Why does a child in a wagon s5v+8ng. rk ,gfgvt)f dvktw 0; :hxv(neem to fall backward when you give the wagon a sharp pull ff vktx;gwgdrk8+gtvn 5h)(n.:0fvv ,orward?

A box rests on the (frictionless) ;m1i2go h s:lxjuw y; /n/ihk2bed 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 standing on the ground beside the truck and (b) by Chris who2l sy;/ihjukn;:2/1hmwix go is riding on the truck

If the acceleration of an object is zero, are n1uvhxuo ,0mjh4;n: ef o forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accel b7 99rvr4ebwzeration? Can it have rewzr74 b9b 9vzero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a fkcye,mg4 *a- xorce needed to make it bounce back up? (b) If so, wheg-m ck ax,*y4at exerts the force?

If you walk along a log floating on a lakef 6 lo7mey xv6uxl n(:;*dr.wh, why does the log move in the opposite directil:xmul .7h rf(o6d6e*wnxv; yon?

Why might your foot hurt if you bl(1b zsx4k t(rnoa9 1kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate cbr .8at ,3 ,dwoptop-4dp f3ws+ f/mgquickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own exp4 w fbo8mp ,cpa-gotw /fdr+,pd.3 st3erience) 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 fcyhxbqm9 +sa. /9c2f rcb0wbb6f9g8nrom the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a sloxfcy 8gqc0ncr9f.9wb6 /a9+ sbbmhb 2w and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg1novl65v 2x pn rock. Why then doesn’t the heavier rock fall faster?lv1n26v xnop5

Would a spring scale carried to the Moon gi0ej3jaky59: ,vwqbyx p0 y3 qjve accurate results if the scale had been calibrated (a) in pounds30bejy ja3qw0xy:jyq9v,5k p, or (b) in kilograms?

You pull a box with a constant force am8+ ras. ,gou7 gb uaez6nlf07cross a frictionless 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 tuezor6,n sf mbg +al7a 78.g0uhe table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under thudbgr9011 xvl rd(;q3j g) bpze influence of gravity there is a net force mg exerted on it b1 qxg;pzd13 rj0) d 9(bvulrgby 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 obj;qh i *nqlge -mm:b*f.ect when you are on the Moon with the force needed to*:bim.gqm-*efn q hl; 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 tsjypf t-(n r0wd39ue (mf86 esug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determinr8s ffp6(3jy nd-(9 wem0t suees which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe the k(0knaoi)2ld cp:8vv (: o0n) 2vkavcdpi8l k“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 is exerted.

When you stand still on the ground, how larg6ne x/acb r,e3e a force does the ground exert on you? Why doesn’t this forceacn r,3e6/ xbe make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s cmpajqlwo ah6 /s8n tpw ,:i0vl*:cy9:ar is struck violently from the rear. Explain why the head of the victim seems th: /ow q pai8n6tm,:09:ll avcpwyj *so be thrown backward in this situation. Is it really?

A heavy crate rests on t2 oue16x5p 6gq0 kflbche bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force gk x5u10fe 6 blo2cpq6causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the blockyentm/3k,f543 mdkn1n 3jj6ubs yv j; reaches its highest point, it slides back dof 133,mn3tu;dnsbje nyyjm k564kj /vwn but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you wei:uwg2 it.7b girmc b))ghed yourself on an inclined plane? Assume the mechanism functions properly, bcb:gu2 itw7g)) r.im even at an angle.

  What force is needed to accelerate a child onl-do(/ -k: vdn vk-m*+f mjgfb a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike anqg.40g d-uw npd 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 if it is used to accelerate a 960nq f:bz87ti eyt h5((i$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of an ewli1+2eccs6/,;v znaj)un $76-\mathrm{kg}$ 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 cargm)jtxkp/-2ac 0x l.k in 8.0 s if the car is traveling at 95km/h? -pmtkjgkca 0x 2/-lx).   

  What average force is needed to accelerate a 7.00-1d:uvnbl n0z.gram pellet from rest to 125m/s over a distance of 0.800 m along the barrb 1.l dvn:n0uzel of a rifle?   

