Why does a child in a wagon seem to fall backward when you givhbctd1n57 qd lc8)f5ve the wagon a sharp pucqlb d t)8n h15cvd5f7ll forward?

A box rests on the (frictionlesstt gkfi+shf7 vf) b*qi3zhw0j *,lh66 ) 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 motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck hvgwis *b0ft67qfj6zi)3fth,h+l *k

If the acceleration of an object is zero, are no forces acting on it? Explaini bnfw8.tlcx3e/6 a 6l.

Only one force acts on an *t(:eeh)e7 ob- zyn+* p heuhkobject. Can the object have zero acceleration? Can it have zerhp b+ee hy*no*7e( et:zh) ku-o velocity? Explain.

When a golf ball is dropped i53kf6 l ,dic9vy fslv,d 6t8:don,hu f2r4cc to the pavement, it bounces back up. (a) Is a force needed to make it bounce id,cv29 6hyuin 53f:c48rdfcofllk ,vs6 d,tback up? (b) If so, what exerts the force?

If you walk along a log floating m9b59ird +6v0/tmktu wnyc ( pon a lake, why does the log move in the opposite directionwc9kuy+r9v (mit 0b/ pd6 tm5n?

Why might your foot hur 2psr6go ,x gm1bbf ea3kz(s(*t if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (a)i ycw+pop*- j+ What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleratioy*+jpp-ci + won of a 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 the same todg:pl5*ksss sh 4*2 jhb; :tshread dangles from the bottom ofo* 5j*s:2 bsd hkh4t:s;gpsls 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 ;l.2m gb1wkcqwc- b i/x39/xmvsd;n q rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall fas; i/kx 3 wcg1/nlqs-.q;b x c9m2dbvmwter?

Would a spring scale carried9lreoa -+nxnc6(0qyh to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b)onye +hlra6(-cnx 9q0 in kilograms?

You pull a box with a constant force across a frictionless table using an att h-qto5oy5v x+ached 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 table), does the accelerati-yhovqt5x 5+o on of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravi i-dh6o46pqxk4x1 ms uty there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object eu mxosi-hdkq 1464x6pxerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) n7(qe15at ycxrz t hb r18o,x2geeded to lift a 10-kg object when you are on the Moon with the force needed obe5tz 7rgrhq1t y,xxac1 8( 2to lift it on Earth. 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, ekn1 4, k*ttbdxach team in a tug of war (Fig. 4–37) pulls with equal forceb,k ttxkd*14n on the other team. What, then, determines which team will win?

A person exerts an upwa/gsq -x(gz13 v 58sxskns:bofrd force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) bn8oksvs-bg(5 xs/ f 13xz :gsqy what object it is exerted.

When you stand still on the ground, how large avtzjhv5 ;jp p 6 wrzj90gxfrj7)+ys(. force does the ground exert on you? Why doesvrj5pfsw 7zrvxzp ; +tj.j9yhj6g0 () n’t this force make you rise up into the air?

Whiplash sometimes resul0lzk ka+9 v6 bw:pq8twts from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in k89b:tpwkvl6w q0z+a this situation. Is it really?

A heavy crate rests o) spv/e,j mzyl6u19ikn the bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. u,ism6 j1yle/)9 zv kpWhat force causes the crate to accelerate?

A block is given a push so that it slides upuqp r2ogp571loudh7 r r:23 xeeqk2o: a ramp. After the block reaches its highest point, igel p3x2:q2oq o or75rup1dkreuh :72t slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale readqta+ff/:7crv b9 4zmc if you weighed yourself on an inclined plane? f+ta c7q:/bc zr4fmv9Assume the mechanism functions properly, even at an angle.

  What force is needed is/obq3* wh6q; /zfehs.3 wwt to accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike ane:jm p2g)v+mw+v9ime q; x b3xd 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 withstanl j-6cz -bd.,nhrhb8e ess3)ed 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 a vkxl-m fg(fc1 o9v -s-$76-\mathrm{kg}$ 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 is tra5tu3 c clor6wn8 3jhud540drovelingtucrc8 un 5w645od3d0 r ol3jh at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet frou/(+eohnv b2 ,kld:4-dd ;do3 wtk dopm rest to 125m/s over a distance of 0.800 m ( el d;noh4:3+kvb2p o,dudt/okd dw-along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water w6r jrtt*hd5t-c,so x/ith an acceleration of 2.5sx-h d/rotc5 6tj,*r t $\mathrm{~m} / \mathrm{s}^{2}$ 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 quarterl g9-+w 0zxu ndozikvw/95gg1 -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 maximum accjl.kc 3i-+wx deleration is 0.0680 g . What are the maximum and minimum+-dl.3ci wj xk 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 bathroom scale in a motionless elevator. q-v)f o w3rs/tkij*k:When the elevator begins to move, the scale briefly reads only 0.75 of thvfsikokw/j rt- q )*:3e person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevatclzu ;.of7u1 ror has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without bruu1crz7o.l f; eaking?    ( two decimal places)

