Why does a child in a wagon seem to fall backward wa,7dfdr zu k7dij*aru v+:y .5hen you give the wagon a sharp puj*vu5rd za ri+k,7yd:df.a 7u ll forward?

A box rests on the (frictionlesbu0s9w;lpf+ux m i :z joct4)+s) bed of a truck. The truck driver starts the truck and w:uljt 9cb;s )um+xi+ f0z o4paccelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces akrr ueq *9+++ b6kdaaucting on it? Explain.

Only one force acts on an object. Can the object haipe k 5fwez2./0awe 1ave zero acceleration? Can it have zero velocity? Expla2. z/50e efaa1ewpikwin.

When a golf ball is dropped to the pafxxip)pm+17 rvement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If sop)rfp17m+ xxi , what exerts the force?

If you walk along a log floating on a lake, why does the log move in the oppot yu6jj1 (6zhsrsb/nm36pi r,sit/n,sj stpj3 iz66(mb yh6urr1e direction?

Why might your foot hurt if you kick a he c(,rh1,aolzg55hsrh 0 *3 fh f2wdhumavy desk or a wall?

  When you are running and want to stop quickly, you must dece m2 n(-jnzdz1nlerate quickly. (a) What is the origin of the force that causes you to m -nzn1 dnj2(zstop? (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 thre0lhnj9 sozkeg6 /4 cb1ad 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 4n6gs lo 9kzec1/jb0h pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kgm k24c9q: 3y04jbur wyjn boo1 rock. Whymqboj rjok2yc9 43: wu014nby then doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accura pc6fv2k:ds-(avox3+yezbe 2te results if the scale had been calibrated (a) in pounds, or (bbfe+pv v3oa-xy: 22(k sd6zce) in kilograms?

You pull a box with a constant force across a frictionl-fle+yge i6fcbroeqm4r(/ 9 )ess 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 th fer-qf(4+b 9 )emcri/y6 oglee table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under 9ggl.oy n 1f*ozhpp.c71 x+jo the influence 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 force on the Earth. Why doesn’t the Ear.f 1 xjn hpgozy+lop*.1c79ogth move?

Compare the effort (or force) needed to lift a 10-kg object w/ro;ag a*epe6mr y1,jhen you are on the Moon with t*e;,ryrjo 1agap6 em/he force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, eb slf.rryv3b4q6m.s 2ach team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which vrsqbsf 3b.m.y62r4 lteam will win?

A person exerts an upward force of 40 N to 4 l ,tu7y 9lnq*ba:ny 5quzds+hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, anq5 n u49lt ,y slby+*q7u:zadnd (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert on/80pbwj xb(kd vlzid42rq8d 3 you? Why doesn’t this force make you ip 04b2d /z8qddx 8k(j lwbr3vrise up into the air?

Whiplash sometimes results from an automobile accident *0cy 2gpuq 97 ejpiqc3when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown ba9u3yejqpg2 7 cpc*qi0ckward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. Whe/am t5q* w 6a(4fmqkkzn the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to acc5*(6ak4amw /fm kqtqz elerate?

A block is given a push so that it slides u:e l cnazi+s7 k1k:ns,p a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on thez71:einks+sn ckl: ,a ascent. Why?

What would your bathroom scale read if you weighed yourseyz , tkhxtc)n6 ;csy.(lf on an inclined plane? Assume the mechanism functions properly, even at an an h)stcn6 t;xyc, .zy(kgle.

  What force is needed to accelera r4,zq bv:)3*ze hzivrte a child on a sled at 1.25m/s$^2$?   

