Why does a child in a wagon seem to fall backward when you give the wagon a sh8(p2 oz vtauwdl.9 0ffarpfoz90l8fd2t va.u(wp pull forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts the tr62jaog/o/ .dpq (w wzf o 72tqwo7.vnkuck 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 Mary standf7(7nw .oq2og//qwa6z2 pv otwo djk. ing 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 n wm6onma13kmcxs45. g .hhj4 oo forces acting on it? Explain.

Only one force acts on an obje07 i idnd.alc;ct. Can the object have zero acceleration? Can it hdacn.d 70;l iiave zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) nj/ pch1;bx, 0lxbdg/Is a force needed to make it bounce back up? (b) If so, what exertxl ; p0 d/bnh1gcbjx,/s the force?

If you walk along a log floating on a lake, why does the log move in the opsn 7bojz; jwh07n-hu3fd*)d qposite directio73b -h sznf)w*o;du7qj nd0jh n?

Why might your foot hurt if you kick a heavy desk or a w1/glp r m:q u2s i8ybn4*xikhx5uno48all?

  When you are running and want to stop quickly, you must decelerate quikhc7,jaescp 9w 3ssaf0f-keo.3 cx .,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 aa f,9..s ho-scx3cwcee 03js pak7 ,fk person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of tyidu-4 bw; 0mnsb, 1mvf:dz*lhe same thread dangles from0-uy,1i*wdvmfb :zb l4 mnd; s the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice ashq(c/h82it z15 8 og m(tczflg great as that on a 1-kg rock. Why then doesn’t the he82 ozg1 /((zfhc58hiltgcqmt avier rock fall faster?

Would a spring scale carried to the Moon give accu)hyj yjz5z zt8z9 pl..rate results if the scale had been calibratezt.pj y 9 .8zzj5hzy)ld (a) in pounds, or (b) in kilograms?

You pull a box with a q:0 b4bw s5mjeconstant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an a e0qwbj45s:mb ngle 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 fallsjv1kn2 u2 6 pc:(imnap freely under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite u(2 k1 ap6pn:jc2 nvimforce on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needeffhdgs * 3qkt nivh;7bz6 ;uw..vx3 (wd to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth.bwvxt; szuhh*g.kq;( w.i6 v3ffn3d 7 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, e3. u wyrjt6ui;ach team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What,ui3y j;r.6uwt then, determines which team will win?

A person exerts an upward forcx 4cwce ;hi/q3*1x pf)y/e1t dixj .yte of 40 N to hold a bag of groceries. Describe the “reaction” for;yxt dy1cf e)jph3tix1/ *x ci/.qe4 wce (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the groundl9 l1.bbicjb(x8 wdj 0 exert on you? Why doesn’t this force make you rise up inj9ibbc(01.8 wx ljl dbto the air?

Whiplash sometimes ree 5r :qmtd;gd(:7rjq+cnw c) esults from an automobile accident when the victim’s car is st+mc ) dn w q:jt(d57ce;e:rrgqruck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truckunlo 5 1y40nfd accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes fnony l1d 05u4the crate to accelerate?

A block is given a push so that it slide664 t 3 y*iq8vmyuxtbjs up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less oniytj63uq*yb 6t4m8x v the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yogzj0hqa:0 7c bxsmbx:owr - 3,urself on an inclined plane? Assume the mechanism functions propc hq-smb:abz :j7 w03x,o x0rgerly, even at an angle.

  What force is needed to accelerate a child on a sled atm04c nf8tc)7,x )w*va vstexf 1.25m/s$^2$?   

  A net force of 265 N accelerates a4w lhvx*5 hsy2 bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a od1ni aogg-vxd+)kw84(q a0f:xz, mv 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ofhjf1;unc3um1 )ev t(o 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 any79l,-h tzlned4:dp u 1100-kg car in 8.0 s if the car is travelned7l49hd zu:pyt, l -ing at 95km/h? -  

