Why does a child in a wagon seem to fall backiigop6m ru5cskm++ 8/,6j xwdk2 o5utward when you give the wagon a sharp pull forward2 um 5uj pk6m8+ks5xw+gi,6iotco/ dr ?

A box rests on the (frict*t syl c;mc- of(7q4vtionless) 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 on the ground beside the truck and (b) byc( s c7 ttm-y*q;olf4v Chris who is riding on the truck

If the acceleration of an object is zero, are no forcesje h )j*g:vky7y rh5+d acting on it? Explain.

Only one force acts on an object. Can the object have zero afr0t2we i+b)ccceleration? Can it have zero velc )2ewirtb 0+focity? Explain.

When a golf ball is dropped to the pavement9*s,mpt 5d3p65kld3 j(gd oufqqzi,ldh r4 *g, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If sft3d, gh*36ip (dmzo4llsgdd u jq5,qkr95p *o, what exerts the force?

If you walk along a log floating on a 5i5 8lt hgmd6xn o(,fm6xq+ag lake, why does the log move in the opposite direct6+i oxqdnglg58mmf ah( 5tx6, ion?

Why might your foot hurt if you kick a heavy :fimx is7f,6udesk or a wall?

  When you are running and want to stop quickly, you must decelerate quick r wd p:,l;*wiasj65 ,g*.mvrxg7zzsxly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your owzr;5gzm6*,dv j sw:ls7 wpr xi*.xa,gn 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 ceferf8g;ap6j h /wunb( 3kz9n+ 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 the stone or above it? What if the person gives a slow and stez89wf;3 ( knbr+fgp a/6nj euhady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1t 8 gp6cjh3-dx-kg rock. Why then doesn’t thghc8xt p3 jd6-e heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if th+ai0ygce4y ox(d* x7ve scale had beencd+7y y04xx(e oa*vig calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across ag0 2ksq1)( qzwvopju*rm.y4 l frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on q2l.gyvj wr ) 4pou1kqs0(*zm 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 net force adrzwkk:h((( mg exerted on it by the Earth. Yet by Newton’s third la( krwzdk( :h(aw the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object wh(d7 q kq7++0zyqtzbk3 bns1z aen you are on the Moon with the 0bbq77aqk tzk sq ++yz1n3(dz 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 + iy fugwb)tce6z4z);law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, deterw uzgf6)z ;ey+t) bi4cmines which team will win?

A person exerts an upward force of 40 N to hold ad(1ugw1 1f6gtx rxm7*; .zlolgfcr9i 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) by what obzrc1xow*x(tlr 1g71 dul ;.9gfi g6fmject it is exerted.

When you stand still on the ground, how large a force does the ground exeli7g2 p .dnzq5rt on you? Why doesn’t this force make you rise u zid5n7 l.qp2gp into the air?

Whiplash sometimes results from an automobile accident when the victim’s c13 m3v)zzigw gar is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it rea v3zzw)mg3gi1lly?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerateswe3 0l 2u*o4i lyq two41q+exx, the crate remains where it is on the truck, so it, too, accelerates. What force causes the craq1o4q* 3u eixt4w 2e0olw+ yxlte to accelerate?

A block is given a push so that it slides up a ramp. After the block rec4z hv,f*-z egaches its highest peg*-zc4 f,zhvoint, 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 weighed yourself on an iwhbuf,f2e(;x+l ji l)nclined plane? Assume the mechanism i,h+u(;leff xw)l2b jfunctions properly, even at an angle.

  What force is needed to accelerate a child on fm5 yj 6rtl9y4awrg6mc4+m )fa sled at 1.25m/s$^2$?   

  A net force of 265 N d:(ju5* vkfqxaccelerates 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 ifnq qad7jr w4x7 ,)j)oe:0oajh it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a 8lu(a 27) 1an*)jmhcv pryaab $76-\mathrm{kg}$ 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 sd -i s()p:y8t(yu qdv zizl)y6top an 1100-kg car in 8.0 s if the car is traveling at 95km/h? t) (q86 up-d iiysz(y zldyv:)-  

  What average force is nn9fqodk b+vzp5zeh, rs z/4k53d9 .lyeeded to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel kbyz dnqo/k+.p, 9ds3r5zh f 4zlev95 of a rifle?   

