Why does a child in a wagon seem to fall backward when +7i6lydcd0f bn:zu :0p.lluvyou give the wagon a sharp pull forwardbv:l l+0udu7pfdlny 0 .c6:iz?

A box rests on the (frictionless) bed of a;nqa:7 1 4 xlb )hhhb:0msntpb truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck an:7) t mh0x1lbhspah4 :bnnq b;d (b) by Chris who is riding on the truck

If the acceleration of an object is zero, ut 3kap3( 55qe lkn,zsy 9(tksare no forces acting on it? Explain.

Only one force acts on an object. Can t:b1ipx yw* ywa ,3:tsche object have zero acceleration? Can it have zero veloc:b yy a, iw1cs3tw:p*xity? Explain.

When a golf ball is dropped to t ,our14ea2amfq7wvwc1 o 5xc3 he pavement, it bounces back up. (a) Is a force needed to makeqv 4c 2wu m ao3o,7r1ewcf15ax it bounce back up? (b) If so, what exerts the force?

If you walk along a log +v1 oep5;ghvce0uw f-upy2r v 3/l3cdfloating on a lake, why does the log move in the opposite directihydv;2w5/ou+1v0 -ver pgcu pcel 3f3on?

Why might your foot hurt if you ki*ec v.2)nywiack a heavy desk or a wall?

  When you are running and want to stop quickk6+8cz7ykhsw ly, you must decelerate quickly. (a) What is the origin of the force that causes you to sto s6kcy +k7z8whp? (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 ceilio6-(4r v*bl-ex*k9itpv hgfing, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and stea6k9-le*fhr xb g*-o tv( i4pivdy pull? Explain your answers.

The force of gravity on a 2-kg auni +w*w-hxp a: e*6 vvgjf93rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall gpavei:h w+*9-3aj*vu nfxw6 faster?

Would a spring scale carried to the Moon give accurate resultszt)buq u4 f30 npenf/2 if the scale had been calibrated (a) in pz /e4tuq2f nb)u0f n3pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table nrb*)2y adj7dusing an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box7d*j d2br) nay 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 of gravity there it 9sa sd2vv0q0s a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on thv 9t0dsq 0v2ase Earth. Why doesn’t the Earth move?

Compare the effort (or force) nee(4c . d: :;p oqsmjc00aa,rlanmpaa/hded to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force nsnca a m qdp;,m :a/4.00olarchj:( apeeded to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig.fi 6 *f)i(wfr-t ikr;qj,*lxv 4–37) pulls with equal force on the other team. What, then, del;ri- rxf)jtvk*i( i w* 6fq,ftermines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe thyj+a)q 9v.tdi0zq(m-,6wfmn yipxo)v 6zje4e “reaction” force (Newton’s third law) byv ).9xj,m zip+ m a6dq-)jz vyei4ony0wqf6(t 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 exert on (t zz;)lut jx5you? Why doesn’t this force make you rise up intox;tjz(5)t zul the air?

Whiplash sometimes results from an automobi4- c t.bvyggqx7 ;p9egle accident when the victim’s car is struck violently fr .- 79ty vgxcpgg4qbe;om the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck acceler u;sp/-dcbouj l91rm: ates, the crate remains where it is on the truck, so it, too, accelerates. What forjr;m 19pbcuold:/s u-ce causes the crate to accelerate?

A block is given a push so that it slides up a rampuq/ghz 70iap/ w 0oc6*faf0a b. After the block reaches its highest point, it slidewgfz/ip67bc/ oa0 0ha0auq f*s back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if wk5gt;tw1 uzzf d6+ *4tzlfm8 you weighed yourself on an inclined plane? Assumwmz *d;1z6ftt8tkflg4 z uw5+e the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled as oiv. j173l qg2 4aqdql(e0u,thsqy+t 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and r0gcc6 gxbx alm o6dz* u4,.:yeider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension mustd:q,try: f uy.4jc v7m9 2d:dxwp4dkm a rope withstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a rfz*z l 28t 0sj:go9zk $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.v b.q+ncd yh8-xs-rz80 s if the car is traveling at 95km/h q hd-rx8-byc 8vns+.z? -  

  What average force is needed :8i9nntx vhl 8c 7ngx6to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a riti8nnh9xnx 87: 6cglv fle?   