  (a) What is the acceleratio:oxb/g h z20ojzaj6 dj ,5/+jazyx n5dn of two falling sky divers (mass 132 kg including parachute) when the upn jz g h:ob/56,x a o2xz5d/0y+jajjzdward 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 hej ew ;v0v4cxj8 vh) yn;up7l:d strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. Ifl jxu4hp c8wejyvv;n0d;7 ):v 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 res7 x;wgibd9qmvhsoao a4.+; l ;ts on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley o;4mgiv; .+hw da9 ablxqo7; sweighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram x:iv/(r h 9fkv/vl4vofor a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagrhr+kv6xj 847j ,pft-w. p vs5h.tm,/kkey wueam of a baseball (a) at the moment it is hit by the bat, and again (b) after it has /.t.p7,y56 - rmfk t 8wjkp4e+svvx e uhkwj,hleft the bat and is flying toward the outfield.

A 650-N force acts in a northwexwe 08 0- z:ppg 9:6ydmtykbhcbdd:f5sterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illus0wd0 c b: xtzykdh5g:p6f deyp:9m 8-btrate your answer with a vector diagram.

  Arlene is to walk acrossh 6( ufspk9-dt a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at t-s(ukdt9 p6hfhe 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 ig ,)pl-anqj08 ;lt imy ,r,jcrf n:(dus 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.d*gh61zhdv)wxp mtk y+ ,06aoh7 r7p j0$-\mathrm{kg}$ 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 na:u6a qh xsg dm/s60o9ew location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum ofh9 /a6:qmsasugo06 d x 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 tw/op0drx 4hop5 ,uk9cxo cars of the same mass behind it, Fig. 4-47 . Dxkpc ohr 95/o 0xu,p4determine 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 up)hxhmdi dektc c 4gr3;1a 39r6ward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herse3 ;ir 19tmhacdh x rcge)63k4dlf 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 began, a 6 ow)g qpu08604+j umz zbv4zar5$-\mathrm{kg}$ 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 bvon;xf, 8/0epdro6 n rlock (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 hor-l;5aapo va48e nkv)u izontal surface are in contact with each other, as shown in Fig8vpvlea 5ako na ;4-u). 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 ajlh.,ismdiufw- r w4 ,7r6:finitially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maxiil6f4 drwf7rs,ui ,j-.:wm hamum 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 cord of n0 k2p u1,dzgxmass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the frepu ,xg102d nkze-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a p( no*:;xb opo 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 8ced7xr k ;6soto 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 tj5vx-zzt+.*6id j*e+0yox9 j uwjb dvrain accelerating at 0.20g. What minimum coefficient of static friction must ex*ddeou+j .- +j9yj x0x*jwvzbz6v5 tiist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car cans ilae.243ynf,v6nyg undergo if the coefficient of static friction betw.6eyfa24 3 nsilngyv, een the tires and the ground is 0.80?   

  The coefficient of static friction0cwb7iy:sj - 5dddey ww7;h:t between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parked? 5wt0d c bwdi7sd7-e:y;jwyh :   $^{/circ}$

