Why does a child in a wagon seem to fall backward when you give the wagon a shjkd/ :nf2x 6sejn:2yd arp pull for:s d2:ye6xnf2jk jd n/ward?

A box rests on the (frictionless) bed of a truck. The truck driver startspmu 9g ;n7f)p,hn) g,wtiwc.s the truck and accelerates forward. The boxtw9mngup7, ) hwp g)ncsi;., f 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 Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object isehl7e82 um.bj zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can it ediew x(*0t8v6es a k*( spsjw5, 5oekhj v5s*es,e(id*t(e68xwwk0s op a5 e kave zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up.h-ccdiq 6, w:z (a) Is a force needed to make itz, :qh ci6-cwd bounce back up? (b) If so, what exerts the force?

If you walk along a log floating o70sr: xobl2 lab5gig0*r k oi;n a lake, why does the log move in the opposite r*a5x7kbii 2 g0o;0llr:bgo sdirection?

Why might your foot hurt if yo6r:0h xdwgf9v kg. tbjub)2dbd.6 wj 7u kick a heavy desk or a wall?

  When you are running and wanr2aa it+gdfx5/.q1c bu ) arw+t 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 running at top speed to come to rest. xwra/5c+)i+t2qf gb a uda.r1   m/s$^2$

A stone hangs by a fine thread from the ceiling, and a ru, )2oq.de.jdktb l 5y/ip b7lyw.:ksection of the same thread dangles from the bottom of the stone (Fig. 4–36). If a pe )t .kb,i2j kp /l.q od5.bwly:rdeyu7rson 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 ( ,oa;uf i 8+iaz2ydiegreat as that on a 1-kg rock. Why then doesn’t the heavier rock fi+i ai(u defy, zao8;2all faster?

Would a spring scale carried to the Moon give accurate results if1tli p aqsp:k4lv i3j9dl ,2h, the scale had been calibrated (a) in pounds, or (b) ,sp:jqpvd4 ali3hl9, lik1t 2 in kilograms?

You pull a box with a constant fob,za6 o+ kd)6:ectrkjrce across a frictionless table using an attached rope held htrb c:,jd 6+)kko6e azorizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of77kljs o)iha/k r 6.g.pfcx/ m gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the obj/i s. r c7/lp7h.a6fog )xkmkject exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or forcah7(l-fp th q*e) 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 object horizontally with a given speedp(a- lt f7hhq* on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls wi7fjkp3z-coeed3 u4 gm ok1 ;/sth equal force on the other tz7 p4o31ogeumke d3k/j c;fs- eam. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of grocerisyk6b tq/ :3bces. Describe the “reaction” force (Newtonq 3 6:ykbbs/ct’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, ho)p7jgzvi g :;xw large a force does the ground exert on you? Why does:v zpj) 7;ggxin’t this force make you rise up into the air?

Whiplash sometimes results fy2 c dyk8c6,hh;k u)zzrom an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems ;hky)czc6dk uhz8,2y to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatiedbarh- 95ma 09tf o4bed truck. When the truck accelerates, the crate remains where it is on the truck, so it, ta9m4 or -h5 ed90ibfatoo, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaciu/m;/omgjlnr 3 yf.8 hes its highest point, it 3l/foj/gyrnmi. 8um;slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom sbh,q,hbwzy 97 cale read if you weighed yourself on an inclined plane? Assume the mechanism fubz, ,hq 9ywbh7nctions properly, even at an angle.

  What force is needed to ag3s f( h fvet+r82fx6cccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike andsv*-0mw a zl*e 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 accelftm1wkq4 ;wowa,z24t erate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of o02/c uae+jy:kce f ;ya $76-\mathrm{kg}$ 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 irn(isi50z; r5j 3wifa n 8.0 s if the car is travelfnir;za ij w505(3rising at 95km/h? -  