A fisherman yanks a fish vertically out of the water with an accelerati p5utgt a4ds+vu (g.o41t/ moaon of 2.5o /pvtg.1t5gsdom4atu + (au4 $\mathrm{~m} / \mathrm{s}^{2}$ 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 cove+gpa pp y-t(fx(js 11pr 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 )pq jg+ 7wdeq:( is to be designed so that the maximum acceleration is 0.0680 g . What are the (p7qedw:qjg + maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a p,iry-o llw*7 bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of thel-*iop7 , lwyr 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 elev dt8 9vol+qo*,3kq bfoator has a maximum strength of 21,750 N. What maximum upward acceleration ct+o9kd*l3b8o,q fvq oan it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two vrfk)p3kr p7,6 s5,z qt ubc;vfalling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of their weight? , ;kc) 3zf56spp,bvq u 7rvrtk  
(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. ck a qyxx766vl4qnm+0 When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (exc+ 7ca qxnlxy 4v06q6kmluding 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 boxxeuf fo- m 28.,pvd6w69tapvp runs vertically upward over a pulley and a weight is hung from the other end, e.fou 6pp9pmt6dfw ax 8vv2- (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 / vd;jrlo6je)for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram ofe u+wu at645z3i;kgzf a baseball (a) at the moment it is hit by the bat, and e a5+ ;kuiz3f6u4w gtzagain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwehu4l hn+wm s15sterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two h4l1hu5 wms+n forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horyf(92 sqa. xyrizontally between two buildings 10.0 m apart. The sag in the ro(9yr 2xsafqy.pe when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a masslob60 czx3278cymh lio ess cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14 wk/55jzbcvp *.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a n q+rtfvyhw(20 ew location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the fft0qvry (w 2h+orces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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, Fi7x,rc u((spm ;kphb;h g. 4-47 . Determine the ratio of the tension in t7 u;p(sr(pchb ;x,hkmhe 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 shoe 7gap w6)iji5wn in Fig. 4-48. (a) How hard must she pull downward to rai)7pg56 iwaeij se 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 beg8xqyj xq. b+pm;tu9e .an, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (maswz7: ;w*blie1mh0p iw s $ 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 frictionlesshnzva pgq py+ngzl 22(bxj.vn3)o80; horizontal surface are in contact with each other, as shown in F jzp3+n0 y);ga (b2h 8lpqn oz2gvnvx.ig. 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 initiaf g,v-33nifgr zt; x:rlly 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 -3rnf ,if3z:gt; g rvxreach 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 connected by a heavyhm vjp 1d plho830d /n63tick9 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 di/6 33 jpdpkhvltm0indc h 19o8agrams 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 a1p-c gymvp0 .friction 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 tog,ykabc8(e/a rs2:4nsg1hh b start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What minimum co5k( 3ffyacjw/efficient of static friction must exist between your feet and the floor if you arek f35ay jfw(c/ not to slide?   

  What is the maximum acceleration a car can undergo if the xpe x,4b zl(9+yuun ;m /qyr7ucoefficient of static friction between the tires and the gro/ue ,(mlr;9xyy bn 4xp 7u+uqzund is 0.80?   

  The coefficient of static friction between8 ,zbsn 3lb( tfyb4vv) hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angl fy(n,b 3vbs8bv4ztl)e) 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 -4.8044p3p n-7y9fdnx ie)jb7 elmf $\mathrm{~m} / \mathrm{s}^{2}$ 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 onltds:y y 1u1uu gz1egz u(8a3- 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 h+c)4g;nv5dg+8ogt*m5wl bbyr pe0 giave a very high coefficient of static fril*dn5gwvbt;)+g8 y4m0 o 5 b +igrgepcction.

