Why does a child in a wagon seem to fall backward when you give the wagon ayng ))qr:jpkw.f+( x s0-suv r sharp pull forwargr kqw.s pynur -) vf)x(:0s+jd?

A box rests on the (frictionless) bed of a truck. The truck rp 1nc(*pgypsdcac2a3h: 1 q2driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motioasr2(1yg321 np :qacc*ph pcd n 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 an object is zero, are no forces acting on it? Ex1 *sn+vfj j.viplain.

Only one force acts on an object. Can the object have zero acceleration? Can ic/l6 (vz a(umqw )e4(wsv. dmat have zero velocitz)(mmd 4.a v((6 w wucesl/aqvy? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (ajhu y0onyn yl (l.*j00) Is a force needed to ml n .no*(yj0lu0yhy0jake it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, whyp1/xopvp(/b h1.1d -atgx9 0 pme4 cxhxpa6l d does the log move in the opposite direction?v. 1o/g bxx6p9-e l 1d4pdxt(xpam/a 0cpphh 1

Why might your foot hurt if n u4vd d6),n3:k6p apyc nmff-jmy.:r you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must dy q*b ;t,ve9l n*qx3twecelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top sp ,q*txbnq* t3le;9 vyweed to come to rest.    m/s$^2$

A stone hangs by a fine thread froobj s0 8:k0rexnnpk;8 m the ceiling, and a section of the same thread dangles from the bottom of thnnbjpe8 ko008 ;k sr:xe 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. Wh6k:ev8c bbh4w y then doesn’t the heavier wc heb:86vk4b rock fall faster?

Would a spring scale carried to the Moon give accurate ry2+ d a)urrjo0esults if the scale had been calibrated (a) in pounds, or (+adu0 r) 2joyrb) in kilograms?

You pull a box with a constant force across a frictionless table us0.es3(flt4go q0 xuuoing 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 the43xu s0 u0.tf gloqeo( table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the ek7o8mgq*x ntz,f -cy)c88nr3xlt/ qu1i5 gf influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newto *zioeq8tf175g)f u xx, nnl c88trqc/ gmk3y-n’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 uw+tcb*c+s1 4fh e lk3when you are on the Moon with ts1c+ l+fk4e*u3 wtchb he 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 Earth.

According to Newton’s third law, each team in v8n5tgtzc*-gpmgo .: a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will -vc.zgtg 8 op:g*ntm 5win?

A person exerts an upward force of 40 N to ho y4 p.krwfq0.pj m7c7jld a bag of groceries. Describe the “j4 cp. .j kw7y7qm0rpfreaction” 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 large a force does the ground ezbprzp f7ou 2h/5( 9iwa0xg6txert on you? Why doesn’t this force make you rise up into the a97ipf2ha/p b6z 5rw txg0z(o uir?

Whiplash sometimes results from an au1:d* epv e-d5bhz rc:stomobile accident when the victim’s car is struck violently from the rear. Explain why tzs5d db rp1v ::h*c-eehe 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. Wh7gptq hch9;udlx-pmr)l8w d 39q, 6,udi j0iven the truck accelerates, the crate remains where it is on the truck, so it,hu 7lq)98- ,u3drm0d j9hqw,gpv;xtpi ldic6 too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides ).6,s 7cj vbxovfm8lv up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its sx ,vl6o.) mjvcbv8f7acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed sdo9u0txs; 8wyourself on an inclined plane? Assumeo xd;08 9sstwu the mechanism functions properly, even at an angle.

  What force is needed to accele/qlr .pfc ha04rate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike xiep-2i59 wcl and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to ac: f qvu(uyjihmq k3 at34acsu:,nt2b-r3 t86ycelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight o-w+ot b5g tj5 maz gid2u28qe6f 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 reqovxfx,j0cz49,yd;q j +mq r6tuired to stop an 1100-kg car in 8.0 s if the car is traveling qo dqcfjy6z 4jx0t,m9 xvr,+;at 95km/h? -  

