Why does a child in a waa/bke m2npl9z2i ,t o18mix 2zgon seem to fall backward when you give the wagon a sharp pull 812o/i expzbk ,nzila 2mt92mforward?

A box rests on the (frictionless) bed of a truck. The truck driver srqhca:t)13 ve 4ozh g.tarts 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 ground beside the truck and (b) by Chris who is riding on the rzh 31ac.h4qetvo:) g truck

If the acceleration of an obj4.rc8-ytb , nqt:4x-zv0 zq/px athl tect is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? ;axsq+3a x8zcCan it have zero velocity? +;qxs aza3xc 8Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is aug, cr t ,j nilkrd00g8h*0b2r force needed to make it bouncr, 00dcg 0kglhjr* , irtn82ube back up? (b) If so, what exerts the force?

If you walk along a log flo wf g)2hc2fvx:ating on a lake, why does the log move in the opposite direffhwcg2x: v)2ction?

Why might your foot hurt if you kick a uqkd bj56)s+dss:/n2nvg qh 1heavy desk or a wall?

  When you are running and wafr)95l4 jabdgbcf o 88nt to stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your8bg5o)dlfaj b 9cr8f4 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 section of the t*u.e(x doq-yir:lx .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 pul-lty*. x ei.(rduq:oxl? Explain your answers.

The force of gravity on a 2-t) ouo ys-9g9cpr9k/tkg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rt9rsko9 yptug-9 /c)o ock fall faster?

Would a spring scale carried to the Moon give accurate );li/+rnym ua results if the scale had b)/; rl+uamn yieen calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a const.zga fu n)y82bant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with n8b 2y.zu)afg 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 influenf5wc2; 5fxvueyb*q4 cce of gravity there is a net force mg exerted on it by the Earth. Ye wv*5qcfx;yuc 5b4 2fet 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) ns (7 uszc3c(y*5xspmck*4 u dneeded to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object4 pkd3c*u szsc* y(7cmsn5 (ux horizontally with a given speed on the Moon and on Earth.

According to Newton’s third l7:ng gsfoq(s2 aw, each team in a tug of war (Fig. 4–37) pulls with equal force on the other te7q2n so:(gsf gam. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of grocrcr9:*uc:pd r v;0ir.i4ohb xeries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, v:hirrrx*puo.r c 0bi4dc:;9(b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still o(k)xbj*.aolm +w-r 5tw rg/isn the ground, how large a force does the ground exert on you? Why doesn’t this kj(ww.obxia gr t+)r- ms /5*lforce make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’ a1m*1 7jlous3blwg +4taqf( fs car is struck violently from the rear. Explain why the head of the victim seems to jaf3s ftm7 a 4(1*bougwlq1l+be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the trsqacl; ;,80nig kl -qduck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What fnq ql0;d;sli8 ,c -kgaorce causes the crate to accelerate?

A block is given a push so that jxvm*s+ 3(uuu x ar(p o)6edw*it slides up a ramp. After the block reaches its highest point, it s6(ux (wp3 vm+usde*u* oj x)ralides 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 an inclinel/txy fq43pbt6 3;csi d plane? Assume the mechanism functions ps ipy tq/3lxbf4t3 6;croperly, even at an angle.

  What force is needed hah ty1u;zc0tb96oht : n5y/xto accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider /yzl pp dj7.0kkq x:-ccthtc0v 8msg7.;i0ypat 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 ug 5mhsa*o .zu 0hok63dsed to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ob5wv2rf , w-6mi+vtajf 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 requir30d3bg f:s2fzlx .mv/.a7 qpuk a5xbf ed to stop an 1100-kg car in 8.0 s if the car is traveli5z v/ ad0 ukbfxb2sqgx f3f37:l. pa.mng at 95km/h? -  

  What average force is needed to1tc/-xqb.,g8k9,k dvi ne xo h accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a riflex9e.x tci,v/1d kq,k-h gob8 n?   

