Why does a child in a wagon seem to fall backwafwx j*7 u gohgbcgtf80+si h*( -8p(mnrd when you give the wagon a sharp pull forward(f s hpguxo0c wh*bjtg8gf(+* n-8im 7?

A box rests on the (frictionless) bed of a truck. r- 0 5+*q7coqtroagb sThe truck driver starts the truck and accelerates forwardr *50ab rc-+qo7qgsto. 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 truck

If the acceleration of ab+zlcp7te3t3ccz 1w 8e,w;bu n object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object ha0jp -7 ,lkknrzve zero acceleration? Can it have zero velocity? Explai klnrp,-7 kj0zn.

When a golf ball is dropped to the pavement, it bounces back up. (a)cgb/0u)-(uh :j0ndo dvkeo.z Is a force needed to makb:heo-o uck /d( n)j00. dzguve it bounce back up? (b) If so, what exerts the force?

If you walk along a log floatingy.xagy ;i1snfr hu-qz ;b, x5eq5xf*9 on a lake, why does the log move in the opposite digf*ai,z f.-51 b e5q;rhxxs;uyynq9x rection?

Why might your foot hurt if you kick a heqz32;;9edwh,3tfckxnm8 s c o/t jwd(avy desk or a wall?

  When you are running and want to stop quickly, you must decele;lvjcto*4p)zb(gk ,kg c az :01s,oqbrate quickly. (a) What is the origin of the force that cauo ztcg,4(v bj*zl ;0gakp):osk1bcq,ses you 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 se9m7fr o7 o4xpuction of the same thread dangles from th9ufm77poox r4 e 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 onipt(2f kxj)8n a 1-kg rock. Why then doesn’t the heavier rock fall fapjit82)x( kfn ster?

Would a spring scale carried to the Moon give accurate rs 7msfwl3u8,8hy iq c7esults if the scale had been calfshl8 ci7,8 um37q yswibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an attav x4t6jx5m7xsched rope held horizontally. If you now pull the rope with the same force at an angle toxjx647 ts5x mv 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 fr i107v6j zyc uq(c;cqqeely under the influence of gravity there is a net force mg 1cc(j06qi;cuqvzy 7qexerted on it by the Earth. Yet 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) needed to lift a 10-kg object when you ar1)hu,/8z cmb j+ h6hqnp tl9ple 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 ozch +)/nm9lq1bpphu8 ,j lt6hn Earth.

According to Newton’s third law, each team in-of; ib gqq)(;kohq2j:hazc ; q-vex9 a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, de zkaghcxq:eoq o h(;9fv b;i;)q2jq--termines which team will win?

A person exerts an upward force of1 8niqnt0h4 q5xfl+ lt 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by sqt8x th5+ql4iln1nf 0tating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how largef /ojx/wr 0ycrn /eln 8l jl7svwe,,1: a force does the ground exert on you? Why doesn’t this force make you rise up into tey 7 lnlsjo1nx/wjec f :, rw/r80l/,vhe air?

Whiplash sometimes results from an automobile accident when the vqg61x h9wy+su ictim’s car is struck violently from thexgh9 uq +1sy6w rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a ftn +;dx :6bcg jg/xlc:latbed truck. When the truck accelerates, the crate remains where clgjtn;g:xdc: 6xb + /it is on the truck, so it, too, 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 it:7ry irn+ vi:8i+iljar ,y(qr s highest point, it slides back down but the magnitude of its acceleration is less on the descent thaair7ii:8j,yq+r irrny+ l( v:n on the ascent. Why?

What would your bathroom scale read if you weighe f8pdlqe s,ct;8gzv64d yourself on an inclined plane? Assume the mechanism functions properly, even at d;v stz,e8fg q 86lcp4an angle.

