Why does a child in a wagon seem to fall backwar 8 d)uthzpzzc 7r ..kv.1bxvq4d when you give the wagon a sharp pu pk.rt8d v1uz7)xzc vz.. b4qhll forward?

A box rests on the (frictiog0pifvn9a0ds-xg ft1f (pn4sc)x x 5qfq7z08nless) bed of a truck. The truck driver starts the truck and accelerates forward. The bod cz 81psf0xn)qpng5fqaf 704 0xg(f9-vi stxx 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 acting oyyea p/7h ijkw9d:esw4,b, xo5o9 h9kn it? Explain.

Only one force acts on an0 s1v h+drbu e(nbm29u object. Can the object have zero acceleration? Can it have zero velocity? Explasn h2u+u m1v(debrb0 9in.

When a golf ball is dropped to the pavement, it bounce7c/5xwxn xmx .s back up. (a) Is a force needed to make it bounce backwm7 x 5xnc.x/x up? (b) If so, what exerts the force?

If you walk along a log floating on ad;oc*0b2tm ub4; , /b k,br+oatruq qjnahz6/ lake, why does the log move in the opposite directi6cb/r4a z b uobahq;0 qr 2u*,t/jomnk,td +b;on?

Why might your foot hurt if you kicku)r6- hynj umhkm37j9 a heavy desk or a wall?

  When you are running and want to stop quickly, you mustt jv ,:,h6iekx l+1num decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed xj6 uk+,:1etm nl, vihto come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the same thremtxy6uw yz9-ln2/4jv81d m hqad 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 pe-mmdyl2 u/ 9q1 hxj n486vwytzrson gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is el ).hbeaw l4deo z3ew/8+b) jtwice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall faewhb e+bjl3e/dle84 wz.ao ) )ster?

Would a spring scale carried to thezqh+ mh3k:t6,o )s;anikox4 4r:f gb y Moon give accurate results if the scale had been calibrated (af rqt:h4,g4 6hmnob oakkyi: s;3)x z+) in pounds, or (b) in kilograms?

You pull a box with a constant force acrosv ulld 22vi;r(s a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to t(vdu ;2 lvi2lrhe horizontal (with the box 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 is a netoaip r/5 idsgo*m+i(2 force mg exerted on it by the Earth. Yeto5i(p 2sr+o /idmig* a by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed 6))ygo u-yd ,(rtet.ytq ien+to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontallru g(y+)qye )ytndt ite.6 -,oy with a given speed on the Moon and on Earth.

According to Newton’s third law, each team74 zrx6 nxjiw* in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will wirxwn6 ij z*x47n?

A person exerts an upward force of 40 N tfnqs-v+hjbo p-n*.q *o hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) os-v .*npqbjnfh q* o-+n what object it is exerted, and (d) by what object it is exerted.

When you stand still on the g+/rz pr6cn vu5g5oioy-i5*zfround, how large a force does the ground exert on you? Why doesn’t this forc55p r iyuori5cgvo *z/+z nf-6e make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s car isclq vjb 8;fcgbaes0526z/z,s struck violently from ;fzs8gc z/0bvc56 ls,eba2jqthe 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 accelera;jgsitfk/ ; i*e:jj o6tes, the crate remains where it is on the truck, so it, too, accelerates. What force causes th6 ;jg;:sfj et*/ioj ike crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reachesquzwck (-w:n 0 5-dtq5a79oo) vze+h f;zmhtu its highest point, it slides back down but the magnitude of its acceleration isdcow7)+5wq m0 (;:f5vteua h n ozk-zquz9ht- less on the descent than on the ascent. Why?

What would your bathroom scaqz4l4f (2f0vvyhr- rt le read if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at qzrf(ftry v4 0 lv-4h2an angle.

  What force is needed to acceleratqri6 tn ifad61,y9( ike a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike .nfwhi6r qf0js- : 8kim.l 5jm -7m8sbh3cvd rand 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 w5q,ikl5auc7rri5q 3 h ithstand 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 ouzo*f1*jcs udpj0,b +4bd*rp f a $76-\mathrm{kg}$ 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 , foz;k ()1tlokt96c c4fhczq8 f l,iacar in 8.0 s if the car is travelinl 61,fo(ct z9f;),fz4 t aloq8hckkcig at 95km/h? -  

