Why does a child in a i)p 6pt4f)dsnwagon seem to fall backward when you give the wagon a sharp pull forwardf) dps6ni)p4t ?

A box rests on the (fri4l/me6d il8gpctionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing o6ild/l m e8gp4n 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? Explainb n .3jmsru/h,c0zk v-.

Only one force acts on an object. Can the object .lp.mee t :ij/s 5f*khtqa.buw/ mr:2have zero acceleration? Can it have zero vel. h fkrl5 p2*tam//qu.jib.s:wm e:t eocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a j8r/8hxgjmw7) Is a force needed to make it bounce back up? (b) If sowjxm78 8r/j gh, what exerts the force?

If you walk along a log floating on a la/- ,a .io)qb/jjy:text3t : 9 gdxkrecke, why does the log move in the opposit,- :tt3e i9 k gbx.q:dejaoy/txj/ )rce direction?

Why might your foot hurt if you kick a he:6et1x5tc-o u dh8an zavy desk or a wall?

  When you are running and want 6jb3 wza bg2- ,:*vlqd9d ykilto stop 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 todwzybb:*, k-lqajg 6ildv 923 p speed to come to rest.    m/s$^2$

A stone hangs by a fine t6t-4w dmvk0ukhd*,tx 2 u(ny xhread 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: below the stone or above it? What if the person gives a slow and steady pull? Expxk 6*t2v,m0 kt x-(whudu4ydnlain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 94yoe2b c0blmqr 3ic8w1sf 9ms:sp-r 1-kg rock. Why then do 2c1q r 4pe 3ol-ymb8ssci99bs:rmfw0esn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results wogkl7udu: +- if the scale had been calibrated (a) u7u-+olwgk:d in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless tablyiy8no (f- dn,e 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 acceleryfn,i(- 8n ydoation of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the )5w 6tksvjyn09 ;eija influence 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 oppos vj65y;jiw0 9ne)t kasite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg objfg.q hnnuvg*x* qdgrx6 1 .6w4ect when you are on the Moon with *g.gx dn6.xv u4*61fhrw gqnqthe 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, eachmw gcj2/.e;ilg+ogo/ team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, dete./g+o l2wmgiej; /gco rmines which team will win?

A person exerts an up ul0t)i4ypc8 l;. nviyward force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c)8cyy4)0 u.l lnivpt i; on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a fof/ +p-m*a,wefj a ru16e)etzkrce does the ground exert on you? Why doesn’t this force maketake)/ rfj,ae6z up +-fem1*w you rise up into the air?

Whiplash sometimes results from an automobilemj /)ak)7m fyj accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be throwk7) ymjm)f j/an backward in this situation. Is it really?

A heavy crate rests on the bbdu yib1x9) (.; 6oqji sq0yybed of a flatbed truck. When the truck accelerates, the crate remains where i.(9 01iqio bqubdyy6)j b;ysxt 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 rampd6w3t k51ee-gt. yuk a. After the block reaches its highest point, it slides back t3w5e-k6ak.uy1ed gt 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 we ca76ocqf0ve- ighed yourself on an inclined plane? Assume the mechanism functions properly, even at an ana e7f0-cc qo6vgle.

  What force is needed tg;kg /*doermbql2lxo: ;d6c.o accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates l27oh sib0 ki.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 accelj9rk6;b w2 5lfaskn) werate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a bchfsy/ppnil 3 *-s4+ $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s if the car is tra,j itj0 6ah2tnveling a 6jat,t2n0ijht 95km/h? -  

  What average force i16d tx :c4 (lfncmyjz;5 cmf2ls needed to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the ba:zc; tm lmy(f14 jnxd6 c52flcrrel of a rifle?   

