Why does a child in a ury(4( hy 2nfxwagon seem to fall backward when you give the wagon a sharp pull for (xhyy4(2 nfurward?

A box rests on the (frictionless) m 1xa,lkfn)4 kbed 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 grokanxm1 fkl,4) und beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object i : m.qjp)sey7is zero, are no forces acting on it? Explain.

Only one force acts on an) b5.7bko3-ijykn:v (bpxcbktm/v2m object. Can the object have zero acceleration? Can it have zero velocity? Ex-kbo7/mbx nkv(:b ck5 p)y.bt2v3 mijplain.

When a golf ball is dropped to the par vjpk.ed.( 47 plw,gbvement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what ej,rpgd.kl4b .(pew7vxerts the force?

If you walk along a log float//7wkeqri4e j ing on a lake, why does the log move in the opposite directio /e4rkw /eq7jin?

Why might your foot hurt if you kick a heavy desk or a rg, 2k+by v+abz l-ns c0nc9li:s(7pawall?

  When you are running and want to stop quickly, you must decelerate quicc;pit-xl99 5wiwd-rk*5fz6ut v8 p sckly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person rrtwvi8 c9p-w*l9u sfkc;z 5d p5x-i6 tunning at top speed to come to rest.    m/s$^2$

A stone hangs by a fine threadmk( i2 r 4app0g9)vnhc from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? ca p)k04 r2pgmvh9( inWhat if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on azyrm (2 tixbda,)j19c 1-kg rock. Why then doesn’t the heavier rock fall faster? d(9camj)2t yxi1 zb,r

Would a spring scale carried q,i;wthy+ 1tg. waa ;ui,kj-t to the Moon give accurate results if the scale had been calibrated (a) in pounds, or t,1wg.at jhiki +y,-au;qtw ;(b) in kilograms?

You pull a box with a constant force across a frictionless table using an attzyb5cjl(/0f70*+ pb feyswq tx s)b y.ached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleratij(e x*z t5l.q+0scbyb 7/psff 0ybw)yon of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity t7rwm g *0tiz n4t2b:1azi6*l7s8dlbv.ep ml ahere is a net force mg exed vt4wt ib bm g12.m:r8a*a7lsll7z i60pn*zerted 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-krr798jub lybpj 7 jd0*g object when you are on the Moon with the force needed to lift it on Earth. Cod u70b9y rljb8jpjr7 *mpare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s thiftu07 9vjq w4erd law, each team in a tug of war (Fig. 4–37) pulls with equal force o9t v0wufe4j 7qn the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Desc c*ne;710 lgnbt7dfdn ribe the bng0tn l7n;ded*fc71“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 object it is exerted.

When you stand still on the ground, how large a force does the ground exert onor -x2pz g6+yt:bk+m c you? Whc 62myopxg-+brz+k :ty doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when e7f5l u5b q.fvthe victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. lf5ubqv e7f5 .Is it really?

A heavy crate rests on the bed of a fl f)pq y8fot08as.uv7natbed truck. When the truck accelerates, the crate remains where it is on the)0tysa vnfpqo8 f 87u. truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it yk1cm +wszj- (jpi0,.c i ig1pslides up a ramp. After the block reaches its highest point, it slides back down but the magnitc - m1iyjpjp(ikz0+.wsig,c 1ude 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 inc(3pgw io+wdzdk 2cqi8 76m t2plined plane? Assume the mechanism funptk( 8 qciogdw37m2dwiz6+ 2pctions properly, even at an angle.

  What force is needed to accelerate arrht fl )o/, oz*a)yai8s9:s/ tpzhg: child on a sled at 1.25m/s$^2$?   

