Why does a child in a wagon seem to fr7kwx) ze2co.0w) bfxall backward when you give the wagon a sharp pzower ) 2.7kx )cxb0fwull forward?

A box rests on the (frictionless) bed of a truck. The truck driver1 ;52x m*e1m/ijn c kyss0lrpy starts the truck and accelerates forward. The bs1nm51 irs2* clx/jyye 0;mp kox 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

If the acceleration of an object is zero, are no forces acting on s,w c9.llflg u7q 0e1.ats.(tmeb1nrit? Explain.

Only one force acts on an object. Can the obj4a a1mtte;.o7g /zl14wk: jqkp ox* hvect have zero acceleration? Can it have zero velocity? Expol4:w1q kpgk;xt /hj7.e4zm ova *1ta lain.

When a golf ball is dropped to the pavement, it bounces back up. (a) 3 )wpj0l,s9 h(cx fpf9ujwd /c.i/gkdIs a force needed to make it bounce back up? (b) If so, what exerts the ffp icxdch9ws/djw309)( p,/ .lukg jforce?

If you walk along a log flo amdhuv8;/*ekzkmj2 0 -zk2ezating on a lake, why does the log move in the opposite d;mkh2 -8mvej /kd 02azez*k zuirection?

Why might your foot hurt if you kick a heavy desk or a wall?(oi5(u , 9jvdti bbdh zjpjig1u8: x)1

  When you are running and want to stop 7 .lyha,t/wbnh 8a8.fyl1q6ijd0jw equickly, you must decelerate quickly. (a) What is the origin of the force that causeh1hy8 w.ell70/ b8 in6fy, qa.tjdwaj s you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine threac;:iozqe.fp 7n s2cy.d 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 thread likely to break: 2i:;qcf.pceo7 nys. z 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 grehuaq qtun91bp1+q39) yh c/ hr wd6o1qat as that on a 1-kg rock. Why then doesn’t the heavie1qq1 h/ hr9p 3)cadbqtwyu q6u1 +9ohnr rock fall faster?

Would a spring scale carried to the dl,dqa3ewnv d. y 0+ ou,4we5wMoon give accurate results if the scale had been calibrated (a) in pounds, dyvwud0we.4 eo+q5dl a3 w n,,or (b) in kilograms?

You pull a box with a constant force across a frictionlesiqo,z,1 ko 6ius table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) rem ,k q6uzio,i1oain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influencgzo:tm;s1k a pm p2e14u +4dkje of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite forcza +4t1o ;g2 mmk:pupdjk4e1se on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) go;msyq7y84j needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare sy4g m;7yojq8the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pb dvir1y b u 44vcdoxc-6y54dha8i*v0ulls with equal force on the other team. What, then, determd1ai8vo5dcy 4vi 6*4 b ucxr0d4yb-v hines which team will win?

A person exerts an upward1i44tuez fihaq zq /c d;6ws4: force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnez/at4wh461i i4 qd;cu:qsf zitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, howy1xm,z9br. sh large a force does the ground exert on you? Why doesn’t thzmb,x1 .hr y9sis force make you rise up into the air?

Whiplash sometimes resultiuhl px8 pj0 96zk52pzs from an automobile accident when the victim’s car is struck violently from the rear. Explain why thzh 6plxpjp8k 9z0i25ue head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the b09 3kfb.sh dx*tsh)kjed of a flatbed truck. When the truck accelerates, the crats.dk9 xt0kh*f3h)bs j e remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the bloh 45gx6kkftl0i 8.hxs ck reaches its highest point, it slides back down but8l6.40kxshx 5tkig fh the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weir 88ujj,okx(o ghed yourself on an inclined plane? Assume the mechanism functions properly, even at an angle, 8jxjr8(ou ok.

