Why does a child in a wagon seem to fall bac yiks6;f5em y8kward when you give the wagon a sharp pullke;sm8fy i6 y5 forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts /3hzctv(y0 rt6t f; tmks0ps;rk; iq0the 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,0fz;y/3kit (t;s0 pt q vr rk0t6csmh; 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 it81nip ng1zu27-v70 bwky s wmj? Explain.

Only one force acts on an object. Can the object have zero acceleration?m0viwo .m t:1; lmecawl y.32f Can it have zero velocity? Explalm3c0.a2m:1fl vw o.w ;tymeiin.

When a golf ball is dropped to the pavement, it bounczq vkru-39g)* da0ff r +8jbtces back up. (a) Is a force needed to make it bounce back up? (b9 g8 zr0+ )frb3a-d*tjfuk qvc) If so, what exerts the force?

If you walk along a log floating on by n/ ix3nhy6u wkq;x0;:8yw ga lake, why does the log move in the opposite d;0 qy ni wuy:3hgxb8kxyw;/ 6nirection?

Why might your foot hurt if you kick a heavy desko3/hmqc f 6 ez8ahi*uk8r+4-rx uuy q; or a wall?

  When you are running and want to sttgpg7 9f//e0 cdkt4cmop 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 deceleration of a person running at/ccm7kf40 pgg9 dt /et 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 tseqm4t8m vbn*9/p ,*2 amie nehread dangles from the bottom of the stone (Fig. 4–36). If a person gives a snt* e/,vq e8e*2mmp9nias4 mbharp 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 onso om *t32sig7 a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fio go3 ts27*small faster?

Would a spring scale carried to the Moonnp;slq/.+)a+rm7r f sfb wg3x give accurate results if the scale had been c bgr7l +ap rf .swmqfs/;3)x+nalibrated (a) in pounds, or (b) in kilograms?

You pull a box with aj* +vqiinyh411 b/sa t constant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontajhsin qb4/t *ia1v1 +yl (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 gravi5h */xcym jlce4/qo(g ty 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 force on the Earth 4*j//5x lmchoq( gcey. Why doesn’t the Earth move?

Compare the effort (or force) needed to li) ee9wevuq3 z-ft a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to thru 3v9 q-eezwe)ow a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’uujm*j (y)av1mk/2 j ks third law, each team in a tug of war (Fig. 4–37) pulls with equal forc( km my*ujvj12)ua jk/e on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 )v st3u 0(xga3gyz56jf )lumrN to hold a bag of groceries. Describe the “reactioy3zagj (0mrsf3 )xu g)vu6l t5n” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, hs4tldlf 2:eez.hj( f8ow large a force does the ground exert on you? Why doesn’. l2 jfe8e:htsl4fzd (t this force make you rise up into the air?

Whiplash sometimes results from an automobile q(g 0iamcn k 31yu45wlaccident when the victim’s car is struck violently from the rear. Explain whywuakymq( 35 0g41cnil the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accel:3 c qusm3er6qerates, the crate remains where it is on the truck, so6rq3smuqc3e: 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 block reachesywsg0ffr: 4k:rb4 .7ft n d 9fk4i2rpr its highfwn 24b:4g 9pf.4fks: 7drkf0 rryitrest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you wei- kn/43n:utybs*xg yighed yourself on an inclined plane? Assume the mechanism functions properly, even at t-/yub4* :yig nxkn3san angle.

  What force is needed to ac1.*c d afp6 o1fedtryuu48 d8qv3sl6u* lqdj1celerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accem)p8edo0zq( 6 yt,k+c vpy:ezlerates 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 is used to accelezf 1 5(sio fbf5c r+c xmeq645sdls(m/rate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of oebh, 7dn s3;)koeey1a $76-\mathrm{kg}$ 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 g3k e:9+8aiby g xoxx3car is traveoxyk iabeg3g x+ 98x3:ling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 12f +29l1eumrnk 5m/s over a distance of 0.800 m along the barkf 1r+9e2n mulrel of a rifle?   

