Why does a child in a wagon seem to fall backward x 01f5*(fdb ohuaw1j dwhen you give the wagon a sharp pull forwardu5(x1 jf bwof d*1adh0?

A box rests on the (frictionl qg-e uv.;3jvpx kk69wess) bed of 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 moti;qpw ve 3. jgk6-x9vkuon of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on itvxpl9f5 f5 ,ai? Explain.

Only one force acts on an object. Can theba0xa f4jgfxp3t- )/s object have zero acceleration? Can it have zero velocity? Explaftb/f sa 4g0axj-x)3 pin.

When a golf ball is dropnz,lciz,x8 *v ped to the pavement, it bounces back up. (a) Is a force needed t,in, vzlc8zx* o make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a .r x4m:y 1fdsp 8b(j6 psiaoo7lake, why does the log move in the oppositp s pb:y(o178m4j6s i.a dfxroe direction?

Why might your foot huftog:kj6 c;4 zrt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate qui8bv5wqea o rhmw:(w*5g)m/u c ckly. (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 speedea muqc/*5wwob( hvg:8wm r)5 to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, an:e.s28g 3dm) ahu:i 08(vz9ohxiwiv dm -hqdbd a section of the same thread dangles from the bottom of the 8 i3hdxi8qw:h2vdg )hmeob(.i 0uam:vds z9 -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 greegq1f+rh,h3b s/yp7 ,fx p/bvfk ey6 4at as that on a 1-kg rock. Why then dfb h, / v736gepk,yqp1r4be +f/fyhxsoesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurat. q)*zq,taxa5nw 1a(g t )xokx 1a+xgre results if the scale had been calibrated (a) in pounds, or z)xqkgnx aaa,rg a+5()qxt*1t.wx o1(b) in kilograms?

You pull a box with a constant force aca- nuex5;91bulj wf: hross 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 tae bua;:xfnjwu95hl 1-ble), 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 ncm5oo fbb hj ,.zl 5fj(,wfn0/et force mg exerted on it by the Earth. Yet by Newton’s third law the object exertsbfhjnj(b5 lc.mozfw0f ,/,o5 an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or f*: l 7 h5)j v1.bmw)c- igdx4xsixussnorce) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earthxm4:-xxgs)iwicdl*b)7jh. vs5 nu 1s . Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls o.-rziz ab7 p-t4 6coawith equal force on the other team. What, then, determinesiz7 zr at6c4oa b-po.- which team will win?

A person exerts an upward force of 40 N ,3hmawrnk *h3q/t,s* v mtni( to hold 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 it is ex3nranik *(mshh,t vm,3tw /q*erted.

When you stand still on the gaq+v/ o;yw8ps round, how large a force does the ground exert on you? Why doesn’t this force make you rise up into the aopsw /v;aqy 8+ir?

Whiplash sometimes results from an automobile accident when the victim’s car )rnemx /qgn-, is struck violently from the rear. Explain why the head of the victim seems to b, rgmq /)e-xnne thrown backward in this situation. Is it really?

A heavy crate rests on the bed o- lx ifz)p1row9gc1.ga e :ycqyd5e(8gx6m i6f 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 accelx69r5 .fcle-y c 6 )8yp(qwg1 dmexigzao1g:i erate?

A block is given a push so that it slides upvaf w5rrc8w84x5bn7 y4yl,z hst0t ob z,q8+p a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on th4nw,zw 8qc4+8p b,flz7 80 ovhy5bratyt 5xs re descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an*tkq x1d .0 d0d 8j;fbavpfi)u inclined plane? Assume the mechanism functions properly,; id)qd 00pxubaj. 8*fdt1fkv even at an angle.

