Why does a child in a wagon seem to fall backward when you give the wagon ag -o6m8letjq 1 sharp pul-tq8 m jl6oge1l forward?

A box rests on the (frictionless) lubbfi r/6 5f0bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the grirb60f5/ bluf ound beside the truck and (b) by Chris who is riding on the truck

If the acceleration ofs*xe35c dk /qe an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Ca(82rnf,- typ w,dlsa,qcq na7n it have zero velonsf c,7lyn-q8(aadp,r, w q2t city? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a forc6j 1:m y4nx *.i-kv5txqx sooce needed to m1 oms-yckx.*6i xvjn5xqot 4:ake it bounce back up? (b) If so, what exerts the force?

If you walk along a log floatir5e-zygk u*) lng on a lake, why does the log move in the opposite directi zgry5ue-* kl)on?

Why might your foot hurt if you kick a l1fqz8;zzuw1i-m cpu1g i7y. heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (a) kbyy86 c2:lzp 9l5bzu w;)i zrW bzy56 p)9ycb ; lzi8wz2:ulkrhat 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 top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the cer0u y, ,ddbqy:iling, 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 :dq0r yd,u b,ythe 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 4trsrd 2fsce 5ov (;d75d5pfo great as that on a 1-kg rock. Why then doesn’t the heavier rock fall far7o4;ddf 2fvc55(r5tod pss ester?

Would a spring scale carried to the Moon give accurate results if the scale hadd00/, hgv xll:u;z ytd been calibrated (a) in pounds:ugv d y 0d,xz0;lth/l, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using adymgr;cb76. mn attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box re ;dby.mr cm6g7maining 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 gravity there is a nn(0tx.7 3no ncmu aaw1et force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and oppo3.7mu 0nac1a (onwn txsite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are on the 2 +wgcdt 7n:ga d**fymMoon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with agmy n7*c a:fd*d+w t2g given speed on the Moon and on Earth.

According to Newton’s third law, d j pn on 628il73o1q*qibue;weach team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will win?j1 2p8qeob7ud; 6w3oi* qn nli

A person exerts an upwa1 fn: xf9acp706amg n. nak5. tb:blphrd force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) bygcafk9:56ba01f7 xl. ma:nptn n p .hb what object it is exerted.

When you stand still on the ground, how large a fo*5 yo8, rizc k6cz3lvhrce does the ground exert on you? Why doesn’t tz5o8vz6 *rkc3,lhc y ihis force make you rise up into the air?

Whiplash sometimes resul0gnr rel8 o5ol 6:um-sts from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward i eurm: sl8no5ro- 0lg6n this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truco o7cc;.(6s o x5q :whwjke/bck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force cause( /b;w.cojwxsqc o:h7cke o6 5s the crate to accelerate?

A block is given a pus+5l y iyt9gy5sh so that it slides up a ramp. After the block reaches its highest point, it slides back down but t tyyly+9i g5s5he magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined planzlb: 2x k6yw 6j:qayn,hwht4v(m(ft.e? Assume the mechanism functions (mjz6.(:kanfvhty w:w6qxb,h l t4y2 properly, even at an angle.

  What force is needed to accelerate a child q ,i5s hwtlf tu+08c9hon a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerat:. + hw xnd(j*nte.hqdes 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 accz rx.weo55 wi3(.yhjvelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a d0kr jxwytuk+41(qq 1 $76-\mathrm{kg}$ 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 cajg6 ab3(a t8aqduuj9m4hw50 l r is traveling at 95kmw(jjubl8 amuq dtah03a6 59g4/h? -  

  What average force is needed to accelerate a 7.00-gram pezi9jis 7 ;yh-yllet from rest to 125m/s over a distance of 0.800 m along the barrel y;9 siyih-zj 7of a rifle?   

