Why does a child in a wagon snp q4cvz s9p*gzyf4;4eem to fall backward when you give the wagon a sharp pull forwan;pg9*pf q4y v4zz4scrd?

A box rests on the (frictionless) bed of a truck. The truck driver starts thp:f nytv5f: v rcai;(8ltt sbup36o *7e truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’t f :piv5s7toan p*lrbu t3f68(cv;:y 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 c o,5 tqk+s-bmzero, are no forces acting on it? Explain.

Only one force acts on t4i.d-fgv c.l1b(wgc/ozz(m wy6y.han object. Can the object have zero acceleration? Can it have zero vel.g(ch. w1l 4vtbgio 6f( my/dcyzz-w .ocity? Explain.

When a golf ball is dropped to the pavement, cjti;h b-evd5jb :4)g +zrfl+it bounces back up. (a) Is a force lj5bt+zh ; j+gvfr-b ic)ed:4needed to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log5al jk:jd43)f,3 lxq)yyvdj jibb)g m; ( 4hee floating on a lake, why does the log move in the opposite direct ,jek35jhlmjyy )4eaddj f3x)gqv)(4i; bbl :ion?

Why might your foot hurt if youj6 iz w:(n;tt)ddr aa6dxae06 kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate 5,f. aewq r0cequickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of5wq ec.0r,aef deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine threan x*5q.2hqtc 8.ppt fepom*-id from the ceiling, and a section of the same thread daneqc* ph.8o fm5x. pi2q-tnp t*gles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as t+ *x 8m/4n4 p) t5cva jn3rnynia7r hnhh6,nwshat on a 1-kg rock. Why th,xpih4an 5nc*hw/+s n6ajhmyv r4 3nr8nt )n7en doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scalen(tfjg12c2ru ff5*uea (80h zzin )d p had been calibc2 )gj8zpzih5 au nrnt(( 2f10f*efu drated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using annx6pnq 8 ni3,i attached rope held horizontally. If you now pu ip6,xnn38 iqnll 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 oanj;z(y +q d1under the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s z+qa;jnoy 1 d(third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object w(s(ast1ja 0xlia: o*jhen you are on the Moon with the force needed to lift it on Earth. Compso:j(*ij1a xst(l a0a are the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s thirjs-p w53dxc b3d law, each team in a tug of war (Fig. 4–37) pulls with equal force oc-p3j 5x3d sbwn the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describtow5n+e 8 vst81q yqa-e the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what ov1+stt8y-5o ea8 qnwqbject it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force do6(fe840v:c d hqpj uobes the ground exert on you? Why doesn’t jovqu68(h4 fedpbc 0:this force make you rise up into the air?

Whiplash sometimes results from an automobile accide31hdsau8r xm /nt when the victim’s car is sts83a1mrdxhu /ruck 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 truqw;c7ai.+.zuu8rb ue ck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force ca;uwc.ur.a i7zqueb8+uses the crate to accelerate?

A block is given a push so that it slides up a ramp-ry k6 r ysrum1x-3ed/. After the block reaches its highest point, it slides back down but the magnitude of its acceleration dyrmx3/kr y-s ure-16is less on the descent than on the ascent. Why?

What would your bathroomg9( yrvx 8k xs*lf ()ikhsqc2. scale read if you weighed yourself on an inclined plane? Assume the mechan(vgf sshk x.y)2ckr l8(i xq9*ism functions properly, even at an angle.