  What force is needed to accelerate d j0upgb9 jz jzg9.l/.qs8t+s a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ridsu*0-mg5y: l)xd c qwd.: pgurer at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to acceof vicmvk 2/;*lerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight offr t,65sabnkn+m6v0 u a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 * 4oemeiqp (w6s if the car is traveling at ewpqm i*(4 6oe95km/h? -  

  What average force is needed to acceler 2o:h9d)uz fvqate a 7.00-gram pellet from rest to 125m/s over a vuh:q df2z 9o)distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the wate io c*cdf*;k2rr with an acceleration of 2.5 **d;c2rk cfoi $\mathrm{~m} / \mathrm{s}^{2}$ 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 trny ;vgkp j j7syo:,6/eack (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 vsp*bku s/x98*h j;on7y0br 9gt6fwx the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the tbrn/sph w8k7*x v;o 9usg fjx96*y0bsupporting 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 bap9 o qf43vx3s, wopu;fthroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the pers ov9f;u3wpfqops3 ,4xon’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 elevato; wrr8n /*as :9mrdsmir has a maximum strength of 21,750 N. What maximum upwa/n* dwairmmrrs9;s:8 rd acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two f xs-dcn*5u ;yxhir 1( 5jqpkr3alling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-four(5hdquxy n kc1*ir;p3s jr-x 5th 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. Whjzp 1fa 3yk*8hnsvo*;en he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excludi3z sh1 *fykn* jao;p8vng legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the boxzo*twthrm/ v;h2 lo4 / 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 box if tvho/t / h;toz*w2ml4rhe 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 player ke,4i hkk 6s3l
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it 6u ;ut 4j9;n xn-efnitis hit by the bat, and ajn fuxi6e;9 ;n4t tn-ugain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second ,voavk 2,q9 uzx, xx4b650-N force must be exerted in what direction so that the resultant of thek,2xa,,b xozvxq4u9 v two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk acroi1b yut2p 7gl0ss a "high wire" strung horizontally between two buildings 10.0 m apart. The syug p1l70 tb2iag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from uepp4/z2/ycekd ;8wqanother 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 1h7( :ndatva c;*bn3zy4.0$-\mathrm{kg}$ 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 McMurdo8mst4* khtijq 3 5gh1w Base, Antarctica, as shown in Fig. 4-46. The sum3wisthgtj5m1* h 8k4q of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-47 .+pzh+b n ,x**w ne/wed Determine the ratio of the tension in the coupling between the locomotive and the first ca +wz **enh/p+ nbxdw,er $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus s:)n tfydm 6j3s(c n 9ndr,inu :po0nz-;z .lfmhown in Fig. 4-48. (a) How hard must she pull downward to raise herself )zln3idc6.-mtpn snf onrzy ,uf:(m;: n0dj9slowly 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 racu0f2;x)+6 lrl5fd gxrgta:xc e began, 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 (ma j oe 70voyhejl0;hw(+ss $ 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 cq vfn-*02s q-:bbu (hrxr0l npontact with each other, as shown in Fig. 4-51. A fo (x2*v-bb:rqnslqh0nfpr-0 urce $\overrightarrow{\mathbf{F}}$ 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 a4n mkm0guku9( re 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 theugn9 m m0(ku4k 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 table a((ina3r djup,+(: 2tgd 9qbbg0e qkkw re 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 si09p u(qd,3a:q gd+ k rgnbb(wt(2ek jhown 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 frictionfp;iq) ve79h z( a+o-3vy rein 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 required to st:-a jup+/tj c9z4kuhs art 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. What minem crcaq0.os ) u0+e7prk2ss :imum coefficienteeoacsum0+k2s7 q).s cr0pr: of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car cannm.kt .s r7e(e undergo if the coefficient of static friction between the tiree .smt.nk(7res and the ground is 0.80?   

  The coefficient of static frv/5k 9vy y-q+fvyj5mviction between hard rubber and normal street pavement is about 0.8. On how s5y9kvv/qfj+v 5yvmy- teep 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 -ls0 m /g)gelx vsx.mk*q,9gt (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 s u68s z7fbr4kqk-ak9 a rough 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 coz15 u)dd0a1*gduj2pffyw . ab ntact with an asphalt surface have a very high coefficient of static frictiondb jguz5*pfy1.0) dfwa 2dau1.

