Why does a child in a wagon seem to fall backwardppb4 wzw: neerb)+6k) when you give the wagon a sharze4wpb: )6kw)bn p+ rep pull forward?

A box rests on the (frictionless) u*y2 s bvu(z+cbed of a truck. The truck driver starts the truck and accelerates forward. The box immediatel(+cy2u svbzu* y starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no yr-ewr:,ia* i forces acting on it? Explain.

Only one force acts on an object. Can thezn3 j 2)k-os6(cdkiil object have zero acceleration? Can it have ze -2n6kiis do jl3zk()cro velocity? Explain.

When a golf ball is dropped to the pavement, it boun1i(poy9v;2k , a8i cgl/jjtum10tmru ces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts 1v ,mu;a ti80rjiuk9 clpjo /m(12g tythe force?

If you walk along a log floating on a lake, why does th g t(9f)glw8hue log move in the opposit)w(gul 9ftgh8e direction?

Why might your foot hurt ifvvv9 *ivj84kf/-ly kx you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decewr yfa-i 5df .v k-;oik n5zf)+hncr3+lerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of decelerata.z+-n kfv)5 -fk;+3dr onhyri wcf5iion of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine threae3lcr jcpf** lf4b:1hd from 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 bccph*:3l e41 f jlfr*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 a.h *fjy pnvne; my((:1bj8eu ;t6ksk rs great as that on a 1-kg rock. Why then doesn’t the heavier rock fall faster tunj86rvb( p;k.es; yh*1kf:(m jeny?

Would a spring scale carried to the Moon give accurate results if the scaleha- j .gfgriuke d ;q*0k7;)uc had been calibrated (a) ik);h* 7kuarfge. ;jdq -c uig0n pounds, or (b) in kilograms?

You pull a box with a constant force across a fy6d7pf nh9v -ep1h(uu rictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, o(ehvp6uynh 79 -p1fudr (c) decrease? Explain.

When an object falls freely under the influence of grav 1k7cfeio5; oxity there is a net force mg exerted on it by the Earth. Yet by Ni1;c x7f eoko5ewton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you/9 kis ox(gg2q are on the Moon with the force needed to l g9kg2o(i sxq/ift 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 )v pkvgeim lz, *kcvev7vd81,u.3f;z mdy/e* third law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team f*mvyp l3, ce8 vi*z,v7/gm )uedkdzv1.; e kvwill win?

A person exerts an upward fogrr;pfx.7n txw637zya xwng * 48j-vhrce of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its drz4xf.vtxw p yh7 ;3a8x jnggrwn-*6 7irection, (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 dod(/ouu9i7o0 5gbx pwzes the ground exert on you? Why doesn’t this force make you d9iw0ox u/(uz5b7g op rise up into the air?

Whiplash sometimes results from an automobile accident when the victeui)i.8x kqyls-;lo b mb1o 7;im’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in ;8ib oq ;71i) elobsx.yk- lmuthis situation. Is it really?

A heavy crate rests on the bed of a flatb)plimgu*irqq6l 0 a9+ed truck. When the truck accelerates, the crate remam9iaqqr0p*l lg6+ )u iins where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After b/ d ld0:6:y)bvgjoon the block reaches its highest point, it slides back down but the magnitu b b::no/jd06vody l)gde of its acceleration is less on the descent than on the ascent. Why?

What would your bathron 2 ob-.b vujtocf;6n(om scale read if you weighed yourself on an inclined plane? Assume the mecho.t2nu;(v 6c-nbf boj anism functions properly, even at an angle.

  What force is needed to accelerate a chilirvk,5gc sqij;g+ x,+d on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerateek a/d j382cuj,dbzs ,kc8:qps 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 b;qd9zg u fo.)5eu9jh a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a ycjvi;ool /zw ,;ft3: $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in qvee)()b,h vf0j .7 dyn7beao8.0 s if the car is traveling an.,v eof ba 7)0q)e jyhbedv(7t 95km/h? -  

  What average force is needed to aig: if8:u wt7m t5xiuj3;uq,/1 hd qamccelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rdx,guq37j;mm i8/ ::a tiiw h5t1uqufifle?   

