Why does a child in a wagon seem to fall backwargm1a*kd8 n8st d when you give the wagon a sharp pull fortd ksgn 8ma81*ward?

A box rests on the (frictionless) bed ofy0je0 ih+ f 4fwwx0,rh a truck. The truck driver starts the truck and accelerates forward0xh,w0 yjfrhfewi 04+ . 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 obje9h j,+z) pl3rnvlg g0lct is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the objecti,)uz )rcm(9lv 3fyqj 0feu: j have zero acceleration? Can it havej( : jl),0uyu icfzv)f93reqm zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is6 n(cvxoiuxc6 vii8 b:023sp 0zye4rc a force needed to make it bounce bir :(cp3 xi2 4icc6ux80s bo60nezvvyack up? (b) If so, what exerts the force?

If you walk along a lo m;3 jiqm l;3/e9.fganttscb)g floating on a lake, why does the log move in the opposite dagmjbie;)s3t/ 9c l m ntq;3f.irection?

Why might your foot *yzifqhf rry:ud162)hurt if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerat*0p 95u ztnhcb9i/kw z91vmffe quickly. (a) What is the origin of the force hf91fbm*z0 cp/n wtu99ik5v z that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of th b6h6h3/lg j2 iysl3ize 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 steady pull? Explainl b6zl2 ig3s3jh/6hiy your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-j1.hup 66y80m tojotukg rock. Why then doesn’t the heaviery806ju tojht.mp 6u1o rock fall faster?

Would a spring scale carried to the Md3 .c mah37nfawg. /19d zbkixoon give accurate results if the scale had beeng/f xkb3dahmc1iw9.d 3 z7.a n calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a ;ao hjv+x+xd 0nps 3b3+( jelsfrictionless 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 p(exh +sjdsx+ 3obn30+jvl;a the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the0ptozc2 jc;f)43 n9wz3(llccoakk;e06f f p d 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. Wc4k wlffjz0tn6e ;(2o fcl9ppc3c;30o zk )adhy doesn’t the Earth move?

Compare the effort (or force) needed to lues nhm33a+9(dy; gls ift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the (n 9musa3sld e +yh3;gforce needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) puvj y;:/ui4lu32 vn aoxlls with equal force on the other t23/nvax:o jyi ;uvul4eam. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag k7l vusx aa udmi5)9it5o -j,ew 2)xw1of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it isdx1l9o7xuwe a wtv ums )-i kia5j2,5) exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force do 5cm3;fe azt uyw77p-1tb /onies the ground exert on you? Why doesn’t this force make yo atw5t zu73;-moib f/7ec pn1yu rise up into the air?

Whiplash sometimes results from an automobile accident wh 0i*k.p icm)v j7w7l xcy9jdf-en the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown b0mvx)-9 dp7if j7* c .ykjlwicackward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed k 5nqo*-:6fvf.axi lntruck. When the truck accelerates, the crate remains n qff.5-6 nakx:* olivwhere 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 the block reaches itssb8 v9pku/ q0nqn /pbvu8s 0k9 highest point, it slides 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 you weighed yourself o/)l4ayctc( kon an inclined plane? Assume the mechanism functions properly, even at an y/ ( akcto)c4langle.

  What force is needed to accelerate a child on 6,pru o) c /0rqnut9bbei /kq.a sled at 1.25m/s$^2$?   

  A net force of 265 N acceleratkc1 l1 dvd(vj/ j.;vqwes 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 accele1i0gn9 )x na7oy 7wnq szuqn1;rate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a b8sb* t; pfqvroc9d94 $76-\mathrm{kg}$ 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*21r bn2m,ryhrnr g8i.0 s if the car is traveling at 951m2r rhnib,n2 y*g8rrkm/h? -  

