Why does a child in a wagon seem to fall backward when you give the wagon dfo5nku y (0czjm.o1.a sharp pull fdfo.0u .zn5 1ymcoj (korward?

A box rests on the (frictionless) bed of a truck. The truck driver sn(n6xc84xkda5 m8wnatarts 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, axd c65n(nwa8anx4k8m s 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 i /+lfcnn4 au6;gw8tmu.td4 p3w w) w.vmu;txnt? Explain.

Only one force acts on an object. Can the object have zero acceleratiun08zw 4m 5/l ;ebkbf 0oi7owion? Can it have zero vewb7ie8mi 45wlfuo0 0z /b ;knolocity? Explain.

When a golf ball is dropped to the pavemjo)- +:o9zj:a r:4 tpzr*una(lrkmvqent, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exertsa ja vq4:*:rmpnku -tzjr+ r:o 9z(lo) the force?

If you walk along a log floating on a lake, tyvg d7j3;) rzq p3v*q 6xdw,jwhy does the log move in the opposite qvd 3j,3x*q r;gtzp6 djwv)7ydirection?

Why might your foot hurt if you kick a heavzqe ee the+tx )*q7d*,y desk or a wall?

  When you are running and wa) lt; ;ua t7x vuk*yv,0z,zwulnt to stop quickly, you must decelerate quickly. (a) Whal 0 z;,uwuu txv,)layt7v;kz* t is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a sectionr oi9dq20z cc0 of the same thread dangles from the bottom 9drq0cz 0cio2 of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as3c((seeea 2/wv mf)l s great as that on a 1-kg rock. Why then doesn’t the heaviw a()2smf(ev3e /ec lser rock fall faster?

Would a spring scale carried 3 jt ceihk0a0k84pz1c to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) ca 43pkzcj0kte018hi in kilograms?

You pull a box with a constant forceul ,y35)c wc.*aq fpnvvvg42u across a 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 the table), does the acceleration of the box (a) remain the same, (b) increase, or yg 23ca,)cq*v45 fwln v.uvp u(c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net lm hqb zt-2za**+7brfzx 7 a(gforce mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite forcbf+hmbq7t a (-r27 lzza zg*x*e on the Earth. Why doesn’t the Earth move?

Compare the effort (or fnd.n8,m p5s4o xbv(2eq lj)rtorce) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Com2 jq5.)xdo8t,n rvpls (m4ebnpare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’fjzbmb0. hwtj.ebv8g iu,: ( ;s third law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determineb,e0hizv.w: jfg jm;tb u(8.bs which team will win?

A person exerts an upward force of 40 N to hold louc5-5uz6yym8 n/q c a bag of groceries. Describe the “reaction” force (Newton’s third law) by statyu8n/y c q55-lcou 6zming (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 on i ljj-:kfwgs2f00 5mb you? Why doesn’t this force make you rise up into the air?f2:5 gjwls-kmf00j bi

Whiplash sometimes results frw;gnt*dnx 38 (ueani713hmih8cxrh 9om an automobile accident when the victim’s car is struck violentl* h g (wc8; 7dannt8 n9xir3hu3m1hxiey from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the trucsg9 miqj 9jia6d/q3g : ).xtzqk accelerates, the crate remains where it is on the truck, so it, too, accelerate j:xq 3igt9d/j9qq)6ms iaz .gs. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Aftew ) uzcpfy8:r2g 4xy;lbc4d 1jr the block reaches its highest point, it slides back c)wb 2 :j;1ydpc8yu4 lgfr 4zxdown but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale re cmg/ tqnn;)u4+ ptq/t0o6yrgad if you weighed yourself on an inclined plane? Assume the mechanism functions properly, qogtm/ty+cq4ng;06)nu p / treven at an angle.