  What force is needed to accelerate a child on a sled at 5*(uei 4p 7iuag x(s6pr6hcfg 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ridp9dby6;pv kj6 er 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 accelerw9l 0d0 ,9jwyffpbt8,nvbaz/ate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a v,p gz+n2/pot $76-\mathrm{kg}$ 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 isdipu8ji0j1 2z gs0k1rgp8qrpm 6e)c6 traveling at 95km/hudpggz01e8p 80 mk )2 qrpii cj16r6js? -  

  What average force is needed to accelerate a b use44ncz /kan5yz047.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the bark sy0u azzc/nneb4454 rel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelerat0nf65+zzzdtb ion of 2.55 zdtbz+ 6nf0z $\mathrm{~m} / \mathrm{s}^{2}$ 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 quqwtmqu,.n)md:(dx+ a.v 9v oiarter-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 des 479 pcn:0hary,cimh rigned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on them y a0ncr9cr:,h4ip7h supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the qf6rz9 rp 6emq5e45hbelevator 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 ofee pb rmf94rq65q 6z5h acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator /eoo5cjg qwh, 3u 98tbhas a maximum strength of 21,750 N. What maximum upward ae3uojctow/,q 8h g 5b9cceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falli fachq,j l* pwqk+q2,,r*/rgf ng sky divers (mass 132 kg including parachute) when the upward force of air resic*,f,aw*k, rqhq /grq 2j pf+lstance 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 tdf.0kj1 a6s tehe roof of a house 3.9-m high. When he strikes the ground below, he bends his knees sk.t0fse 6 a1djo 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 rope tied to the box runs verticaldl,47w ,cq b7hsh0or xly upward over a pulley axl47s ,,or0b7q dhw chnd a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball 9x n7 i2bc0u2aqv;kv gplayer
(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 rk:z 6i:jcfvetzy27( (a) at the moment it is hit by the bat, and again (b) after it has left :e c2( j7zrtfi6yzvk: the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 65nn j)vud46iq5 nweh5 70-N force must be exerted in what direction so that the resultant o5) j46vdq 7nneiw5nuhf the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high ,qok/ dr/ee 4iwire" strung horizontally between two buildings 10.0 moiek,4 q/ed/r apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless cord frv/f9zq-xt vx*00 kqns ,aa u4tom 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.-5 t 2glpzx: j(/ojp;iqrtu p.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 M meomq5 4x4)ltcMurdo Base, Antarctica, aq mxo5 t)4e4lms shown 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 pullinoq +v7i8tm;l*9j4 yjy vvge1pg two cars of the same mass behind it, Fig. 4-47 . Detepgmv;84l7tve+y y 9j1vio jq *rmine the ratio of 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 show zkaw nbal uq651l1(*lla* hihv) l)j5n in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at jn)a1avl65)qki 1bhu(l lh**law 5 lzconstant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 6xgz63m)8 nfsb3+qo9 lpsa9gwsk fg /75$-\mathrm{kg}$ 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 blvew03t+ d 8jtvock (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 horiz.2kl:amr3 k heeoio3( ontal surface are in contact with each other, as show o2(kh3or 3ak:lme. ien in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each inozdf9f 0a2;rxo50 w2wxbhg, bitially 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 after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity ata2b2d o ,;hfxr f0gxoz059wbw the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on ap 4o s,9dhnh va/y42va frictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each env,h9 dhsaov/4y4 pan 2d 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 friction between au-fw368hfamj 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 required to stadt v0l yp2/7jcn5q h7urt 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 stand53.lpk od**n47kmsich .v 7kmt lrpv6ing on a train accelerating at 0.20g. What minimum coefficient of static friction must exikt p dr4*vm7im 7.k6hvpoln3*. lcs5kst between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can underbfu:9*e)tx+i j 9 bwblgo if the coefficient of static friction between the tires and the ground is 0.)i:b9xwfb +j *9b eult80?   

  The coefficient of stati. 2ls2 z8ttbvic friction between hard rubber and normal street pavement is about 0 tbl. tiv82sz2.8. 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 -lgt;x716s( hp5q q0n a,glv o)6g rfiu4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 restr g2nn gxtk6jv12e1d + 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 contact8tb,w0mz;,f gaf7yj b with an asphalt surface have a very high coefficient of static fjfb m,0g,8w ;fy7ztbariction.