  What average force is needed to accelerate ag.z*ljymd ;( o 7.00-gram pellet from rest to 125m/s over a distam;*.zo yjlg d(nce of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration t qfys03 m37ul;j:qr5/ mj qflof 2.qmqm70f5lsr:u ;y3fj3j t /lq5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 tw t2r:jcv * x2dv-z7ocover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so th e86ga:d3jqoa 5iw2w iclq*)kat the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cablwkdw5iq 2i*la e63q co jg:)8ae? 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 elak rnihra:v).)n )cl+evator begins to move, the scale briefly reads cnhv +a:.ni) lka r))ronly 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 sthb lwe* s/;sr6rength of 21,750 N. What maximum upward acceleration can it give the elevator withhew ss/ *rb;6lout breaking?    ( two decimal places)

  (a) What is the acceleration of two v::+9nib + upe/azetbfalling sky divers (mass 132 kg including patb+/e eu z:ivn :pba+9rachute) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from thn9+sdvy visnx:bbw l;zin848fw 5( b)e roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso deceleras;5l :8vn9dsn (v)ib wi4ynfw8 xz+bbtes over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N re c)::1fc9 ug fenxo*f.ongh:z sts on a table. A rope tied to the box runs vertically upward over a puofecz*ou:fc g .1 nh9 :x)nf:glley 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 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 pl(j j*+r(hebzm qyj) g: an+qn;ayer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagnxq;;2b v6vs5t7 ubev ram of a baseball (a) at the moment it is hit by the bat, and 2v bv e5xt6uvbn7q;s; again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 6rwrg gg l*,-mq339ta h50-N force must be exerted in what direction so thar3ggr mla, h gt3wq-9*t the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "highu d)/j:sz8u-0.fum 6ghy ee ax wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the mi)gs. eeh6f:z/ x-udam ju08uydpoint 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 fry6bg ;y;mr uu p:s*gc.om 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 14.0y 5l,wn/q(5 up.uffhr$-\mathrm{kg}$ 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 tl. r7f vobw tq/tx67;qo a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces 7 vrq tloq.wxb/76; tf$\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 dpocq.,9; lobs, ,g;/c* ;t/p speesajsk *eqpulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tensio/s 9**opjqdpb;/;le atc;c, ke s,g,sspoq.en 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 apparatus 4bi t,bwh)r4vshown in Fig. 4-48. (a) How hard must she pull downward to raise herself slv4 i, bbtwh)4rowly 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 bd9fo0efky* 7g egan, 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 b26()g y 48nknl5;iwwbyels jwlock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with eac 6f0g. r85h zpfnxc7kzh other, as shown in Fig.fh .5pz7f0kr6c 8xn zg 4-51. A 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 eachud.3wo s+njkqu e.we:u n 6 xjw-.fj.) initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it dwd)x n .jneu:j .6kj.+quef-s3ww uo. oesn't hit the pulley.]   

Suppose two boxes on a fric/g.epkd4us a9tionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams show/4 u9.asdeg pkn 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 between ak/ vj 0ox)c(qxw3ti c, 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 isjx3a6) qo eu4rr;v:dk required 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 trc av0(d(eoa/5h3k )iq ej0vqoain accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floordv(e cjao0iq3/(akev5q ) oh0 if you are not to slide?   

  What is the maximum a:dxu:iv*.t: cpn/a q-d4gk/ qfn2c 1kjr;iwh cceleration a car can undergo if the coefficient of static friction betweiir v j:k-q4/:/ :tcg p.an1 f2d wchd;xqu*nken the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and norma*p0;x x7pzk pkl street pavement is about 0.8. On how steep a hill (maximum 0kkxx z7*;ppp angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4 dco wr7r6/9cxdf*r(r.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 onuh9 ,y6)zzyap bqvj.; rg 3qe7 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 contact*kxk6b( ugktk +-c8e y with an asphalt surface have a very high coefficient of static friktk*xe bg (6k8-k+uc yction.