  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 acw jj+y:3tww *t -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 pmom3:lx3 d5 d o)n;iq30$^{\circ}$ 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 9w,-*0fa; ruerzrohyamx* t- very high coefficient of -uz orr09;,yw-*xa *tfre amhstatic 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 kinejto0ofaer5 8pnln -v1d**pr 3tic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would bog+r rf5k rfv97x A have to have to prevent any motion frvfgr5rrf7 k 9+om occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far f/vqur+ s6xr0/jd9 bd will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial spejrudq0 r6+dbvs9/ /f xed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg fmxnqwc w 6*p6p) 8n1 ;bxa2ypand 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). A 661qanpp* yx n pw2m6cfxb8; )w20$-\mathrm{N}$ 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 coefficient of 8:frv w a51eoustatic friction between the crate and the bed of the truck is 0.75. What is the maximum rate15w :vrua8eo f 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 parking your car in youi jdajjt5u(g4pzpg b s)3 epnc/589(gr driveway, which has an incline ofud3 j( p9jz(pb e/) sctg5g4nij5ag8 p 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 bqzc-fxt+ow i:/bw ro97g4 o)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 anax,8 tdgcw- 1mye()e( xqa3cn 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 s. rx 1otixn*mmu(k b+j9 8li(vpeed 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 steepes sd qp *8*5kdlhauiw12t 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 8-6 ;d gjvucvn tj1f3tpl8a)vin place against a rough wall by someone pushing on it with a tvnd) j vlf8tv;j83ua 1-cg6p force directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as they melt. ,dk7q:a cdcmsienvv480k9v/:sjn4 jConsider a chunk of snow at thed csv, ki kav8:sjde4qj/nnv 04m:79 c 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 travelindo4d* 8ih.z kl(jbv 8+kmo 5pqg at speed v is equal8 +. p z5v4dljo(mk*kqhdi bo8 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 d c(d+:p1yab2iwd 3spsash when the driver decelerates from 41p3(ywc+p2:sd bis da5 $\mathrm{~km} / \mathrm{h}$ 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 inisi)ww4xl 0q: htial 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 ajhb11n2qa/ k.faq.yzwl 2pl2n+z 4lcre 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 izya12kcpq qlw z2n 4+1.l hfal/2bnj.f the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic friciq71(+wshyn-,b t b n3epxmb 5xig7d9tion 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, yiz2.5*k di/ rbxem8gw0 msq4gh 1qk 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 mammalian heart, at each puc ha0z8 cn(-fib )i)vflse approximately 20 g of blood)b fic)v- n(iaf0hc8z is accelerated 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 ofl mt;(dd a2i:s surviving an automobile crash if the deceleration is no more ta2m:( dd sti;lhan 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 ac;hz xf u73b/alm.ys8tceleration produced by an earthquake is a , and if an object is going to "hold its place" onxa ut l/h3;s.8 7bzmyf the ground, show 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 *ke6 g/l 5nrwtau,6or9g )hptof 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 initiatk/r 6,o* ge9 pr lah5wt)g6unl speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means thp fluj.l: nw5u (n8)vy;n 8bna+wplu2at 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 traveling 55 m? (a) Ignore fricufn2uw;p+vy (lnl):bu l85pa8.njw ntion.   
(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 s)rypkhxnn 4( 0c1un 8Pisa and falls 55 m before reaching the ground with a speed of What was the average fonn yu(1nh sc04 )x8prkrce of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enter--kj /,rnkovq5yb ;w 67 nadwxs a muddy stretch where the effective coefficient 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 6rbwyxav- no k- q5k;7n/,wjd will be the speed upon emerging?   

  A city planner is working on the redesign of a hiu2 xols;ioudzcxzyl. 0/6k t;lf+- 5flly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hi txu+2i6 oluy. zx;;l s5fok/c-f0 dlzlls 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 likesl3o(1 k:(,z pdmubfpq physics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig: 3po1 ( zflqkm(bp,du. 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 au1o,p:+ zhib,ru ii+e:cbh b* re to be several ramps connecting different phhib+c, b i1b:+p,*zi u:eru oarts 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 .x+9 *pqfqig+x8pa qw needed to lift the piano (mass M ) using the pulley aixxgqp9wp*q8++f.q a pparatus 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 r-iw nighs0;m 1y,qv6$\mathrm{~m} / \mathrm{s}^{2}$ 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-rebh46mis* . whastraint chair, an engineer considers the following set of co.bhm*6swi h a4nditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 660 metricjruvpem9 f3z)(p ,;nt 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 o 9x0-4-z*jc si2 ftldf rjg4vi+hg5 xaf similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a stati+dg4g2 zi 4h tjfvrc fxa0x-sj9*l5-ic rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat l v3mr)ll.9 ls /nq1guis using 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 reacxgbzpfkmvy+ *q m; ifbp;+2o7 a 810yzh a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice-mv/l 5)+(mjwvzhmdka-)v rq field inclined at 21.vhz k5-l)(rmj dm)vaw/mq v-+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.