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 frs1lxtl( +ie9n.2 k yqxiction 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 (Exag1g pn 2:6ngkdmple 4-20) how large a mass would box A have to have to prevent any motion from occurring? pg 6k :2ngd1ngAssume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acrop,g e3vfso ,,dy/am z8m.,zkgss the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts a3m, ,./s fzmg, vae8,yd zkopgn initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kr gb.(k8f/rsig and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). fg8bk r /rsi(.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. ,:5rf 6wi 6b h,i3fgkz g2yvqgThe coefficient of static friction betbr3ff 5k 6 6,vwghi ,gy:qgzi2ween the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has hy q2(hl pa+exs,i66ban incline of 12q6e h ,h+(2siayxb6 lp$^{\circ}$ . 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 scqnx8 px6r abt5/i q64lide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in rfy(c1t7zm 1pbrgz0ovcd)wf ,eru 68, xb-5 dFig. 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 speevc zv6,u+t bmtog3b;9 d 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 the stee5ro) m)6* z dtc 5qjfpz*u*sicpest 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 roug;zh3i 3r0g r29zcyuj bh wall by someone pushing on it with a force directed up bzrczy0u r;33hj9gi2ward 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 they melt. Clkbd1 )169pu o4vkxpea7yw6 konsider6ol1wedby)47 kakukv6p1 px9 a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum sto1d9k5e fpy )4dft x;zapping distance for an automobile traveling at speed v iyzpax9 ed;k4dt1)5ff s 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 das f/s, jz15/dmbut.djhhboard of a car slides forward on the dash when the driver deceh.,5 ft/zsbm1uj jd d/lerates 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 initial speed 5qvy5t dyv)z6 n0f9zl $ 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 e(ptf e 9y*h9intg7)epni36swhere they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction b6ept eignp yti9sh9*(f3) n 7eetween 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 kinetps*xfo cr5 :4*;(bw6k ycki wwic 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 65 kg (including tv g(y+ qr*)zjahe 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 m l qmbwo(+:y4codel of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0.25 wqbc l:y4+o(m$\mathrm{~m} / \mathrm{s}$ 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 reasonadx3eoj5af +45u hton 3ble chance of surviving an automobile crash if the deceleration is no more than 30 " g 's. 5e3at hdx3oj+5fn4u o" 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 acce ;cmcvlh12 8 i7vsnj)cu0vn,- gow:hzleration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficiecmnos) uc7i0,j gc-l vhzw;vnv 281h :nt of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the vc q c 8rwr07lh49fv2escene 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 0qv0 lv 8h2ecc 7r94wrf.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rollingg9/ln.,3 r ,b ftaggob down a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches g/gb nr3gbf l ,9ota,.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) f+8v+r ohnew7 n+vod from the top of the Leaning Tower of Pisa and falls 55vd7rnwv )e+noo8 +fh+ m before reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a mudf(kxdx quw 1j w+i5.p:dy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without hav ik( q1:x5wx+ fudjpw.ing to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a ciga ejk d4 .qirm5 *4i..dppv7ity. An important consideration is how steep the roads can be so that even low-powered cars can get up the di5.pv4eaj.m7 dg. pk 4*iqri 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, dangles :ms3jb3ozks,lx mk;(her watch from a thin piece of string while the jetliner she is in takes off fs,bsml j3z:;3(o kmkxrom JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be several ramps connectin 9opdkvhz xadi n7 tip9.hgi,i +9626sg different parts of tpsodn kithd h a9pvii,z97.i96 2x+6ghe 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 2ep/ :f2wmeos tfh3x6 M ) using the pulle eo36:s2 epwfh2tm /xfy 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 accelerating at 3ve lt- mgo-)6wtw4eq9.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 engineer considers the .k, i9.;l2 yqj;zpmn pqvr vl)fol2.v9lk) rmp;y,zq. ij;nlvpqlowing set 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 metric tons4t* k* gvgbx7g5au v+c (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 Kare/rsuqzxtiwg: (c z- 8oproxk5 5k)3c*n, 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 lr3*zoz)/- w cr qg(uxko5itc8 kpxs5 :arge 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 " 10o5as 4wyfe9q/-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 afli4t +l 6rt5ajh+e1 dllowed 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 togeth8n a*. /c1 yehq hopqlnhr2j23+l+pyqer are ascending an ice field inclined at 21..1e3acpo pj+2/ n8qhqh2*l+r lhynq y0$^{\circ}$ 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.