate distanc4r h cb,l1w*4 ep8kydhc kvt51e 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 the box runs uo)-fxf 7z/i .5r1j.rbfhfb avertically 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/ uao) ribf71xj5-..fz bfhrf 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 diek*x csyju q:j c 8w9,jrkj3v5r9nb/9agram 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 (k26nwl6(nogm sn(5u)thykm 5 6;xrdua) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward thnkl6 hgud25uxrn mwokny65s (t;(6 )me outfield.

A 650-N force acts in a northwesterly direction. A second 65l* cj(5tzb,no b wamx+gv-6zv1v, ( mt0-N force must be exerted in what direction so that the resultanbvtjx -,m (5 +nv,t1c(l b aom*vz6wzgt of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between tw 87 3ncrlm4aw 59mfytfo buildings 10.0 m apart. The sag in the rope when shel9wr3c t7mf4n 8m5fay 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 buci:qyujky,8 u 3ket is hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.0(uy,i cq9qmd:$-\mathrm{kg}$ 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 at McMurdo Base, Antarctica(.kw 1xdz:ujp 8nzb78 d ywz 1rit*oatn s0)t/, as showt a)8z71jtd d nts*i 8x:1rk (zz.pyow/ bunw0n in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind8 zgf,))eojxf it, Fig. 4-47 . Determine the ratio of the tension in the coupling between ex)zgf j)f,o8 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 using the buwy9bl-un9 cdi6 e1v(ecket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant speb el1v9du(9 iy6ce-nwed?   
(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 0pxsb4w 7 o9 36lcvw.23idtqie npp:b65$-\mathrm{kg}$ 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 bxlax7 e4u *n/24emhizlock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in c-hyuk8r 9y1m eontact with each other, as shown in Fig. 4-51. A force rm9e- hy1 uy8k $\overrightarrow{\mathbf{F}}$ 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 glo cg: 2)wjdy0l 2zga(round, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object rw ldgcyz aljg( 0)o2:2each 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 fr7n9x o7 dn3d t6ky+gkgictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each bogx+y okt d3d96 nng7k7x 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 frictio aj) -b3:zypkav3n 5ian 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 0*qu-z pj-58 0)4ls 7ddnfd1o7xureqmljohnrequired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train arn-t + m37brmaccelerating at 0.20g. What minimum coefficient of static friction must exist between yo-3m7a mrtnbr+ ur feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can +3p+m ) hk lva +j2n(wkgpg*qqundergo if the coefficient of static friction between the tires and the ground is 0.80k +*)+w+ nhv(l2 gjm3p qqgkap?   

  The coefficient of static friction between hard rv6v ,/o rb)y1h( o)js+ijfdfuubber and normal street pavement is about 0.8. On how sovhf,yid )bo 6f1/u)+jjrv( 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 -4.80 y a(gzwl+q2gt i.)l5t$\mathrm{~m} / \mathrm{s}^{2}$ 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 n2aq(-vm.q,lpln:ta t 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 h, ,.2wja x9euu9dq(uy amm+n with an asphalt surface have a very high coefficient ofj+u, mx.u92a n, q9hd(yuwmea 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 fpv z0j b90o:9dca kif2or 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 Fi 2;noe cofksh6fy9(rd ,6r mj-g. 4-32 (Example 4-20) how large a mass would box A have to have to prevent any motion from e-n j;r6s(y9hkc,mff6d or2ooccurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How facv gxduis40 g :fn5m76r will it go, given that the c7 5xg6ngmcv:f d iu4s0oefficient 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 , a3a5*mawhy h3v re in contact and at rest on a horizontal surfm *h35yhava 3wace (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. The coeffiqt;sx v7/8kh(thf3k l cient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still ah t(l k8k;vtsx7/ h3qfvoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in yvw/r* bav/z kf(yd:*tour driveway, which has an incline oab*/d v*zrty /k:f (wvf 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 sl1noq3th r)9tjz -,lhshlzt72 ide 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 l arhb 2ouws6wc54n0ij:/.jpst d06t:r d bnk;ies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initia agr)+diyz/,e qp)a*ks9l2z nycuz .*l speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with al 7 k)u83b 5j8revoimi 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 roughv /cud(k-ru1v wall by someone pushing on it with a force direcd/ (vuk-cr1u vted upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as thebge/k1)tub: ky melt. Consider a chunk of snb tb:e)k1guk/ ow 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 automobif 8yyozm/o04p le traveling at speed v 8 0o4y/myfpzo 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 whyt4 o h5fcni14en the driver decelet4i41 y ncfo5hrates 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 , u14k syab6fmis given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to the pat/k.hmf k u4b7 2ufe,acking 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 between a box and the belt is 0.60, what is the minimum transit time for eachu4 u2/kh f kbfmat.7e, 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 bi aurg/sd6(,.cays s :zak xqz3k/03between $m_{1}$ 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 bicycl:si q6ihjd8lu069i h x(3evwgg id 3-ve) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian q8)wjkz5v e sgi 4 lh8b(j0bzvik:*k5heart, at each pulse approximately 20 g of blood is acc 5b80i*8ksgvehj54:zjkbwqzk (i) l v elerated 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 a eno/7,d3t( u 7cvh7cqfvdt0tutomobile crash if the deceleration is no more than 30 " g 's."7fvh7 /ct,(03qdn7ttedv c uo 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 d*j8 ,pe cpk1oearthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient o8jp,k1 epd *cof 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 4y. xa*g jj7zcan accident involving two cars, measure 72-m-long skid marks of one of the cars, which neaj7 zj4g .ycx*arly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hillau/,effkk ;nh6h )9 oyfh+j-x (1-in-4 means that for each 4 m traveled along the road, the eleva )-ek k+6ujy;/hhofa f,9nfxhtion 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 Leaning Tower of Pfc h+(wg/bo- cisa and falls 55 m before reaching the ground with a speed of What was the average force of( +b-ch/fow gc air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy /rld( f*uj(qo yjy;.m- n0gdbstretch where the effective coefficient of friction jo mq-rgn judf;l(b/*(0. yydis 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 on the redesign of a hilly portion of 15y-wv0ujq atl s.yr8b 4s0c pa city. An important consideration is how steep the roads can be so that even low-powered cars can get up the h1yb0sq r8 t4uy0ja pcw-.l 5vsills 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 physics experi7q*vute 96rqkments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that tht r67ev9qkqu* e 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 diik5 g/ 8aku th );p91bmj:w sklw97zpzfferent parts of the/w7 a )1 t9 :;zk8zwgju9mk5spplbkih 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 n06hcqf (j)c6k(h oq fteeded to lift the piano (mass M ) using the pulley apparatus shown in hf6j)q06 (tcc oq(hkf

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating at 3.51 m-4(nk jewvaw2 r;ul $\mathrm{~m} / \mathrm{s}^{2}$ 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 considers the -vy,fy 9v 0rlh 4xseh4following l9eh,44y -hfxvy0 svrset 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 metric tons qc/)q9uf5i w q)zeb 6a (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 : hdxua4 rxi:i9d+o87e*rgso8kogd1 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 rogd o 8agx*di9dsi1h8x+ rk:oe4o7r:u pe. (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 usinrfz 0ksqsnt1xrl g6wu*k i43bv1 21n .g a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building ;rklml 7 /dum xyu-vy3//r9zx 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 tsf2ymngb/bmi2 )8; c mogether are ascending an ice field inclinedb8 s g byf;2/mcm)imn2 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.