Why does a child in a wagon seem to fall dl70(pffyu 2 n sri(7t2 nt8soc5 /enqbackward when you give the wagon a sharp pull ftni0snes u 2 8oydqf(5(pc t2l/ 7rn7forward?

A box rests on the (frictionless) bed of a truck. The truck driver stardcr l1)09:f imq gtjofm.qcvn,4/ fz4k r1mj 1ts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Dr,id.t0c f4k fm1 m/g qz1)fcjv4mno q91ljr:iscuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of y wlx5a md pan.;s/8o*an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. k svqjkd9t,l +jw6lyv 9v8 eg6vvc7 24Can the object have zero acceleration? Can it hav6j,c6vv4 2q+tdw jsv lel9k v8y9gk7ve zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a2u 7b (qv++huxfsef*ru b.0 gx) Is a force needed to make it bounce back up? (b) e+ bsxu(qgxub+ fr7hvu0 .f*2If so, what exerts the force?

If you walk along a log floating mixy /t*gc5h *sv -nf2on a lake, why does the log move in the opposite* tv2shg /cifmyxn5* - direction?

Why might your foot hurt if yozwp;gh2pk d9 a2 1bk)hu kick a heavy desk or a wall?

  When you are running and want to sto0f 92pwtjjg(x9 m zmn1p quickly, you must decelerate quickly. (a) What is the origin of the force that causes you jwng2 m(9z9ptxm0 1fj to stop? (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 the ceiling, and a section of the same th9y9lc5q+x nu cb9yyp,read dangxcly+ qyyc,5b9u 9 np9les from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. e7ws u9o2tspx*5p8ieWhy then doesn’t the heavier rock fall faster 8st5eppie7*2oxu 9sw ?

Would a spring scale carried to the Moone 5p ,0ub*r lf rxcp.8tcam)9n give accurate results if the scale had been calibrated (a) in p8e*.mbax , rc0pp5nt9fl )c ruounds, or (b) in kilograms?

You pull a box with a constant force across a friction)b*w id/ez 6vdless table using an 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) decreabd*i/dew vz6 )se? Explain.

When an object falls freely ux c,zmfe: ic.6nder the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third lax:e ,i6 zfm.ccw the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when y3cdo9gy5 f v5aou are on the Moon with the force 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 Ear 5vd cfgyo593ath.

According to Newton’s third law, each team e zv1zumu) uia10hi94 jdkp4)(:etkqfrt:6j in a tug of war (Fig. 4–37) pulls with eq:kt(fh 1mu 1rd p94 ji0z64vj:i)u uakteeq)zual force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceri 0h6uimjkao; 4es. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direct4 0uia ohm6j;kion, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the gr(g,ov+wbke9s0d 7 ipsound, how large a force does the ground exert on you? Why doesn’t this force make y s0g p7e9od(+i,k wvbsou rise up into the air?

Whiplash sometimes results from an automobile accident when tk s7,wok*8sz 5xyr2n ehe victim’s car is struck violently from the rear. Expla7yws 8 2,sekr*nz5koxin why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. Whej 7bruj0f32yd hrz g6-n the truck accelerates, the crate remains where it is on the truck, so it, 6y j7d-h rbzg r230ujftoo, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches itov tvnyq8( 0q;s highest point, it slides back down but the m;q8 (n tqvo0vyagnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself e) 6d9fa g1rqo2qxcv/on an inclined plane? Assume the mechanism functio9q6e rvfo2x qgdac/1 )ns properly, even at an angle.

  What force is needed to accelerate a child on a sled at 1ce,mq3.v p4 jfnf.o( x.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider)4 gwk49tcaz p at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must upw3:k,:i acm hc* kbxf(g ):ia rope withstand 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 of addiy/l:c*z2e 4ftrzfcis858 vb 2/pf $76-\mathrm{kg}$ 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 6 lisxlni42iee p5+ s7required to stop an 1100-kg car in 8.0 s if the car is trai2s4lenp x +5li6ies 7veling at 95km/h? -  