  What force is needed to accag+d 7n+36vge,5rein cq 2imhelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceleratesb8d )a n +6gp33oyx06qhiipz h a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it j 3qnnvrg(.e 7is 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 hc)z1,d4j key*qq7 eg$76-\mathrm{kg}$ 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 f/-c 25n 1ng1gnavtb tstop an 1100-kg car in 8.0 s if the car is traveling at 95km5ctn vt 11gg2na /fb-n/h? -  

  What average force is needed to accel*9b;shd b ueso hpiq(/4*4uzd erate a 7.00-gram pellet from rest to 125m/s over a dis(ib4h;/poh d*9zebdsq*uu4stance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of 2.5ue-ip fy+l0 r5 i+e-r0p lyu5f$\mathrm{~m} / \mathrm{s}^{2}$ 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 ;zma(nr .;lz ctrack (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 designh 9nk a6x )r3b5hh3kobay97eoed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supportingb9ka h)nr9bohoe53 h3k7 xa y6 cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When th5)sa b* 2zkij s-:mp f6(zcnoqe elevator begins to move, the scfza(5kinz2o*:- s6q)pbjm s cale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 212 e1njfe ykq04+5-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the e0fj n4kye1+qe levator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg in,ol*io*jvex(s( g w-oa, rh0fcluding parachute a eh,o oo-fx*vs*g(ril,(j0w) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the w5.e2 tt4gm pjyypa+*roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his t 2 jp wep*y5t+4tam.ygorso (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 rpw.pfvo t(h7 o8eg:6 auns 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 ofvop.a: w(g8eto fh6p7 the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball play0zvdw; nkhu0)er
(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 basewm be3 zq09jm2 fivdk7 cj-; v(rp(f.wball (a) at the moment it is hit by the bat, and again (b) 7mqjp dvr;0(cw9f2ib z3wm. jf (k-v eafter it has left the bat and is flying toward the outfield.

A 650-N force acts in a noj:c 9dw.qg i 2q;fzus7rthwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector 2gdiwu 9 qsqf7zjc.: ;diagram.

  Arlene is to walk across a "hig uwv0m sc7/7jth wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the mujt7/w s0vm7c idpoint 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 by4/w s u cv2dzf)jp5g-h4exc d+ 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 14o:y;hy ,e nh4qxd:km7 .0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, Antar +3k2 zu rx;pkgj 66rqoh;*gqxctica, as shown in Fig. 4-46.hxggo;zk+u* q6kj6r pr2q3x; 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 kz dajh/az*8bszs/ ,:gn2e. 0y 7umxk uwu*4oit, Fig. 4-47 . Dk/.s* *z a07kjws2uox, m z8 uu4b/h:ynedazgetermine the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using th/6y own-(l2vk ens e5ue bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at cyn2eso nweu/6(5 -lk vonstant 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 7ul( u o uh1bp)i4+q*ylh:bjmbegan, 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 blockh90 pxpm4 rn4 b0bn*cawf3mh+4j4tta (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 qf5:lsm; 8rjz5vt,y1l.cty) 8s mbjware in contact with each other, as shown in Fig. 4-51. A force b1js,yl.c5m)m85z t qfy;:sl8 jvw rt$\overrightarrow{\mathbf{F}}$ 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 e 6d8 ewa:hn;e fa68 zxcmz(z2nach 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 lig8z2 eaz8na:6wze ;xc(d m6hnf hter 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 onqs5ad 2g ,mgq8 a frictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cos 5adg8 mgqq2,rd, 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 kineti+ avg1oc6bht *ik(sbqa)h 3q* c friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to et q -/ xn,md;u+-cj2f-xd gbmstart 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 train ac k,6 a;:)/rbuja2pduv*wio svcelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and th,v asowki2*ub;ja)v p6 /u:rd e floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the co:9,/i3ij: b7z;ecxoad qtpf p efficient of static frfbocieta3:qpij 7 :p9z/, ;dxiction between the tires and the ground is 0.80?   

  The coefficient of static fri77j-6r3 t4nlzhiky cexj 06uolq ()o pction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum ax utc3ojk0-j7yp r6z7lqenh ) (o4il6 ngle) 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 ez*b5wv90j7 bqudr 7p at -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at restxl-i (s1 4gljm 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 wittiuj( ;b k v*agi9.l0e x17e /w;xwhpfh an asphalt surface have a very high coefficient of static friction. jp ew;aw.lt bexih*7x9v fugk/1 0 (i;

