Why does a child in a wagon seem to fa4x:pn2e :rfjfll backward when you give the wagon a sharp:rj x:4np2ff e pull forward?

A box rests on the (frictionless) bed of a truck. Thji*j- f1ilonq(/4 ky a0 ru5tfe 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, a*it j 15q4akyuj/ i oln-r0(ffs seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on ipl+) o+2larcwt? Explain.

Only one force acts on an object. Can the object s7msyzqr 7d 1/have zero acceleration? Can it have zero velocity? Expdq/rs z1s7my 7lain.

When a golf ball is dropped to the pavement, it bounces back up. q488ggih .nz +f(x sbz*bwkq,(a) Is a force needed to make it bounce back up? (b) If so, what exergh s z8(fk,xqn qb+i.z8*4g wbts the force?

If you walk along a log floating on a lake, why dosny,2 fs7pgs+f7noq +es the log move in the opposite directisgqn77fof2 ny s+p,+ son?

Why might your foot hurt if you kick a heavy desk or a wall?498 j8acf0 :frfimyza

  When you are running and want1of8aer,q/znap f7 u g:im83t to stop quickly, you must decelerate quickly. (a) What is the origin of the 87toi1qra3meaf:8pz nfg ,u /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 ceiling, and a secti/8 (dh0xmuy avon of the same thread dangles from the bottom of the stone (Fig. 4–36). If a perdy8umv0 (x /ahson 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? Explain your answers.

The force of gravity on a 2-kg rock is twice as gr0xapok g jd(-1eat as that on a 1-kg rock. Why then does 0pa-jgkx (1odn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate riyj20a4bgz w0ca)k n8 esults if the scale had been calibrated (a) in pounds)z8y0nk2ai4a0cw g jb , or (b) in kilograms?

You pull a box with a constant force across a frictionlessvz-rn ,p/mw 35h3gvlz table using an attached rope held horizontally. If you now pull the rope with the v-p,zwmvnzg 5rlh3/ 3same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gcn ixbjozvw7)*2cys1r k pe ::sjy+ (.ravity there is a net force mg 2wj)nc +jexvkc*:1rsz obi(ypys:. 7exerted on it by the Earth. Yet by Newton’s third law 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 ob+7tjp1jz9v s ( iopj0cject when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to thr1zsp pj vjjo9c( +ti07ow a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug *vmby 2 (brqxko uoly2f.,4r8of war (Fig. 4–37) pulls with equal force ony,y 4(2lm2o.b xr8fo*r bvkqu the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N k-5e*pq(wt b0boi : afto 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) by what *wb btp5okafiqe0(-: object it is exerted.

When you stand still on the ground, howphj*5ispv1-(ck.x 1vopdj x7 large a force does the ground exert on you? Why doesn’t this force make you rise up.xc (jj *pd -kv1pp s571ixvoh into the air?

Whiplash sometimes results from an automobile accident when the victrv46l xoxvg rl.z6qp/ hk 4k(+im’s car is struck violently from the rear. Explain why the head of the victim seems to be vk46lqkpr+.6xo4r(h lg/zvx thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accef j7 :es/khz/.d/e+iwhdhcj8lerates, the crate remains where it is on the truck, so it, too, accelerates. What forc/ei.sc:j /jhd hek/+wd7h8z f e causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block rea( woij-syv,m +ches its highest point, it slides back down bijy-w,o+ svm(ut the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you wbw*4e4eu/9 zo omo-wr eighed yourself on an inclined plane? Assume the mech- o4/we4bmz*w oeo 9uranism functions properly, even at an angle.

  What force is needed tb2rezs tq4u/ -o accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceleratesqr/wy svrtmhz; x 1(09 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 a0nu wcfj6mbmm5u5i1- h yq:s8ccelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a hai:y8c*r5 tfn:w zk7 $76-\mathrm{kg}$ 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 bn 5jd4k4t*6-i0)fn pkj 9 +xjtgd qfcis traveling at 95km/h?f5q 9g)tp6fc* +xjj k-d0tnbj i4nkd4 -  

  What average force is needed to accelerate pk dfeqdm+ry4j0mq:o 08 h1reh+ 3sz; a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the bar+ yj r8q0e3 m;4p:kqddro01zhh+ems f rel of a rifle?   