  What average force is needed to accelerate a 7.00-gra0v;yip hpo ,m2tl( *,vowhcw2m pellet from rest to 125m/s over a hpw( 0 whi * cpm;o2vto,l,2vydistance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish verticalltznp7*ap j4mav x 6fy*u:3wt1y out of the water with an acceleration of 2.5 4pa6uv1p7 *xta :jf 3* wntzmy$\mathrm{~m} / \mathrm{s}^{2}$ 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.xba*5 czngp : 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 the maxim /5qd3lt af nl58rdks1um acceleration is 0.0680 g . What are the maximum and minimum forces the motor shoul rn t5d/8dq5l1f3sakld 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 in a motionless elevator. When thev..5n d22t4 yw*utf.u, bj blg23jrrpeo .axy 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 acceleratioubatgn fr v.y.*er.yplwx53t.,2 j 2d2j 4bo un.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a ;0vcd kblwt e8ky,t+1maximum strength of 21,750 N. What maximum updt; ,0lkk1bcyvw e t8+ward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falliqy*u h: 7a azmkf7c79nng sky divers (mass 132 kg including parachute)f 7z:ankm 7q9ua*7ych when 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 a house 3.9-m high. When he sjlohq1 za)00). j11 u4n-nnnoshbz hstrikes the ground below, he bends his knees so that his torso deceleratjzn )njonl0s14hho1n ua-0s.q)h1z bes 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/2gx-k7nvedoliv bjd . 4 uspo5 (d1p) vertically upward e4d d xnjb /v25-7(kip su.pv)d1ol goover a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the 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 player hj.nkhcxx+d,zei/8/*h qm , u
(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 mbrbn,f:goh0 mi3 d t n(p5us8+oment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfitprn(nidm:o3g 5 bhu8sb0 +f ,eld.

A 650-N force acts in a northwesterly direction. A second 650-N fo:nlkq7cmy, w+nrm(x ( rce must be exerted in what direction so that the (y m,ql7r (nwxc:mk+n resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk acrosqzjw11; ll 1q ,rhro:se( qi0ss a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10.0(1ls0i ,qsh ew1z q j;1rroq:l$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from another 3.2 x ,cvut:1(zuesvg /h-5 cyd/2fcm*e j$-\mathrm{kg}$ 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 14cj ;c7 q.r,qnorsomld09/ 2 *4jtj xob.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 housd4q8j i20b 4gwxfn(w ring unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4- 28gndw04 jrifwxb( q446. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behingu3 y2kq t2z:wv6 tc ug0w7h,vd it, Fig. 4-47 . Determine the ratio of the tension in the coupling betwee2u 2uctzww3 hyvkv7,qg tg:60n 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-pulmiw7z50skxogt( c3z : ley apparatus shown in Fig. 4-48. (a) How hard must she puzzs gtk:im0(7xw5 co3ll 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 -d esf:obl i(z)+qz(pbegan, 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 (massw34fu nccw03j $ 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 withlbq.h p;vah4 (sm3u9:5 e bede each other, as4vlmee ;bh ub :.e(sa35qph9 d shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above tnw oue43rkov)/wzz89k r6-p b he ground, and the massless frictionless pulley is 4.8 m vo9 ur-6ezw 83z/k4n)rob pwkabove 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 the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cor7 ua2s 4dvuzn5 v+try2d of mass 1.0 kg t4sd+n2 ua2v5y7zu rv. Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of 7sx8wt7 hpn w8kinetic 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 required to stq .)gfv2o z8jdgjm85 /f p d-khsk)up8art 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 sjb5 uj,vc2ct-tanding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are n ,jbj -c5uvct2ot to slide?   

  What is the maximum acceleration a car can und-4vp0anh+ ,(awdpg oeva-h0 c ergo if the coefficient of static friction between00dne ha vg-caop4wp+a(v-h, the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber an- s(chstg-: y zis+kr84c1iu ad normal street pavement is about 0.8. On how steep a hill (maximum angle) (c:8-st- kg+ihss1iy c4u za rcan 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 deceleratefmcj32u .oowl(xr .66:m fjx c 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 on a rough 3d;v f2 o rcyt9x*33 8ka8hekhq0$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coefficient ub8 mgeo5ag 3gf7lb:( of static fric gl8a3eg(g57 bf :bmoution.