A fisherman yanks a fish vertically out of the water hqo+r 06)pxwf k+-shz with an acceleration of 2.5 -6fp+r shk0wqozx h+ )$\mathrm{~m} / \mathrm{s}^{2}$ 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 (40/ /3ve yvzquyr3m( xw)2 $\mathrm{~m}$) 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 designekq7-cw *d:y +;mvc6umg uvfg 4d so that the maximum acceleration is 0.0mwgm 46+ vgd kvc7f :-uy*uq;c680 g . 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 mo+(gqw0 s.mz bztionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of b q(.+zgws0 mzacceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of yvi mpb sui551ea wkj0g+*3d/ 21,750 N. What maximum upward acceleration can it give the elms v0dijb g p+ak i1*e55wuy3/evator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (m hcu9k nx95poe.weo0yoe48z) ass 132 kg including parachute) when the upward force of air resistance is equal to onexekp5h80z4w c 99.oone eo )yu-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 room 8684gcbk etb+qe,nk f 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 hg8,m6n4bc+8 ekb tkeqis 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 s dq u fm9-gb:hvn232zt+9tmntied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on them-dfng ub9tnvs9 2qz:3m h+2t 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 diagram for a basketball pc( 1 og8ial6p//t0ha*n; u ayhelkzp3layer
(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 hittjww865wi x;yz 48hv )-v/va2v yogywwg,t ( h by the bat, and again (b) after it has left th 6t8( v/v, ;z8axtwwjhyoiygww wy-)5v vg42he bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force m 7k71(e l*vwmvnl3ufoust be exerted in what direction so that the resultant of the two forces poi(7 7*ovull nm1 ef3vwknts westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung )la rcdj/2z)p h6dx 5if4 qkh9horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the m)) 5jld rzf pihd9xcqa/462kh 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 by a mass.nn5q (udse*pless 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 14.0mdxn v6jy n+;/py* x2:xtfe(c$-\mathrm{kg}$ 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 ho7: a-jo ld* )wc2gibtmeb *8dxusing unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46.8 mtg*eidc)lo bdxw*a7- 2bj: 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 it, Fig. r0 e wi62sc+as 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first0aesr+ cs26iw 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 (x8+vlzn+ zxtbucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself sl++n t8 zlxz(vxowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a au/9lpr ead9 .g( to4q 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 blo;0kd1m/e jj ysck (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 frictionlesbc,w(rnt +ci.2wg ku3s horizontal surface are in contact with each other, as shown in Figr,bcu ng3iwk 2(+w .tc. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are eachw ( g:mubk3h(g initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m awm(hu: 3 (gbkgbove the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord lff(glz 107i6upp eo)of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, ppuflo1gl6 7 )fe(0z iusing 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 8c;g1gvag g9j9 9ygwy 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 5.wtmd,/42 2uccod 6bm k0$-\mathrm{kg}$ 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 acceleratingoa/ nk2tj7) qfps16pt at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to sls j) noapt2kf6qp /7t1ide?   

  What is the maximum accelercwb lbjb byk)/j*9 zr/ +/mrh2ation a car can undergo if the coefficient of static friction betk/* zbjbl c9 r)yhr/mbj2/b+wween the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber anun:1 w; (jcddad normal street pavement is about 0.8. On how wc( ;ju1:adn dsteep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4.8;y,bp4u.co.3neih*ze -h2u z ja 6gl9ejusb:0 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough 3k-01u,hsao 8nzco n1q0$^{\circ}$ 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 surfacb8 jqbl(lp/ j2e have a very high coefficient of static frictionp/lbl2b8(q jj.