  What force is needed to ac9j4umcepwc2 ,celerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.30+u;aal1)z wn b8.qh zt$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope wiem/3qq/dq:t hvn4za, ogh 1hajum:,*gh1 f4j thstand if 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 p6*x7:4+eraposg 6y1q .vc*1bye* ghir nuxpa $76-\mathrm{kg}$ 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-kgszdzv ) *8uu8yb (rm d)yw b9:drj8;wb car in 8.0 s if the car is traveling at 95km/h? - 8 rv8z9 zmdy;u:)rbj(u*bsb8w yw) dd  

  What average force is needed to accelerate a 7.0.mkmy baeu )dn27 tx5*0-gram pellet from rest to 125m/s 2uydme nt.kaxm57b) * over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertica4tn v3-s2t yf i qz3k5+cexbk,lly out of the water with an acceleration of 2.5 cq5yzf 2e3+k xisv t 43t-,bnk$\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track (402 ,al3te) zfzy. $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum acceleratiei++ w hjjq.c0on is 0.0680 gq.jiwj ++ch e0 . 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. /xkml.hd m;oip6ps : bm8aevdzik-g;7j5 m;2 When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Ca iogh /evj l6pk ;2- .85;mddsza:xmkmpbmi;7lculate 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 strength of 21,750 N. ;k;uv u 9qa9uoWhat maximum upwu99 u uvk;;aoqard acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fhd;dqvhw 8n/ygc4u cdy0 p03 ,alling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their weight?,yc d;30 nuwd0 /8hpgdch4 yvq   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes /sp-2(pvdbol +t 8in t (e4phythe ground below, he bends his knees so that his torso decelerates over an approximate distance 84pn+ply(/hode p t (i2-btsv 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 r3o9pop ho,d4rests 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). Determo3ph pd4or9 ,oine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball p v-gwf9a4dbjfh* j 64alayer
(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 bas7;dyfqg a,oqm gg qc6x 3m9k2-eball (a) at the moment it is hit by the bat, and again6dfgy 29om xak7;cm ggq-qq, 3 (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N foo.)1 t jbpf(lhrce must be exerted in what direction so thbfp j)thl1(. oat the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "cb7xk44wmi):fi yhry : ku2e 9high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is a) y4ibhcefky2xru:k9 i7m 4: wt 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.f3g)pr :zfz l22$-\mathrm{kg}$ 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 14go(v6dp tav .i/ z iz/*)an3ob.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 tw1jxvpx j493 co a new location at McMurdo Base, Antarctica, as shown in Fig. 4-41x x4 p3wc9jjv6. 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 2 ;qrocrf5l:nnieg11v .o8nq same mass behind it, Fig. 4-47 . Determine the ratio of tro1nnfl r15 i v.8:q;engqc2 ohe 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 usala.,er10u7er0s8 i9.qb fykius0 dyh c 0ub )ing the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly atb0,yyau hes081 7 .9ksua drc.iqlrui )ebf00 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 6c-utrl(i l.lmnms 0)e,iuv(n w40np, 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 (mass 4dy.9s;ly lwj$ 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 horizonfil:d90 q ;j5gloxfs0,vj 7k qtal surface are in contact with each other, as s7ildvxj f 5qf;90o:0jskql, ghown in Fig. 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 ar/qu*p3blut g98f i v1*un9xt qqr6 3+ummx +ove 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 afv8l*vtmr+ mq3n9/ 3+x ftgi quup16uo9*quxbter the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connecpd p(x) y q.*v,mcwqdl5 +tiff q+t(s8ted 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-bodsq,plfv*w)di x( qd8m .q5(ctt+ yf+py 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 frictiom+y;c; pk, heon 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 5bqkiw men chy57+ f qk s0ft5c,)hn()0.0$-\mathrm{kg}$ 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 accelerating at 0k 3)x6j d;ocor.20g. What minimum coefficient of static friction must exist between your feet and to ; 36okcxdrj)he floor if you are not to slide?   

  What is the maximum acceld4 l3h*isvka q*zo22dzv c 2-rohu0.reration a car can undergo if the coefficient of static frictio 4z2rl2hs -zv3.cavi2 *uqr 0khdood* n between the tires and the ground is 0.80?   

  The coefficient of static frictio:(p 6kdbxbc;r hyyu10 n between hard rubber and normal street pavement is about 0.8. On how steep a hill yrb 61bup y:0(c xh;dk(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 -a 9r 1te.nh2sq4.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 at,um flg+4 o4v rq-qfuc:qp83 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 contag atp1n0xg.07ozf4hj ct with an asphalt surface have a very high coefficient of static fripgofaz4.n00 j g th1x7ction.

