Why does a child in a wagon seem to5u :/m 0vl5e/hunahdsf: y)wq fall backward when you give the wagon a sharp pull for550y hu: h avw)e dq:slfunm//ward?

A box rests on the (frictionless) bed of a truck. The tf*9 rv( uar1 m4w6rnvaruck 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*rnvm4 1(rw fu69var a 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 it? Esou,0+encmmer p3- m; xplain.

Only one force acts on an object. Can the object hv3j02q6 m0aa jc*awsbjehz9od1 f v92ave zero acceleration? Can it hac*0b203z2j1 s 9daqve oj 6amj h9vafwve zero velocity? Explain.

When a golf ball is dropped to tall :4(e +lxcwhe pavement, it bounces back up. (a) Is a force needed to make it bounce e l(c+llw4:xaback up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, +lrii(v.v) q*+4 1xpn e e pfx68pzrnbwhy does the log move in the oppositeflxvp( 8eqnir6+pvxp+ .n iz)r14eb * direction?

Why might your foot hurt if you kick a heavy dessjd- i*rprj48emp(jx ) 2i0t xk or a wall?

  When you are running and want to stop quickly, you must decelerate qu5cwlxqqvyf3uq+9 ly73;q.kq sk+f , pickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experiencqsc+fqw +q5 ypqluyq .v;,9 3x lk3fk7e) 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 th+c-l b:*/z,xvv je yxr,pcvp qgr775de ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person givc/ ypd,: x7+b vrg,przle-*v7 xvjcq5es a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on 7c loxyh2l87m3r vabo47wrj 7a 1-kg rock. Why then doesn’t the heavier rock fla7b oyc4omj73r 7r78hxl2wv all faster?

Would a spring scale carried to the Moon give accurate results0p6(npdep q7v if the scale had been calibrated (a) in pounds, np p6q0d(7ev por (b) in kilograms?

You pull a box with a const g9-k lg/7q,;)srsteth/-bo6idclx ym5k x 8g ant force across a frictionless table using an attached rope heyd9xtgi85lq,-h6 g7 se)c x/ ms/go;bk- rkltld 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 influeocdyc06 9,3jjd:bkb9if: s srnce of gravity there is a net force mg exerted on it by the Earth. Yet by Newtjr06cib:kf , :c9b o sddj3ys9on’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) neex+)mozkvb9 : lded to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Cb):lo +zm9xv kompare 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,m,0o(x,zbpxc/7zyyq st 0n u/ each team in a tug of war (Fig. 4–37) pulls with equal force on the otycyz/ptz(qxmsonb 0 ,,0/x7 uher team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceriesaoqw)u 4qj:2a. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object q jaawq)u o4:2it is exerted, and (d) by what object it is exerted.

When you stand still on ( va 4sqxrvj05the ground, how large a force does the ground exert on you? Why doesn’t5s( 40jvr axqv this force make you rise up into the air?

Whiplash sometimes results from a99b)dizhf8m m3 7yt8l vo9pinn automobile accident when the victim’s car is struck violently froio8vh3piy9)mf7m9 tl dbzn89m 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 7a cwfc o)nin i8lov4i7 o62q+bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force caus2 c7w q)+4io6ail ocfvo7nn 8ies the crate to accelerate?

A block is given a py,kn kefinzsz1gj* 0*u8)f8dush so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude zsf0k8k)8g1dnfue**jzy, in of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weigh2.q 3b woq+ebng j0buuqi5*4 : 1lpctaed yourself on an inclined plane? Assume thbq uq5tojbq3:.i+0 nea1w pg4l* b u2ce mechanism functions properly, even at an angle.

  What force is needed to acvz2y rx/r* f)qcelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a7 ftw sndf1 nt xztxp,(:d-/4y bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstandb+xlg0d uw6e: 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 of8 yf;4p 0hyj )kkgzaa9 a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 s gjpel:7 .xe5 bif the car is traveling at 95k.lje 7: e5gpbxm/h? -  