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 fr jy sk aj57;sed2)wdfx(6kr x/iction 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) 6x *gnr8.d cohhow large a mass would box A have to have d r 8nxhc*o.g6to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the9c *xg6akcl4t floor. How far will it go, given that the coefficient of kinetic friction is 0.20 anctlg4 9x a6*ckd the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kcw3qrnh y*rb6exz 6 /8g and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). 63 n* 6qwr xyh8cbz/erA 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of msmk*/:i-ngmstatic friction between the crate and the bed of the truck is 0.75. What is the maximum ratemim/ng-s m*:k 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 your driveway, wh,wim-utf+0 wom+wu 6fa 5cj3r ich has an incline o 6 mfu iwr-f,5a0twu 3+owjc+mf 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 slid8 ck,ot 7+nup 3vdj2aze with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane t: 5sqf,(kb9sq df9 wrsilted 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 rfz5uh/.ok)r initial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill wif 6p3kkfs3i+ pth a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone p o zs:h52dr;deushing on it with a force directed dd; roz:h2se5upward 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 sliw0lucyo(2*y0da h 7hw4 .dsxoppery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge o.4lhd20ow7y(hdacxsyw u0*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 minimx8ohoo jzt54j pw7xl .mih.( 9n/cuf4 um stopping distance for an automobile traveling at speed n4j fz wo ui5.8olomtc xh7/h 4p9x.(jv 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 of a lgd+m;z1i 3ew car slides forward on the dash when the driver decelerates fro;m3+1d ilwzeg m 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is gix1ftl; d0 4wp u+jiuz9ven 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 u(m:nag-3i:ran yufx 0p .u 2gthey are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of xay- :mrgiu20 3p auun(gfn.: 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 friiutvx:bb6 2g, 9eed -mction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down akl yz a(k)u8k3i xhk wg-g1n+ 0t77fzs 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 fe4o),mpai79 ,poe )npx:ogturj 14el w4-n rmodel of a mammalian heart, at each pulse approximately 20 g of blood is accele )pplj7e,o i,m-or:444p frno1 te)x wgen9aurated 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 * aou0w-uv:n zautomobile crash if the deceleration is no more than 30 " g 's." Cuna:v 0w-ouz*alculate 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 by an earthquake is a , and if an objed+i ta06y ;tmcct is going to "hold its place" on the ground, show that the coefficient of static friction with the gri0t;mc +6 tdyaound 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 anhv6 )mei nvtuq0i w7nxc9:ydx9 ;*)rv 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 ix0d6 * thwc:vn9yi9q)e;m7)rnv u x ivs 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 4 kwxq33 ((jzx3bun rtu*5 f9xf m traveled along the road, thjxqurk x 3bft3x3u z5(*9f(wne elevation change 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 dropped from the top of the Leaning Tower of Pisa a4fy zr 9 3c j6dnoe6ql:lcm) mz5n.i8end falls 55 m before reaching the ground with a speed of What was the average forceqc9 i) l8 fl:66jzcz5. e4n mo3emrndy of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but m1 ap.t 5x9zgnenters 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 will be the spee9 ng5atm 1xzp.d upon emerging?   

  A city planner is working on the redesign of a hilly portion of a ci6 hkrx*4y7 ouh5cgmx)wi u) p:ty. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular smallpxwohxrhk) c:4uu gm6 i) 7*y5 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 watav.i 9b7 o:qdfl0vu0 g(o i3coch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of fb73vu0oog c9(d l v:.qaii0 o25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps cor62nrscq+ y t1nnecting different parts of tsr n 1c+qr26ythe store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using the pul84us+(zf3 pwe zx9 wiqley apparatussi 34z+fqup8 (x9ezw w 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 atl;)/vb5lo;w1zk pahd bs :5hf 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 9dx 1+6pluqnemx o;l +the followiq9lnlepdo6+x ; m1u x+ng set 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 metriyjz og 79nyalsi07x7iryhe166, gq 2q c 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 K82.gvsr u)ltkaren, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the 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 trs.8v gklt2)u he rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is usds ,a8: k56+7 1ybp cnmggyrlking 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 reachp.xa dw(s(ufdjv/a1 / 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 whtga1gnz4)x2u6w2uxz x ilc* 0o are roped together are ascending an ice field inclined at 21x)24 2n itua60 1uwxczlzgx*g .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.