  A net force of 265 N sdrnw p71++l4d 0br gs(2gaxu accelerates 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 oc9c3 kcd vinbhhxa.d9:2l1wk1k/32ns iq (yaccelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of7sq6cjafh-+z2 2ct 3tu d .e.fbme3sz a $76-\mathrm{kg}$ 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-kg8,q+t xy bwj4r car in 8.0 s if the car is traveling at 95km/4t wr8x +jyb,qh? -  

  What average force is needed to accelerate a 7.dyf txd q1aj2(ro1 di3sr3f8; 00-gram pellet from rest to 125m/s over a distance of 0si8tj;o1 21xfy ra3d fqd(rd3.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water wikrb((x0d5n 55 a ecq/ld/:nx rul)fqhth an acceleration of 2.50 n hxdk/5 l( lc5ndru)a(5qrb/eq: fx $\mathrm{~m} / \mathrm{s}^{2}$ 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 coverh ,(8ozv-4itn fmzm+x a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed 5 getm(x,g*cpso that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces thegtcx g,me p(5* 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 bathr lj9v)n)nswcw u4i-),,g0y l 1e fhlacoom 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 achvyfcn,l 0-)uags9 1ln) ,w)e4cwj ilceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator hatv.b7;lng e 2ts a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator witt 7l.ge;bvt 2nhout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg iee i69jof* vop17,xvk4z - flincluding parachji4ke,v1p6o9*el fv 7f z-o xiute) when 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 hfhjs)dd8,0b)(hq qyl fkvf0 2ouse 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. (jhh)vq0 2l )kq 80s ybffddf,If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box r7/z vcolm2i7 euns 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 c/lio7e7zvm2 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 pl0;gkup 0m;qe layer
(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 mvukx18ily m af*z-q2.s9vwn )oment it is hit by the bat, i* )-vkvsl8zxam.2wf19ny uq and again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts i* rfziad n-)k4n a northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illur*iz d 4na)kf-strate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betweenc18 iyklh (o)c two buildings 10.0 m apart. The sag in the rope when she is at th c8lyoi h1k)c(e 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 p+sb7ckqy):i ih * m3)risxv 23.2$-\mathrm{kg}$ 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 14.0)ptp)bzfms-, 7nk oh/$-\mathrm{kg}$ 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 3/gzg)go.cwounit to a new location at McMurdo Base, Antarctica, as sh cwggo z/g.3o)own in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulup. kv;gn7 ca80yj,paling two cars of the same mass behind it, Fig. 4-47 . vy k apn.j80pca;,g7uDetermine the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward usi(8 ( .3fr uee4kk zlp*isksh0ang the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at c(i8 .a4e0zkhrekl *pu s 3kfs(onstant 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 6qtrpthpm,m)zkm8w2(3nv6. z:b(e yq 5$-\mathrm{kg}$ 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 (massbdyj 4x 1:,a2saevc)szt )kis 6f p,d* $ 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 horizontal5 9skb9bd1pqcftm6xxs9(q -x surface are in contact with each other, as shown in Fig. s-m9x9d9tbxx sf 1 6cb(kpqq54-51. 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 gwi/d*v+rdgq la 5+lsb5 ak rg)k+ 9e;kround, 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 velocitalwir v g a*ksq);5k/+deg9b++l krd5y 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 fric rtzn+py(e o;9tionless table are connected by a heavy cord of mass 1.0(+;erpoy9n zt 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 $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 b (3 y dlbad;os- c9 2gig9bvu5kyy*qm8etween 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 requ 7ei2 bwj (7lm5aq md(/;upafmired 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 standing on a train acceleiz nemz;2o 0o3h/:gkkrating at 0.20g. What minimum coeffici oz; i2mk0h/ 3oen:kgzent of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of9 3h*nuwm)klu80 omak static friction between the tires and t 8 whl9)0a3 *nukmomkuhe ground is 0.80?   

  The coefficient of static f78eogkxr6 d-uriction between hard rubber and normal street pavement is about 0gdur 7ok6-8 ex.8. On 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 at -4.86os( ;s/ nsqsq0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 restmp- oz)ne jk4) on a rough 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 erm h32jl ,98s b jvhe5dl3)dmsurface have a very high coefficient of static frictioj)3hld23d8bvs ,95me jrhm len.