A fisherman yanks a fish vertically out of the water with afm96/10niamm .wr y; ztfd6 lan acceleration of 2.5mmd.a1/6a yt96f w;inmlz fr0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 co2wd*f1peeeoy;9 g -betk 1da;ver a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the maximumxv lok22(l yv6 ml4hukb s1v59 acceleration is 0.0680 g . What are the maximum and lkhb2k4 o6m s1xvl(vl25vu 9yminimum 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 -s 4roljnz7bg(f 6l0hthe elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevagr 476bjf n0lhsz-lo(tor, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator hd7kewtq8mn *)br19d modpym 4:w40slas a maximum strength of 21,750 N. What maximum o d4bnr9ysp8* mdklmw:4t mw)7qed0 1 upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fallingj bcikj was6o4;i32+ enkjvkb1*w u3( sky divers (mass 132 kg including parachute) when the upw1u( ojb*i v33aeckb k4jn i s2k+j6ww;ard force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the ground ecm6v .um3b,s g;u(ktdc h(m7below, he bends his knees so that his torso decelerates over an approximate distan(.,3b(6m e7;kc cummhgtdu svce 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 vertically uoz/qnzboo tnyb7 ;- 59pward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the fobo7oz5-ntqoy ; /n9b zrce 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 diagramy18jway0 -hbj qd 12wq8hbd g0 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 bzg x .sz)ufl9r2mw:x6y the bat, and again (b) after it has left the bat and is flying toward zs.: z62lxmw r9u)gxfthe outfield.

A 650-N force acts in a northwesteroxm w0(dgqp +.ly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westwar0+( xp .qwdmgod? Illustrate your answer with a vector diagram.

  Arlene is to walk acrom48a gtt0)+o2f rkvatss a "high wire" strung horizontally between two buildings 10.0 m a ttako8) t4f r+gvm0a2part. The 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 i ,-5ol fcyq0jahs1;ois hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.0zblkaq1 ga9obw1196 agqhnzts9i/ 8 8 $-\mathrm{kg}$ 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 uniti* +;hhtv dljb h.ix5) to a new location at McMurdo Base, Antarctica, as sholbvid+x;5. hj) ti*hh wn in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the s3wa k1*ujt5oe ame mass behind it, Fig. 4-47 . Determine 3k51eau ojt w*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 the bucket-pullevv:m4h:a9 x diy apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise hersehvdmx va4: :i9lf 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 racd / /6hmgzrs.n7lrp, ae began, 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 4 0bw3) oudfsm.z4kci ufir;l+wij .*ass $ 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 are in contact with each re*g3k8: ydmzfij-gfp 5xswj .s*sic2.1;ezother, as shown in Fig. 8m: ydicj;-3jk2wr xs*ep 5g.s1gf*.zs i ef z4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are eacm8hgc6u s-snkhv59.c h initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum5s9h-gn 8vcsmh uk 6c. height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy corjo:-awkm79; kz*bd iwh :td9 pd of mass 1.0 kg . Calculate the acceleration b9odjp;:dw im*hk9: 7ktw- azof each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a ; 3vkn40hi5rxjs.od* gh30*n)lfb pkrf1dpm 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 5.3h flm3;yx 6ufqp0jp*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 trai3b-fgnpc4j w /n accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet an4 n/j3b-gwfc pd the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the51udxy,ba klvx1yv o/t.z63/ow k h)b coefficient of static friction between the tires kby w b13 vu x/a,k.v)yh6odl/o15 ztxand the ground is 0.80?   

  The coefficient of static friction bs8vx-)tl h:iv etween hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) vxtv: i s)h8-lcan 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 -4.887h4-)yaa f8ocn k:7 vjuescw0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 3lbz ann+p8 j: wds2-9o0$^{\circ}$ 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 con - ga-b* saz;)q;wbtzntact with an asphalt surface have a very high coefficient of static frictionnwz tgaa;-* zb;)b qs-.

