Why does a child in a wagon seem to fall backward when you givecjf ,*ze9 ww: o+to2ci the wagon a sharp pull foj tco,owcw 9+ze2i:f*rward?

A box rests on the (p4poojp -ktmv 1)snsi;ut9fv,l09 3g frictionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary stapi9 ml;-kvp9)g,p0v1 s4f ujs 3oottnnding on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on i7 ja j; 7uum9sjpoqj96t? Explain.

Only one force acts on an object. C)jz+va3//jbe 00ywlyii+ i mman the object have zero acceleration? Can it have zero veli ewz iy+/am 0ijby+/30mlv j)ocity? Explain.

When a golf ball is dropped to the pavement, it bounces back +6;woe kt.eo6ysxlo),mu) zoup. (a) Is a force needed to make it bounce back up? (b) If so.;so 6mkexuo 6zwl,)oye+t)o, what exerts the force?

If you walk along a log floating on abt5ae.sr;( (ikgu mi1 lake, why does the log move in the oppositert(esui5; a(k1mbi .g direction?

Why might your foot hurt if you kick a heavy m8f/7/ayckc m7m aqi ,desk or a wall?

  When you are running and want to 4u38wa 1muvknkf.y n:stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stouw31vn. ua:y4k8 mkfnp? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from th m), rf0zjueaj98j; ehe 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? Wujf9mzre0 j e8 ahj),;hat if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg ywr4 dl4(uwkzu78 r n3rock. Why then doesn’t the heavier rock lr4y wnu47zuk3 rd(8wfall faster?

Would a spring scale carried to the Moon give accurate rz vb917ge6cus+ jt *miesults if the scale had bee79cs+ue*v j 1igm tz6bn calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using alw4b:g ww p 8 3m6cbo s75/h;-ykgpbjsh 3sn1on attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decre/ :6 5b h3gm7bc-pk8howynwsosjpgb; s3w1 4 lase? Explain.

When an object falls freely under the influence of gravity there is ad:wxs; rte1m h+gcah ,;v)p x+ net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and oppositewedhgrh+as)t;xcv:m+1 x;p, force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lipckw+c+w- i* ift a 10-kg object when you are on the Moon with the forceiw c+i+*kp-cw needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pullsili f1w00 ,h(xme lpt1 with equal force on the other team. What, then, deterhp wmelt1,xl0i 1f 0(imines which team will win?

A person exerts an upwi35dft2x) rewex shid5q96snjk:e92ard force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it i)h 5e5ext2j ki9srd 29 n:e36fdwsxqis exerted.

When you stand still on the ground, how large a force d33kxfjawwv8 *, z dem5oes the ground exert on yomxz*3 f3w,vkj8d aw5eu? Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobi3zm jxa1d. v7u; ciu:: kjd)vws65y zple accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this sitm:z1)3uydvizvajd . cw6x:k ;up57 s juation. Is it really?

A heavy crate rests on the bed of a fld ;aq lv51qr7gatbed truck. When the truck accelerates, the crate remains where it is on the truck, so itvdr ;q5g ql7a1, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that i//,do e3o mwe9.bcwtlt slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. w.t,lee dbo93wocm//Why?

What would your bathroom scale res7trf,avwqqj h :ki e)w(bfox.-0r 1 :ad if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an angl,his xow1a.bt0 rv::7) r( kqjffq-we e.

  What force is needed to accelerate a child on a sled /fr-4vol/zjbtg /g2 ue sua ;) at 1.25m/s$^2$?   

  A net force of 265 N atn9y daw-)5qv-l-qm h ccelerates a 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 withstand n6o/hg fcl1 5rif it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a o,/uo dks(q :j $76-\mathrm{kg}$ 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 11n .hcozqqe yb4,ac:car in 8.0 s if the car is travelqhno41:cb 1yz .c e,aqing at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest tce-*ijrlp6t(7 nq6h mo 125m/s over a distance of 0.800 m along the barrel of a rii (q7emn-cltj6 6ph*r fle?   

