Why does a child in a wagon seem to fall backward when you give the wagonv dr2 aj:f-4ld5) xqpw a sharp pull 2al)-pjfrvqw4:x5 d d forward?

A box rests on the (frictionle-.9 m* x(uvo- 9nor g5cfpgohd m)g1kmss) bed of a truck. The truck driver starts the truck and accelerates forward. The box i( o1 mc-g)mhxrn-p.*5dv ugfko99mgommediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an ob9srpf/h,0dto * qpqk 5ject is zero, are no forces acting on it? Explain.

Only one force acts on an 5;p4imo(gkof6b h *qnxtma(7 object. Can the object have zero acceleration? Can it have zero velocity? Explaingmt4m;7oo(qx( phk f i5na*6b.

When a golf ball is dropp6sv7 4)5oyhr* )j0a:jqkl w q6valtpbed to the pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, whato*vlrpjt)sl 6b0 45)w avhj6k7:a qq y exerts the force?

If you walk along a log fl,v*a/ r mibk:.5wkkn4 6uo eggoating on a lake, why does the log move in the opposite digk n. a,bk6rk:o umiw*4ge/5vrection?

Why might your foot hurt if you kick a heavy desk or a f2rmdkq6d p:7 wall?

  When you are running and want to stop quickly, ym :ks4 t2eu:x(boxq kdr04 hm2ou must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (usu:bk sto44xkq:d2hxrm20em( ing 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 sectiono +edozp7+yfzzg3gc,o /0w6a of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers. ofz+ /, 6wgzaooc z73 +ypegd0

The force of gravity on a 2-kg rock is twice a)9n-i*t poldkvm bxr3x*5 3ins great as that on a 1-kg rock. Why then doesn’t the heavier rv d9*x5lo)irkn3 *bnmt ip-x3ock fall faster?

Would a spring scale carried to the Moon give accurateos+ 1kazihk.wi ,3;zi results if the scale had been calibrated (a) in pounds, or (b) in ki1i.z z+wk , sohiak;i3lograms?

You pull a box with a consta f/j+g a;,ci * (cnhfa unhcuts74+yl7nt force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the sauau*l 7(7fj+ +cytgis,; fcn4 hca/hnme 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 gravimv+ny4,0o dwuty there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts a ndu,4vo+ y0mwn equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-k1 qy6/6bysc)utbczw cdc :. ;rk1zxp3 g object when you are on the Moon with the force needed to lift c kbp u/:r6c6;dtw3 cz.1yqb sx)yz1cit 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 e.+c4z s sun/ta tug of war (Fig. 4–37) pulls with equal force o.u+e tczs sn/4n the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag n-zbn3stg-wo :ps tcfh:s k.3h-7 5bc of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) i 3f-b7pt5-ngt :c:b3h os.zs csh-wknts 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 for7 hykr*7s 6cgb2 ecwc3ce does the ground exert on you? Why doesnhkr3ccg7c6y*bs w 7e2’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when t. 5f5t tkclmp zu )bsb6,bc(b/he victim’s car is struck violently from the rear. Explain why the head of the victim bk) 5.f/lbu(ps5c,czt bb6tmseems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed ofp(2 sj ;gz*gzk a flatbed truck. When the truck accelerates, the crate remains where it is on g 2 (s*k;jzgzpthe truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a pushw+i s5l pqyo:)kpne36 so that it slides up a ramp. After the block reaches its pws 65q+oley 3i )pn:khighest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on, c . nbn42liy5.xiftxd+uc(v an inclined plane? Assume the mechanism functions properly, even at anyx4.5+t 2nblnxvif cdc.iu( , angle.