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:+mig :0ax+6 z/qjtzx fj9md9lthvo 6iction 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.6l9cn4 oo.xf lq9x p(b 4-32 (Example 4-20) how large a mass would box A have to havcof p64x(9bqloxn . l9e to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How fatgt/g 1 sw(l 4fu96:fwtr:ntejq0gy : r will it go, given thy fgrw tw4s1:0(e6tl:jgun 9tgq/:f tat the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and v1s53c rjyf*k--a2cx lo) fe t110 kg , are in contact and at rest on a horizontal o5 x13yc2seaffk*jrct) -lv- surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient g5j(p (6dwd gbof static friction 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 ( 6gjdb(wgd5pthe cab of the truck?   

On an icy day, you worry about parking your car in your driveway, whij6 m1 gbur8ry0tviy; 6ch has an inmvu 16yiyr g;tbj8r06cline 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 *c) u1-sc xnatslide 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 plane tilted at an angt,he0rtvkw 7:l6ojx 8 le $\theta=22.0^{\circ}$ 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 speed of* hbglzl0e b;5l u,i-g 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a6b 6) dag ipx0m1ds5lo 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 someone pu;nh ;di:r uj t)arg/a1shing on it with a force directed :uian)hg;/ar 1jdr t; 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 dangerous proj;g; y,9h g7dmtp.jbyrj ;nf+l2dg4tbi8 k c) wectiles as they melt. Consider a chunk of snow at the ridge of a roof witjn .;tyrim bp+bgk;c;tfddygw,72)j 948hlg h 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 minimumgru2;x hu00(d3yej.9e ywq oa stopping distance for an automobile traveling at speed v isa9oygxwu de0yhqu2 30.(je ;r 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 the dash when xfgjva vtsgf x/e.7e32fc7 83the driver decelc.aex2s7 e73v 3t8g /f xgvfjferates 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 gi3w dvn:m-n*k rven an initial 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 convzceq1i 8cjr blf 5.i-6eyor 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 f. rclze- if65jq bc18ior 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 kine2dm 5t,pj0 nsstic friction 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) l 4h6p ll/tt77xo0yc*6w dsc ycan coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammao(s2; gdr dlt. +vw*jtlian heart, at each pulse approximately 20 g of blood is accelerated (ojd*+l.srwt2tdvg; 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 4x2*6q 6 s +bawd9v xktlezf07 r4otnisurviving an automobile crash if the deceleraot i6tsl *v 974f6k0nwxd xzaq4e+br 2tion is no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration productihm sz3562hged by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction3z5h t2gis m6h 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, examin kji0i uu3h3 /ad hs1(qgv69juing the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic frus6ik3u/ u3idq1hjagvh (0 9jiction 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-;ek:jz b(1pfx pr4 pw04 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fa 1r z(x4wepk0b:pjf;p st is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Lem gtb-p,wg 8qu2x)b 7upl3r 7kaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the axmplqk p 2,8utg)w7g-bbu7r 3verage force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a nnrm w 2tabn,mh6a.1zi7ln 05 muddy stretch where the effective coefficient of f 0n1mw56 m2rilnbhn .zna,a7triction 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 wo+89sk i4np gftrking on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. t8knp 4i+9fs gA particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her wa7msjx24o+*kj i) pwvdtch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 2wjo42d*s)mk+xi 7pv j5$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connecting diffem 51cpo, i:zzerent parts15 :coez,mzpi of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (madx w7+o(8kraxm(u :nass M ) using the pulley apparatus aaodrxk8nw(u(+7x : mshown 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 acceleratiu2b l,0+p o6ezpl ;xbleho+2xh9k9-mtyc z /ung 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 5 /qcuio* ny0j4f drx0/mv8kz9hs e g4child-restraint chair, an engineer considers the following set o r4g0 ed8 nv5/y/9mo j*0skx4uqzfchi f 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 toeh( *pw*exlu y6+nx 138ifg;umr (z 9yj)t qhas a mass 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, Bilak-f.v-asb c*dwly 8+l and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic roks+l.-d *fa-w 8c avybpe by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-1 qfmg - )uj-vq(n ddimph(mh6y8/dt1qot z ;5 5$\mathrm{~b}$ 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 spvr- g g0:fozf/ 8e6crieed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice fieowx5kzzsjr 30 eprs2l(:y 37k ld inclined at 2s3kzwkorel75 x(j2 0 : zrys3p1.0$^{\circ}$ 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.