Why does a child in a wagon seem to falm8 w;kpg48b+c*psiqqxvv cey*c;g 47l backward when you give the wagon a sharp pull fm*vigq8;cq 4xe+ys*; 7vpwp k 8gb 4ccorward?

A box rests on the (frict7c 9 flcbkjeg5/f1 *bbionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box imf7*9jg5bl k1e bcc/ fbmediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? Expdr217i ins ild.i10ff lain.

Only one force acts on an object. Can the object have zerod i gooa.pv flc(. 68ot.n-yvw091l tm acceleration? Can it have zero vw18la v lt(.- pm itn9og0 coyvfo.6d.elocity? Explain.

When a golf ball is dropped to the pavement, it bounces bac 8peww5bp f7n uo*d)/rk up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts th7 p*er5w)of /w8nbu dpe force?

If you walk along a log floating on a lake, why does the log move in thyq23)3d c8mww yew2cz e opposite direction? d 8cm2c3e)3yz wy2qww

Why might your foot hur:1q il9ebyyg) . / yxceu9*hunt if you kick a heavy desk or a wall?

  When you are running and want to p l6 ,( tpsg*4amjm2n2rxbg(ustop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of decelera(ta 2lgbsm2 p,4p 6jng( rm*xution of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine th(nf3;(bp wzrcsi2 ag;read from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the t; faz(n sgp(3r2 c;wbihread 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 i)z)j1mlhse4;x al ,utwice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fxlumiehsj;1) )a,4zlall faster?

Would a spring scale carried to the Moon give accurat n; 23f,ih ie4cglr/nhe results if the scale had been calibrated (a)l4 hnhfii,3;e gnrc/2 in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an attai pib05pw /y2 n-/mgqoched rope held horizontally. If you now pull the rope wybwq- ip/ /mo2n50igp ith the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravu k ec/*2bdpn5ity there is a net force mg exerted on itnedpk b2 *uc/5 by the Earth. Yet by Newton’s 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.utggklt0yr7e o59 mv g: e))m when you are on the Moon with theu9lmeggk.: m et)5 yrgo0v )7t force needed to 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, ey5+3yv pda7kp 8na 3my93hk*nel s +ugach team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, detvpgm kud3*yyn9a+a3p8sh57ke+ nl3 yermines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceri*kre ,vhf/*u1fchd5*f (s0x pw-fv lses. 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) fru(veh -/s*w dsl hvck1f *,0pffx*5by what object it is exerted.

When you stand still on the ground, how large qqn 8pouk:2kn2 f2o 2qa force does the ground exert on you? Why doesn’t this force mao2kqf:nnqq2p2uk 82 oke you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s ma;+dckc*mld9 lw* 1q car is struck violently from the rear. Explain why the head of the victi* camdwc;k lm*dl+9q1m seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbeb4- kk xt .o;,rihxbf4d truck. When the truck accelerates, the crate remains where it is on the truck, so irto-4b ;,4h. kxixk fbt, too, accelerates. What force causes the crate to accelerate?

A block is given a push so5daq w hxdh,6jx 4djyjs: 2i t*zb:(o6 that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascd6ob2*45 xywz6h i ,atd: :jq hjxd(sjent. Why?

What would your bathroom scale read if you weighed yourself on an inclin a;jvtuiz5 -1 /3azasmkw0xc-ed plane? Assume the mechanism functiocxasa3i -w a- u/5kz0m jt1;vzns properly, even at an angle.

  What force is needed to+ l-4ql)k/h nqrk k5xj accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ril2z tqms4d1 owql z yy.e-t; /+4bfm7sder 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 gv38m 8e0fq7+kuu i/w.uh ctuaccelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight o stac;jln ej(;jxk:8qxb 46 q2f 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 an 1100-kg car in 8.0 s if the,c,8e 0yd2,afx(jy ap lcozaju+*-fu car is traveling at aa( ocux, ,y edj 0-yacu 8pf+2z*l,jf95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest tors cyb 7 23pc,+g/nlgt 125m/s over a distance of 0.800 m along ty/3+nt ,7cg l sgcr2bphe barrel of a rifle?   