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

  The coefficient of kinetic friction for ab 8/ iqft)(tpy $ 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. 4-3e-ul, z h5w44h3 bcnuo2 (Example 4-20) how large a mass would box A have to have to prevent any motion from occurrin4,eo uw5z -bl h4c3uhng? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acro)1lh4l izgsbu/d.1u kxq .c/*/w y wusss the floor. How far will it go, given that the coefficie*dl qus )1g/ bc1ywhs.x w//lkiu. uz4nt 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 kgy,of m8m pk/3y , are in contact and at rest on a horizontal surface (Fig. 4-54). A 6om yf3 /myp,8k20$-\mathrm{N}$ 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 o6 g,n t5jm:k umh1s0 x:*regxcrate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate andnj gm:u1gx6 *,srto 5mkxhe :0 still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your dy96z cilq:y/kriveway, which has an in/qkyyc6:i9 zl cline 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 a 28slk 6v itqa 6uif0:n-,$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an0fy3e 4gc8os d 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 an7)t izixoyridw . bc +*9p1aj: initial 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 of7x4 h ij/ljns4d2 wnmlkt0 h7; 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 pke 1*5kgrwn2u9,+ gf 1fyp wldlace against a rough wall by someone pushing on it with a fo+wl1y 1 grngke9u2f5wf,kp*drce directed 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 can become dangerous projec*tpu 1 wg(2xthzuj /f 3zj knb;z(50dttiles as they melt. Consider a chunk of snow at the ridge of a roof with a uh0n zzu31kpbj( t2 *(gttxzj;fd w/5pitch 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 automobildk;,-x *x1mdgsc3 tta3ca- r fe traveling at speed v is eqcdgftm3s x3 -cak,t1*ar ;-dx ual 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 slimqf79qr)e3;s*eb dz 6-bwx o+* yzz andes forward on the dash when the driver dec -yewaqznz*b)xmsfb odz*r+9e7q36;elerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given s7.ga,g,r+wc/e 3i o+wg lfo vodx .:ian initial 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 ar geq9iev4s-de37 a kn0e filled to the packing station 11.0 m away. The bel- geiqns v7e3e49a kd0t is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient of kinetic friction betwee7 eq:57sw7ae 2kgf5nz2 f okuen $m_{1}$ 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) /go) s /ymbuj1i zi30cx 6xjli b0w-k)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 lq1n- l6,f.who 9rhp-a3vhrt of a mammalian heart, at each pulse approximately 20 g of blood is accep 3-vql,trlorh1hw ha-n .6f9 lerated 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 reasonablhk/by*/p t q++a rcxm-e chance of surviving an automobile crash if the deceleration is no more than b-+/my*+phxq/ at kr c30 " 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 cij14 vks-m ;uv7v:m qproduced by an earthquake is a , and if an object is going to "hold its place" on the; i:m1vv j- kvcqs7mu4 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 opzmuv z;4gyck640g)vl6q. u gf an accident involving two cars, measure 72-m-long skid marks o;p zm)k. guu6q46vlg0 z4gyc vf 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 level road.   

  A car starts rolling down a 1-in-4 hill ( f576o+di.jf qgn.en j1-in-4 means that for each 4 m traveled along the road,j5g +on6fdi.7e fnq j. the elevation change is 1 m). 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 c/hdalj5l3 p n* ;j s*.apfr(yof the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of Whn a3jr( d*fa5pshl /*.lcyjp;at was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/x ic)78jjcsc bkd.-0ns 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 mudj.c)cnx d0c 7-b ik8sj lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the rq .);gl 2oanj-fxi*0r gjg0siedesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 2 *aioj 0- 0.nxjsqi2 gglgrf;)1$ \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 experia1rt j- h7*0q mzpwae:ments, dangles her watch from a thin piece of string while the jetliner she is in take0q7ta*: -mpjzre1 ahw s 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 a v1eyj;x )z6ylgq.kt/ re to be several ramps connecting different parts of the store.);t1j./ y e6gqxvy zkl
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using the pul8;.u/yyy.yvsjj , tm dley apy8 u. ;ms/ yjyjd.ty,vparatus 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 acce -sjay6 /gjin2lerating 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 f4f-6k5 zo7:(twrcfnsv0i pxa or a child-restraint chair, an engineer considers the following set of condit i-zn o p5afc74rvtk:w x(fs06ions:
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 maqkul3rabg..: 7a vw l7ss of 660 metric 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 o7 c2 ah2q7r(vf wp)fnvf similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a s7wf rvc)7a 2fpq2(vn himilar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-1xnecb/gps, 5* $\mathrm{~b}$ 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 -/v d0vx6m i3ieyswv(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 who are esy .hobfn 5k h70o;; gewy.o6roped together are ascending an ice field inclined at 2 b.kh o7;hfwoeoe 50y6.ngys; 1.0$^{\circ}$ 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.