A fisherman yanks a fish vertically out of taae60hivcw: a6t4lq-he water with an acceleration of 2.5 qiahc v6a0:awl4t6 e -$\mathrm{~m} / \mathrm{s}^{2}$ 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 o mj9s dq497u0rgxo;b (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) 5 9bbd io1 .aknwvvtlg20-yw ) is to be designed so that the maximum acceleration is 0.0680 g . dvwba l5n2 -w yo9tbigkv10).What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the elevator 63w s; (egxm m(q9zbs ba)9ltkbegins to move, the scale briefly reads9q3btske( glb 9mxzs6w) ;a(m 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 2125-kg elevator has a mchbw+ 5f kwnc54ni+ u;t8 1bccaximum strength of 21,750 N. What maximum upward accelera bckcc nuwwh5i15n48cb +;+fttion can it give the elevator without breaking?    ( two decimal places)

  (a) What is the accelerativ vtl 46cfq9u;on of two falling sky divers (mass 132 kg including parachute) when the ftl6uv94cq;v upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house tgx ckl:f: cz l19*ger4y1;qe3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distat e ec9fgxk4clzgl r*1y1: ;q:nce of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertica+k /z.w 9bcbha*:v gyjlly 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 h/9k+jg :zbw.*ac yhbvanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a bask 0id4rtvw:7d m ebz,e-etball 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 x cc.5sz u,tegec) 8c9the moment it is hit by the bat, and again (b) after it has l9ex t,c5gus8.z )e ccceft the bat and is flying toward the outfield.

A 650-N force acts in a nort l;f ulj1lbgdr (po00*hwesterly direction. A second 650-N force must be exerted in what direction so that ;rlg0*d lj01oul f(pb the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontal 2i)i+uru:yu lly between two buildings 10.0 m apart. The l: 2i)ry+iuuu sag in the rope when she is at the 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 is hanging by a massless cord from another 3.2mu.w 2gv8. st-ntn jdjz:q1a1$-\mathrm{kg}$ 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 11fntoc rh2w j0az7b*dk ;jj 8.4.0$-\mathrm{kg}$ 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 n w,fvt7oag5 .iew location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forcgtfa o5i7.,wves $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 ct8ab3roy t z8.ars of the same mass behind it, Fig. 4-47 . Determine the ratio of the 8r8ay. tzto3b 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 the buckkuzsb;a, 9: - zftqs2)gati: b+cg;wfyq/ 1efet-pulley apparatus shown in Fig. 4-48. (a) Howft z;ab:iqt f wgukf+ y;sc1za-q, 9eg /):bs2 hard 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 beganc(0pzw 9m ;8k qdbp/:hprrh y(, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (m ek.y*zavx 09:*ql bxwass $ 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 horizonb8fg:yif*nr s+; n0emtal surface are in contact with each other, as shown in Fig. 48nfg0 ;y*i+ebn sf r:m-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 zat+i;)c h, qu m;gml00 7ymgpare each 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 determinygq7m t)a g+ucimz0;,h m; p0le 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 coh2qbs9ukyp*j cg 3 n :j4..pi/i5ko utrd of mass 1.0 kg . Calculate the accel/qk.b 3np *i9uou k.g spjj ic2y45t:heration 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 kjy2, stnww.e(g ijw08 inetic 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 start a 5u3;sppzc hgl9;fe 1xn 9q22 yj.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 stap)s,wsr px/ +tnding on a train accelerating at 0.20g. What minimum coefficient of static friction must exist bep,x)+s/srtwp tween your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient 4ew+uh t 94w9 so3ddliii*9hbof static friction between the tires aw+u9 lh*s owbi3ed9hiti44 d9 nd the ground is 0.80?   