  What average force is needed to accelerate a 7.00-grawj p)p-be*m dx v9s 61o,y+8;b2qql0igsv v hrm pellet from rest to 125m/s over a distancev,6+wg l miyq*-bp1 rhqs8evs)oj d90px b;v2 of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accb0b2sldgtv 0*eleration of 2.5st 0 02vdb*blg $\mathrm{~m} / \mathrm{s}^{2}$ 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 cu-- /lqfhp:u+k9mbevah2tu *over 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 des1w47 zgfkz 0h0.abmxwd:0ufpkm0 v( jk w.za9igned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motojwzxm0.kk uz k 00mg91.bdwzwp407 : fahfv( ar 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 elevatodn;mq/5zjp 1z ttp3(;rllo)or. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. 5pm ntp;1 )(lo o3jrtzdl;zq/ Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elwy: gh6i+,tj l dny9 :nv1tr0bevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevatorl61t+ n jh v0 y:it:9d,nrywgb without breaking?    ( two decimal places)

  (a) What is the acceleration of two fall r;dw40i4,rlhk8 wn pi;h k*fbing sky divers (mass 132 kg including parahrwd 8;h,4i;k0inbkl p4rfw* chute) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the z;.7s0kkel p ,xdp;ate 3ej/ lroof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approxime p;k,tjp ez/3 lek7axd.;sl0 ate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs verticbp/soe k .816n kampa3ally upward over a pulley and a weight is hung from the other end (Figb 1ak./onmpa 6s 3ep8k. 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 dic:meez-j6 5 yo4 ll2xoagram 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 baseball (a) at the )6i a jf7xgp2omoment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfieldg762oxj ap)f i.

A 650-N force acts in a northwesterly dil8 bido y-c7r+rection. A second 650-N force must be exerted in what direction so that the resultant of the two forlbi78-d or+ycces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wkrvkb mq1 awo+/ 7(kl0ire" strung horizontally between two buildings 10.0 m apart. The sag in th10q(kw r7mvbl /a+kk oe rope 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 from anothq:.e cs3nb9v1 /o jjyrer 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 1inx0,b d,.v2ouq rkxmpp,*z/efu , 0y 4.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location a p6 8vb75ebwx9t mog+ekfae*7u7cn- ht McMurdo Base, Antarctica, as shown in Figh7ceenb6 g9m7ew k-7*+ vu5ax8btp of. 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 of the same mass behind it, o 6,htzkxr47ivple4, tp-kw+ Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomo wktlr 4o,zx tvepk6i4 h+p,7-tive 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 buckjd(2o7 x;a tbu7 w+3so1bppbaet-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at c3 7 (pboob;xab wt7p1 j2us+daonstant 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 .8op 3 +p+y qwurfa)tvnx4.jz, 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/c won6.k0zwq 2s fg) 24pmeik (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 contact6tci f,)e5o- j8nz*hz.egfh nv4k)-ory s5sh with each other, as shown in Fig. 4-51.5rf.6ine5 z4hc zf ,jyog-8e)vsk not-)sh*h 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 ar)yha.swq z wb4jpe*+(e each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velap(*wh4s ej+ )wzb.qy ocity 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 l;y*owq .1ykf by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at eachoy flw1y;* k.q 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 betw-*: j 8ykqzf kubqbqvv3* 3id;een a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to dgh/f5s i ,c/rvidrs( ov(36estart 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 standi5basg x5jc2m,6e) nh/ixice )ng on a train accelerating at 0.20g. What minimum coefficient of e5 m)b2siij)nch5ge x x ,6a/cstatic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if th 9 ),5awq6wudwgma -vnd35s nde coefficient of static friction betwee6uw)-wd5qnsmvg ,a d an d9w35n the tires and the ground is 0.80?   

  The coefficient of static friction between had+ shp5x-6 x d(rgpraip ds3od3(.ku.rd rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a -sk hx.6ps .3+rug5pdd di x3d(aopr( 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 prq6x gp3k/cjmg9s6*c (n(rvat -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 :sfp1tj-lk:8bc1:vavs x.,fm xyk n7rough 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 surfao5czvc382 yg0uwia/tce have a very high coefficient of staticvai 5gtw z8oc /u230yc friction.