A fisherman yanks a fish vertically out of the water with an acc qzpq7ed +eyorc w06 *:v+f;oeeleration of 2.5 oew+ 0ezfvdp*yr+qo67 :c; eq$\mathrm{~m} / \mathrm{s}^{2}$ 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*(r w)x)cac 9en;.omdjfj(a d cover a 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 tz mami 9v/zr0em)o)w oihu0xa 8z+y 1ow,nn/ +o be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces thewrn ez+y )mw/ o+z xi90mo,/mov18) nuiz0aah 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 the ele5wqhj,m 8s:x1:,w:k 9fpogw lhf* uxrvator begins to move, the scale briefly reads only 0.75 of the o 9khm,lxxsq *,w:r g8f: :f5u1jhwp wperson’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a /.rfsi.hs22- ) dswrev9ia s 6im4jo umaximum strength of 21,750 N. What maximum upward acceleration can it give the ele4af /ir6i.h-o .2ud ssejs)92 v swrimvator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falebm/ z;3 8. 9erfuwybofu0 bn nl(+fr3ling sky divers (mass 132 kg including parachute) when the upward force of air rel o.ub/r+fu3e3 f rm;b z9y0 nnw(8befsistance 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 strikes the ground kc ll*)i +g8jsbelow, he bends ls) l8gk*ci+jhis knees 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 cw v ,6r; vw.l.pl;i fvbv5jm1nm7g4nrope tied to the box runs vertically upward over a pulley and a weight is hungnnr71w5vv .mb6 4w v;plgicv;mjlf,. from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagrax9xa ,g4wdl5i m 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 baseball (a) at the murn la9g973cg oment it is hit by the bat, and auc9ggnl9r73 again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must bp2vey, p8d r8k3hk 3jee exerted in what direction so that the resultan83ve pdkrh83e p, 2kjyt of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung hoj1+ ldreqiw,m ,(lcv;97rsfo rizontally between two buildings 10.0 m apart. The sag in the rope when she is at tredf1 iw,l 9,(ms; c q+rlj7ovhe 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 hangi ,;m n(jsji vpc1:nhzo jl*f(8ng by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 1d 6 1k aka.86r fdlsfmkwp2 e(;dj/xm34.0$-\mathrm{kg}$ 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 McM yzh1 ,fu9s5jburdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forceh sf5u,zbyj19 s $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 puo)2vs nd-py o k..rg:flling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the couplingk2o..y -:r d nf)ogpsv 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 pullk gqw+w;irwl3bxd2w* zum*j g;k-.g:s herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must;xu3* m jbgdz+k2w wq:gl gwwri .k;-* she pull downward 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 began, a 3icl2 .c irqplgla65+65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (o*** be. hbrx b(qsi)gmass $ 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 how8kd mt 08 w3;wux4y/c up1lj+gw;qp orizontal surface are in contact with each other, as shown in Fig. 4-51. A fo;83 w wxtgjucqywu+p 81/pml4 0d ;kworce $\overrightarrow{\mathbf{F}}$ 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 inr qq/ ;w7e6)/g5ye hvoxowe/5 ecedd , Fig. 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 the ground. This is its "launch" speed. v ; eq/wg)ed7qede/xwc/o o556e , hyrAssume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless k+ (lp17jo*8k endmjltable 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*d(n1 lo 7kl8jk+mpj e 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 betwod 6q)9y vkybut ,l6t9een a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to scxm(q)pu b64k9 txhu8 tart 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. Whnc vqhf,k ,x5-at minimum coefficient of static friction must exist between your feet and xknf-, qc,5 hvthe floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of n+gee a(zsra62s(0dyc ,yf h *static friction between the tires and(sye * f0c2+y6h,gena r(a szd the ground is 0.80?   

  The coefficient of static friction between hard rubbplk- jf1i*x9*h h sz*ger and normal street pavement is about* k9- i1jphhzls gfx** 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 z z9g-9gnhrhr8mz;w jn77 -ku$\mathrm{~m} / \mathrm{s}^{2}$ 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 roughlu k3yz4 8w-yj 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 veonzq :d0 6 w(gtkh8*iary high coefficient of wod6*zn :ahitq8 0(gk static friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of ki 6c nhudsqwevg1x: qgx r,v 8:9/d;lp2netic 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. 4-2ds4t, n5ktb2qazb0 n32 (Example 4-20) how large a mass would box A have to have to prevent any motion from occb dn2 zna, tt0sq452kburring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides agha ez6zmj5vn ),hvqx 95(g3mcross the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speem5 59anjezxzg( ,q6 vvm gh)h3d of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and ak/wp 5m*tzo 6ot rest on a horizontal sut/o5*kzo mpw 6rface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate.g,nosssy9q. c*g k2u;76m w+mpwyh )c 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 driver can decelerate and still avoio +7yc,6mgk)2cnw.ss gmw; *y9sqh p ud having the crate slide against the cab of the truck?   