  What force is needed to accelerate ahcu12 vq:zg,y child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike ae82nzs 8 /vae 1kathwss q yoz)4k3m-:nd rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension mus5hyrmsjol 7 zu;(l q;40ec;p /prkfs.t a rope withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of amae 4p(q,6f 1hac: jzg $76-\mathrm{kg}$ 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 ca:u,w+zqb* vb9cl .pha1k *u hrr in 8.0 s if the car is travelihv wl*:b,qr1ah*uu cz+kbp9.ng at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pelleq*j- uq7uwl s/kb p;j.t from rest to 125m/s over a distance of 0.800 m alo;ljj-bqksq7w*u /.up ng the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accer rk,vpp +on(-+iw 8vbleration of 2.5 bv+(r+rpnv,o -kwp8i$\mathrm{~m} / \mathrm{s}^{2}$ 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 p,xul33 x2dl9gzhd2sui ;j6e 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 ) s-d nztt6v6m5 is to be designed so that the maximum acceleration is 0.0680 gn6t vs6 zd-t5m . What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom3emwa o2e- 6*o bxobv9a xu;g0 scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s reog3ve abuo 0ew6a*o -xbm;92 xgular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,75xmr )o/)dngr/ r.6wk r0 N. What maximum upward acceleration cankdr r) )o/rnxw6/gm r. it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky diverp679oh ( 26vwxcevd hl we5cb 1w5+slbs (mass 132 kg including parachute) when the upward v6x(b2lwlv6e cwhd9 wp55 +s hbco1e7 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 cayu.8feo1( i4n i2bb 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance bbo.ii24(a8uy ec 1f nof 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 vert12 xk,u c28h o:vpsj++f kepmp7)qi zbically 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 the weight hanging on the other side of the pulley ++bqvp2,)zp78okfxp2c uijm :1hsek weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basmase+w4)27pbked b cg r i m2v5nw9;k.ketball 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 by the ba+c (n2 pzdo/sht, and again (b) after it has left the bat and is flying tzdc/h(n2 s po+oward the outfield.

A 650-N force acts ixpm7 kbllh s(orgd,3 s -s-7h+hv* n2xn a northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of t2dnglsrk, (7obp*s3 sv mx--l hh7x +hhe two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between t b-qi8bz2w )q+uqnz;y wo buildings 10.0 m apart. The sag in the rope when she is at the midpointbqbz 8-y qz +i;q)2nuw 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 i+sijht8xr cf *os 38x)s hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.0p* o psj:paricdf x8,ph* +8o .uau.gfnfu.-6$-\mathrm{kg}$ 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 kp 2y:x 3s fy0+binne,to a new location at McMurdo Base, Antarctica, as shown in 0snf pbne:+,y3x2ik y Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. o +72d l(bj4ok4zch -isr7 +ecpq*ymd4-47 . Determine the ratio of the teql oo+ j4d ci2-h+*4skr7p c(d meb7yznsion 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 b(z)k ;jnj *ce-zyij xbp0s79aucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at consta 0( jz)z;bnjkaj7 spi- 9x*cyent 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 begana)6 rf4n glo+l, 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 (m9asur km 5oh88ass $ 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 arehjj)1ymm ( efs1 g9-;(ara oyp in contact with each other, as show ;r9 )y gjm(y phj1(o-1meaasfn 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 :/ ozwpj6yw*vlj2 *m szl j9u2each 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 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. Thi 2w m2*ol wlpjv/*6uys9 :jzzjs is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heaz0u k42cpyy 8mvy cord of mass 1.0 kg . Calculate th cum0 py8ky24ze 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 kinetic friction betwe38vb;p zjmn 4.t k s4zbn.e;vf61lnbnen 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 requwz89w yjlg, t(jyq h0qi)1e(qired 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 traidjyi:; u77 xsyn accelerating at 0.20g. What minimum coefficient of static friction must exist betweu7dy7:xj;iy sen your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can uno7jxz ,q m*9rz g(7wkmdergo if the coefficient of static friction betrq wo79(g ,xkzmmj7z* ween the tires and the ground is 0.80?   

