Why does a child in a wagz2f4lh,;y cul on seem to fall backward when you give the wagon a sharp pull llhy2z4fuc ;, forward?

A box rests on the (frictionlespv g10f.bcr(t9p9ait nw 5a6 es) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground0t a5ncpga i vwbfe(p.96r1t9 beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are 2 ubmgcc8dz4 3no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero qt, )yx :-,gdb vlbhh3acceleration? Can it have zero velocvbq xd, b3)lth y,gh-:ity? Explain.

When a golf ball is dropped to t 15bw2d:.deh tz unl uc.1avj73y7 tmlhe pavement, it bounces back up. (a) Is a force needed to make it bouncelvul 2h1m t5cyn7 e7.1ut a:zjwb d3d. back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in oi7+sp) hl orx19xjq i+vk1a:the opposite j1s7vi19) k+ po+r: loqiax hxdirection?

Why might your foot hurt if you kick a h+awy 31x tt1rz 1xvs0zeavy desk or a wall?

  When you are running and want to stop quickly, 2uji vkt*n*m8 maeg (6p4 p3i7ru mdq-you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of d7dm(8pi*a *3uimjteg r n4mk6q p-2vueceleration 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 section of the sa g/tz (pjjgc;lg, 2q4ame thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the j zgpqt,4gg;/ cl( j2adangling 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 agp v6gr:btmfy08tek7se 6 ) j4 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fal8rfgy)7m40 jts:66vebtk e pgl faster?

Would a spring scale carried to the Moon give accurate resu),gbukg7u )/nccvqq/lts if the scale had been calibrated (a), u)/k/7qgqngcv)c ub in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionle7ng 2u8ozw0 cess table using an attachedeog8 zcn207u w 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 (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net force gim( 5)l7ghcunssu - xb0 q1e2 xh5li(qseg 0-)m 17nbc2s guumg exerted 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 obrg0fut0ar2sq7 f db -*ject when you are on the Moon with the force needed to l 0q*0tf rau g-rdfs72bift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pz1: x1g+jszetulls with equal forcez+j1 tze1xs: g on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a b(p, a2hj a1vyfag 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 object i(fjphvya ,1 2at is exerted.

When you stand still on tbpdf875 kktd+ he ground, how large a force does the ground exert on you? Why doesn’t this fopb78+k fd5d ktrce make you rise up into the air?

Whiplash sometimes results from an automobilxymg-yc(4 e +be accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it reaby 4x (-ygmec+lly?

A heavy crate rests on the bed of a flatbemdit 2w8ewi42 d truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to acci84diwet 2w 2melerate?

A block is given a push so that it slides up a ra)r;h nrtok x;2mp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration rnxk;htor);2 is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined plab06iim8 mq2 yyfhs b3l8f )q4wne? Assume the mechanism functions properly, even at fw2bmybhy4s6 3mlq8)qi fi0 8an angle.

  What force is neededf n7g6x) t:(n usmq:mg to accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bik5r htrp8x3edl 0g1zx7e 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 tsop2d8(w w8a ;pfv i8if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a ui*-i8qvzb i:s 2guo.dg.+ /6tg 4tb pz(qvq u$76-\mathrm{kg}$ 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 t9 +3upqu1ksk7ejkxd *3r tc 1an 1100-kg car in 8.0 s if the car is traveling at 95km/h? -st71 d*3crjqukkux31+ k pet9  