A fisherman yanks a fish vertically out of the wahr 0.96 c yhsw;up0wywter with an acceleration of 2.5 rhy6yw. hw0wu9c;0 sp$\mathrm{~m} / \mathrm{s}^{2}$ 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 quarter-mile track (402 h.w k b)o0uhgw9u4dw.3r;iusz +* wfx$\mathrm{~m}$) 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 to m2tg2bi-jn( he maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the suppbg -m(it22njoorting 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 mom 43pud*sxe :*netv5 htionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the accelerae* dm*vx t3pnue: h5s4tion of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength o. hxlh 85g4 -m-wwihmvf 21,750 N. What maxiw8l- x5m4mhi .-ghhv wmum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (ma;bhd5z t 45gf6u)we gwss 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of euw4 d5;)b5 6tw hggfztheir 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 strikes the hpx,:7 bnxe b3:t hu3jground below, he bends his knees so that his torso deceuxx7ht b3 3:e:hbp j,nlerates 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. A1:+ : osjjtpay rope tied to the box runs vertically upward over a pulley and a weight is hung from y so:1 +jjta:pthe 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 diag61 wk vs1jxj miel4+e(h5m5sgram for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit sqoa6 *e :atj*eh9 1xvby the bat, and again (b) after it has left the bat and is flying toward :1oe *9t ev qxsaa*j6hthe outfield.

A 650-N force acts in a northwef5+bcfh) zkdv9bx; g/ sterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illusthb;gv)k bffd x9 z5c/+rate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buildingzcf;o*zgj1wzp-c z 83s 10.0 m apart. The sag in the rope when she is at the midpointozz;w fg -8*1cp3zjcz is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a 9g.l x (rfy3xx4n a.llmassless 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.ymnnuf-ss)g lv v;3 )30$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new 2wtdj 8 ,z:1s 5cbbq2iw r:ynz3ltq.flocation at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces :w5.l c3t1 tf:jbbs qrny,q22wi8zdz$\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 ca 3tsg6xmx+iqe+m (b/irs of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the qxt+ 6 ms+i e(/mxigb3coupling 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 m5+ul(dwd savy 5) 1g9ot2qqnbucket-pulley apparatus shown in Fig. 4-48. (a) How haryqgtw ms (uvdo)d912+5nqla5 d must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race be4 )c9 uponahbd) lfj- 73gad.jgan, 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 blooz,puw yd 5i05l; l-o2 zv(wsfck (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 horizontal surface arekd; 5/kef0z u8x7vi ze in contact with each other, as shown in Fig. 4-51. A force ku izxvdke78;5 e/z f0 $\overrightarrow{\mathbf{F}}$ 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 the g;s78flfcl 4dpround, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after tc8p slf dl4f;7he 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 a3zekohmp2clda9z (.*re connected by a heavy cord of mass 1.0 kg . Calculate the acceleratizk2d 3(oep*9a chz. lmon 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 kineuj t j9 w8rnh2x3 n/wg:qe*6qltic 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 tbwgbr,:zk s, 6pt o6*njk7my;5b2r wb o 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 oobi s6/1 y(g 4qltxz1train accelerating at 0.20g. What minimum coefficient of static friy1ts 1/l(qbiz6 4oxgoction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffic cu;c/2:2cj acffv o7vu-rj2vient of static friction between thejuf2c-af7jrv /v :c2cvu2;o c tires and the ground is 0.80?   

  The coefficient of static friction betwee6 o fqtie9mj(0n hard rubber and normal street pavement is about 0.8. On how steep a hiletm 6jqf09( iol (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.8 1 *e56xw nzmwaszgy+-0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 35 lsw6b/pmdy/-eq u p00$^{\circ}$ 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 x 2s jmw6c+gd. czsh e*.g;a*mhave a very high coefficient o h.gw*c.sj ec*6 a dm;g+m2zsxf 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 fricti nafru8 )mtbbps2bb9 cqm97p c;5vu*i/ 2(hyd on 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 largut4gsy*2 jst4irxiewz;8g), e a mass would box A have to have to prevent any motion from occurring? Asg28xyutj 4 giwr iss4) ,e;t*zsume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floo74wjtdf .9l 0zqc uo4lr. How far will it go, given 7 qcw. 0z44fl t9udoljthat the 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 an j;jnw,jsv*up9d j7+kd 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). kj9jpds*+wu ;7v j,jn A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. Thjy2 ,6dzr .igxe 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 decelerate and still avoid having the crate slide against the cab of the truckij6x ygz, dr2.?   