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 fr( 7 :sx yfs4atg80rjtu.rf/viiction 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 ao+-z3 .xstelb.+pt ix mass would box A have to have to prevent any motion from occurring? Assume. xe.tt+ixsbz p3- l+o $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How b: d6ue vmu7h4far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 ehdmu:v74b 6u$\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horizoy wnj.yb9(lf4h g8axgy(p9 /mntal surfaj y 49fwx m9(lgy/hpgyn.a8b(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 coefficient of static fricti0gwbls25mizy r.;b( msnv2n1k:mqv ,on 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 against the cab .k; qmvsr5v2bbys0 n1m z:igw,m l(n2of the truck?   

On an icy day, you worry about parking your car in you56 0f0h+zbdwyh*d xx or driveway, which has an incline oho+0 fzx*d50xhy w 6bdf 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 wit j77n+p8u(oxpoq.tq g h 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 planu1 o/a8a oy.vde 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 ansn 3 xc(hq+c nkn6-9n7v2vplg 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 the top of the ste;qdt19voi dc9x6 3tbu ;lx e,mepest 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 by g8um 2h8wz.dt someone pushing on it with a force directed8mw.h tdug z28 upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become lxwrrx30 of06oe 8fwb /2e8zpdangerous projectiles as they melt. Consider a chunk of snow at t/208wx0 e eow3z r plrxoff86bhe 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 distancux ild5b08 g,ke for an automobile traveling at speed v bud,5k8g l0ix 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 slides forward on b-crsa* 78 dkfthe dash when the driver decelerates *c fd-rb7sk8a 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 spee0(.mut;+hxd zqx 6 +h1 oiymeed $ 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 toz:u.)c pmc :rf 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 )c:m.z fr:cpu 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 ,oeu:3va45fez1 fthp 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 a 6vo:z5b; msg4v4qvxg 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 apprw8 l4t md8ya.noximately 20 .8awl8 dm4tyng 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 automobile crash if the de ou: ,*fwuxrfw 07lz/qp mmo24celeration is no more than 30 " g 's." Calculate 7f oqmlm,wofu/xr:w * u02zp4the 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 earthq vajy2 y cl0:4 b+:hmx)rqtt8zuake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the groundx tam vyrhtc: b)+84lq:0jz y2 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 ba4z00) xvr5m75xmlu b +bgsp of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop befp5)gl0zb u v b mxmr4705x+sbaore 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 thabd/zvsqcc2vx* xyea+l :/qt g- g-,d9t for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reachd 2xz-e,d+gc /b/vxv c9 qa*gt-s:qyles the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top 9v:p .t v 6(totuvchg3of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average forcotv9tuv vt3 (g.h:p6 ce of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch wherm:afx 8c1v )+qkv2b0y.xdem we the effective coefficient of friction 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 em)vqa0 .ey 2dk+vxw1mx:8b fmc erging?   

  A city planner is working on the redesi k+92lqfb 6j anj)ziv(gn of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to b6 kq(al9f zj +2vj)in 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin piecpcxiyd**fd;8,5 (pk noi xa6t e of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle o ,x ;8iip n5p*6*kcyotxfd (daf 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 severaf63xp p1.zh6,m zqw/epeoq*ql ramps connecting different parts of the h6q*o.eq m, 6 /p 1pwzzex3pfqstore.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using vd;oy6 1 l3frithe pulley apparatu3;rodlyv6if 1 s 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+9/is+w2mgs ujkynn4;ec nxje6a :m8rating 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, a(p,n7cv,cf z ln9us,pn engineer considers the following set of conditicup nf,n9z7pc,s( ,lv ons:
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 meto*7f2d. kni0yop)ke r8+ ,yumd hh3u jric 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. Karen's .e5ha 5)me j:4a nmx)t qwxc-u71y cguaeec-,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 about5ey,7aca- u. )wce ):h qx1xm -acej5 meugn4t 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 times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boatvzu+k3xaf) m7-f ori;jca62 j is 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 3.5 datkdgyr.4 r24+ uztk22sh g/$\mathrm{~m} / \mathrm{s}$ 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 climbersl m n4ex qchi2odg3wj(-l++)y who are roped together are ascending an ice field inclined at 2+ih-o4 +qg(cdwem2 j ln3x l)y1.0$^{\circ}$ 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.