  What average force is needed to accelerate a 7.00)q +i dk --ez)kv-geyc-gram pellet from rest to 125m/s okq- kez-v+ei)d -g)ycver a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the waterb49f r o3ia1bx with an acceleration of 2.4xb oa3 i91brf5 $\mathrm{~m} / \mathrm{s}^{2}$ 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(nho-qf a x4j+-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 so t zm)t,o6lha1a hat the maximum acceleration is 0.0680 g . Whatm)hz 6,oa1l ta 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 motionp96brf w+ k j4 i)baq,.xsdba.less elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the perswxpdj 4+b96barq ,.sf .bki a)on’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of mdsbb n j e:d.,ht**ln*pcu8 ;21,750 N. What max:s n8,bdnctlbdhe *m*pj.;*u imum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 lqg w anmy u2u()4c,fm g*g,6kz4o;qfkg including parachute) w, 4gac ;)y6umg4qq f(woukgln* 2f,zmhen the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he xiskrd)r9m1m7 r/u1 ostrikes the ground below, he bends his k)r1rirx k7o1um/m 9s dnees so that 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 tied to y3ztfqd q07r a1+q 3bxthe box runs vertically upward over a pulley and a weight is hung froyq z70qdra3x+1q tbf3m the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a i-nxsyu 3*: llbasketball 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 momen c /r/cudtvqbo, a0;/w:f )oobd e(5opt it is hit by the bat, and again (b) afterb q;/pco0fr uo ve/,o/c b5)(taowdd: it has left the bat and is flying toward the outfield.

A 650-N force acts in a bv ndf*n,r37enorthwesterly 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 7,nrevf3n*bd vector diagram.

  Arlene is to walk across a "high we,yfg4 yr 5p3w 1kyok5ire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at they53,p k4kyr5gwyof 1 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 bucke xa-, 2:t; p(tabvp (ghh9 qmzd+fbe1gt is 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 14.0*ir. ffz9g1ymo 52cg+sf cth.$-\mathrm{kg}$ 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 B*4 aufiv0 1wl2 qkifn+ase, Antarctica, as q0ifw* u42f+vln k ai1shown 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 pulnl 1xbpb)o98 .qx/kgqling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomoti1xbq8.g pnobql9) xk /ve 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-pulle..xt x ilca46ty apparatus shown in Fig. 4-48. (a) How hard must she pull downward4tat.cx 6xli. 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 beg mm6ywm .fxo66an, 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 (cf 97l:2v/hvhskqvb ,mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contactu(n;cr zz kunkf9 3:8d(bu(hn with each other, as shown in Fig. 4-513(dk(nnrn; zk u8zb(ch:f9uu. 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 ,s o .onuqvt8 -22 fuamy.b;ldi7yos:each initially 1.80 m above the ground, andio2o-l. o q .uabfu; dn:stmy,7s2v y8 the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a fri a6 z1c9q3g ;vlr3hwwxctionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assum6qga913zvl;wc h3w r xe $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 305wz (px(,calzk1oy elr ) qdbetween 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 t4m nm6e* 6/tn .voposvo 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 accelerating at 0.20g. What minimum c d/g ef*p7fu4-ur5fu ooefficient of static friction must exist between your feet and the floor if you are nodof f7r4ug5uf-e /u*p t to slide?   

  What is the maximum acceleration a car can undergo if the p1 uu8po(ycf8f zv5 +bcoefficient of static friction betwv(ff+z58u c1ybp ou8p een the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal s2dniw iz23iwr 6 5ld8ktreet pavement is about 0.8. On how steep a hill3k i6l225 rww8 zdidin (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 atheuss:hts3h ( m 4f)5x/ sjih) -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 restw ej.p / py e.6nuicbg0eq5w+h6,ce8b 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 aspo48m,si68-p4u jx o 9ovrwhly cv )v;mdkc29xhalt surface have a very high coefficient of o2) ,pmk mh8vo4jl4 s xox;ycwu-86i9 rv9cvd static friction.

