Why does a child in a wagon seem to fall backward when you giv+jpt(o v-v61c8 n8qrgkxmq2l-1 jrso; ooe l:e the wagon a sharp pull forrole+s- 8qt cv(gokoxq:v6 1;1on-8 mlj2pjr ward?

A box rests on the (frictionless) bed of a truck. The truck driver stargkm.s.o*c4n uts 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 n*os .4uk.gcmterms 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 is23dk9v h0fx gs;c,9y 06f vcfwpsl;sw zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceky*v t82zb4vi be+a-n leration? Can it have zero velocity? Exvn-+k*i v 82tzaey4b bplain.

When a golf ball is dropped to the pavement, it boo 15 vjyeg3ne:unces back up. (a) Is a force needed to make it boun onej31:vy e5gce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log -7u-rao) .wamqo 0vxr move in the opposite direction?m r--q0).x7v wor aauo

Why might your foot hurt if y-pl1obs ;1g+y xuisd: ou kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must deceler0i*rnknd59mky9r rl9 k wh l;)ate quickly. (a) What is the origin of the force that causes you to 99k;0ry* 5)lrnd rl mwhki9nkstop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section ofgf- :hm da-;tjpo6/ kuiiz (i. the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the oa-mujh t:i;i d/(-gi p.f6kz 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 rocky y7:7rj 3q uwnlth83p is twice as great as that on a 1-kg rock. Why then d ht3rlq 37w7ujpyn:y8oesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if thep7t4 sd90xu(q86h lngapbc7f scale had been calibrat 9pcu40tqxl s8dh 76 7bpgf(aned (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an attacy m.1;gt+ vdhxhed rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the bovgy t;xmh. 1d+x 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 freely under the influence p0j:q64e-et ,u6 ud1dgzzebzrdmy8 , of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite fmeu6 eqpdz0egd1 jrbu8dty -zz6,,4 :orce on the Earth. Why doesn’t the Earth move?

Compare the effort (or forcinq 45 cjhq;)re) needed to lift a 10-kg object when you are on the Moc5n r;q 4)jqhion with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, eg wf:2ok1s3lf )(dnr n7:r)/hzx ikfpach team in a tug of war (Fig. 4–37) pulls with equal force on the other team. Whatx/d1f whrn :2l)(kk7 :z)pgoif3 r nsf, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag o*v1 ordv9q6saw, n1gnf groceries. Describe the “reaction,6 1drnqn vo9wv as*g1” 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 lar 9u: p8ckiss (.p6*yy foi zda-hw;*yw 2o4xmsge a force does the ground exert on you? Why doesn’t this forc(d.ypxc4wys:f69 s ; -*im8osa wzp hu2oiyk*e make you rise up into the air?

Whiplash sometimes results frnz kgm92 kwvfg6,qpe9 ;vwu94 om an automobile accident when the victim’s car is struck violently from the rear. Explain why thm;vq9f,9vwg n94ekz6g kp 2 uwe head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flsrc;p*- gokqg(*/z h/dqx/ j tatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to ac/pszk (j-dcgt o; *x*h qrq/g/celerate?

A block is given a push s x8mqa9ya ;zeh2ud83eo that it slides up a ramp. After the block reaches its highest point, it slides back a2xq8a ee ;zu389 ydhmdown but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighedihw zes* +2t45f bqkt/ yourself on an inclined plane? Assume the mechanism fun* e z5k/2iwt4+thfqb sctions properly, even at an angle.

  What force is needed to accc yb l8gu;l-(l- pjfc d.ac:t5elerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceldw f -v /,fnsdif(+x3fa e3y(igzz: 0terates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a 960/t3 ytunb zdiy-ge72 3$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of auem 79lxs 1 i)/ujwjr* $76-\mathrm{kg}$ 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 11u10ah u +seni200-kg car in 8.0 s if the car is travesu 1iae2u+n h0ling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet fr;gn66iak eo6f om rest to 125m/s over a distance of 0.800 m along the barrel o 6efna6kg ;io6f a rifle?   

