Why does a child in a wagon seem to fall backward when youd 6zf ik+idj90 give the wagon a sharp fj ddii6z+09kpull forward?

A box rests on the (frictionless) bed of a truck. The ti, cm 3u mb*n:9jfilkf9-v n:xruck 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 seen (a) by Maluiif:jmvnbck9x3fm, :*-9 n ry 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 no7zayi j7gen 96(5dm6,c fahlk forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can icyj(focd:yjcr5,t u eir+ip8ar97 3 ,t have zero vr:d7(coa uy ic 9f,p+5r3jtij8e,rcyelocity? Explain.

When a golf ball is dropped to /qtsz97 l mk+xthe pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) +97kxl sm /tzqIf so, what exerts the force?

If you walk along a log floating on a lake, why does the lo5pzcw2a bwb2y/omgo, z 8gd4.g move in the opposite direct2ggpab w2zc. d/y ,o5o bzm84wion?

Why might your foot hdu 1;ncku8wlze 3a)7f*m irm 9urt if you kick a heavy desk or a wall?

  When you are running anze 3i(a7dsz 7x9 5eafbd want to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person ru973zsi ebax5 ( efz7danning 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 sa m2v3za7cr /xime thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person giv7vmxc3/zrai2 es a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as +m,g,poulw +agreat as that on a 1-kg rock. Why then doesn’t the lp +amo,,uwg+ heavier rock fall faster?

Would a spring scale carrb0hs,ig8ust4p )m +0x stza.ried to the Moon give accurate results if the scale had been calibrated. ,zs0 ssh g+mi8br4ta)xp0tu (a) in pounds, or (b) in kilograms?

You pull a box with a constant force acrossgfonh(y oy2vs uas(e8o128cr, h/3tt a frictionless table using an attached rope held horizontally. If you now pull the rope with theeahs n21s (8,ytt y2vurf/g(o3c hoo8 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 net gbgdff*n78 p: )0rq zf rn))xpforce mg exerted on it by the Earth. Yetg*bqg)0 r8:dzfn)pfp)fx rn7 by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10- ;,j4,ey 7fh kjbwbyc(kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given wbjj ec,74fhby(;,ky speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 5t0edky4*k5lm, kx do4–37) pulls with equal force on the oth o*,k 5mxtl405ke kydder team. What, then, determines which team will win?

A person exerts an upq/-mmdx(x y.5tzk)wp ward force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its dir5wqt / pk(mmxzd.y-) xection, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how larg3abig om3*+b; t1m(zm dvyd4k e a force does the ground exert on you? Why doesn’t this force make you rise u +3vdmmzo*13k y bm itad(4bg;p into the air?

Whiplash sometimes results from an automobile accident when the victim’s car isu,h *37 oc9i z any55s(pipxuv struck violently from the rear. Explain why the head of the victim seems to be thrown backwarz5 nx3o* a5puy7(9 iuvi ph,csd in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. Whez ;/ysp :xs .no2c.u iab+yve9b bq2.vn the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to.q2o+9/ usvy n.cp ab. s;ze x:bv2ybi accelerate?

A block is given a push so that it slides up dvr6+1rl t .ioa ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the desc rldt+1iv6.orent than on the ascent. Why?

What would your bathry4kl/4x5s gp0o3jx m doom scale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, em0/g s453jxoxdpky4 lven at an angle.