  A net force of 265 Nbnze:t 15g )3/ qekptx accelerates 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 isp s5; ll(qucs2 k2bt: jvtx,i8 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)o4. 6 5tu(up lbf)eedjnxl(s $76-\mathrm{kg}$ 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 zoabl:z9ja0 98.0 s if the car is traveling at 95km/h: 90zzbaj9ola ? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 12g5vm 35aajn5 xgwz0 q4dxv 60v5m/s over 05v0j w g45md6xv5vanx azqg3 a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out e0wr:g u( u5:st gcc)sof the water with an acceleration of 2. g):5use0rwcgcsu( t: 5 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track y:o: m4za hgev8ljc4 9gx*g4 a(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 bhr 0 p9p.h t(qfiwq0a:e designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the ra q9w hpfi.h0:(pq0tsupporting 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 5bni+vz t( uz)scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the nbt)5+z vuz(iacceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg,g wrkdbmc)) +h jv14t elevator has a maximum strength of 21,750 N. What maximum upward acceleration can i1 b)w,d4jg)k cv+tm hrt give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling ska1+l .gy qwaf0 lxtu/:y divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth .la/ul+1aqg0f t:yw xof 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. Wher/mdoltnm/jdi akb 3 0:m*u9- n he strikes the ground below, he bends his knees so that his to: mj*da9b r lit0/ n/m3kmud-orso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a tabl(dxad. zy*m z el9rc//e. A rope tied to the box runs vertically updzl e 9/a/ yr.zmc*dx(ward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight 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 basketbai:(8h vvtiu0,u .kxecp gf9 c5ll 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 mkhbbjny9o +;4 ;rzgrxk 1w0s1oment it is hit by the bat, andgnk;0ow;b1rzj1 s +xkh y4r b9 again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts iny jfa *14e9o ypfp-iq7 a northwesterly direction. A second 650-N force must be exerte y af7y 9-f4pejpo1q*id in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high w1be1u ,r-dkelu (*,aog- fznpire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is un,dp ef,1azu(*b k1-o-reglat 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 massless cord from anothee edn-f1) 86)gkpxcr2php e1 xr 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. k-v .es.dehk*v8 w)cz9u5nca0$-\mathrm{kg}$ 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 7p5kby(yv5g g unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. g7y5 5v(yp kgbThe 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 szoag)i2as vd4/(-tyfame mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotio/yg2d - asfai)vt4 z(ve 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 pull:(iqho)kg ; pls herself upward using the bucket-pulley apparatus shown in Fig.;po q:g h)i(lk 4-48. (a) How hard must she pull downward 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,y *sikj1;,i-z-48e0ik au.odblqt b+f sxz8 t 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 blo4d )l(o c3zt i 3a7iry;ooxc(eck (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in c26c,bi fujxi( ontact with each other, au2 cjxi,i(f6bs 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 1.80uuiw(m* upvoq1wzmh))- jw0 . m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" s)zwu uwv0 q)jmh(o1pm. *i-uwpeed. Assume it doesn't hit the pulley.]   

Suppose two boxes onqojno2)s89vpzh*n v) a frictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleratq n nv p*)2zs8jvo9ho)ion 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 friction between (oulqlp; h;),n(h soq 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 required4uwy5 3 7ybitg2u9r jh to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.c0vu ovdtp 24:xb4q m120g. What minimum coefficient of static friction must exist between youvb xo41mq04c: pvu2td r feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of2 -p:f p+fqo46vvmxnv static friction between the tires and the ground6pqxo+ v vnp -m:vf24f is 0.80?   

  The coefficient of static friction between hard rubber a1kmjzc h*86 m2c8 xtlend normal street pavement is about 0.8. On how steep a hill (maximum anglx2me816cm*ckt lh8 j ze) 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 ato9jmgfv*sr3u*u 5d c0 -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 ri e ttgq)bpr,:j9 w+y6ough 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 h2:jm;fykghplzp28 r dzn1( 6kigh coefficient of static frprj; k( p2zykz 1m:n6fglhd82 iction.