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 kinetit 3s. 8l f9wlbc1evk7puy4ix)c friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box A h8;a:d2x;ci ho m9p rgsp8da-rave to have to prevent any motion from occur-id;h: c;8 rs82og radx9ppamring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, 8e-mpy9;f7m.i,6uhgek sw wm given that the coefficient of kinetic friction is 0.6s8fi y;,em 9 kuwmehgmpw-7.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg a:d kp v6xry2 )r9)fjtm0k ua izap3p5.nd 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). A pkf 5u mv.pxj: 0tpdrkz)a3r2y9 )i6a620$-\mathrm{N}$ 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 ofr;eb.rp;pb, w static friction between the crate and the bed of the truck is 0.75. Wh brpe.bp;;r,wat 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 about parking your c cfa-5 if51 g*(fom.cl9yt rikar in your driveway, which has an incline i 9yfcgcko5. a1m *-5riftfl( of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide wifzqw x7 /.v:cqth 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 atpb)i)afyb8kx.n; r :l an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.hgk:;k,kh j/ 8ajvea9 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 reachesis zxb2 */onmunv0+j3 the 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 i qt*(h,a2u dhby someone pushing on it with a force directed upward hht(a*uqd, i2at 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 n ;)n/ u6vglemroofs can become dangerous projectiles as they melt. Consider a chunk ofgv6en/)u nml; 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 au xd k.r(r2cq(xl ce*9w+ 0 wlpfn1.ebotomobile traveling at speed v is equal to n2.(x(1 wr0o kdxlqcb*rlw e9fcp+.e$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 the drivex cp s-b*6j2bkybz*,z r * b,- bz2p*jbxzc6yks decelerates 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 a.mxf3. y4kz)kxtc+wm:bd -v5 (rgu ysn 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 conveyor belt from where they are filled to the packing staj/ ;qenep/z; ntion 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 the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit tin /n pe;jeq/;zme 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 betweenc4ls-3 hjh8+lx2iy.34 r9tpkt wsmcp $m_{1}$ 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 -:/1gdbme9lj 1v biuy6.0$^{\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 ofppl h099y z-nkf.(qj l6;nzxv a mammalian heart, at each pulse approximately 20 g of blov9 yp-nx pq0(.;fzhk6z nllj9od 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 craf(0+h *9n brl8yqy1or8ef xz tsh if the decelera8 bzxoq y *8frh +(l9yt1en0frtion 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 acceleg5l:caru 6fnd- h tq):qw g:a46n2ky sration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of2-du5y: gf hkngac:s6t46: aqrw nq )l 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 investigatorsw a2ax7wr 0g8d, examining the scene of an accident involving two cars, measure 72-m-long skid m728wwd gra0a xarks 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-in0zdt+8viycn k uygze71 z,p9/-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after tradz+u9z, 07n8yz/1gekciv ytpveling 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 L+.1ais vhoyf h/um+dy-poj(. swb;+ w eaning Tower of Pisa and falls 55 m before reaching the ground with a speed of hh.mu wb a/v -owf y+dpj+o;1i+ss(y. What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of uj,z p.x ob2j,xiw,a,12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if th zu,xjb wjaox.,, i2,pe mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portior c:,*m7y vwdyn of a city. An important consideration is how steep the roads can be so that even low-powered , w:7y ycvdrm*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 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 experixuayr.ri8+e2cow 0k 0 ments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices tha20uxc+wraok.e0 8y rit the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ra 6mbj4p oclxufg 9p k5(22-tklmps connecting differentmplxlg4-29p5k2 o tb(fc6 ukj parts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M y5tlupg0vt 0th3.j8jtw7r: )*nb s hk ) using the pulley a7w ntkhs5gy0v ) 8rhl3u.0pj*b tt:tjpparatus 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 accelerating at 3.5 4n:g lf t8aug7$\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engp bfdv((/(o myineer considers the following se (dy/ pf(mbv(ot 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*sq; x;kyh 3jf1xeo ;l of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Kaji) 1lo t5rk(v4+g cw-kmmy 9nren, use 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, assum5-nk+41o imj v( gr mcwlk9yt)ing 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 ispc0pc 4ws6 yhly)+i/ gh8nn.p 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 alldf2w7cq t+,/w-vd g: -dvk5wvzak y2lowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending ane5 bwf)p8 4 b5tev*upovu0m 7h ice field inclined at pev * 8) w54b07v5uepbfuh otm21.0$^{\circ}$ 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.