  The coefficient of static friction between hard rubbei(syd/aep j( a7qx2 4sr and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you eid2s(jas yax4/7(q pleave 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 -wb-vz/06nwww0o9q q x 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 rou:7 (k3khb .tymmpsk -ugh 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coeff;x) lsflm j5t6mt 7ubm:::eugicient of statml t;:):mubjmt7:6 el gxs u5fic 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 gr6qt:k :/qzl 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 box A hav z5v j/cr,7mx7x+nrs ce to have to prevent any motion from occurrinx,c5r7x/ vsjc r7zmn+g? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor.xoo)gd i:cx(9np 7m(sc2ccg 0 akdr9* How far will it go, given:)g x (doos 0*k7n md(cxga9pir9c2 cc that 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 and 110 kg bv; l ;snm(tshlq; l/(, are in contact and at rest on a horizontal surface (Fig. 4-54).l;h tq bls ;((sv/lm;n 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. The coefficient of stat+9c ymlaji 7oo:ov6e+ 7nx :xguw 6;hbic friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can deceleratlv uwjecob: 97h xo76ymnoga+x+: 6i;e 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 (n- j(sh zs7 0idysi1rdriveway, which has an incline7 dyz-i(sjr0hin (1 ss 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 d9a y3pph(sy d0iv-4 pslide 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 planneo; alf*(z i/e tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initia) p myzan0jne8x-tq-;l 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 1rv. 1x qh2s hwp-o9c-zxeriq qu -8c5of the steepest 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 in place against a r7(0rndw7 uhm*kbfv(k ough wall by someone pushing on it with a force direcv(f7rhkd*bm 0 n uw7(kted 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 k x4f:*ueea 0vthey melt. Consider a chunk of snow at the ue0v xe*a f4:kridge 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 sto;(cp;xbsb jep)h yqc 1m7d g2*pping distance for an automobile traveling at speed v is ej cd) *;x ;cb 71hsgpe2bqpm(yqual 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 ofvrwzuh.;x4p d0h) x(.. esxss a car slides forward on the dash when the driver dexh(huzv.r.sx4ss dwx;)0 p .ecelerates 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 mass m is given an initisqpbozea .b /.e;-4bmal 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 a3nas3(px )jihpr ,f 4b/xsp m9re filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for eappxbxnr(/ms3a 4h j)s,f39i pch 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 frictinr .h*3gnvmj *. tii2o3k4ru hon 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 e c., gn6hk r206gylf(uf 8zbi65 kg (including the bicycle) 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 rnuomeqe 6v0dfl2d o (,+u ,hlw1)6qyof a mammalian heart, at each pulse approximately 20 g of blood is accelerated fr l+m661f, rywl(dv,udohe0qn o q2)ueom 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 automobile crash if the 2nory3. b2 nejslo-j2mi0. rx deceleration is no moreb r2 josymx-03e.2 n jnli.or2 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 acceled45vtk4m )gq-1n(gb: cdm qa zration produced by an earthquake is a , and if an object is going to "hold itdad-bgv4q4m)qk1tg: ( m nz5cs 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 theng:fi3o4 z d0:*gqage scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. Then *i4q:0ge :g3aodg zf coefficient of kinetic 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-q9m /ulao2 rs+4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction. m+qo/us29ar l  
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leanwmsb5 j6t e7q(ing Tower of Pisa and falls 55j sb (wtm6q57e m before reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s buchno,nmex+wey9x+ 0()iig,f t enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having giewn(o )9+xemxf+,hi0, cy nto pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the rtk:s45 msiq p klriuwz1c8:+7edesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can amstu 7rl4kpcw 5+:q1izk i8 :sccelerate 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 experimea fd cryp8,z..nts, dangles her watch 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 za,p 8.dfryc.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 supfgwdhh(- f2 fex. yf/lfq1(t.ermarket, there are to be several ramps connecting different parts of the store. (/dff x2tl1 g-h(ey ffw.f.hq
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 pya2:) c,/so5g trcfz hulley apparahyr, :)tc ofc2sg /5zatus 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 cbl0m4;hf/g v at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint c ,b5lnvku;1dx:m fb bv50em)+w nh jd-hair, an engineer considers the follo)xj5e10v, vm5-whkbluf+; dbm n :dbnwing 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 metric tons (660,000905u 9e3qek*r a ygod76rzrks $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of similar len zgli/;q m)fb:xv6sf(gth. 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 6v:zfg;)mxsq/ ifl b(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 " 10as)1ifqz 2a 724bs 4wws4vciy-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 bm).a( txxw; ehuilding 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 togethetd 7jklvqn) 7o/5: cgjr are ascending an ice field inclined at 21o:k jv dln7j5 q7gct)/.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.