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

  The coefficient of kinetic friction .;w( zi e2l.msed7klb hmno8*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, e:j/ z6bijpj0rxk +u-32 (Example 4-20) how large a mass would box A have to have to prevent any motion from occurring? Assumej e+6ji/:x k,brpu0zj $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How fariaf (z;zzxt8idr-5r3c/ 8r,i.rm svj will it go, given that the coefficient of kinetic friction is 0.20 a 5zc83dzi(r m/.rzii; arrx-svt 8,jfnd the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a h 3 fs*tcao(st-orizontal surface (Fig. 4-5ca-o ft*s(3s t4). 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 n/5dhv.qguy w lpg5:nhu1)0j heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maxd05gy)1 vhnuwg l5qunhj:/ .pimum 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 about parking your car in h z e:e. 0efds4p3jp03 jus(f2ehdi8f your driveway, which has an incline o de8h0h3fzspf:4 ejef2u.3s jd0e(pif 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 , gz1vg+al9ee a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an angle 42za ; :jur jsm;(fjev $\theta=22.0^{\circ}$ 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 ih rj2i tjdxr )8;3.qxsnitial 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 of the steepest hill with pj s(equec (i,g( gat 8xn3f05a 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 i31*5sq*ihu t ak udtv4n place against a rough wall by someone pushing on it with a force directed upwarh*s*4i t u1td5k3auqvd 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,fkh- r8i,71/ jii vkf 6yd)ia +xa ldppet;(g roofs can become dangerous projectiles as they melt. Consider a chunk of snow at)kp1i,v+peh-j (a f8tig,7ayix6r ;dk dif / l 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 auto.c za-og1m *xtmobile traveling at speed v is equalm*-a gx1c.t oz 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 wheb x 3t-tmnalf105vr1 mn the driver decele3 -t 5f1mlvbx0rnm at1rates 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 an initial speexw1 r3e7:kntgp j)j 7gd $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are fz2qhyr d uir59i)j7w q+v4vg)illed to the packing station 11.0 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 c9 i 5vrzijwqhv+d7qur) 2)gy4oefficient 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 fricml r 2n tjre3.,h7+rtv+u-yfp gc(e fg+ (:edstion between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (includ; htzsuh, w5hpt0m* y1ing the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approxec zy91c d8e8h ;fqv,tn/ j e2sf.er4kimately 20 g of blood is accelce sqez.1r;f e/2c fknh9y je 8dt84v,erated 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 reasonabdwdu0d.66 rm /o,wscnle chance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the fow6oms n.r/u c0dd 6dw,rce 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 acceleit*) l5qc).mmsbf3v 4-ydknv+sy2 uzration produced by an earthquake is a , and if an object n f3)b+mqdukl 4mv .)yts c5s2z*-yi vis going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accidel2j:n .bcx z)t) 1mtmbnt involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car astx btlznc1bmjm)): 2 .suming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 m0/ t9kg9x*cirfiwq14ue ee w vr()5cveans 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 travelv9 ecqi1c (wk u*wir/e4r0v)gt 5fxe9ing 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 Leanih :i.pibmz3w:as wo/ 6ng Tower of Pisa and falls 55 m beforei :hzpi mw b36s:o./aw reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a 1fl++rg/ b d9af cnno8muddy 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 speed upon emea1 ofb+9fn crn/d+ l8grging?   

  A city planner is working on the redesign of a huzukwypi (i41bt*; *q illy 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 dowp z*t qik(uub 4i1y;*wn. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes phyb5 ubh ynpypd:n1:a( ,sics experiments, dangles her watch from a thin piece of string whnanyp(dh15y pb :u:b, ile the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connecting diffovs 3fm0 np+(zxs)dj/erent parts of tsjf) nvop (xzd0s/+m3he 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 neednie5 3:cy sg: zme.rz,ed to lift the piano (mass M ) using the pulley apparatr3,:. sege cz:5zinmyus shown in

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

  A jet aircraft is accelerating lnig0+(hp yn-*dnvyvu:f1otr ( 9g-fat 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 fo ;kaqvp h3in4b (oj3 j kvf(+*qs*ayh4r a child-restraint chair, an engineer considers the followa+q 3k ;(f*n *(skja44ojp vyiq 3hhvbing set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of y mz jr1hc))o)3sprl7,spit3660 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 Ka 6i s)p nklo9w:c8m4bgn6 da/gren, 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 in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fg6lmis awpn6bc: )49g /ok8ndig. 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 usieh7zq qicye6o83 - ry xbxe+(4ng 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 buildin5v zvxw9: 1hmig 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 ascending an ice p an*1hsgttv0sd. tu lg--03hfield inclined at 2p nh0 dt-0t3ghsu.g1-svl*at1.0$^{\circ}$ 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.