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 fo)l.qe q5c oe3/tvi:jbr 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 fjzjqp.g 6qc4j0 :pgu.6a/ isdfka5 7mass would box A have to have to prevent any motion from occurring/6i6qp :40af7d jf cgqkg5. z.jujspa? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far willu 5uw8d6lslyhf5m3 3 b it go, given that td 5y35 hf8ubl63m uwslhe coefficient 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 contact and at rest on a how,ht t8c.oapk9 7ib,erizontal surfaha8,9kwt.i cepto, b7 ce (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 heav-rru5v9y t .f1wce*l(ti3b7l imnt(sy crate. 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 decelerati*ve3wb(-19lrs(cy u7t 5r mi.flt nte 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 i nxs( :pym::zpncline of : nz:yx(pp:m s 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 d3e g+xc6 h3hgs 6c(wwge/i7j a slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in q r.1lbzo -o6lFig. 4-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initiabvasscz5) d 6/v-4xpol speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speedj64l4v wrvh ,h 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 somey/mz9sd c7x s,6 8uqylone pushing on it with a force dir/msxydusyzql 8c, 697 ected 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 7nwti c-2tm*v+l. i:hl n u5gudangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pm+ hi2-7gvu inn*utlc wl.5:t itch 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 fz;apjha :wy;q qi*: i-or an automobile traveling at speed v is equal to iw *;p z-qyiaqaj;:h:$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 da)2aq 9rkwz7juif ys60shboard of a car slides forward on the dash when the driver decelerates aki zwf q0j 2rs9uy6)7from 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 m7rfx gvck m7/v8+4g2y: mda bc up(8cinitial 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 beex4ae .hz6j n0:t2qu :y 6ejba 9g7iublt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the h :bij7jtz0xqa eu2yen a64u. bg 9e6: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 frictio:nav o,c*mwnyw4bp6 +sn w 84mn 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) can coast down 0k 5yf1tt3bji a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approximatel9tl hw-*+zv 3qzlxt-9poobh9y 20 g of blood is accelerated from 0.29+olvt -o-3z9 qh*tp9z lwbh x5 $\mathrm{~m} / \mathrm{s}$ 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 k vff au-b7fib149 gic)j 55rd)ic6 geof surviving an automobile crash if the deceleration ikc1 fg6e) 59dr bfgv4af7icj5 ib)-uis no more 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 bwb9v2jo7b oztq5 f3 s)y an earthquake is a , and if an object is going to "hold its place" on the ground, sho2jftwoqo9z )vs75bb 3 w that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accident involving two cars, mwju*4)p12 h wmprwd. /spnq- teasure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic frictio1m/)-sprd2p 4 w qhjp.utwwn*n 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 ttusf-h 2q*zipj/js.k vmk,r-e(s,q5f) h5a i hat for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches th) *puhezhs(k,-jqi vs /i .mkf f5qrt-aj2 5s,e bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pid6;5/u pkrbf isa and falls 55 m before reaching the ground witbu6fki/;p r5dh a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed jl;y2tr8g35 qr fs3rm of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Willq;f38jm3r5sg 2l rtry 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 wor76/y) ;0cdwxo paji eaking on the redesign of a 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 hills without s6c odwyj0)ai7e/pa x;lowing 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,ta4e+vr/plp:, ozgpmll2vp(2 o9 0d t dangles her watch from a thin piece of string while the jetliner she is in takes off ft gv2vp:l2 +( oopde9, z04palm p/tlrrom 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 diff+;n3mhubdx5zk i5y8w erent parts of th; y 8dhnmw5k5iubz +3xe 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 1d 0p:k pjkxnpl; uk8:the pulley au:lp; jdk :x1pknkp80pparatus 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 accelerating at 3.5 j:)a, r pf1(mi udbia/$\mathrm{~m} / \mathrm{s}^{2}$ 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 38m -jdo vg1fdjbw+3x engineer considers the following set of c+-dx3j3omd1g bf jvw8 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 Italian train has awqq9t-( k3 az2wat n2dcu5k5e 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 sr5qko6 u/ lbdp8vs*s .afety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the q6o8l *psdk/5vsb .urrope 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 usinu,2/fmxx( kq h/ j4qszg 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 spe*, of9p0doji. svggp/ed 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 u vm*tdh;ru5)are roped together are ascending an ice field inclined at ;tdh 5rmu)v* u 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.