  What average force is needed to acceler qo q1/tvdtkln; -tl20ate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alonkvt1d -nltqqo;2/ t l0g the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration ofn54ag *c m+u10q7l,jng aghoe 2.+ 1j h0ug,gcgaaneql5 4m7*on5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 -kwjm d2l) h2rcover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that zms0rp.+ kq x-the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor sqpz0 s.m +xk-rhould exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale pkzh0u1 : reg,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 direction of acceleration. ,p 1g0hrzke: u    ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum jx,,(pvds ;0k9c iqbpstrength of 21,750 N. What maximum upward acs ,;cip(09jdxvpqbk ,celeration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration o0: reqd5 qqg*rf two falling sky divers (mass 132 kg including parachute) where q*d5r0qq g:n the upward force 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 jhvj/y7um1kzh)ifs 9-z 1n rwc.4 l9xa house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of vsun)jh yl9jx czz4/1mh i 1f9-r7w k.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 th(c;3a sth,yp/s r1la ve 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 the3 p,s;c rysla(/avth1 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 diag 5rjwjvk7c*fi,mj fpdn9 oryd;1z .: -ram 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 (a) at the moment it is hit 3m*xe jc *k:shh6 0jw+hgow.pby the bat, and again (b) after it haok mhjp 0w*: +sjxc6.gwhe3h*s left the bat and is flying toward the outfield.

A 650-N force acts in a northwest +pg84x4) revgi2wybb erly direction. A second 650-N force must be exerted in what direction so that wbv iey2+)rpg44x 8bgthe resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontaloq( gh,(9fh5yyzww(e ly between two buildings 10.0 m apart. The sag in the rope when she is 9hqgw(zfy h5, e((woyat 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 corcr;(m 4h y.mkpd 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. lcpvekq9w;g /j-vd 8(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 McMu0z7mxw.g-78wcc vl vlrdo Base, Antarctica, as shown in Fi0wvz7.x-gv cc lwml 78g. 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 k y* gqr0 nvyiz/grdhh:kh7) ync.*4; same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomo0/h;:ghh )riv k *r k qg.yzy7dn4ncy*tive 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+;bew ptoam7 flmao l08i( 9p9 the bucket-pulley apparatus shown in Fig.0 im p7owl(;ba9ml9 aeop +8ft 4-48. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race;u81 xfkd*h (m:psgs g began, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (masbkl y:qp21 2sls $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with each otheeitm n r3),-cdr, as shown iit,mnr-3ecd) n 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. 5e,jbvjwfp ki,cm er40jnth ;)q :87 n4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach afh n minjvc5,;w:fb jjr7 e,t4keq )p08ter the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by e*d;9)f8 br xr1 hkerka heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the eh brex*r;9k8rk) fd1cord, 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 between a 35jnr bdq nc tb)l+5-o15$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required jbs*/ )pttu9:dyile;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 accelerating bk:pm+2e hf9lat 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are nob2lhf+pk :m9et to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of static/ -s*)ab6oro z cfn, jwd9aib. frfo/,wab- s9 i .b6jcza*n)d roiction between the tires and the ground is 0.80?   