A fisherman yanks a fish vertically out of xp6hqz. bgh7 i0 n;)td7zllt-the water with an acceleration of 2.5q)xzt dz.0 7gh-6 np; lb7itlh $\mathrm{~m} / \mathrm{s}^{2}$ 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 quartr5pl+u(vyc ops s +a.uw6z5 q5er-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 that the maximum ac0i68s exxa h.p;z nmd;celeration is 0.0680 g . What are the maximxx eh8nz6; i.smap d;0um 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 sca. f3 y*gp 8bu5dbnnqm8le in a motionless elevator. When the elevator beginb8.b3n gpnq *ydum5f8s to move, 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 strq/z b.09iok fyength of 21,750 N. What maximum upward acceleration can it give the elevator without kqoi ./0bz9yfbreaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg inclum w5pofy -e;l tzz/ 97s(nxh(oding parachute) when the upwarsno thx7/z mz(p;ly-5fo( 9we d 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 house 3.9-m high. When he sfl+e-c fwp1)strikes the ground below, he bends his knees so that his torso decelerates over an appflscpef- 1w+)roximate 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 t d: ;6x-zw+jm*jov bbt gb;m.yable. A rope tied to the box runs vertically upward over a pulley and a weight is ;tobzb v6gxb;j m.y +d j:*-mwhung 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 baskeeje wv5ao(v/l 6 ) uq*j3swq7ftball 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 baseba)+s- ydc,6vrwt2jre3e 1 )ib y .lerzsll (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfiec.ee es3i 2+)rbyrwyj-l r 6v1, szdt)ld.

A 650-N force acts in a northwesterly direction. A second 650-N force must brpmdvo5; l+c f fc;7mn+;k1iw4 iytj 5e exerted in what direction so that the resultant of the two forces i+;1 v +df7 kl5f niommpj;4cytr;cw 5points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between twos.ih i rfaq:3:/+ wjbn buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10 i:hbfir s3+:/q. ajnw.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 rs)fl+pu:0p t k6n ou0a 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 1u yvif44b7a(80f ikn ,yjq8pb 4.0$-\mathrm{kg}$ 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 e3m7n2-gd n/wn kbv,r unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The dnr7w-3 kvg ,2ennbm/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-m4qi*nmn l9t it, Fig. 4-47 . Determine the ratio of the tension in the coupling b*4qinlmn9m - tetween 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 shown in iwngsw+lhb:2, ;;6yq q8( r hlwiz w,xFig. 4-48. (a) How hard must she pull down ;,g ;lqwns wyh,8i(2+wirlxh6wq :bzward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 65*y+ j.z2j qnhotgvc l7fh7;+g$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mas*j;g 2* yrx*az)( wmeafvw4 sns $ 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 frictionle39o. ll8 g i4cl4gpppgo0j6(f i;jbcrss horizontal surface are in contact with each other, as shown in Fig. 4-51. A jcip3b jog. o;0 64(ipg gllrp89fc4l 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 eq vx d6+a9 sh)xlwhy,0ach 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 momentx6a,h+ds0v ly9hwq)x 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 connected by a heavy cord ox- azak(ue9, c c9z5uaeoki6*f mass 1.0 kg . Calculate the accelerakc6(9u 5aaek* zc ui x9e-,azotion 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 frictiony:v/dspb2 s 0gjo)-tq between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start;0c4dv2mt6qyd g;qkj kll.h nh4 -h+w l *1apm 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 standuns3t n4u )o, 3scj.eb6j(jxj ing on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not tojn(,t3ec.bj 6n3j)so4ux u sj slide?   

  What is the maximum acceleration a car can undergo if the coefficient of st m aqallzj5pzkt4;3 x5b6p 23batic friction between the tires and the ground isz p5kzpl ja6bl;343 mqxatb52 0.80?   