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 frictiony4mf4wge1;m q 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 have yrpg.8d 7awm2to have to prev8yrd.7aw gp2m ent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across 3fbmd ne/ v/h4xv eh.5the floor. How far will it go, given that debe/m.h/ 4fxv 3hvn5the 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 anq p99- r9fppto8rvse-po/ e(ad 110 kg , are in contact and at rest on a horizontal surface (Fig. op8oqe f9(t -prrsppa9/9 ve- 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 ca/hrggk o5 *e1lrrying a heavy crate. The coefficient of static friction between the crate and the bed ofoh/ggle5 * kr1 the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry aboutga9 18sa t42vcmsrov: parking your car in your driveway, which has an incline8asvo14msc gv29a:tr 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 amzr qaoq kc.24j *.0tm slide 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 Figueoa16y5;3knbh4 q2aezr8 w( zef3 1lfof mm5. 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 spqqq6j b-hoy)1eed 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 to1f ( huhi- nsdq5++q 0tolpd3gp of 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 rouzz/x:c-pls, ez tz kw4qf/v bc 9o;c8,gh wall by someone pushing on it with a fo/8-v e zzl ,ztc/fpsxq4b,w c:o;k9zcrce directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slip49 //rchew*btoy 1pio pery roofs can become dangerous projectiles as they melt. Considb4e1h 9/ *ro wct/poiyer a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveli* kby nd,;adc ;uu(h3kng at speed y( c*adu bk;uk,dn;3h v 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 car slide7xb f z2d)i0oqs forward on the dash when the driver decelerates from 4z)fb i0q o27dx5 $\mathrm{~km} / \mathrm{h}$ 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 speed i4bcycz z6yv; ( 2id;x$ 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 k(q t 9zkyxdt/j9:pc1 where they are filled to the packing station 11.0 m away. The belt is initially stationary an1pqz tkdjx: (t9k9cy/d 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 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 betwexv3 ph4groqd-uv3uo w 493hl3en $m_{1}$ 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 (n)g2ptxj9xn79:)bdt;pz13 qn h bm buincluding 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 of a mammalian heart, at each pulse approximatelnv7acyiiwphr oj0 o79s7q 8g ;g7h3+hy 20 g of blood is accelerate 3 ncorqo7whg +80 sh7a7gii7vp9hy;jd 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 - q 1u6t6fyhvzan automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a 1hq 6 yv-zfu6t 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 acscy*5jph+v 88nwhdbj 4c c+/j.n 1vphceleration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must bewy h8c18jsj. n+5 phvn4/cc+bvpjd *h 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 ac ao) ; fnb8tbfaclz9xz.bo:4 *cident involving two cars, measure 72-m-long skid marks of one of the cars, which 9f:8 a4bz;c).ob z*nxa otbflnearly 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 hill (1-in-4 means 1cc* fy6 gfd9tthat for each 4 m traveled along the road, the elevation change is 1 m). Hoc*fg6dtcy f91 w 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 dropwwz/, sxgz5b, tyt5t4 ped from the top of the Leaning Tower of Pisa and falls 55 m z x,s gwbw4t5tt,5z /ybefore 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 but enteyjj9dy s z:d 7m;)b7msrs a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muysd 7) s7y9m:jm;bzdj ddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is workiwzrra aqe3r*/6;o x1x ng on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills ;r*wxr /a3 a1o6reqx zwithout slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a bku u;) tiy1ui,an (7wthin piece of string while the jetliner she is in takes off from JFK Airpnu;t,bkiy(7 1wiua)u ort (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps co-3li,ek4uyyue 17ju2q) jc sznnecting different pa j) u,-keqziu1l u2s43yjyec 7rts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M c qz,syw7xj60hmlemh 6v1r 67 ) using the pulley apparatur ,xc6wm7zm1h 06qeh7v j6sy ls 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 accele/ a*wqmcq09l0md5y w hrating 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 6(zzcont. j ehtsbf61gig:8+chair, an engineer considers the followitzg .js+t6 i6b:cgfz (81eonh 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 metric ton06r:rif 1o 3jomwyw*ks (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of s 5hwaad e9a*u bg4b3b:imilar 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 tbba b3u :5dw9gh*ea4a imes his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is usieea54of d/vo)fhau:9a( p ,pi ng 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 reach a maximum sw onhitxa5 7(*peed 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 roux1r9 whr -.*vuic,l8jcamr3 ped together are ascending an ice field inclined atri* ucjv8rc1,-wmuxa9.h lr3 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.