A fisherman yanks a fish ver;ly ; n9uk9wxyahq (qet* 2/gq9 g(oidtically out of the water with an acceleration of 2.2oyx;q(nyet h9 ;ak i uq9g(wdq9*gl/ 5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 tr ,itfzw8p1 u221(usr opyavg1ack (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 designedz;d* uzl,(rckql+ t2v so that the maximum acceleration is z;qltlc ,2 z*u(rk d+v 0.0680 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 motionless elevator. When the elenvlf mka)nd( :2oy+:d xq2 ,nul; zzq9vator begins to move, the scale briefly reads only 0.75 of the person’s rnoladx:,z uqqd;n2(v9z+ n:) f2lkym egular 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 maximum strenblvx ,h4 poy t1, 61))qeconlngth of 21,750 N. What maximum upward acceleration can it give the elevatyon),npl,cx1h16)te bl 4 vqoor without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (untm:+r;bv)jfusle,w 6e1 m5m,bh:p mass 132 kg including parachute) when sm)u wp: je nf;:,uebt,vbm65rh lm+1 the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strik-e4dbauw c8 cvy0hy; f;t+ wf5es the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kb8;c 5e vcuyd -+4fhtfy;w0aw g, 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 restsz) kdn f8i:um7jdq380 snfo,r on a table. A rope tied 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 the box if the weight hanging on the other side of thes 7n88),zmfn: kq 30 jofidrdu pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball player izcm3 sl8pf(8
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body dfsg2e / uwsl)4iagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward twue)2sg4/s flhe outfield.

A 650-N force acts in a northwesterly direction. A second 6hl:i py3us ;9s50-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagra 9h3yps:u;ils m.

  Arlene is to walk across a "high wire" strung horizontal24u ;niwe9 zq4zr ubk2maaj61ly between two buildings 10.0 m apart2a 24;ak r m1ewzjuq9un6ib4z. 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 is hanging by a massless cord from another 3.w:oae c*tcbt(9zhc5 .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.xl (:1uoc98xtlld q s-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 neff+lyf0n3odcpl3l+ w. 0x)i ew location at McMurdo Base, Antarctica, as shown in Fig. dl w03nolf0fcxp .+)ef3 y+ li4-46. 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 same maspxc*o-oo:icvh-u,* - e z)jj ss behind it, Fig. 4-47 . Determine the ratio of the tension in tpxo-zhe:u-c ojs*v,j*o -)c ihe 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 bkvql7i; ge3qg +v t8)kucket-pulley apparatus shown in Fig. ;gltgv3v + qkk) iqe784-48. (a) How 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 rk ,mx-3hx1g ,e bvds+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 (meu pm6;ie.2 i;1cb iarass $ 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 jhqvl ;qh o60:contact with each other, as shown in Fig. 4-51. vl0qhqhj; o6: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 inl:uviz.wo; i9 Fig. 4-52 are 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 determine the acceleration of the lighter mass and then its velocity at the moment the heavierv z;9io:iu. lw one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a fric)i zbr5f. 7ajytionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume i7b)arj.y 5fz $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 yy,u 5 s17pws7kizl:zfriction 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.-yyfi:*z82ud y0 qobe0$-\mathrm{kg}$ 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 accelerating at 0.20g.0 m 7r m ixe/ic:6ngsn284aciq What minimum coefficient of static friction must exist bet8in4/xes7 m0rc:gmc26 inqiaween your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffic+f8b/w7rkui a39gu pqf y, +.0fcd ocrient of static friction between the tires and the ground is 0.fk p+wi+ ua9uf/o.frb 7,crcyg 80d q380?   

  The coefficient of stat+ecqf5x3fb h*)j9 wvrcc-su / ic friction between hard rubber and normal street pavement is about 0.8. On how*f)rcc3f/vs -qu9 hjx +ce 5wb steep 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 -497t4bemt m; m:5fe gbm.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 ro8z(x trbb kzjvxv****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 cny3.t i4uqrg1k p50uc82k6ntrskn9 very high coefficient of static f0k ui96.3 prnucny2kt1snq k8gct54r riction.