A fisherman yanks a fish verti3gzfn0el0c. vp- f a8pcally out of the water with an acceleration of 2.0n-f8 g3 0p vfl.acpez5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 quartek0oillw .5.8:msc gql0yan/ br-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 kgpl3 4*fs,vqso )rb dr6 ) is to be designed so that the maximum acceleration is 0.0680 g . What are the m,prvof4 *rqss lb 6)3daximum 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 db yrs ;sy)tuq ex//2v*8m-rxbathroom scale in a motionless 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 acceleration.r qv)d;/xy8s* uxme-yt /2sb r     ----待选择----downupward 

  The cable supporting a 2125-kg elevator h*l)u v;ravsk;as a maximum strength of 21,750 N. What maximum upward acceleration can it give the el *;r;vuav )kslevator without breaking?    ( two decimal places)

  (a) What is the acceleration of t; mzm hh( g7q7.m kysra47oxw/wo falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of hz7h4(xrgwmm k7 .7smaqy o /;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. yc1ot7jx3 *wq9-m high. When he strikes the ground below, he bends his knees so wocy7x j*q1t3that his torso decelerates over an approximate distance 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 tie,q x+ wdk)i y)s4ma:xtogp6:fpa8 0tvd 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 vt8qp tmp+ a) ak)xoi4:d:6,w0sxyf gon 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 diagram for a bas/d . 65e1gncb/ufc8ygvx1xgz ketball 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 g8 e76r1jz efcty bllc(z15 0u )tkz.pmoment it is hit by the bat, and again (b) after it has lc0 y glklz7()tj.r5 zt6z1ucb e18pefeft the bat and is flying toward the outfield.

A 650-N force acts in a northwestui p6u ,xmb kv28aph v9b;xt60 7fg sl4(ntnt:erly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector dpt6aiv0nm2ng 9x4suutt ;xbp7(,f l hb6:k 8 viagram.

  Arlene is to walk across a "high wire" strung horizontally between twovqwd yh3/0w2 j buildings 10.0 m apart. The sag in the rope when she is at the 0dyjh wq/v 23wmidpoint 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 d n4e1lv 1i.f mvww43qis 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 1rs;bj v;szt 5mx9;pv/ 4.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo pkcpe-q4 cs8rqt1)l n87xr,rBase, Antarctica, as shown in Fig. 4-46. The pr7n -)t1xk8,e8lsrp c4q rqc 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 mr1d);z,j be g,c e2 :t)lb+;bvybdft the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling btdy gfbmejz e t) ;)2;,:cbd+bvb1,rl etween 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-pulley apparatus shown*rt,(ni5lnr z in Fig. 4-48. n 5,ir(*rltnz(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 began, a u7vkswoa w 0n3ew(b* 865$-\mathrm{kg}$ 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 (mass hy + ie9i0mj m9h441dqc- brzy$ 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 otoew5. zjc ,*ko9 t mnv33f6dysher, as shown in F n93k eo*ojm 3y.vc ztfd6ws,5ig. 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 each initially 1.80 m above the gr+gs )sysstg )c v+:l3yound, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after) vgt+)s ysglys+: cs3 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 fri7i+p0 8(uyxcgep+r ulctionless table are connected by a heavy cord of mass 1.0 kg . Calc+yriexgl 7p p08+( ucuulate 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 $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 bet2am6mxjww5 , eween 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- ,n9bhv kcu4lkurl+z8h )f4za w 1m5a required to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are s0dqq4wp3*sk p tanding on a train accelerating at 0.20g. What minimum coefficient of static sq04p*q dpk3wfriction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if tcl+pd.3e rv*r u k7t4vg)wu(mhe coefficient of static friction between the tires and 4)lrw7cv m3vpgdku ur*.e( t+the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal mkv.w6g0spxuw5l9: k street pavement is about 0.8. On5gklu k0x.vmww 9:p s6 how 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 a,yz*7exw d1 fct -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough 30cq fo4vmv 9l6;$^{\circ}$ 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 suo x8 (/ayg1 cogbb4 om.v8go1yrface have a very high coefficient of static friction11gmbx /g.(4g yocvob8ao8 y o.