  What force is needed to acd9isz f)tmym3ni* 1j3)j8jityk . to 6 )p/kwrcelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ift+,wh5 30 yl3 gwoev28da iprider 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 acclu2jh lov3m((+ eq y.q:n(r)scaae* relerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of an 5l)ft8.pa2h5 m n,vt+snrhw $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s if the e1j2ap4u6 ll fu5pftno f6:m 3car is trav 3effa5ufpjulm1l n46: pt2 6oeling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to ps8-s8u v5oga / az:ra125m/s over g8u8 5avo zssarp:-a/a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically ou7;wt1 qkln:v -u:xp ent of the water with an acceleration of 2.5 pq :wk- evnn7;1tx ul:$\mathrm{~m} / \mathrm{s}^{2}$ 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 )/ oald.8*xvvifx .p x(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 design z+kq;uk:f81p duliw+ ed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max i1:d+w kplq u8+ zk;fu=    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 bathrooij 5(hr4h,bre m 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 directh,rj 5i(bher 4ion of acceleration.     ----待选择----downupward 

  The cable supportingwa/spz6qmwlw4j//-a 9u kf-a a 2125-kg elevator has a maximum strength of 21,750 N. What maximzl9/au- jw-/sqap4k6w/w fa mum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg in)l 7il ob3 0ibrv j6zwvke:f)+m6t1w hcluding parachute) when the upward force of air resistan)vzm o wb7r61 0 eibl3hfl)tv:kjiw6+ce 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 roo;q q7rx;sx4 qt1poq/(n hwfy4f of a house 3.9-m high. When he strikes the ground below, he bends his knees 4 o1wxq(fqq py; h/q;7trxs4n 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 the box runs velog;2n 5jd3ybrtically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determin25l doby ;jg3ne 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* eoiutyy/;x 2 for a basketball 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 bavvp19(s4 b3y bt ci g,-2fbhehseball (a) at the moment it is hit by the bat, and again(2,h14i t v39sbyhf vbe -cbgp (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly directiplx4pn2g9 (sk*hg )vpon. A second 650-N force must be exerted in whapxn2k4l*9 ) g s(pghvpt direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung hojx 5rj (wmu(fx8c h(e j7d+pq3rizontally between two buildingsp q d3ju8 (7j5xe(frjc(wmhx+ 10.0 m apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless cord from another 3 o(1xl,,bikv pjei9zk);)mv i.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 1karea 1hs )gya3f fi 49dm8s/74.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo o cb+/:i5 mfdx+ bijnpj1u0d eg.c q7o/6m;dyBase, Antarctica, as shown in Fig. 4-46. The g.bo/d px fq d0c+e/nmy1djji: iu;+ 7mco 56bsum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-8e*yhmk ; 8c td,azegsp8 8n5 8pr2sut47 . Determine the ratio o n* 8yghrpzetac8um8;dt5k es s882,pf 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 us+pil+/ o.zm nging the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise hm pn/o+l +zig.erself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, b0mnq:31ts8r/lr uyq l4j1t da 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 c/8b25 tw7buc5 xekc lblock (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 icvg/ /zwkozu88e1w e 6n contact with each other, as sho u v8zz/cg e/oe861wwkwn 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. skqt .-;spabk,g:;vs 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits ths;tpb qs,-.s:a;v k kge ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a fribapb3 x*o1f0p bweu+:f8b)0jl y wgl+ctionless 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-f3a8b ubbfj+bpy0w)*1l+ olpg : exw0body 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 between ; u md 6 i8e0rqic-yq:;hvlg+xa 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 sta8+qr*ywoa b b,rt 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 trp z.n8eq uw dygvoyrc 78783ref )yg37ain accelerating at 0.20g. What minimum coefficient of static frictu yc73epez8v g3wr7yo8 .7 n )8gfydrqion must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo i2qf +ay4 y;zsff the coefficient of static friction between the tires and the grouzsyf+;2qa4f ynd is 0.80?   