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 for a l2vo l0da018h gc t1il$ 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 mass8smo,6/xj tmz+/kwds dfr1k 9 would box A have to have to prevent any motion from occurring? 6dj8/ r1mozf / w,dkxk9mss+t Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push soe h. o i(i.k-ear8i*zh that it slides across the floor. How far will it go, given that the coefficient of kinetic friction i*i k8eohiizr .-a(he.s 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg syn(f 8imxe3, and 110 kg , are in contact and at rest on a horizontal sx meysfn8,i(3urface (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 coeffcya:b8hsp1c ;;otycnc 3j)h91,lam kicient of static friction between the crate and the bed of the t j8nk; :cc31b,)hpccatyl;a1om hy9sruck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parkingiw:cvel u88j7on pyb6ygm80x )ph)6l your car in your driveway, which has an incline of 12ub c)8 hg)nwlv6p:8l y 80jpyme6io7x $^{\circ}$ . 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 slin:g f22uk vyzivza.x a8 )bb62de with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at *ttj .jp1kx( san 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 speed of 3;)fo: z ya7e+q u6lgqxc ,--0yg ejumb.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 ;c( ec6ilene:viu /sf;l(j 9kthe steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing on it wtf10y.:2or xybee ax +ith a force dirxf y:ta+ e01y 2roe.bxected 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 d.- za 29ritp-tpiv,xg angerous projectiles as they melt. Consider a chunk of snow at tgrpz9x-pv ti a ,2t-.ihe 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 travel8 l qyrr7:pd-aing at speed v is eqap r r7dq8-l:yual 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 whgn71r. rpcr t3l:j3y g5p4w wif0qkc 2en the driver deceleratescrlg j01 rwtpf 3y5kwg2.3 q p:7rnci4 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 dk-q z(-4jvqp 5b :jwfinitial 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 pacv 9 cd/cuq/z(nu)1a stves20e king 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 es9v/2 cu0sn1 evutac)dqz /( 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:j l ;ldt78oso of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) ca/a4bee.d+yv3i g7ffln nd t: ,n 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 mammahwa8p i- 6cjlk f;y5vnn *hj12lian heart, at each pulse approximately 20 g of blood is ac y p;hflh1j5nn8 6jik2*wac- vcelerated 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 automobile c e9dcf)vcznlbi( 4l;7 rash if the deceleration is no mzdi 4vfc9 )n(7llb;ecore than 30 " 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 braekuxgur,b)-tg; t+tb* y0vuv)1 (a y an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static frictioart 0 ubb -1t()au; ,ke+)vgtx*uyrgvn 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 ina,,f/hb+zlrzv q, u 7hvolving 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 p lr+hhazuv,z 7qb/, ,favement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling dowg0r0zg p) 3o6rr zo,tpn a 1-in-4 hill (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 the bottom after travelin) ogpzrortz30r g,p 60g 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dr4 fn ha8a x +yah2 mtvpy3s:rqrm5:l8)opped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the f+rmya 8q ltmsrhpnyx3) a5 :v8a42h:ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but ente 2sshp3es l/)vrs a muddy stretch where the effective coefficient of fs sl3s)2 h/evpriction 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 tly*02 b vh6cecykg:( v2svf 5zhe redesign of a hilly portion of a city. An important conside0*cy2bv6gv:2v(yz5kf l eh scration is how 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 thin piesj.w2uw 1s4g gy 2sx(0hr3uxvce of string while the jetliner she is in ssy r0uwg 2x2xws 1gv.j3(h4u takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be several ramps connecting difgxq kj t8 as16+6eo.seferent pae6eotq81sxj.+ sk 6garts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using the pmlk+vs0l tk(6oz cz4 (ul z+mkllsz ko(6v 4c(t0ley apparatus 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 acceleratin g)kkw2 fh9uz1g 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 consqdsl nv6mlymd9y)/6 1iders the following setmv66ydyl9d1/sm nq)l 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 t oq a7owuj)l3-rain 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 length. i.kaph .usat 5sz r)c 2him93)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 .3zac9ss5h2ki)uh a )p.mr it, 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 usi3f i 0bz,*)ugnlf ai.ing 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 is allowed to reach a maximum speed ofj(z cnmo:vn* )1 kwxy3 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 a azmj73-:eaxure ascending an ice field inclined a:m3xu7- eajza t 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.