On an icy day, you worry about pa4su+h:.p1jvllcm w:arking your car in your driveway, which has an inc4+a1p v hlcl .wsmj:u:line 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 withh,n p agii.1vez7t ,vet-yg- 3 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. yqdj6*fqqjn0axx9 n*(l z0nr +u t1m,4-55 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.a 9)ilgm34i6 u n 0co/mxt 0txy);ben g7xyrf50 $\mathrm{~m} / \mathrm{s}$ 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 at:iv22oi7n6 cw+fhe 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 pnrmhgw*w04xd c 6i4 l+lace against a rough wall by someone pushing on it with a forc nc0wg4r4ldim*+w x h6e 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 da*9hlm zou 2b4 21 zai8seomzc:ngerous projectiles as they melt. Consider a chunk of snow at the rida2oz41sz eih b9c82l*uz o:mm ge 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 automouv7c 7 8jfkzr4bile traveling at speed v 78 kc7jv rfz4uis equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward msm33 k jcraeiid-p7/og:b*. on the dash when the driver decelerat cpi3o7mbs-:/3.ij dgrmea * kes 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*/rfj ga4; rol 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 conveyor belt from where they are filled to the packingcu/dwl+ mfj7wu(a:qn xp8l 9 + 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 trip. If the coefficient of static friction bdlwpw +l 9/qu8ua7n :cmfx+j(etween 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 flgdcz fyn 1xsk +bp4)g2a82s4 x(qe; friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass ;md(:es4tsro65 kg (including the bicycle) can 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 mammalian heart, at each pulse approu9nv v :0h6kumximately 20 g of blohu9n u:k 6vmv0od 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 if the df37. sop +pq3tjhen0geceleration is no more than 30 "ep q.3ojpt3n0g+hf 7 s g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and if an ob-vg6khdms. 7aim+ exk+s n4,;nv*dcn ject is gok +d+h*;n -6sm,vms4kx7 .gavcnd eniing to "hold its place" on the ground, 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, exame h38u;q2dxuf ining 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 hx 2ef;d3u8u qof 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 thatf/e(wmh l+ew 9pe ng, :r4ra-g for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom 4 (w/gp rfmleg+,n ewhr:e-9aafter 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 Tower of Pisa anmmpf6q d5+:v ud falls 55 m before reaching the ground with a speed of fp:v+5 qmm6d uWhat was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 1i d dxsq:ln8l0-: djh(2m/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 so, what will be the speed upon emerging(j:dxns: ilqdd-0 8lh?   

  A city planner is working on the redesign of a hilly portion of a city. An impo q*56fetl+ pc2d p7dgyrtant consideration is how steep the roads can be so that even low-powered cars can get up the hills+efd* d 5t6c2pg qy7lp without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, d031f:.jqfdy ade +d qnangles her watch from a thin piece of string while the jetliner she is in takes off from J.nde dj1dqf: 30f +qayFK 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 several ramps connecting din 8*8du xggmet,dbc6em.o , 3efferent parto,u6 gtxd dn8 g ,c*em3.eb8mes of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M )fue1r 0dxw 4znv2 ,;v t2io/ 6luds)za using the pulley6 1rt 0 dia2,uwv;2so /fe4l)znvzudx apparatus 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 acceleratinslxy, *xd81l wg 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 chair, an enri, a4.a,n7la rk*gl ixl j70jgineer considers the following set of conditi*arlklijx ,jnarg77. a,l0 4ions:
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 v 9zm2pv:h o9ric qqwh3dp 0;/train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length. s)(hhsvo udb5q :/z8 kKaren's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not reco:5d8bs uh /) zvk(sqhommended 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 us.e ;aonz0c dldlhr4yi, *szx3*c b),fing a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to re8z4 v2 z/w khyh1q0ov :/rcmlrach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an63 sn.oyijo8q4pt z/e ice field inclined at 2e 6ojzns/q4 8.ot3y ip1.0$^{\circ}$ 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.