  What average force is needq90 vp xio2.teonvv.4z z,1xoed to accelerate a 7.00-gram pellet from rest to 125m/s over a dista ez4tiqpo1n.xv, 2z0 .oovv9 xnce of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with anoenqr7/6e.(d ym m:nl acceleration of 2./e(6le n.ry o7m:q dnm5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 s16 p 2; 39lpvvhfa(3o;vhoboso,cip quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum accd3r v1 t8ibrhd,8 0thbeleration is 0.0680 g . What are dv ibh1,t 0 388brhrtdthe 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. When tp*moh n3kp1,h he elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceler3mnopkh, 1 *phation.     ----待选择----downupward 

  The cable supporting a 21x)ntcg *6uj/s 25-kg elevator has a maximum strength of 21,750 N. What maximum g*su/6 )txncjupward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleratio:iqso( ju6 du81(knqxn of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistsdqu((1u8 xji6 n:qokance 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 stringxb0bru m* l0w.d,-w kes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (erg nbm-wu 0w*d,blx0 .xcluding 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 ryt mzfi 0kxsky58c80uq6: o/m ope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determinec8umsq /ftiyx60m:y85zko 0 k 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 g s3n1d/ lo0f *fmdhv;-.exxq 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 moment it isbxpfb/3n8tez4a v96 0: nogy e hit by the bat, and again (b) after it has left the bat and is flying towa69bx0nbe4e gyznvt8 f3/poa:rd the outfield.

A 650-N force acts in a northwesterly direction. A secon .ris 6)h(o i)ebgss+fl -ie)cd 650-N force must be exerted in what direction so that the resultant of the two forces pie.re(s)lc- g)si+ fb ioh 6)soints westward? Illustrate your answer with a vector diagram.

  Arlene is to walk acros5/ .eq1xvc: g2n2o7banf bie ls a "high wire" strung horizontally between two buildings 10.0 m apa enn :1x2 l.e5q7vbbc 2ogfa/irt. 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 frocq f5lq3) lkosajnz/d (;u8t2m 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 14.0w0gjo5i.s j z8$-\mathrm{kg}$ 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 uni/6m8c vd*bk(lv cf :)+8mlbzkc r2hdkt to a new location at McMurdo Base, Antarctica, as shown inm8kbk z()rvfkc:/l+ bm826 c*hc d vld 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 pulling two cars of the same mass behind it, Fig. heq/u;q:6fxz h 0h /e(c9wqsu 4-47 . Determine the ratio of the tension in the coupling between the(9c60fh/;qhq u q: hez /wsexu locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-puz*q c t5v 4dkgd;df((elley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raiszqd kde fgv*4c((5 ;dte herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, m8wfuxy,m8xe0kdg+) 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 blocfr d-ijf(x; mv2jlbz,po)7 ;jk (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 o058a mllr143rxlx2 fi7rwlq.s+lunm jb 86 rin contact with each other, a5r i2uans wm rjlxlf+ .x8lqm6 r10olrl843 b7s shown 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 are each initially 1.80 m above the ground, andv+ 8y m .nx+hxdw*8,(veqese d 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 + v,dmv8 ns*qyw he8eexd+.(x 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 tabob dc2*nn:q .8,hzfrictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the t n2.bd8zbqh:,n c*at oension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between kr htw g 9fl8mv0,06oxe2fk2ca 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 is8a ;yzc62.o g/(b*djhsvhp k b required to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a mu8w5o9;d yy imxj e7lx(dfgg,ep)6 8train accelerating at 0.20g. What minimum coefficient of static friction must eyxm9l u ex,8; 8p 6jdi)7 wgedfom5yg(xist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car ca 6maf9o9 (zvwn-dlyb /rl i:)sn undergo if the coefficient of static frictiondzmvwsb- r6:f/ )y l9 9ao(lin between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rub vemy fq/9j 1ut*)h2xcber and normal street pavement is about 0.8. On how steep 9mjxy2t*cvq f1uh )e/ a hill (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.8wsac( q6,tor30 $\mathrm{~m} / \mathrm{s}^{2}$ 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 ayh6rjhn l* m+sk+/s+ 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coefficient y5 anh5 gs9n)oof stat)o 5y g5n9snahic 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 kkj t/7py4sa0k inetic 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. 4-1 qmmb xm3ew1hk ; )xru/f)1r-*mhw xq32 (Example 4-20) how large a mass would box A have to have to prevent any motion fromhxw;/ fbqx*m1 k mw)humer)131 q- rxm occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor/l)(d lykh v6p,ltvvbzd 07d :. How far will it go, given that the coefficient of kineti) ptl:hyv,7dbld 0v 6l/vz dk(c friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are ue0bko)c gta.-q k7o- nvz8h1in contact and at rest on a horizontal surface (Fig.b-81 no).gk7 ca uv0kz- qoeht 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 codm+n 7 5 npti .;snh*3a3pynpwefficient of static friction behitan3w n+n d7p;ynpps m.* 53tween the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has dj7tvn6;c1byan inclib 1vcny6djt7; ne 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 atj cw9b i3 5k/cefl/7r slide 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 atmh ll gwum.9 k+)e/g7ysr utqd0+03,ortca4ngle $\theta=22.0^{\circ}$ 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 3.0 ;qle .m;imr i)$\mathrm{~m} / \mathrm{s}$ 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 h21*jm3h ovqqp yz1o*-q:fysbill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place against a rough wall by someone pushing b;eil 7z9t)m/rsz 4bj on it with a f9t l4s/;rjz7mib bz)eorce directed 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 canpo,*5uq7a r lz become dangerous projectiles as they melt. Consider q,5pa7z*lr oua chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopq8+e, vje3lpit/e )reping distance for an automobile traveling at speed v is equ,elie 3/qvr jpet+8e )al 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 al0z.u2*ysu 3bncv1i fcsg 7x33n u)g dashboard of a car slides forward on the dash when the driver decel3 f3i0g ulgs71cun)vsza *y .c x3unb2erates 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 giv ky*/h 8nk jvndf;.n ,rbbo)d0en 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 conveyor be2,0o,2h pleeo gexk rl 84d*dflt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the tk*rgeo d8f2o42 ,l,pld0 ehexrip. 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 frica0adnv f7fl;9tion between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast do:kks15is iq z-wn 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 mammalian heart, atd p5/n) hta1jt each pulse approximately 20 g of blood is accelerated from 0 a1njpt)5t/h d.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 autom0 yik4/1-1rtdk u;u gz a;fjrjobile crash if the deceleration is no more than 30 " g 1frtku/jy r0 ;-au z41igj;kd '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 acceleratiouj 5yvikoq z0:no 0 a;c9xq::on produced by an earthquake is a , and if an object is going to "hold its place" on the groo9; 0:nak:ujo iq ycoq0z:xv 5und, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involy nayn y gh//gyk7ac2; m)6k8r(ng g)mox i;:qving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a sto i6m;gxy7c g:agqa ;n /ry)yho k)kgn82m(/nyp before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for e o452gejtkc .tcj u.*fach 4 m traveled along c4jjf2 o5kt.tugc e. *the road, the elevation change is 1 m). How fast 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 Leaning Tx yop x1st)59qower of Pisa and falls 55 m before reaching the ground with a speed of What wassp9)xtxo 1 5qy the average force of air resistance?   