  What average force is needed to accelerate a 7io/mhhyv kt9xt/ * i)8.00-gram pellet from rest to 125m/s over a disio)ivk8xy t*h//mh 9t tance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an aydr-dp w2(w2 z:b9no ucceleration of 2.5z (:dydnb2uwro 2-9pw $\mathrm{~m} / \mathrm{s}^{2}$ 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 ca.l30 rk h;ao3alorkc 3r can cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so th c3skfup y8.p0hkn65k6z j p. zk6d x3e;5kbswat the maximum acceleration is 0.0680 g . What are the hdpxkk j s c0ppbkz 5s6nuek3f6y8zw.6;5.3kmaximum 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 scale in a motionless 01ctcbt9tugk9i2 ig8 t+ )nrxelevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular wb 2g19t r) tkt0unxi9t cg+i8ceight. 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 strength of 21,750 N. lwmp(+b6.b- b. ;gxcxws x9wwog-0wx What maximum upward acceleration can it give the elevator wig c(.blb;- mwx6.b w wsxw+9 wpog0xx-thout breaking?    ( two decimal places)

  (a) What is the acceleration of two ft;-hajby m-ui /b(vs9 alling sky divers (mass 132 kg including parachute) when the upwa/by 9jm;-bt hva(-is urd 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 st* 5 )s/sustpoqrikes the ground below, he bends his knees so that his torso decelerates over an approximate d)os*tp/ 5s qusistance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied tu8 n.mxy *c;u2fn0zgkyt8 9 eko the box runs vertically upward 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 hangingk.8 ntxyek8u m; gfu0 *9z2nyc on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diag*v(um2;nd4c k9 afsbb ram 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 of a basebah-p 9ryf,;b(/zb 5e(dp wawbkll (a) at the moment it is hit by the bat, and again (b) awy9b-;/depwafh b5 z(,bkp( rfter it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly directi0509/e 1n r pz;wdv,uxyseox jon. A second 650-N force must be exerted in what direction so that the resultan1 er0/0pj;zsyud5vxxnweo 9, t of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire a8-h9vcju0rl 5+x,ge4 x lxjr" strung horizontally between two buildings 10.0 m apart. The sag in the e0+a,x -4gjujc h5v8lrxxl r9rope 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 massless cord fro5jxdsm:-t ecxlv8m y+;/vy(p m 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.j6m )n8u j 5uuz-rqm2e2jifl5 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 new location at Mc*p6g:dfy5)rv i7prhgMurdo Base, Antarctica, afhydrig7:v 5g6 pr*p)s shown in Fig. 4-46. The 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 o5l ldjz0di (-nrkoch5 2 .gc *x5:ert,/ck fjjf the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between tdj/l5n ir.jg0l5- ktzjde2r:( cofc,5hk c* x he 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 usi/hnok-zh 9u6teg 2i 0ang the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly u6t i29nzoa0h k-eg/ hat 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:r)m* npp sthnx46r3 s$-\mathrm{kg}$ 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 (k2k 9 iw)ifxd)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 ssgj e* *msm(bfw x3max sn(t(8f+uf92 urface are in contact with each other, as shown in Fi (xb mx8sjf93gme((t+ mw*assf n 2fu*g. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above the ground, jt.lox.m 8e:d wsa6ngag68 k4and 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 k8w86jtao lme. 4an.dsg6g: xand 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 heavy cor-i 0hv4yf8kte lu )5gkd of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. tgukvk h )l4 efi-5y80Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 kine u/lro:zoco 1gzi*0 2rc d+k;utic 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 requiredk qoy s1.*r0l/fw)msua5ioc 2 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 0.20g. What mib rgmdj *3i5lx4zzr 0+nimum coefficient of static friction must exist between your feet and the floor if you are not to l5 xizgb3rz *04jmdr+slide?   

  What is the maximum acceleration a car can unv8shp -bm af,-qztpi)1ri/g2 dergo if the coefficient of static friction bevpfi12-r8s-/p,h )z b i tgmqatween the tires and the ground is 0.80?   

  The coefficient of static f,n)ze b kau/ tnx(h:s9 -mllo3riction between hard rubber and normal street pavement xnh9- 3/b:slnez umaklot)(,is about 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4.8mh+p :kzg5 s 8uj33oue0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 aqx1nxjnz 0vfba,v, wv, j7k1( rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coeff+ p zb6wtnz0mbi5e 7k w-9mg6ficient of static f-ngtwm6bm6k 9p+7wefi b 05zz riction.