A fisherman yanks a fish vertically out of the water with sbnp)h/kn, 65 8ubvzal;nmxr-c-6y gh 2d lj9an acceleration of 2.5 s2b xjyp)rk5nl -,l ;-9nzm6h6u hd/ac8vgnb $\mathrm{~m} / \mathrm{s}^{2}$ 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 trslmqs.(-d:1j-:vi-r o z j7 xcwwpr2r ack (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 acceleratir, /;kfa7k3cwm 69myv3qmf( a)7jpbq c(cma son is 0.0680 g .ac ,kq(3f7y c/p 9awrbkamf 3m(mj7 sc;mq 6)v What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in a motionless e+;6g 2/a1guh1olryyt*a mq dwlevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calcullqmr yd1ua6*/2;hogag+1 wytate 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 ofwt(3 aakekk38 s6crff2m j-0r 21,750 N. What maximum upward acceleration can it give the elevator without breaki0 k6j(f3srk 2k3 fme acw-a8rtng?    ( two decimal places)

  (a) What is the acceleration of two falling 5jqv .etk;siioh/6.k sky divers (mass 132 kg including parachute) wheks .j.o/k;ih e tq6v5in 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 ay:vd*x1j xf*c*- rfe. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If thca*fy:xd-f r*vxe1j *e 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 restsl8 0l:qd g4njp(0vjga 6rp )bu on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the bol g(8d0 bv:j4uaqgjp rl0pn6 )x 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 playe v 0+;8 +sygnc -ehp)ei7 im5iafqw0xzr
(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 momenb y v3/ xkxdt3+p6g)gdt it is hit by the bat, and again (b) after it has left the bat and is flyingggdvp/63x) b x+ydkt3 toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N forces4fg6a 3m4o+ tco0n4f0wj kw f must be exerted in what direction so that the resultant of the two forces points westward? g6 0+fs 4otk4omwfwjanfc034 Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two buil3m 3+0zhh; zr3pu j0r+ qybmnedings 10.0 m apart. The sag in the rope when she is at the midp3herh0m r; bmj+ ny+z3 3zu0qpoint 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 anotherdi*3q7 jknrd7 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 14xpc3/f6 on j3ok33aop .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 Base, Antarctica, a w/w xh1k5vl a*8j;kwes shown in Fig1w w;*8wkxahkj e/5vl . 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 b,s oc9ba+as6 cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coubb sa6o as9+,cpling 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 herselwrk 5 3rc() dhcexzlqz3;f37df upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull dow3)7 r3qde;35rzfc dkhlxw (cznward 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 amxvk4rui dd02nt3+ 5began, 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 blohzz q/z(s09z wck (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 contact with eo yc*u1dc5 vq7ach other, as shown in Fig. 4-51. A for 5u1ocyv7*qd cce $\overrightarrow{\mathbf{F}}$ 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 ini lgnpg:r, se.f c+2bt ej+s(t.tially 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 the ground. This is its "launch" speed. Assume it doesn't hit th:rgnp+ts egt l c eb+.2(,jf.se pulley.]   

Suppose two boxes on a fr su 552naz .y*i4:gr)ibp * nv;vq: zgqwga;ptictionless 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. 42v p:pwn)rsiub a*y.5:g qzit*ng;;g qv5azAssume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 kinxkdv9z)s7svmv mo /9-etic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is kf (s 9dvdl76jrequired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g.45 2a /w/o5mus0z x8xkz4kxsz4 nhmxr What minimum coefficient of static friction must exist between your feet and /5oxkn40xmamk4s xuwz sh48 r25 zxz/the floor if you are not to slide?   