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 kinef3l 3 0v0fpy 8sudnb;gtic 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) hu,pdqbj-t )s3zgj9 )oow large a mass would box A have to have to prevent any motion from gus-pjdj3,9)q tozb) occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides au69i pr611isgl gjh9z cross the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial s 6g1h lj9zigirs61pu9peed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are i wzkb57e iz-h:n contact and at rest on a horizontal surface (Fig. 4-547kezwh5 i:z- b). 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 static f*bh sqt)uq( 5 8oqn 2.e;o+sox5yfxv triction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide agains8e*+tv5 qohs)xqs fqx(ou. ; nob5t2 yt the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has a fu +sp- 2nbk3y7j0gion incli+n2j0 3u7pys kfi o-bgne of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a +; ajlhzuj8vruu) k+, ,s9xlq28$^{\circ}$ 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 planev f2z2,vyqq 6zpx -qr1 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 speeoe9;ciq 2v27 zacy:jdd 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 steegh1q 9* ygi8lalo88afc3f .. :qcqypn pest 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 pelat8i+ g2(qt56hvv against a rough wall by someone pushing on it with a force directed upward at 6iqv+hlt5 pga28v e(t28$^{\circ}$ 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 dangerousmvflefy 4(6m9yuqb5 56twfm 0 projectiles as they melt. Consider a chunk of snow at the rm mv9y (0b54f e6u5w6yqltm ffidge 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 l0dv6 v5way:f distance for an automobile traveling at speed v is equal to ay6v0lf5w : vd $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 car0w kt*pry*gu(l,k fi* slides forward on the dash when the driver decel*y *kwu*gki,rp0 f tl(erates 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 spnz)g ci(q z*9heed $ 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 are filled i8i;k;8;al .zdg bkdb00spgb(7i yzn 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 decelybl; zkaz7gi0;ip 0( ;8gsid.d knb8berates 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 betweeugh5v tir)0 l*ujzwbvc,a ;1h70.mbu6 a5nknn $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a 6.0l;uv9sou5 *ol $^{\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, a5 c.awruq2x j1t each pulse approximatel5 2wqcar j1xu.y 20 g of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automob p(nsxycq32 r0bjl55tile crash if the deceleration is no more than 30 " g 's." Calculate th2 jr5tyc0b5qlp(n s3xe 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 earybkv;z) n-:a1bce5z ythquake 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 be at leaa)-:y k5zbvcyz;n b1est $\mu_{\mathrm{s}}=a / g$ . (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, examining4iej94e(:phgd z8 6( vfckard the scene of an accident involving two cars, measure 72-m-long skid hr pkd4zce 94a6fdj((:gev8 i 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 hil2veszm/gz5 n llb.w/ +l (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) Ign l l+zw./n/gvezbs2m5ore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top u s26ftjmencn4;+ j .emaz3;bof the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of +;sb6je .2n3c;n muemt4jazf What was the average force of air resistance?   

  A cyclist is coasting -3udp rk)o 48 d bbbg*l)jzks/6udf .gat a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of fr36 z4lru8f/g* sodkukjd.)-bb)gb pdiction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly /zsfhk4+e 5yi 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. yf5szk+h4 /i eA 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 exper1 yu(hqi.l4o8;*v7xt th8ukkvjz s- r iments, 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 t-s4*t8 vuv;ryq8oj hzk(xlh.it 71u k he 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 supw/gmy q b ht. 2.c+:i7a3z tk.d-fbeygermarket, there are to be several ramps connecting different /3t ky.ef+ 7. -tmd2h.b yiwcb:qggza parts 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 forco r/t91cc. pl daga1 yf84omn*e F is needed to lift the piano (mass M ) using the pulley appa*. of rt1g pccoa1da4lym n/89ratus 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 acceler p f,fhrz1.dpuyecz4;*i41 nyating 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 chair, an engineer considers the fo woign ww4om0o0)jns3 /r84)+ dji6vco2fbzjllowing set of3w)ic w4+m4w vbr8nsni /6go)ofjdj0o 0z oj2 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 mar.x, oida4yg saw*qf;a ; au5y 6vj+4hss of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length. Karenx0h nuy bh81kx8:ht 3;tl-c 4m4dmdo/h( g mlz'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 strt;mt4dx ll4:nh(kh8zucd1-hbmxhm o 8y /0 g3etches 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 awu,as ; oqrb8 lc:2vc+jqk)0 aji d10w " 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 allo2umt.q atl4gvt4j89m wed 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 to,s 31yvv8j zsggether are ascending an ice field inclined at 218,1s3vzg svj y.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.