A fisherman yanks a fish vertically out of the water with an accelerat6vw n)z o7(vjbion of 2.5w) (67nvbozjv $\mathrm{~m} / \mathrm{s}^{2}$ 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 trackkk3lc2zrf b -2 (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maxilg2 gzm .ztb+6mum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable2 z+gtb. zlgm6? 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 e j:jdw 8ou.cxq 54ws2glevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the dcj. jgswu2w8 :dq o4x5irection of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strec9-i,.rm a5qs(p bdm cngth of 21,750 N. What maximum upward acceleration can it givr pbm9.m5ac-(s qicd,e the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky dclg tzo;1sd,u9su;(fivers (mass 132 kg including parachute) f( utcuz 9,sd;1go;l swhen 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 the roof of a f2z0m.t 5pnpc tgi(-ehouse 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an p.zct02t-(m gi5en fpapproximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically uqbdqm:t t-t .8pward over a pulle-q8 t:. tbtmqdy 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 baskd p ra.+t6mwc*etball 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 momela4+e * fwnj0x .d8/8xi zpcoant it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfiel8laxz fi*j w0ax.pce /o8 +4dnd.

A 650-N force acts i,zsgx p0)r;yn9 lnxh3n a northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points n,; ngy039h slx)px zrwestward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strunl*p4:uvc-smjw-t2 x zg horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is tv-xp:lm4wsj-c z2u * 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 anotheag v((m.cho6 jr 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 14.0.3ve. kz5f/fh26 s qswui:ecj$-\mathrm{kg}$ 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 Mcxbwkrz9j-h92t7aq 8 -6 u:odptoe 2ndMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the force2q ba6d99k:2 jxwe-dn-zrtouo7h 8t ps $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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, Fivi kcx -n amh0fbovmx;7g31d qk/6 -4bg. 4-47 . Determine the ratio of nhv-k1cogm;/ d6ix3xqb7 4a fv0-km bthe 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 pullshc,lcv21y vj5 6cnbg3 z3lvq o9 mi50c herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant spl 6v51j9o05i2lcbgnvyh33c,q cmczv eed?   
(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 )o+, xfk5 w ujkpof)s9began, 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 blgua5 2ovus:.kfe7 l-6l(8z1 tygai.ujvi 8 zaock (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 frictionleuts+gdj sg jvs;:+::f ss horizontal surface are in contact with each other, fsu;:gs +vt: j:+gjsd as shown in Fig. 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 each initially 1.80 m above the groundwv31ogq(frrq( k.htyb y ;( )js5w1kr, and the massless frictionless pulley is 4.8 3r ryy rqo; kbhjwvt1(fk15sq.)((wg 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 doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connkaaqojp,pd 6y5u)vf (y;8m2x sy ;z2bected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown ijq s z 2a ay6d,;)5(b8vpyu xkmfpo2;yn 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 frun ,x q5qqmm x+k7n)b5iction 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 remevw- 0y(m4hm-vt aq2quired 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 accelx g w6(r5 5-r/kxny ovo5lm/gserating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to sl(-gxs/o5nk r5m r glxw/y5o6vide?   

  What is the maximum acceleration a car can undergo if the coz ec9a/ ,q4zpwefficient of static friction between the tires and/a 9pzeqzwc, 4 the ground is 0.80?   

  The coefficient of static friction between halm;vcabwq h/19 mf:6* a84ly40 ojd5ak bqgqy rd rubber and normal street pavement is about 0l*6hbcyv w9:adabmq1/k4 5q ja; y0qgo4l 8mf.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate a1v sz.kog6f+at -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 resc0agoqh*j v( ;t on 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 with an asphalt surface have a very high coeffice8;qp)sdhi -zz82h a9wmdw)fient owm2;8i ed8h p w)qd-zhsaz )9ff static friction.

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

  The coefficient of kinetic friction f7uyk x1ho/r+por 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 would box A have ,yo /bmpqdt60w7wpb9 to have to prevent any motion fromy/b6p ow dqwt0 b9m7,p occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How fdqlz)s3s mi;x))qc p9ar will it go, given that the coefficient of kinetic friction is 0.20 and the push impar) cqp)l3 s9iq; xmszd)ts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 11jadb52hf k*n 10 kg , are in contact and at rest on a horizontal su215* nd jkfabhrface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static frict1 mc :bicxb rh(:( pz bb:8.wg0smram+ion between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide againstb b0m .m+b1 g:rh:c8pxmws icar(z:(b the cab of the truck?   