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 friction qo ,hl; tn+,nwfor 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 1j6kri uk)ig-o25j+1rp m cwx-32 (Example 4-20) how large a mass would box A have to have to r1w j1uomc 2)j56+-kxigirpk prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push s4u,f y-f92gjvs*qhr c0 5 fjbvo that it slides across the floor. How far will it go, given that the coefficiengruc,qsh0jfb4*vf2 j 5 -yv9f t of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at re e6c,4+hvm.fktfj - lkst on a horizontal surfaef,h.j-4ktm6 kc f+lv ce (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 heavy crate. The coeyd:-g9oe- fuy fficient of static friction between the cra:f--ug9yy e odte 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 against the cab of the truck?   

On an icy day, you worry abouem;: oe,s4 wjtu/msj2 t parking your car in your driveway, which has an incline ,umt2m/ sjeo:;4ewjs 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 s v2a )p4a:xt,mycp/woy.me)a*p az1j lide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a eeqv+21-a 1 :uxat*sikzcj l;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 anw2gfe949r :6jxq4zr uqy t7lv initial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches t-d:1) dgoigmu he top 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 rough wall b/snb5. tvz cs.u,6kph/ zw1f;e :qb gqy someone pushing on it with a force directed upward at 6:k.g//e w uphc51qqbt,;.z ssf nvbz28$^{\circ}$ 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 roof8hh::imcu z-r1a v0q kl* dj*ss can become dangerous projectiles as they melt. Consider a chu1 0* hrlmc: q dv-hzk*aj8:uisnk 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 autq)r7 k.d+eubnd o*x3momobile traveling at speed v is equaxuq)m7 *br keo+ndd3.l 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 slides fpgaw;8bf /,l y:.ms qo+l)os j;lh)foorward on the dash when the driver deceleratel)ss y:;,jal /oo;bflgfwo+ 8h)p.mq s 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 initialaer/-3-w hbtdpw )w 0e speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyorbylk) a-fn:jz446 td f belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If thefbktadyjn z:4l)- 6f4 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 f,yr;4hj9e3uhrikjr(nv 02e x riction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down z w:e(xem70 gka 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 mfb1f3i0 e p h.v/1*5bndi xbknammalian heart, at each pulse approximately 20 g of bloo 1edbvfn f.bk0ib 5*3hp i1/xnd 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 automobile crash ifn/z 08+:p geduhli ki(h9f96uc t h9hf the deceleration is no more than 30 " g 's." Calculate the force on0nu /+hf9hi 8h6 klhe tdg9f:(uz9 pci 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 m +7,ttla f(v b.jw,kpan earthquake is a , and if an object is going to "hold its placem ,.j,at +v7(kpwtlbf " on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an a17 c8 dvejdvk:ccident involving two cars, measure 72-m-long7d ve18k v:djc 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 hill (1-in-4 means that for each 4 m traveleo7m *s ff,rcp8d along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (arf8 *cmpos 7,f) 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 Pi7sx1csy, +djssa and falls 55 m before reaching the ground with a speed of What was the average force of air resistay,j1scxd+ ss7nce?   

  A cyclist is coasting at a steady spq5 u3kbu0/ 6st*qnqsweed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0* uqn3qkwbq /5s0u 6ts.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 bsz enq 5xo*b1b+jc- 4na9 9cmredesign 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 wi+9bcjc 1zo a nb*5s9x4-nbemqthout 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, 4vudw a)i 9jihmbt825dangles 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 thjwi hv)bidt2u8 a45m 9e 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 supermar 0*pk3 j4uzqkpket, there are to be several ramps connecting different parts of the storej zqpk4pk* u30.
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 neededql:) uma8bs;h to lift the piano (mass M ) using the pulley apparatus shown m lh)b:u8q ;asin

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 ace2ew8ydx c9fq fq73c*celerating 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, 0,kj)ixi :in(iu)nbnan engineer considers the followiuix ,n)kbjni(ni:) 0i 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 tons (6 /)k2swykl yb,60,000 $\mathrm{~kg}$) . 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, uspv8kx ut5y/(i9nz + nme 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 frnxz5(n/9m 8tyiu pvk +om the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is(y6 77f1ult4pt jlww c using 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 speed of elxi/i,q1w :u 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 r8svt xyq za1le/to 7a;l 25m-ct-q- lkoped together are ascending an ice field inclined at2 ctkts;eaqa/yx 7l -vzo 8mql15-tl- 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.