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 f/qhr2.3a( *uhzl+ kdynuq,m uor 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 mass w75og* q)d y6ju1v ;4;mpr0xnmkk lxlf ould box A have to have to prevent any motion from occ7jk0qrm ux 65lxy1*; mol nk;pv d)fg4urring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slidtr s6p5s6kt0xes across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push im 6p0rtsk56ts xparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on ag11s7 oji- fn6 r3owgc1wot q6 horizontal surface (Fig. 4-54). A 1i-q3rogw1n6c1oj fo7gt6ws 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient:c s(v9(o 1ycjwj.f la l-rjx; of static friction between the .(v(9al1lfcsc j w:y ;orxj-jcrate 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 az0fe6u3jsm,4 o/gadt0 l)l xdn incl0 /el4dtzo6, ls dgmxfu)3j0aine 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 xu*;fc qw/lv /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.qd lb+.*7 (x7nwiy*bbmlrcvwt(b j )* 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 initi (j p9 i ;k.5 cdd4l;n)m9tl2yeujeyqgal speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of x8 ;o4dm+ n b5yjv*euv2.krmdthe 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 wall by someone pushing o ww+y frtdg 3q.*a g3jfj.7tdbiu on2n5- h/6mn it with a force directed upward atd-5fho/md * wg r.t.yj3njn witqf67ub +3a2 g 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 akz hfm+ aw61v 2azy:6+woxt 0become dangerous projectiles as they melt. Consider a chunk of snowtwvokfz6 +6:+a 0ay1z amw h2x 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 .dl6uumr +36qefc:r jstopping distance for an automobile traveling at speed v is eqq3jmeul : dr+fc.r6u6ual 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 sli45hb l 71syql7o;n pz0vfk/ wkdes forward on the dash when the driver decelerates from 4w1 k7 qf;hbk/5o svynll4z07 p5 $\mathrm{~km} / \mathrm{h}$ 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 in3ht t ;do6hx .dwvn7h)itial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to the po y 8kbj c9(.htbsbn82wi*, wwacking 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 between a box and the b o(wj.2w 8c ,ybbn9 bhw*st8ikelt 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 frii41* 6vufsdmk f)x g/+xx8 gyoction 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) can co4ops;w /1zugcast 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 approxi2 /2yo.+;m g2b.w ickyrvobirmately 20 2w/.iybrkgm 2byo 2v.i+cr ; og 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 crash if the)hao wyxii(1+ deceleration is no aiox +wy) (i1hmore 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 acceleration produced by an earthquake is a bxmkj qv 1 *3p9o5hoz59f/hik , and if an object is going to "hold its pla9*fo/z h m5pi95 3jqo vhkkb1xce" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examini48)jvyn xppv; ng the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rvx84pn; v)jypubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4sv ,pen 0e+nj8 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is ,njne8sv0+e p 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 dro:vg. lh dq,g1txr2vxfs(nu)y 1)di 8apped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistance s 1fd)ng)rv.a:u ,1t ig(x 8yl2hqdvx?   

  A cyclist is coasting at a steady speed oft5yf i6jv9 r+dow k;.j 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emergingjjr fkd9oyi5v t.w;+6?   

  A city planner is working on the redesign of a hilly portion of a city. An p, ka 24o4ldtyimportant consideration is how steep the roads can be so tha akt 42py,4dlot 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, dangles her watch from a thf;ock xy)h7w: in piece of string while the jetliner she oc;hy7xfw)k: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, there are to be several ramps con-o56yf gfsad5necting different partsd65of-gfa 5ys 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 jc7sty2, o/584 l tihom ouk4:wbfa8xlift the piano (mass M ) using the pulley apparatus sh/8 wsk8 i uo24cx fyhlmtb7o5 o,at:j4own 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 accelayy.zvh*tf ):)3 gtz, x 9 -rlpqm(ryoerating 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-re y01js f9q/ ui ozhm2t.93lomastraint chair, an engineer considers the following set of condm29fl1 zt omhj3q9 au.ys/i o0itions:
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 3h4kaes+tf7y, 4 6tv b5sv/pzyko hggk(+l g /tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar len6mr s18xdme5dd,h6 ns gth. 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 ab, 8d1r5msmed 6n6shxd out 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 usingvd5a ln* e ba-5p:eu,erjn.8a a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum s1,qh:m ev3ufjpeed 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 incliwu17 q7 pq0a6w+jdmjei dttq )z4.w*sned at 21.tqdtwiwpam +e j*7d )q.u6js0 7w1q z40$^{\circ}$ 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.