  A cyclist is coasting at a steady spee6ledq3s lv r. 4i2;( qhp-mhuld of 12m/s but enters a muddy stretch where the effective coefficie l; l-e.vsh 2rmpu(iq6q3ld4h nt of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a b fbt,3sd3se23 coya7 hilly portion of a city. An important consideration is how steep the roads can be so bf33bd2s,coe 7yt 3sa that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 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 x,;b 6bn0yf ksphysics experiments, dangles her watch from a thin piece of string while the jetlin;6k,y0 nbxbf ser she is in takes off from JFK Airport (Fig. 4-58). She 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 severtsvg/yq;pt(9-vx* + gr5 gvdval ramps connecting different parts yg( 9 ptqvr /*5xvtgs+v-dv ;gof 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 th n+*f6qu /dt; wxcb7mae piano (mass M ) using the pulley app*a;7+q x ct mun6dfwb/aratus 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 a.f 1kpr)g bz3f6 dvh4wt 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 -asbl o zg*+*7-fqfk oa child-restraint chair, an engineer considers the following set of conditions:ol--zf*g *fb okqas+7
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 660 metric tons (660,x km ;+qw*5nbr000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length.ax l0r4d:)i2n67f ujzdft ao. 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 (Fif2iz fx6)04oraal dud7:tn.j g. 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 " / +b4bv5fexz)js) hp n10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reachv b0kzw 1g;jd1 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 asy0h .a8y vnz6vcending an ice field inclined aty vvn z68a.yh0 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.