  What force is needed to accelerate59-dn6nexa:)4uw b ckefv- r a a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bi;hfn)4rxy7s2 7/f zricu sct.4ktcf5ke 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 used to accelerate a 960or5*5x(go as0x .-. ;zhdl -lohakdft$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight okw7 8m h(u4jw89snnsp. pi;ywh)s ir .f 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 7g76 usypw9,y pzo*z aan 1100-kg car in 8.0 s if the car is traveling sygy6 wa7u7pp9 zz *,oat 95km/h? -  

  What average force is needed to accelerate a 7.00-grvbid0(1 1 4wo3hfe xv6stl/eqam pellet from rest to 125m/s over a distance of ( ldtfvq/v0se 3 io6hexb41w10.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of 22 vnou54oyyjfk/ 3e0c.4yo0 /f y5ecojvu 2n3k5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 tracfq*nz :po5r:6 rlhx5 ek (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that :r 9;n2npzmra the maximum acceleration is 0.0680 g . What are the maximum anm2 ar ;nrpn9:zd 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 bathroomm./iwzj+kf hf /q5:8yxq(pf a scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the directioax(8fw/p/ .:hfmi+jq qyz5fkn of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elev wp*-5ek rpx9rator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without rkw9*xrp -ep5 breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg h9ohdje. (kz. including parachute) when the upward forcez. hj(9 hd.koe 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 ow*spv0kjce4-0 js mb5f a house 3.9-m high. When he strikes the ground below, he bends his knees smce0 jks5 s0p -b4vj*wo that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A 2okg ;,s li0myu(cpx5rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine til o0g;yk(xc52s mp ,uhe 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 plzf*j0o: l (t-tm ;+v( oencvwo/d w7kuayer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body dukq5ho1o3jjxex/*m -+b n2p 9 bnw b3wiagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the nwkjn xq*/-o3bpxebw5+jb9u o3m1h2 bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direct ct3najn72- 3xyr hwp6ion. A second 650-N force must be exerted in what direction so thac-w2 3p hnnjx7a6rty 3t the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "xxet1 a ;wd- 3j8vyhez.w 3e1ahigh wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpx3 eyee1wx az djvwh3a8t-1;.oint 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/- wzgx(/u4kruh 2zcjt7drn 9 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 14kl+w j.h6 gtuj 0.ydrkr56q.y.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, Antarcticapwlt /qao9(t6 lxj;/r, as shown in Fig. 4-46. The sum of xa; rl /p(w tqt9/6oljthe forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4(ng) f uh1vffo*,dhu2-47 . Determine the ratio ()1gu2 * vfn,dfo hufhof the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus kuh-4r 9ehul* shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowlhrl4*h9kueu -y 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 bw6 79)pdv ;s3gd hgyyregan, 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 (massc2cosqh x 1udxv8frrips,w,w.: (j. 5 $ 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 s ,a3* oip o64uxg:flzcontact with each other, as shown in Fig. 4-51. A force sa6x: oilu,o4g*fp3z$\overrightarrow{\mathbf{F}}$ 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 gr5vt 1 5(1kuodnmgvf3e/axzb) ound, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration 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 theu ob1m5et/3k)zg v1 5x a(dvfn pulley.]   

Suppose two boxes onhvix r0t*x;b g8hr1g2 a frictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each et8*0 i rgb 1hrx2g;vhxnd 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 kifj0:o met)2co netic friction 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 req r.zr8l50t+ 2b8wcujkmiz2 c -hx9prtf9 tk u+uired 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 standiomleqv) kt99-95du 8hy4i otlng on a train accelerating at 0.20g. What minimum coeftem4v5i l9)9 o-q9otdh8ly kuficient of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergonym a:- (tx/mmq(ie( cetdcgp-47 j* p if the coefficient of static e(gqc mjptxp-(im*4 nc7y:-/ t(e mad friction between the tires and the ground is 0.80?   

  The coefficient of s;p3lt87 iv5zjcac ,kl+ri-wd tatic friction between hard rubber and normal street pavement isi7kwc v +dlj -izlt a5p8,;r3c 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 d6s1yx8 4 +cu: 5)ro*j0jqsuhuky p am -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a b5gi-n3ioe klezs hl2.3*o/ wrough 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 0mma44yn3deqof8b7c an asphalt surface have a very high coefficient of static frictc4eyqbo8mmafd3 70 n4ion.