  What average force is neede ()e*e 64 arvyorljg5pd to accelerate a 7.00-gram pellet from rest to 125m/s over a distance o*go6r 5p) v4erja(yel f 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of+a7 i yo8ks/ov the water with an acceleration of 2.o+7i8 /ovsaky5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 trackb qb gg0jo4,k+k 2hcg. (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 acc- jef.g(-fkzj1cfajjs b5k. 8eleration is 0.0680 g . What are the maximum and minimum forces the motor shouldszefkjg1 -bac5(j-..j8f j kf 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 scal p(xx*d(qpijenbec,q 2d9q- r a-3s f8e in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular wef*9b-jxxancqp,-rd(qe se2 diq (8p3 ight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator -kqls*;4b4yr*mhtsd 9 lm)ps has a maximum strength of 21,750 N. What maximum upward acceleration can it g94lss 4 )y*;kds-lp*qr tm bmhive the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration yrjwgr1:teqm9lgt8 : 7t4mx6 of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth wy:6 19 m84tel rjrmt:ggx7qt 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 vxt.hu w.rf10 the ground below, he bends his knees so that his torso decelerates ofxv u 0.h.t1rwver an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied toni+x yw3/jb , /hzbve- the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that tx+eihbwz,-v3 yjb/ /nhe 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 diagw .xgx(t-9q njln3.yj ram 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 bam.t3xgw1n 4k xrm 3me/seball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward n3. ek1 xrw4tm x3gm/mthe outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must bz y5nf3r-mwy2e exerted in what direction so that the resultant of the two forces powyf 3z2y5mnr-ints westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high li7csq. ydq id;yd;;5wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at theid;y5; c7; ql .dqyisd 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 mavv3 -u/udzg 7dssless 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 14eg,uuhj5.kyo(g v5o 2.0$-\mathrm{kg}$ 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, Antvdr4.+,8ka hbvdvf z4arctica, as shown in Fig. 4-46. The suhz4 4fa ,r8bkv+vddv. m 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. 47-vooa)me3 llu : pyd9t00wty-47 . Dewd-3 oatelu)y7o00v9 m:lytptermine the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the buckeyncg2c1 2mlh 0,q vh8rt-pulley apparatus shown in Fig. 4-48. 0h1rnq822c gv,m l chy(a) How hard must 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 b2 b*.jdf3oh05rw4 tvpojc(t, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (massv di030a hyw4fkvm*x) $ 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 co(nmu( jspdlu9;/zxe)x;jhug8/0sf 1f z1fi entact with each other, as shown in Fig. 4-51. A for 1mjs 0/hfux8u)neli/z9zgj e; sf((1dfxpu ;ce $\overrightarrow{\mathbf{F}}$ 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 eachmd .obj*/d xfvk56sq) 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 accelerat5db m/ 6*)vfxjs.odq kion of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless ta jzju,5xp6 xqto)mr2e jq-q.,0x3 wquble are connected by a heavy cord of mass 1.0 kg . Calculate the accelerati xoeu3,,quj 2wzj6)m.j 0-rqqx pxtq5on of each box and the tension 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 betwee okn 7c6s8f:hdn 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 rem4o3b4ko6 nyyhmxe 2+ al8gd- quired 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 tatb;ytr * labc3udb4c-j5iv- fmfl h+ 72 7tr1rain accelerating at 0.20g. What minimum coefficient of static friction - b4 1fjb mr72utt+tcb ac3hra 5ly7;vfil-*dmust exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of ste(- bh qf6,k9cvviw (h+7qnn uatic friction between the tires and t hqie9 cunb,(n w -7+vh6q(fvkhe ground is 0.80?   

  The coefficient of static friction between hard rubber and normal stz01qxicl:p9oioj,nmo6 / /ur reet pavement is about 0.8. On how steep a hill (maximum anglnxlop1 rmic 0q:u,/oji oz6/9e) 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 ag:gbi6x9f c8nt -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a r +tnutbz2/o;u:sf/ ;nkk ,v*3gy 3mov d(wbd mough 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 ks 4:bcoi kz(t2v1/rxasphalt surface have a very high coefficient of static frictionx 2 bo s(4tk/k1zcr:iv.

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

  The coefficient of kinetic fricz2pizeu:8w36hzd m gsyf(z) 9 tion for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a maj b:cjc,,-ng l0jezz-ss would box A have to have to pre jj--gj ,z0b :enzcc,lvent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so-( kcb1y7,owubyr7xv h,e;of that it slides across the floor. How far will it go, given that the 7h7;kr vxu1obyf,w-eob ,c(y coefficient of kinetic 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 in contact and at resx20xjh7 kn*yrpuwmp. b;7f;g t on a horizontal surface (Fig. 4-54). A 6 ;2krbn 7 jgypxh*7u f0.x;wmp20$-\mathrm{N}$ 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 static frictiom2*midf/ en)h:af,ih8s yf3hn 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 avoid having the cratie:mhdfmf)h ,sa*ih8 2 f3n/ ye slide against the cab of the truck?   