A fisherman yanks a fish vertically out of thec2w e rs1*3mv; hxxq-c water with an acceleration of 2.xw*-2vs3mce1;hq rx c 5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 track gb 8,*wnr epq; (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 kgy ttjm-h-fe25u8urd: ) is to be designed so that the maximum acceleration is 0.0680 g . Whattt:j-mf uu25h ey-rd 8 are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the elevvtl, 6 ihk28zkator begins to move,,hvl2 6 iz8kkt the scale briefly reads only 0.75 of the person’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 maximum q(mfzq;l 85fbk, stivtcsx.;p/z1 ( sstrength of 21,750 N. What maximum upward acceleration can it give the elevator without breakinxvcp ki/( .tq 8sfsz(15z sft;lq;bm,g?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inclz * , bhea*,rqa,zk;ieuding parachute) when the upward force of air resistance is equal to one-fourth of their weig ;e,* ,b ,eazki*zqrhaht?   
(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 gr0w ha 5ibtae(ht9/e6found below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 mh596/0( i tbtwahfeae. 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 ropbsl4i;m:2 lofe tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight has:l2b ;fl 4ominging 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 for7q-a45xf z ncme)2rhz 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 moment it i;ncqk 6 1nqu,xs hit by the bat, and again (b) after it has left the batkqxnu;, c1n6 q and is flying toward the outfield.

A 650-N force acts in a northwestxrlw,(0o-nvf txn: u/erly direction. A second 650-N force must be exe-lnv0u ,:ox frx(w/tn rted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung ho+2di)5kawn ljng82 z, o4so. hq xqr2krizontally between two buildings 10.0 m apart. The sag in the rope whenqlnx 4d 8kk .ja5s),h2+woq z2g2 nori 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 52zbjaa +lyi9ejfm k3tfrj/ge 7q);) hanging 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 14 cm no2jraq:ium;)y;m. qwr3+.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 locat6 3o7zearz b-tion at McMurdo Base, Antarctica, as shown in Fig. 4-46z7bz- 3e6raot . The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. cv dpjw+s k7;o: -hff/4-47 . Determine tsfk :f-p+dv/ c ;owj7hhe 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 bucket-pulley apparat2as4x/tbrdt7 l, 5x lous shown in Fig. 4-48. (a) How hard must she pull downward to raise7x/d52txl4tslrbo a , 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 xvvsp;cc 9lkez (n+gzf+ -x*: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 bmee92+mrri52v/wz flu ;(qz klock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionly ie1 o2v(aln+k(y j,iess horizontal surface are in contact with each other, as shown in Fig. 4-51. e yyki 2((+vil j,noa1A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each i*1t et+ z newr+tgq7,gnitially 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 hez1++*rgq t7 ,gtetwneavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on ap + zz,cjh1rh bj vpav/f6yb))-3t +vu frictionless table are connected by a heavy cord of mass hh/aru6+ztpv cj )3bv pj 1)bv+,f -yz1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. 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 frwdb+ / n:hq3tli*onsf 52e 5uniction 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 requiane036eg5bz*a ow 6p +dgoig 8red to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What minimum co5cp:dgq vb)hrq97+ eye ublfg :7/0jr efficient of static friction must exist between your feet and the floor if you97c)l7e+ u5gg 0:d vhyb/fj p:brq qer are not to slide?   

  What is the maximum acceleration a car can undec5 g./. anfhhmrgo if the coefficient of static friction between the tirn5fgh./ ahc m.es and the ground is 0.80?   

  The coefficient of static friction betw.a gg87xu8pfzp hi+8gzw, y9deen hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can yoy,xf79zpwa d i8. hg8pg uz+8gu 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 a0jxg3i 4t()f yjnqb v:t -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 rough 3tn -8be6zxgc n) t5h0v0$^{\circ}$ 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 asphalt5 3niy 9 dtzk)fa1l,bb surface have a very high coefficient of static fr di )f3ztan51 lbkb9y,iction.