  The coefficient of sta j ;4vpo4 sde3tn/ld4:ubg)bwtic friction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you dg lvts4w4:jnb;p3 e4u)o /b dleave 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 :bqilplu* hco3 m-;z*at -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 ono)yak58o ,oc /:d f:fhxxf e9v 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 h+s)3.wfm;e)mhp zvs/-g us ysurface have a very high coefficient of stat-m+;hmey /fp)ghswzu .vs) s3ic 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 kis6v6pi-eduf/ 6a9 :y a4nf)v o+ yslvanetic 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) hodl:m 8uq/)e-5ne ) upmnavw1wr9l )f pw large a mass would box A have to have to prevent any motion from occurringq1e :f)nw) md5/-aupn8v p)we9 llru m? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far willjvu5/s ;n52 :2 fxkim dc8rhhoojv+t7 it go, given that the coefficot8v dvj522 iurm/c fkx; j+h7os5: hnient 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 in fwjgpo0o1/c8tm9 g)acontact and at rest on a horizontal surface (Fig. 4-54/cmaw01tg )pjf 98 goo). 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 - o ,e2.f34npzdaxfzicrate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decfx z z-,i23e4opdna. felerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry abouurnw 0zvs;oy 08ru+,w t parking your car in your driveway, which has an incline of yrswz8no + 00uv; w,ru 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 5px / 9v7+vq etpo2mxck1 +pmbwith a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane til tisen. fc*ldkd(905 ated 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 se5w sdgo;zespg.e ,y ,fl*j52 peed 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 reache 6mzz9y 7minsfc1 j i(dgdf)n)x;3f/ ds the top 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 plaejl7 1h9gdv9oce against a rough wall by someone pushing on it with a force directed upward at jh 97g9vdole1 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 canw9)2/ bw42xrbl*zf ro xgkz0e become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a l b e)xzr*2wrzkfwbg/ o9 420xroof 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 traveli:qnr fazkbts )3(3bdkek*( h)ng at speed f(k3nr3as kdbb k)ezt qh*) :( 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 forwarq vk0ieuj/j8xlp6a8-)pq,i q d on the dash when the driver decelerates from /8klqj i)vq60, iae-j8pux qp 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 ggqc qkp-v*s5,iven 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 packin8m/gj nj(:-h6r 8qc5kmbe s1)vcn uxv: roe3mg station 11.0 m away. The belt is initially stationary and must finish with zer3jnv / :-b:ksjc8hnee(m1mr6o5uqxvr) 8gmc o 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 of kinetic friction between 7t+ .fn2diaoj2 z )*icxc ey)k$m_{1}$ 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/j mjkcb wh sb3qn/so)gw3/7 7 (including 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 simplified mod:: 8cdguf :1ev( nbpjsel of a mammalian heart, at each pulse approximately 20 g of blood is begc:df :v u:(n81jp saccelerated 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 chancez k h.upp/m+* y8.ayjm-.afod of surviving an automobile crash if the deceleration is no more than 30 " g 's." Ck.j-.f8umma/pdyo +*ay zp. halculate 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 :azw3hycr+f*e)o(;* r eer mh produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of staa cfyeh+rh)r3 zmw ;oe:e**(rtic 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 /4d + )xo*vadxvnc7f5xxh;l can accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly camc x7)* xd +vlx5/dn4xfcvao ;he 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 hill (1-in-4 means that for each 4 m traveld:m1qdgo(xn 69 zfvj2mnt8fn .j ;q8ted along the road, the elevation change is 18.g f v8;zdt9j2o(6fm 1dntnm jqq:xn 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 lyz* f:/qtl38 3zx rwjfrom the top of the Leaning Tower of Pisa and falls 55 m before reaching the gz3ytxlqlj*z r: fw83/round with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s buqfp wria4 *1).r7dme rt enters a muddy stretch where the effective coefficient of frice mqa*1rwd rri7 p)f4.tion is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesig-pc8td vx.( hhly28tin of a hilly portion of a city. An important consideration is how2-yl8vhix c.8(tth dp steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thel-nafr u c iq1nio4:l;1*4i0b h, iyvin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string bi1lna:*iiu4f;rl oi 0v-y q4he nc1,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 vcgs tnj5)kz*a:2q/ z several ramps connecting different parts of the satns:52 kqcz z/v*g)j tore.
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 ) u yg25:;)vd ciep/q tgising the pulley ap)e 5/ic vy qgg;i2pd:tparatus shown in

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

  A jet aircraft is accelerata( d 2e,:zg5r3ula6v ytg/qiiing 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 considers the fgu1)xu0nd o-idamk41z 6li (hollowing set of cal)dh z iun 106xokgmd4i 1u-(onditions:
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 Italiaubdz hy/3. 8qjp/l4 win train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar lewmg qvuq*5) lyh f:hex-m ;y0;ngth. Karen's rope is more elastic, called a dynamic rope by climbev)heg hlqwy0mxyfu*q; :m -5;rs. 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? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 1xhw.h 85 swmi;-p0 gaj0-1 $\mathrm{~b}$ 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 buildingz(s d+1v,kvw+e 9szd c is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice fq+t iz asdg*7k1n:w 4hield inclined at4wgh:d *iza1s7t q+nk 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.