  The coefficient of static friction between hard rubber azil8i))c;yj*ra; :7 mszacu 76vnomg :cm7l fnd normal street pavement is about 0.8. On how steep a hill (maximoy *zc:7m7gfnlmsr6) ; z):a;8cijvcu i7lm aum 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 -4.9+j kwn, y/dbtn ae )-rp7tke(80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough 30s im: pi9)vec0: uay2bll o9s1p 6sr1a$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coeffi :n)t;bc9d*/i ud ngcacs58hbcient of staticct;b a dc:nbig5/n8c * s)uhd9 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 kinetic friction forop8cwj3b 0 hj07vjq kg j9q5k( 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 bob cv+yze; l+2z i9yndw +.buh4x A have to have to prevent any motion from ocu+zzc+y9+ni;e bv 2hywd.4b lcurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acroo,c l c(f-x07um;8*lyf k8mywo-v fxts . gu9tss the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and 7m 8- w yoc ; x8lu-0svkglx fcmu9y,ott*f.(fthe push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horizodr8 az pr9p 24g0op 4vy.oz;ybntal pdp z.r ao;y2grz489ob p0yv4surface (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+9 g:x jef6xdfw c /vl,zmg:p3 crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the d:dwpgje9+f 6vglxz:,fc /m 3x river can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about pa7xy4aptfe6a d.b: *q xrking your car in your driveway, which has an incline of 12:.*yqfatap e7x6 4bxd$^{\circ}$ . 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 slidpxe0k1lv * k -vka4rjg 7m(s9hu+xd ,ve 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 g hw9yg.x86 had 1ovk0an 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 58t i : ab*8nf1gh lu;cvqn4qaof 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 a speed of 6. *xi,gqo7e.ap0$ \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 sompw+/w4zau g *reone pushing on it with a force directed r+a 4/ *wguzwpupward 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 slipmnm-jvfbzw*( c ) nj,0m7iyc +pery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at j,*n0zjcm m +-wf)7m bv( cnyithe 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 automobile traveling at sp,pn t0p7swc6km0v4p6c l pqw1eed v is equal toq1sl mtv7pp 60 p0ck,64 nwcwp $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 ivf+pjf2w p 9 ,isl*n8car slides forward on the dash when the driver8vpfwsi +jp 9f*il2, n 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 n/ tz.er c6zl;m is given 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 co s)l45o;dfw 4bbh0xirnveyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of th) 45 ;w x4lbifdoshb0re 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 frgd+, ud *(sh/;yqqaw ynxw(c0iction 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) cwzrs 7 ujn6-4woe5 q:ian 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 mammaliacf dx7a5b.asij9i. s/ r- 3kmmn heart, at each pulse approximately 20 g of blood is accelerated from m.-jmfa ib ks3sc d.x5/r79ia0.25 $\mathrm{~m} / \mathrm{s}$ 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 tfya1y spezr6 f8 rr7:*he deceleration is no more than 30 " g 's." Calculate the for:eyr81yrsafp6f7z * rce 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 earthquake is a , and if .b5f aa3 0(gywzrsw -san object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground mus g0fsr bw35-w(az ya.st be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving tm58 tde j hrjj q(z,8e:4/btkswo cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before collid5j tdt e:q4bk8eh r,/(8 jmzsjing. 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 hiy m+hf -v-/efr+4uwffll (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after travm/ +u4 rev wffy+-hff-eling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is droppedi*esd tb 8w;(f from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the averagie ;8 w(b*sdfte force of air resistance?   

  A cyclist is coasting at a m 08 8bmg-jddssteady speed of 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 the mud lasts for 11 m? If somj- 8gd08dbm s, what will be the speed upon emerging?   

  A city planner is wor. tr-uz l;l: dzig7;a2iva t67xup,ecking 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. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rt;7t c g 6.-,vd;ulz pu2z7iil:aaexrest 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 watch from a thin pier rkbb3cc r;t 1 )3z5p,r9fjuhce of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). Sp5f1;3rrk9rhtb ju c ,)bz3 crhe notices that 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 ramps connecting d o5 9osmeloni z4 bv3);ctwv)7ifferent parttl)ncwb e3z;7i45o s9vm voo)s 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 theoq2 t 9ltlg .+qs-kwz1 piano (mass M ) using the pulley appara s9l.gkw 2 -qtq+tol1ztus 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 3dibb ; :ylkcl)7a-rq 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-restrmtludj n53v h: 0yu1.m 62texraint chair, an engineer considers the following set of conditions: urnv .uyx5m1t3e j0hl6 :2tdm
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 mej)9/z f0q l6 bhqfs3(hwnb n7htric 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 s9ytloa tr t941qn /gx5imilar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope yx14 tntrg/9 q5taol9stretches 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 3il0 9zulful u(m ol+)" 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 allow +/1eisq:1mmuu) 4n9cvz .odnn eebmu 66b(pwed 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 xb mh9 y(x/s jw0v* 0yy7wwxy;who are roped together are ascending an ice field inclined at 21.0jxvwxh y9s*(0 xw7m0 y w;y/by$^{\circ}$ 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.