  The coefficient of static friction between hard p engua 0.b1r cmzt r*9phcx(g*w0*n*rubber and normal street pavement is about 0.8. On how steep a a. 0b9hm*zgegnnrp*t(c 0c1rw x*up* 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 3y(e:h 9a t;fnjqb3lyat -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 retjvnbmy 3+l :6st on a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a kw69rn (qjk0 wvery high coefficient rnq kw9k6( jw0of static friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic frictbzo 12c.xoqv2 ion for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box A ha95mhw/auv k6y. s77ai(s*wkzbnw4 e ave to have to prevent any motion from occurring? Assumw7nzaw6 *ek5m b94aiyu 7. hks(vsaw/e $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, gig3:3y2bv ycsysae2t8ven that the coefficient of kinetic friction is 0.20 and the push imp3esv:ytg ac83yy2b2 s arts 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.zzfj9zmfck7v5 7f ,:gk/ oju a horizontal surface (Figgz57, kj7.fvczf9 kzj of/um:. 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,:wl a)o utw9zdvfk l( kd9r;5 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 cano5d9,dw :(w vz9t;lura)kl fk decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which h;agc3-q): ha(zbfwh has an inc3w agazhf:b q)-h(; chline of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a g i ;ogutvbci7 )0j;,j i u,gty/rzz7y;2/ing 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. /ojv+*sjc va)a6e9 r1i 0vu dn4-55 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 initial spr h.yb(c7lw-geed 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 speed of/ik 8 gy:,v- jfxc4,b,o4vmwnk taxkd 52ea( n 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 wr*:q l*c2 j: .wqjog35kg r i/htl-rzin place against a rough wall by someone pushing on it with a force directed upr r :kz*q/rh-oc53wq*lg.g : lwtijj2ward 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 roofq7 ars6ntp6vlhc 4f1 .s can become dangerous projectiles as they melt. Consider a chunk of sqn.flva47 h6s t 1rcp6now at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling at h+hci+qq(vc3 speed v h+q3c+c(iv hq 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 oz.u , vrn 4i/,1mcok7j jt5gnof a car slides forward on the dash when the driver decelerates fronjz1jg.omcn, 4ivr,ku5/7 tom 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 mas dcl gg6f4a ufjx5228fs m is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are filled to the packing stn yk -ifxrc9872lgha60 .fwqtation 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 t 0xinfrkhw8la.f6q t y7c 29g-he 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 7kp +l vs*x)6mkizvo 7 $m_{1}$ 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 fr tc,z,mwdmtd(,(;v 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 mammavk+*9rv tq*h xlian heart, at each pulse approximately 20 g of blood is accelerated from 9hk*r+ q*vt xv0.25 $\mathrm{~m} / \mathrm{s}$ 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 reasonatp .g*xa y+ia , :rn+p xekanc (erb3,h:2pri5ble chance of surviving an automobile crash if the deceleration ir+p,c a+y(exxb5na *iaprigr ,k. 2n peh3:t:s 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 accel.rj0gbe 0a,l als 0(x fkilal .y,4vz*eration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be 0eiz .l yla bgsaj f,xl.*va(0lr 4k0,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, eqaf9orld)5s x 6n4bq3xamining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial spex s or6q5qfb4a)d 3ln9ed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-cqnvql045)myn l)0 ha4 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 boyln h qlv)qa4 500nmc)ttom 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 T/)xgd 9w y6mbl;hi( rkower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistance? xgmkl) y6 9(hwr/ibd;   

  A cyclist is coasting a ;mbzr2 a ee6yj68cu5c4 swcj3t a steady speed of 12m/s but enters a muddy stretch where the effective coefficie6ec6ybc4u2jmrs;j 3w5 8eacznt of friction 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 redesign of a hilly portion of a ir.9 tv;e v:vmcity. An important consideration is how steep the roads can be so that even low-powered cars can get up the hillst evrv9v i:m;. 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 mbx, vdk 9-2a rnn+/iea thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notn +dbvnke9-a/,mi rx2ices 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 sev0o jjgx-4:p7ur ip su6eral ramps connecting different parts of the store.:sujpi-j47p 6urgxo 0
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 neededk0ihi,dh(xr4 to lift the piano (mass M ) using the pulley apparatus shown (r,0hi4d xh ikin

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 accelera9pb w: 7/:fd7dhsexyl02pi t oting 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 ths +vrfstg( oig q2sy27d6( l6pe following set td+ qssys7ol( 2r6(f26gvigpof 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 trom0nj:c,9j l2mp0 j2pl hc9 zvain 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+c68h fi*y ssvkzf9) n 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 2i 89yhc+6sznfs v) kf*.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 "mk j9716zpumda)u+qriv6 *o u 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 builh u8+i/nzu mv;ding 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 ropqxon; asg.u p+q;vww s)) vm/.ed together are ascending an ice field inclinesmva / ;gv+x.. wuo)wq);snpqd at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.