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 fric)m 2,xl -r4f)t ypgdhwtion 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. 4-3fhkj0 y7 h-k-u2 (Example 4-20) how large a mass would box A have to have to ph7k- f -kjy0uhrevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. y4v l71vs7 o5;p k)(smrod xysHow far will it go, given that the coefficient of kinetic friction is 0.20 and the push mrs 7)(spdl4 1sy k5 x;v7voyoimparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at2yret1 *: qy1cdvfji ; rest on a horizontal ;c:ve *yj2y1 1 idqtfrsurface (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 coefficiengeya1uup4h8 6t 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 and stille yhg4u1a8p 6u avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in yo pj*bgdo)z-)1e94;fwzwdd dnur driveway, which has an incline n1p dgddf)ow4;jwb)d -z9e* zof 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 q5 8x q-boge2nj hlm fi2e(7nt6o*tu(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 at an angejzz-j*h 6 qh8le $\theta=22.0^{\circ}$ 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 l/,zwz.ne6 r (n zwy-se pjb2-f2dgz)2 x+dxt3.0 $\mathrm{~m} / \mathrm{s}$ 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 hillz5 i ;xiypcx; 2l4jei/ 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 push; b my -xqg:g94it4lvn3z2tsting on it with a force directedv4yb t3:2tsq9zi g m ;lnxg-t4 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 bec0ffzv 9tvc:,rb 2wvc- ome dangerous projectiles as they melt. Consider a chunk off2z 0bc:t,vvvw-fr 9 c 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 stoppinpl1cqyop qb - q4(iw2,g distance for an automobile traveling at speed v islp,2oqqwb4( 1 qi-c py 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 dashboarogz onrfde d.pky5r;l,d:uw 0 s-14w(d of a car slides forward on the dash when the driver decelerates from ogk.; soe w14pd0rw:,d f -5dz(r lnuy 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 isq,;l(9 syc g2z*-y scsc6fe px 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 convexaq+4 qfvu.x 90w*k0f nye;mgyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary anqxy.kgw +0 f q9e0f;*xvn4a mud 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 between w -zy)sjq * 6pmmyol28kh6v2z $m_{1}$ 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 cosd805cw g1dnuh2vv7yast 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 m xpv7k+b zxr0p* g-ks-ammalian heart, at each pulse approximately 20 g of blood is accelrp xkkx 0s--b7pz+g*verated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if the decek hz56ckg c9u*leration is no more than 30 " g 's." Calculate the force on achgkk6 5*ucz9 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 accelerationsddbkg(ky3 5,obey5 4 produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at be k4,dkogs(y5y5 d3bleast $\mu_{\mathrm{s}}=a / g$ . (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, examinin+fw +rs 1kx+tmg the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop befox kt+1f rwm+s+re 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 db meb l, 3ax5bp;run83own a 1-in-4 hill (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 after traveling p3nxa5le3, ;mbb8 urb 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 top5zm(; phgw)lg ga/zf. of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speedlm)w / h(z fgggp5.;az of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s :um- 7:hrnr gngue5g8 but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 17mh8:ng -guer g5: urn1 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly porv:cun;,1n/ e g:kqys2wpth1n tion 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. Aq:1t:k ce; ,sphyw 2/ v1ngnun 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 physicf82wc :4bqqpt s experiments, dangles her watch from a thin piece of string while the jetliner she is i8tbpwqq :f c24n 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 ly0yo-x 7tu/aare to be several ramps connecting different parts of the stoayly 7xotu-0/ re.
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 knwi 6m*)uk k q;uclwl;,51q w(mass M ) using the pulley apparatus showmc,nlwqlui)w61uwk ;5kk;q *n 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 accelera ,eb:+p4 sbh hm+xj;pjtbn6y ;ting at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer corkdo-ojqi5jlzj y /e 4-*x3-ehp7 d7l nsiders the following set of 73jo jdeo-dry z4pe -h*ilk/ jx7q5- lconditions:
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 3 .ih:px;k+hb lzs+lla -lx 5vof 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, Bill8osjujgf e04 * and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes js8 g 40eo*fujin 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 usitaw/md0 7v0q 6kh) )wttzy,(zb once:ng a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reachec9sa4ik .q2thk* sq4 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 (m5jc6giw:9/,j smj/ u jah ywascending an ice field inclined at m9 / wjmy/ iahs,wucjjg6j(5: 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.