Why does a child in a wagon seem to fallsz0 vw;b2k9p qi 07qrv backward when you give the wagon a sharp pull fr0vq9wi02zbkq7sv ; porward?

A box rests on the (frictionless) bed of a truck. The truck drechmw uo)drd310;/ga iver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discu )hm0d cdeo1; /a3grwuss 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 actingr :lxsf0i/p1g on it? Explain.

Only one force acts on an object. Can thenqzp sr)wv )vbaagbi /*6.m*2 object have zero acceleration? Can it have zero velocia*aip wbz/.bq )r)gvmv * 2s6nty? Explain.

When a golf ball is dropped to thedka*zx00sgi r3iam4m)an/doc,7 p )q pavement, it bounces back up. (a) Is a force needed to make it amkria0i4/ ,3ocgz s0d q))am*dn7 pxbounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, 1:ub562 +vj6o df uyv(rvfmdn why does the log move in the opposite dirjdrn5fuv u:(621b ov6mv +fy dection?

Why might your foot hurt if you kick a hesvcpnh k:85qz( ,u bc2avy desk or a wall?

  When you are running and g4 kcopo 6la51want to stop quickly, you must 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 to come to r 1cl4 6oa5pgokest.    m/s$^2$

A stone hangs by a fine thread ob 0ieeoot9 p7/5em o8from the ceiling, and a section of the same thread dangles from the bottom of thmoo e ot7e8oepi b9/05e 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? Explain your answers.

The force of gravity on a 2-kg rock is z ,m,56 wncskj53j/uer hjt ws:ewt*7 twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall fasten t*se : wj,,ruhj5/53 ts ckzwm6e7jwr?

Would a spring scale carried to the Moon give accurate re uab6 xlopo d60lb**c.1ok4 pjsults if the scale had been calibrated (a) in pounds, orpabk4* uo6 dlbj*xp0.ol o1c6 (b) in kilograms?

You pull a box with a cofj4 k*ts/srv o,z+b4o nstant force across a frictionless table using an attached rope held horizontally. If you now pull the 4 *fsv/s ,okt4 bj+rozrope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely ut :dq6x qc)5 m16 (sbuftxw:kcnder the influence of gravity there is a net force mg exerted on it bykm b5:twcqxx 6s6u:t1 )q (dfc the Earth. Yet 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 to lift a 10-kg object when you are on th:f8 xyymfp t-p:s 5g7b8:qjdle Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed:g:7lfb:yt 8jy-p fm5 xq8 spd on the Moon and on Earth.

According to Newton’s third law, each team in a tf6;qm2g.ggxywsh j7s (w 3jz;1 or)cdug of war (Fig. 4–37) pulls with equal force on thex; zghj6dg cjr37 f)12ow m;ssygq(. w other team. What, then, determines which team will win?

A person exerts an upward force of 40 N :cbavihsz *9h4 g+*gz23pad k to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitubiscdka pz2 3+g hz9hgva*:4 *de, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does t1k4y7srcgwp /) twmq :he ground exert on you? Why dpwq4c/ys w r:)g1tmk7oesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the vicm *mdb:/n/awb4cgv3 yy a p/m1tim’s car is struck violently from4da* yy3bmnpvwg/ m//bac m1 : the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. W: j.f8xo6u y) ;qoez83yxluya.( nvpo hen the truck accelerates, the crate remains where it is on the truck, so it, too, acco ay.(opju.fx 8q6z )on yx;v83l:u eyelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the blocky *y0 mew-ar4u reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on th4yae-m0r*u ywe ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclk ubd676k a6y/iyxfr9 ined plane? fx/ d6bu6i9ykra7 6yk Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled ameegb ).0 n+fdz+ i3sst 1.25m/s$^2$?   

  A net force of 265 N accelerz* -(,u wju ap4ubpj4,*tmyz eates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a 96+lejwka(87 cz 0$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight obe a8oo85 nq 1l/odq(yf 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- b10o p,(govurvc 4rk1kg car in 8.0 s if the car is trarkc1p1 ,0rbv oo gvu(4veling at 95km/h? -  