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 kineticgmh3k+lnxgj j8 j )q)4x;fb j, friction 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 to qr11 u;hyg 0nnhave to prevent any moti ny;hq 11ru0gnon from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across theuo wwz7he1-sjh*8e-flcl1 * n floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 *ow ehh7elz11*l8 jsc u-nfw-$\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , alj2qhvo z3 87vj 8e(wsre in contact and at rest on a horizontals78 olzqjv 32e8vhw(j surface (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 cratewn*. ef( xyl8x. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driverwyexx lf8*(n. can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has an 5rrwrqjj(gu8 lg6 u;(incline of lr qgu6wr5;g r (jju8(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 fmq4h x6.d3pr)u2ng f 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a ptztsp7oofw duedt.26l*k, 07lane 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 imga3dg9z: rc;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 stee9we.nb0oh x: ppest 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 2(wor inx )zk5in place against a rough wall by someone pushing on it with a force directe wx(kzi5n2 or)d 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 projectilest0d *pq42yhd e as they melt. Consider a chunk of snowdt2*eh40 pydq 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 travelint 1o,a,.6fs mpyog *vpg at speed v is equal to1app y.vtfog ,o *6m,s $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 days i 2jvz27-:eszawv 4shboard of a car slides forward on the dash when the driver decelers2 -4zvve2w y:zi js7aates 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 in cyj 8 eo1 fw)0os1nwzu(ij,a,itial 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 th,c:px;qd1ef-xhu1poj w k6 *mey are filled to the packing station1p6 *dm p : uw,1;hq-ofecxjkx 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 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 ,t3s- ub 1ppgm go.r;aof 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 (2g d4,vkoua jpx )/ey6including the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplifv+ ( sbxdn6cs8ied model of a mammalian heart, at each pulse approximately 20 g of blood is accelerac8sdv (+xnb6 sted 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 automobilpn.bi6v*i vfdm/xa614.pscre crash if the deceleration is no more than 30p v sncr. id1 xmv*4/ia.6fb6p " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an ear(2b ,ig sglfp 5c3tyl*thquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction *yb23sgg ptilcf ,(l5 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 invot-4z30yio3uyy g2ss d lving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estid 03zg2 tsyi sy-yo3u4mate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hdyw1xi3 5 e51crd7fogill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches d ec 573ox dr15iyg1wfthe 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 tqs/ng qpx3d2m60qx/ jhe top of the Leaning Tower of Pisa and falls 55 m before reaching the groundn/ dq/px6q 2j0qgm3sx 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 snk, i ce8klb4prbv48u s(;q6ytretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if p kbs,68 4q8v4k e;ybclnr u(ithe mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of aaps1-ch j6qn -f)s )f,1lmj h51exudr 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 hn eu- j6-) flda,shmqfp)r151jxc s1hills 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 experiments szx3d+.t nkp-y 228snpqvf-l, dangles her watch from a thin piece of string while the jetl +s sdfl8p2pxty3kn2zv--. qniner she 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 gk,dtwz;gyep* k w6,4 are to be several ramps connecting different partdy g kp wt6*z,ek4,g;ws 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 Fjpg/41xgm q5 e 4:z )ey,xwzsd is needed to lift the piano (mass M ) using the pulley apparatus showmszw5 xyg4/:j de4q)1,pxe gz n 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 acce+g5j r 0 zz;xmihcy.,rlerating 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 chainzwaf4t -44-1prtxnk 6 i7hsgr, an engineer considers the followinwfz4n4-k4g1ap-i h 7 6tnsxtr g 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 669hh1 i*9yvaw i0 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of w*e0x 0mb-p lksimilar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recomme*wm0 -0eb xklpnded 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 " 10q*zkxx6opfw--bsx9q .tu3z, -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 allon9.)n wghavd9wed 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 quywkie* m,e01 ea+/broped together are ascending an ice field inclined at + /0e*u myqkwa,iebe121.0$^{\circ}$ 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.