On an icy day, you worry about parking your car in your driveway,33ih)ub - jzhb which has an incline of hbjb33 ihu-z ) 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 ak t,c(4mrnym2 slide 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 tit9 5ziegtb thp,/+g +onq/ ijam7p(+ylted 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 initiamhx2.0p4 bzz el 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 th:w.yu uaor.4j) z9;ayt eogf; e top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough walt58 evjq2+ogt(uqg ;fl by someone pushing on it with a force directed upwavtf o;(q q58+gjegu 2trd 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 projg 4ccjx9 ,y(nhectiles as they melt. Consider a chunk of snow at 9hxc gj(cy,4nthe 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 automobile tr6h (: f-kc77ra:yhyx3akwl4 k)n a oizx2u/ twaveling at speed v is equt4)hz6c7xha(3/wr wy 7-ok i2 lnxuf: ak:ykaal 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 forwar ,a2pwy;opn s4) (w 6qfdji2ozd on the dash when the driver decelerates fd f p4,zpq)jsi ;on62o(2w wyarom 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 initcto o0g-o vax2)*)n krial 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 fyflsk :al2n83a;i)l g illed to the packing station 11.0 m away. The belt is initially stationary a 8:gs3 2la;iy )lfanklnd 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 frij q;j.sb8 p1hzd641ifq nu,ugction 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 coast down a j5hqcrjjw(+ 1 vs+t5l, dzqo- 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 approxim t9.j frk.t-m3 kh:dblately 20 g of lk3t..9hm b r-kd:f tjblood 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 autj(1k;qgh dsav/(9l 2wrp+gmq omobile crash if the deceleration is no more than 30 " g 's." Calculate the force onqshd(/rag+j gpm9; (qwl1v2k 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 produ/kk;x:3 nqwk/yr t tq6ced by an earthquake is a , and if an object ikk ntxqqwy k/;3/tr:6s going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving two cars, me 0f5r jm-lry2ujg8+ stfz( 1ulasure 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 0.80. Estimate the initial speed of that car assu0mz8-r5fu +g2lusr fytjl( 1jming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m traveled3 cx tfhdq)s3yp/5wza ryl:18p3- inq4pn3t m along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) s a3lip4c3yq1 n)3 x w-n/dymp:hfp8tr qz5t3Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of ttlfagdkl dbf-2r,*/jw(7t :j he Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What wa l f dlajg(rw2f-tk*:7d jtb/,s the average force of air resistance?   

  A cyclist is coasting at a stead2jud6s8oh8zabm0y h rmxj125 y speed of 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 themma huho6j8 85 rsbd2 2z0x1jy mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redrhjb/i0 ;n2( 9wxhwr mkxc; z)esign of a hilly portion of a city. An importhcw )w/jr x(rb2n 09;hm;izxkant 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 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 experimentv3u 2p r-up* fqg+b6res, dangles her watch from a thin piece of string while the jetliner she is in tu-rq3 u pg e+2r*vp6bfakes 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 t3v*v 8ucuuakr6fb9js ym4/ )wlo 3:pconnecting different jpycvmu /3r :4)6*9v ao8u3kwfbtls u parts 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 lw n yntb95l6ec -i;yh(uh83ha ift the piano (mass M ) using the pulley apparatus showchh-n( 39uthye8y ai l;5n 6bwn 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 ac/oe-jr/od4 u5ch9(/ vls is hccelerating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer consider4udoqxtsx n eg -4sr-b6e1w+6s the followin4bn-xwos1edxut6 6 eg + rq4-sg 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 tons z0h h8n71ijba9dn r-u(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 simila2xcqs9-m m qj*r length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large s2x -mqj*q9mca force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is us )1 /k2g;yiwrp wgi9gt bfm)*qo(qjy(i h0ut:ing 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 builwgn ovb:o540 fding is allowed 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 wp*78 v5gj wmxnhkisugn7z(6q; e25v6b pczx. ho are roped together are ascending an ice field inclined at 21. vusg2 knp6qvxe(gwz5bp6;h7ixm57 n.8z j c*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.