On an icy day, you worry about parking yourl0:9 kf:ss3lx/hepht ; 1d ztj car in your driveway, which has an incli xfhs j/0 ;9ktzpht3el:: ls1dne 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 2b rqmj n)c)79nsa. 3+m,qgy jv8$^{\circ}$ 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 tiltedt 8 vyi1t qvw/*6fl+yc 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 speed ofmj0ui4.dw r-7s zv ae6 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 hee3,;71qgnv5gs( r. u. 0h kd4lmnfud4rjnsa speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushfjtt,e* adle6x1, y c+ing on it with a force dejf, c6,+e* ttd1lxy airected 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 projeto r)id8ilh 7,pe(/c9q soc1fctiles as they melt. Consider a chunk of eh 7ct9sp/1fr8 ol(i)o ,icqdsnow 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 wv5yx, s25( vhv,ems2acqn / adistance for an automobile traveling at speed v is equw 2ssq c,v5ym(nv,2aa 5xevh/ al 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 ofh:/1nf/1 f+yta lbetc a car slides forward on the dash when the driver decele+/ f:bfyalt1 n/1he ctrates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of masg /13qyo/8dilzs8 mtp s 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-u:ogu5:(z j4by 5 gisra sai- conveyor belt 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, 5b:- z:yaggu (u5 isrs-aj4io 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 kinetiy6)fwt( 9zwnqtqr- / ac friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicyc9e7rtp9ys)q h,: (nnnayt9yp le) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse appekvd7;dtc 0 2groximatelydgtevk; 7 cd20 20 g of blood 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 of surviving an a6*ex46lqx /mr 9xsmhvutomobile crash if the decelerar 6m6*ql9xvme4/x s xhtion is 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 bczhu91rak6 l3y an earthquake is a , and if an object is gcak9uz6lr 1 3hoing to "hold its place" on 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 of an accident inv;e yc7i+ tots)/n v4xcn*rf 0zolving 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; o) * vysn/ce0n cttz47+ifrx friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each xwsr,0)6dcbkc:r b 3b 4 m traveled along the road, the elevation chrb)w,c :c3rxsk bd 06bange is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is drow s xwr76c/o+g czkm77pped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resismc7w/o 67xzws gckr7 +tance?   

  A cyclist is coasting at a steady( pn4 )masmzy3 speed of 12m/s but enters 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, whamym4 z)3 (spant will be the speed upon emerging?   

  A city planner is working on6mba5z:nhx evb i7 und np 4.zpp3y)5( 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 :nz m5e(z)y35bx pv4pn.h i6a nudpb7 up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics expedb,dru52gjew (b +el/riments, dangles her watch from a thin piece of string whiee,2 bj+/ r5wu g(lddble the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramp-7a5;qut; x2vua -x uijaozs ;s connecting different parts of the;5uuvaixaa- 2jus7t;ox - zq; 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 ps4lhp b r*/1eviano (mass M ) using the pulley appvsp1le*r4 /bharatus 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 accelera 0d1vla(bz w3s m6;ewating 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 child3qyi.:2 fnf6fv * 0ibi h ;.vcbiz.-g/dnpcvx -restraint chair, an engineer considers the following setb.ihvq . b-d vipngn3fcc.2;v yf/06* iizx:f of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 me*bo)-d *c6x o i,lbz9q e/-*uxferg vltric 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 h*2n r2vv y(t70gvdclwx 59syav(p: w of similar length. Karen's rope i s7dxly r(n 502wvy*w2hvv9(agv:ctps more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, 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 " pz/t,g7 l keo-e*my)s ru(xy510-1 $\mathrm{~b}$ 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 buil)uc7r4/ nj zilding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascendijx7 36f*gcyro ng an ice field inclined at 2*g3 rocjxf67y 1.0$^{\circ}$ 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.