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 friction for 6,bpsmleluv ,1 cgp :6ije4 zm+ hmg92a $ 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 larg sb.2,umt kzs9 30sshde a mass would box A have to have to prevent any motion s d2z s0s3hk,bmt.su 9from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it :c1b 0rochp bsy3g3h1slides across the floor. How far will it go, given that the c 1bp31rc0b hcysg 3oh:oefficient 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 a:ggy7,xkzfb7 nd at rest on a horizontal surface (Fig. 4-54)yxbk:gg 7z7 f,. A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The cod1 jfzaj n c/h9mr,,)7(slwvi efficient of static friction between the crate and the bed of the truck is 0.75. What )vjdzw m(9,c 1a if/rh7jsnl, 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 h3m8nct 1yt4wqenb5md)( nhf: u* -gtq9 fo in5as an i:m 1u* fqn)ec(54y9q w 8ti nhndg oft5-t3bnmncline 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 slid d()yftjoh 19oe with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at z(ecut8 l:o rb*de;6uan 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 s2f4sy-ts(.5ds b* zkf eo;bs:gnqvo6 peed 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 y v4+y h-l9+q37ein jkxe9vrgtop 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 rough wal) n5 5tqqmc4cul by someone pushing on it with a force directed )c5cqqt5 nu4 mupward 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 ang6* j+p(c/uqr(bg lbecome dangerous projectiles as they melt. Consider a chunk of snow at 6u abl* + gcqpjg(rn(/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 stopping distance for an 29 b omi4 g6 vq5axs3fakk8hbp(0fy9oautomobile traveling at speed v is eqmhq 4b 2s30oy9(ak8fipf a6o9vgx k b5ual 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 ;r6mjg t vp-lp r37kz-on the dash when the driver m67 k3zr- rgjptl-pv ;decelerates 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 sp 71j e-gsfqfp+m5fed7eed $ 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 ar0-q 1,2rksi5ahts vcd.q3jwq l .7rzge filled to the packing stationz-j.hcs 0l 5vk2drg3. 1tq,7wiqr sa q 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 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 frictiqag -i, mms7gn1cw9 r4on 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 bi; ok d8z9 cknh y:)utcwcbte 8,7i,w8lcycle) 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 appro4xh9idogp5 3 1epw 2qoximately 20 d o 9xiw54ep2gh13qop g of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crasv +xwhc ls6:g8hy,kq*h if the deceleration is no more than 30 " g 's." Calculate the fo*hskl:vwq6h+8 c ,y xgrce 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 , andbyjnwe )uavyg*+8s/) if an object is going to "hold its place" on the ground, show g+yj/s)8) nv*uaye bwthat the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the,nuxtf pp8l/,t15t(q2vox yh scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 15nfxu/ otpty p, x2tv(l ,q8h0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that qajz7x)p r/m8 for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going whm x) 7/arqjzp8en 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 o 4*0jxtl+k h-2 odzxmand falls 55 m before reachingxzo*h+l d-j 2tm40 xok 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 muddy stret bffr7dq xe9efbyu0*d2 s*.m-g0u5ptch 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 eu fbd dre5m fgesu.f0y790qx2*t *-pb merging?   

  A city planner is working on the redesign of a hilly portir* 0uq9g5i ncsws:d1 zon of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21ri d509 cguw:sn *zq1s$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watcko4pm 2v9l+t1pxi 9)z bs nhg0h from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the stb+tl4z9 ppvk)90mogxi2shn 1ring 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 connec8 7g-bt 7d(xujgws luus5 c-5eting different parts of the store. cbg87 wul-ut -5sdux7(g5ejs
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 wlm6g z9ke s;5c:r3sothe piano (mass M ) using the pulley apparaws 9 lk35mosz6 cg;er:tus 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 accelerati,8 qjj7; 1seelwo3fjxng 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-rest)qiy trbw s0bc+a gnd- o:*)1araint chair, an engineer considers the followirb y+*g1t i) o qa0:scdb-nw)ang 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 tj , s cryjf-4;k3wiro+ons (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. 7b3pg eb7s v1vKaren's rope is more elastic, called a dynamic rope by climbers. Bill has a staticv7pv37 1segb b rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-6m*3jy,wz3,kdzvzt x 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 txf 1nk5;1dik ip eh5b4o 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 together are ascending an ice field inclin rvn(.9c. dl3uh9wngn- :r+opf0r lnned at g dn.n9 lv9r.ro -3lcwn np0uhn: r+(f 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.