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

  The coefficient of kinetqs; ;,iej)u+gbjipfl a f (g76ic friction 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 cn6/9uz 7-q/)*vhd)htjerlnuhm xn ;a mass would box A have to havej)*z lnnd7/mcquv6h-x 9e h);hrnut/ to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so th;2 5b m i0xuvlzeci9v4at it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial svulx9iv;52 z 4eb0i mcpeed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kgi :w.8 cnb xnug6vva3, , are in contact and at rest on a horizontal saux nivw8bc ,6v3ng. :urface (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 hh:(w5:0m ub snps4c w nf.p 2upt-4wqcrate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What isp m4wh.hwcnuft5(: 2-4np0bup:wssq the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry fef2 4k-1t th he)plz1r1r-fuy4sq 5pabout parking your car in your driveway, which has an i4 fs) 14hft- ep-1huzqrkf1 tyl 5r2epncline 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 pec ,; ky6f3p(*ggypnx7zk(a og (2ey 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted z xe9d*s e:s5xxub 1jvq e-4p/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 os1s- nh h+e7tl* awmv i93klv1f 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hqmjzeell sr62+mi7b.w1o 3u:aa w a/4ill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing on 69jj5f r 8armf,w8pcym ct9n) it with a force diremyjc nj) m58fcrf98w69arp t,cted 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 projectiles as they melt. lzk9dy: /b0kq C:d b9lzyk k0/qonsider a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobil-9 slsas di81rwengmhe* c618e traveling at speed v 1s1sl 9smw rdein8-8*ch ea6g is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when the drive-c-szd/ g9gcjl+i r,br decelerates from lg+/s jg9 r,zcc- bdi-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 b treekr3k v4;i8a ;p2 m is given an 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 conveyorz36sj*5f2t e y5iw 8pa *inbiq belt from where they are filled to the packing station 11s itybwp5f*iq* 23a5zij8n6e.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction bet otgt4z7(7qyyq)q kn(ween $m_{1}$ 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 coa3j7jvp8 sm, f68fpy6qthlq 0e st down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each ptf v.x t:tnoa+/s(rti9ri( z+ ulse approximately 20 g of tf(tr toa s.v+rzini9:t/(x+blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash u,f 1px5-+k w kj6zaxoip80 rgif the deceleration is no more than 30 " g 's." Cjg+0urkzkwf px5,8-1 ixa op6alculate 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 produced7u7px4x2f fp vmocf. 5c7 bsr0 by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of sta5747ru20.c fvpbx m pc xsoff7tic 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 caryq* +rte0s x+ds, 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+*d0t sqxy+er car assuming a level road.   

  A car starts rolling down a 1-in-4 + +bzjxzp99 b*8bcb yihill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom b9z+ b*+8ijxcpzy b9b 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- mu 248seb* kytfp;em Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force o;ty pku8b2-s* 4mme eff air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a0v: fu:z,: tol zh8jgu muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the spe: ut of0 jvlzzhu,g:8:ed upon emerging?   

  A city planner is workingcw5j3 mamj fiw,-;t ;e on the redesign 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 f;tjmi;f am,35 jww ec-rom rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from 3j 0vlyj/klw+a thin piece of string while the jetliner l j+l3k/0w jvyshe is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ram1u bk ss-ot,k31g (m-w mty7gdps connecting differenw,o1 g(km-ud7b 3t1st gsm-k yt 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 n .u a* 83t-jslo/,ojrwjclnz1n (lpn7eeded to lift the piano (mass M ) using the pulley apparatus shown (j ,urz * na/3w.7ljooncl18p-njs ltin

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 r : wsqe+8 jgxv,c/.4jn hmo6xhxak74at 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, a6r6*z0;kt d)gnuv nmj n engineer considers the following set of cv0jgm;u6)dr nk nt*z6onditions:
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 q/5z5yq7plp y Italian train has a mass 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, Bil*o v1hy:pkxnzak6h 0)t k ea53l and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dyk khek xao0t :51za36h* pnv)ynamic 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 similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " 10-1 ) 7ei9dx r6rvt0pae.i$\mathrm{~b}$ 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 buildinfmyeb akx.y.b 5n d8i63lvj-)g 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 who are roped together are ascendin hyi/-iagnubu r-/q 1,g an ice field inclined at 21.bqha /in1-u-/ uy gri,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.