  What is the maximum acceleration a car cjow+nsy 0 a6,wan undergo if the coefficient of static friction be,a6j yn 0osww+tween the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal st:n 6y6kf9yce6 x*da/ fjpxn( kreet pavement is j x/cxk6ndpe:yk n f9y6*(6 faabout 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4.80 ku 52)+vj+rpwa8mu um $\mathrm{~m} / \mathrm{s}^{2}$ 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 30* t zla8ft8k8b$^{\circ}$ 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 wb /1z/ kat-1eafbm jw4ith an asphalt surface have a very high coefficient of abf a-w4m/j11/t ze bkstatic 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 kinetp o8t /ukdo 3(h3ze rif*7ka-ric 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 4::yyakj qaff:l*r- ga mass would box A have to have to prevent any motion from * ja::: gfryl fa-q4kyoccurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the fjssmx vi)h ,27;txdi5loor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial spees imhst;vi7),x xd 52jd of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in i dl j 2qerxwsv715hu+iy1i2ca /2i -ycontact and at rest on a horizontal surface (Fig. 4-54). vi ixdi2lui7qe1hs52+cy/1 ay-j2 w r A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of statid,v atea pb opq .91,76zuu)w*w;to b;r jitq.c friction betpiw bz6;q,jp;w 9 ,qu1t v7ua.ottea)or. *bdween 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, whic p(nyu0xp98xe kd57 feh has an inclin p097k(x n8ye5udfxe pe 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 with3 /vri aqg5 mag01;zb(ropqm8 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 angle gd +6vxgsxm;57dp, ,d,uo ek0b0bfix $\theta=22.0^{\circ}$ 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 initiw63o8linfk,x dbk14l k a,ry .al speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of thr0fue *mgsh1j t;98tee 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 agaif-d b n.kl+qu2jp 5dijo+6s.gnst a rough wall by someone pushing on it with a forc ub 5d2g +q.sponjdl+k6i-j f.e 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 can become dangerous projectiles as theyz4:z zssi- .fmi:se-h melt. Consider a chunk of snow at the rid-e4 : fs- :szhismzi.zge 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 stoppe-4vq) n2it2og-y d jyq2wj.fing distance for an automobile traveling at speed v is equaf-4wgqn jj. )2d-y eivoq2yt2 l to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash0dlp ,c2w9:3eam mv3xfpu iazb9 51 dl when the driver decelerates fu abc3v , :9mp0z x9ilf23dp1admlew5rom 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an init 0pt3 3osr+: xk*+ zagopr,tswial 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 conveyo+eah:tjwrx) v.x3mjb, -x l t0r belt from where they are filled to the packing station 11.0 m away. The belt is initially stationam,0tb3 w+ aj:x vjxe)lhx-rt.ry 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 time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic friction betdsybo3gnk(fucxy:2/ tt (w(u/hbt) - ween $m_{1}$ 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 coastki0j1e)i -ehn uq1l .ad5o.n g 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 mammalian heart, at each pulse approximakb (4ur;ynrq ,tely 20 g ,uy;( 4nrqbrkof blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash i k3uke(at9cqde x3n03xii : v-f the deceleration is no more than 30 " g 's. kii (xkenatq0:3 33ceu9x-dv " 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 accelv59b q8q y)tbheration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of staticv bt5qb98qy)h 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,x, h+b-n ymy*f0xv+i v examining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road. bvnfyx+ +-,y himv0 *x  

  A car starts rolling down a 1-in-4 hill (1-in-4 means that fort,fd3g 8 qj2jq each 4 m traveled along the road, the elevatigqd8 tjf23 q,jon 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 eks2s)nd 3rxe0yn 4g *from the top of the Leaning Tower of Pisa and falls 55 m before reachisxe)nn * y 3dekg02r4sng the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a stea(*6mq6dj hkgm;, xfsaawi,1 e dy speed of 12m/s but enters a muddy stretch where the effective coefficient of frhs,k,iagx(a ; jm6 ef1qm6d w*iction 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 ojl6*o ygdw 0 5-/elzhbn 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 onjg 6-* wloyh lez/b5d0 a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a9irw:ot8m8 4 i)h smdhep,fu7 thin piece of string while the jetlini:7h 9m p8ts ,)h 4i8erdumwfoer 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 supermarke77nc f .p8qcsjt, there are to be several ramps connecting different pa 7cfq nc7j.8sprts 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 8/wc.v3gz/xza khp d5piano (mass M ) using the pulley apparh.5da kv c/xzgwz/83patus 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 acceleratingta gxk0jr9.y - at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chairfgf9atiut7(fw..k h 3, an engineer considers the following seg( tf3.f wait.u7hk f9t 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 o3yd*syv nm (4:t )i(ik;2eefwmuxy*kf 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 Karen, use ,ivtpfp.gm 6 /safety ropes of similar length. Karen's rope is more elastic, called 6m/pi vf., tpga 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 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 usa- ;4ru;ze v3z0wgm" 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed ow0zq9b ;2:p:dsbz mp yhn59l wf 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice fil dsn*+g, dk am6z 7zg8t(6djjeld inclined at 21.0*76g 6jal zskmt ddj8+zdgn,($^{\circ}$ 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.