On an icy day, you worry about parkinggr,ml65s s2hsztec3fd 1 i:*d your car in your driveway, which has an incli2 s:g cdh63tdiz,mfs el5*1 srne 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 with l:dsfa r. wv*5wq3s2ga 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. aknw7:jc 1-mx 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 speet-. y)ep*o 3dzyy o6sod 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 thk)r5ia;dfw6rn y.:6 y,jhyu;ls * ttye top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rou*z7fqal * po 4pc(uw,xgh wall by someone pushing on it with a force directed upward at 2p *a7fz,o*x4qu(pc wl8$^{\circ}$ 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 y; w*pvj1a5/ 2hhrpc hprojectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitch 5a 1hh* pcypvjhw r;/2of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling at spex 0j32cljf e2oed v jo20 l cf2ex3jis 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 on the dash when the dr i5z9qj8p 9ip me wz*xp(2f ;j/aehkodb9,z*aiver d;pxe98 moqj5pp a9/,i da2ijzwh z(z *ek9b *fecelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an phz ui4 s5s);sinitial 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 conve h4y;em3t6uq ,lx 7hrdyor belt from where they are filled to the packing station 11.0 m aldmxq6t3 uyh,7 ;r4eh way. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit 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 frictioln9+-u my- y.uf-dbjzn 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) ca2oz7* wuxk8rkmz2 .9ntjg( vjn 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 kc +a8tl,,t2 5 le/kp 26uwkqx by5vvaeach pulse approximately 20 g of blood is kak,v 65b/2 l+aly e,twv2qxutcp 58kaccelerated 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 reasonab 7 f4vjfq rwzk8,z.k1dle chance of surviving an automobile crash if the deceleration isqw4.f7fz1r vj d,k 8kz no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleratioam l9f4hxjc5nxzw ex*)1z 9r,n produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static *xfw9 9x1mcjhz,5 zlan4)xr efriction 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 involving two carsh4ajit8,q3b4 u berkl 3ic4x 9, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction c3b43jr 498t 4elhbqixui,ka between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling naom9o/f :- clp1i1hsxp,z5kdown a 1-in-4 hill (1-in-4 means that for each 4 m traveled along t1 xa oh ppi :zn/cf-ml1osk,95he 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 Tower of Pisa and f7g-hwd /2.plfl a h*nye5;didalls 55 m before reaching the ground with a speed of What was the average force of a.eaihd;yn*pg l25f d /d-w l7hir resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stgox -*n,jt*ku hs:(yxretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy strets hy:j-xon( ,*ugt*xkch 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 3 3(ah/rc bcfkthe redesign of a hilly portion of a city. An important consideration is how steep the roads can be shkc /af3bcr (3o 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 physics experiments,156af 4uq,em qck1lyb r stk)4 dangles her watch from a thin piece of string whiltqe )r4s1aycfk uml51b 4,k6 qe the jetliner 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, therf9uipd 0sfd )5e are to be several ramps connecting different parts 5i9pdsdfuf 0)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 M08 2 gprzntipu5ob: 7w3ib kgty (w)k7 ) using the pulley apparatus shown in 5 i iwz380( wrgupt:7 onk)7pkgby2bt

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating at )zah-c o.tkk/ 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 engineer77 uvr1sd y3h+ 6doidr considers the following se6dud h 71+drrvi soy37t 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 of 660 me9 njxrcy(/iu8qvo .8stric 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 andsm6a 0akwh j812fi k6gyp5xx 8 Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.x1sgj5my 0 i 6kxp8aw28fk6ah) (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 " 10 zt asl:np2w0y8,p ol-g x()hub 6bh4d-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 allowahu6 olm+7 lal,np1r1h,g8:ymxos 5 bed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped toget-6e6fx .uz zqwuk edh*9::9r,tgtubnher are ascending an ice field inclined96e:qfn hu-9tz u z*gk6 :xut.br,wed at 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.