  The coefficient of static friction between hard rubber and normal street p4ej1:uvx xdy6avement is about 0.8. On how steep a hill xe:j1yvxdu46 (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at d p+-+c wm)la6kuyd 6z-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 30u x( y3yau-a3o$^{\circ}$ 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 co7ezop0wbv. 9 fum3ob8ntact with an asphalt surface have a very high coefficient of statiz3 w9veb u 80b7ofmp.oc 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 frictions0xv z8.naszl ;0ki :jp7,wsb for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would bo rzx5tge**j- 5tqtpnx( sr09 jdan 3h;x A have to h r3st-n;* tjrg5 *x9qn pe(jz5 0hdxatave to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will f 7r3x d.u+5hgau-bl1(awng bit go, giveng. 3wl+5 ua1 nfba durbgx7(-h that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at j 1bc5ykd(ry6(eu,ulld w,f2 rest on a horizontalr,ek1uj y(lyl, 2(c6wd 5bduf surface (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 fe;p,- lg0 6o3rscybgls6d+gu riction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driverd6g;lo3c0 gs-selb+y ug6p, r 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 zju49dbw(*8tbu 7 s r7jxqiw 0an int dbu 9jzs84wqx7i(0u*r7 jwbcline 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 qb297yai *alv 7ikn c,x. ha*ua 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 liesnii+:+rqduwen ,/q u. on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of iq flg v02rs+s1la-e4 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 reachq0nwst*ng:, k es the 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 wall by ow9)f3lwi9 v5qxfo(q ab5* l rsomeone pushing on it with a force d(5*a qloir wf5f9b )o3l xwq9virected upward 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 c pxs j1n+r-5 rpa ms3wi582cvdan become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a p 23w8p15pixdv5r+rj sn asc-m itch 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 ff8p.5xtcurz 7or an automobile traveling at speed v is equal to .tufcxz75p8 r $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 for/*zmbri bw7x :zuil0;ward on the dash when the driver decelerates from 45 z7zbwi:0l /i ;bm u*xr$\mathrm{~km} / \mathrm{h}$ 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 speedl - ,4awq-xkfy $ 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 freu. oa p;cvdp2).y(ks om where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The mo;p.do acseu(p.)v 2ykst 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 friction betwee3 g/cyeulh/hn5gv b5,n $m_{1}$ 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 bic /n g;yvz h2u(vo,gh4wycle) 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 hear9.ur 1:viubd it, at each pulse approximately 20 g of blood is accelerated frouubv :.ii1 r9dm 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 ch -toqjrlcbwjj9 ooq:+( yiq;/id m -23ance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a +q;o-jb y 3:qwjlqri dto9 mi-oc(/ 2j70$-\mathrm{kg}$ 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.ok b/z z,kq d.7vuqj3 by an earthquake is a , and if an object i/k3 q .v .q7,kzbdujozs 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 involvi+x+j ;(d mb hgrje/9ua*6bstgng 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 0.80. Estimate the initial speed of that car assuming a lrmg/ b+9j gbu xe(jsh;d6*a+t evel road.   

  A car starts rolling down a 1-in-4 hill5bt ph amg:+9w:p c0xa (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m 0w:ab+ ga:9m5phxtpc ). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa andel/ ;f f mgryvu0/g)+zz 1 /ga;qyyk,c falls 55 m before reaching the ground with a speed of What was the average force of air res ;zue gl/0;,+yfkvy)1mz/qyra / fcggistance?   

  A cyclist is coasting at a st wg5;je)y7m7hzn dso:eady 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 pmg; yndz7wj :e)oh 57sedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. An imporw*6n n9 tls)jah0u2iktant consideration is how steep the roads can be so that even low-powered cars can get up thl )inwskh*u620aj nt9 e 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, dangle421f o r,8skynwq4z:+fsly cc s her watch from a thin piece of string while+1sqnko, f4wz: 8yc2f cy slr4 the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be sevec5y13l v1r qzvral ramps connecting differen1vz 13lcy rv5qt 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 lift the piano (ma4 ux 0hw)e-i fk83-ranc jcrh8ss M ) using the pulliwr en-ja8u0- xrfk843c) chhey apparatus shown in

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

  A jet aircraft is accelerating bw+izdv og9/n e) /2ayat 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 engine4) 35 hrl xyzat:-ycm -q5daqper considers the following set ofa tzxy4q5h -d-q3l: crap5y) m 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 (660,000 ofxmansn-1(e 9+v 8f s$\mathrm{~kg}$) . 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 lengtrkydf6s(5k 5/8nm v zlh. Karen's rope is more elastic, called a dynamic rope by clv55l(/6kkdf zm8srny imbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (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 kxe *8 hkdnyq, z2*eb-2k*e qn6 su4mra " 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 buildingx3has7 o00 dg vbk2ki8 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 8m7quf/pzucsc . 16e je)du p-who are roped together are ascending an ice field inclined 6su dfc7qepcu1ej)z.m/8p u -at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.