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 friof .emlfok-jk z tq8m*5 -;5vmction 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. 4-3 (w)9bc-. *cklef.*gyd wu hso2 (Example 4-20) how large a mass would box A have to hclfye.w-* )ckdh(*9suo gwb. ave to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. z3 0ukk aqx2h7How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed ofakk73 qu zxh20 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 1tg uu935grnu7,7uiw8q-v jbm10 kg , are in contact and at rest on a horizontal 7umubq 9tugjrv n,8wu375 ig -surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a(ir3z s q(*zjp heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the (*zpq 3i(srjzmaximum rate 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 c .z cmvoc8r(r,lb:5(se4ix dgar in your driveway, which has an incline of b sm 8vcre,(r(ocix54:ldg.z 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 sl5vqeys:i 9/s wide 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 Figi vyuiwh:tx0,f zw (9;. 4-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial sdr30pw gvp rqy( )z zqy9l(59ppeed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of c3uczv(wq q;3:nqqp5 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 pushing on itler)r svujkj7,4 pjg+a:s;hcq3n- , 6rcq/h r with a force dir jhrh,vqec: jcnr grs4 +;u6- 3jr7ap,klq )s/ected 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 bec1 rhez,p7 x rjz:/aui3ome dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitru 31a ,zrh:j7xziep /ch 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 stor9n5)gx8x blepping distance for an automobile traveling at speed v is equaber g 98l5)xxnl to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car , lnb9fbzf 8m6lj(b*z slides forward on the dash when the driver deceleratesf6 b ,bflz9bn( mj8lz* 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 initial sp(jri6yh ,k h-aeed $ 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 th(vz,em*u v d0pu6 lwwfj2+1ohey are filled to the packing station 11.0 m away. The belt is initially stationary and m0wu j(zovm p wlvedu,*1h2 +6fust 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 each box?   

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

  Suppose the coefficient of kinetic friction betweemn7xdxu)m 77fm3 wuw, n $m_{1}$ 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 vjnq3d(g8 re-(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 simplifiedmm) mke r3fvt4u0x2(b/ 4gciy model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated fromb fm2(y4/3rx i)eg0ktvcmu4 m 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 d3y *k ;jdgurz4kzbd0x +lsi8*eceleration is no more ty*bgku*j+3l szk8r4 xd id;z0han 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 by an earthquake is a , and if an i dx 2g21ujta0)jz ak7object is going to "hold its place" on the ground, show that the coefg1aadzkujj x0)27ti2 ficient 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 .77cpgvr5cdb e;dmn4 accident involving two cars, mea pbgvm.77 dn5cc; edr4sure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 yd/psh + .0k)-vrowcchill (1-in-4 means that for each 4 m traveled along the road, the elevation. )owy0rc sdhvpc/k -+ 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 Pi 8;+n w:*/bifo.ivmdxf sg8 jgsa and falls 55 m before reaching the ground with af*v: g+ni8x g b8f;mwso/.ijd speed of What was the average force of air resistance?   

  A cyclist is coasting at :e ; vsis.xphkgy/8 kx4c- 0okr8bbj6 a steady 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 stretchb4x/s:v ; j60e k kro 8gx8k.-bchisyp without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. Al ksh;(p g8c)dn 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 o hc;(l sg)d8pkf 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin piec, :7 v5ufyobute of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes:v7f ytobu5,u 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 sever(s w.jh3 yss teel9kil, :4w/oal ramps connecting different parts of s/soijlh e4.:,(wwsk39y lte the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needemif7fh0wl62p ( l 0wwxd to lift the piano (mass M ) using the pulley apx0ilhwf0(w l7f 26mwpparatus 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 atg3 01e*zkenvpwhz2* (byc o 7rn,o4rk 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 -gw 6cic:id/bc;p ; zj0efza- chair, an engineer considers the followz6j-biec-da :wz0;; cc f/p giing 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 ton1ca:ck 7medem +o -gr0e9s28 uh /ghkfs (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 andjcf9y6ea.l c 0 Karen, 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 manj9eyc0ca .6lf y 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 " 10- .kni,nj-q8ng7- y8 leean4i*frc 5 ot1 $\mathrm{~b}$ 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 reach a maximum spee z;gne48u-( *io kkzpsd of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice field 6oc ui;bqv-aad72,mm1vhp -c inclined a,im a q-ob2- 6 cuvdv;7mhpc1at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.