  What average force is needed to ac kxebf/ c*utr1y9)n(/iuqdfhh5,1s i celerate a 7.00-gram pellet from rest to 125m/s over a re 5x)h(u/si *,k1y /niqhudbfc19 tfdistance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleratiohv 3+y4y*dfmo/ k tgdr-;;top n of 2.5t* ; 3hop/f+y oyrdk;4t-vmdg $\mathrm{~m} / \mathrm{s}^{2}$ 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 bgt6 zdre+ )uj8m4zkuol( moyp4l5m0 w8 96qtcan 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 4850fe+8(*q//2r vi gpw/hz1j u-yv oeytn kg ) is to be designed so that the maximum acceleration is 0.0680 g tj/e 8y +(rqy/u/g-1hfnoipz2ev*w v. What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bae9r3f rjx 3gsz- (cn)nthroom scale in a motionless elevator. When the elevator begins to m j-fr(n39z3xsn)c r geove, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21vodmhcv 0+ d y4013lurk4zkv( ,750 N. What maximum upward acceleration can it give mhdokv4u vzc1dvl (3 04r+k0y the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg l+4c uyqep 3j.jyxx-9including parachute) when -qx3 9eyjc+. 4yxjlupthe 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 roof of a w0 4 1 vn00usky ia6;bk54im+dngj;do .wg wjthouse 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (1bam 40;wyt nnwku. g+v;dj k5ii w0sj4 d06ogexcluding 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 bo.qs; p(t8kaon x 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 hanging on the oth tpnoas.(8;kq er side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a baskmzc *pc kc(p1ysjx r8zn9r:3/ etball 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 bah p9j4z)l yvb lmd/w6x:6 z8 o50lxnc:lffwn1 seball (a) at the moment it is hit by the bat, and again51/w h f6xy:v ljzldf0onwmx lp84 lz)c:n96b (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a nbp)q(/vfrl . morthwesterly direction. A second 650-N force must be exerted in what direpm(/ rflq. )vbction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung hhc,up- ;jdu(xl by;j9 orizontally between two buildings 10.0 m apart. The sag in the rope when she is at -d (jpb; ,l;uj 9hyxucthe 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 bucha3.b/h7reer ket is hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14./ qf., spq,;ogu/wc hywxj/ l40$-\mathrm{kg}$ 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 bs5sl-eq1i u,g 7hjs4 a new location at McMurdo Base, Antarctica, as shown in Fl4 e71gs5bujs hq- ,siig. 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, Fig. 4-47:h 2u, 4eitsfq . Determine the ratio of the tension in the coupling heq:fts2 ,ui4between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herqv02iwa fyv n16(. pxaself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard yvxaaw6viqn 2. 1p0f( 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, atqkk xhi v g2;uah3,vk3/-x/m 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 (mj)tbfw1;ohh3 ktpyz+ p+ue9 5ass $ 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 horizf g3j b)ad2lg.ontal surface are in contact with each other, a. afl)j3bdgg2 s 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 1.80 m above t lv.ts oj66bk 1agqdy6 o(7g*hhe ground, and the massless frictionless pulley is 4.8 m above the ground. What ma ja6q1tlobgko .7y* g6(vd6s hximum 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" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of mass dkv4v;nu2tjo;7- +s f7uqgog 1.0 kg . Calculate the acceleration of each box and the tension at eas4j k; o gutgo2nv7u f+qvd;-7ch 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 kinet:qbr )qv taje.37x tan *+ykd7ic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required,ejr0 f 1i7 r,i.6aae7 bz)ilgtzdcn. 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 m4+ji)obsjbz v:6xphi6n3ra ; inimum coefficient of stati v 6izb;ohsa3 rb nx4ji):j+p6c friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum w)cwjrkum81ln2l zi5. (*vefacceleration a car can undergo if the coefficient of static friction between the tires and the ground is 0(nemljl)28* cui wk.fwz5r v1.80?   

  The coefficient of static frictiysn2 s1ew9,a6g sft4 non between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angleg9nes y na, w1ss2ft46) 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 at7im1 vqrw3,mt -y2 hxi2p5pc *vujkt5 -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 ro0(6im v2zt8twspkt t/8bwv:8 ,wocyough 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 coeffici 2pwz cxr* o01sjg.z5bz9k6eoent of static friction.c9 sk2 zzgx0eb6j51w ro poz*.

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 fri1qbt ;2uvv5yoction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box Ahfq-ik kij0 8 oywj0q(;,d lufg0x0 n4 have to have to previ4x 00 f,8hi(kqognfyj0w0 ql-kd;juent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it sxxdl n7 8ajrx 2:* g 3puvv3-/g3+irizx.hzaflides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an +i32z :auix8nf-pg x jvl 3d7/rgxxz3rha .*vinitial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on vey ycr64er+yswe ,4 istp6ir 0b308ea horizontalw64b0+sr0 yi6 revst eeyyrep i3c,48 surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy cra 8zwcfynv ,nl2xac .:0te. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driverw. : ac l8fn0z2yxnv,c can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which hvrvzx,ca.bl9 *d- arr,istr 390 yqo-as an incline of z,yr-bir r3so 9aav9*,cdr 0 t.qlvx- 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 ot 96hhc j )v 2,e3wlto+jm-pa28$^{\circ}$ 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. 4-5fb l9m-rl-9:(ift s* rcs7bw0+ddn vq5 lies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initiazpqs4 t1y9a/d l 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 a speed of 6.0n ycf+s/ (c ha54shps ()xnqw6$ \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 pushl7h.vy er2nr xm v(-0x2o5wmxing on it with a force directed . 0moxvr xlh 5ey2nvmx7w2-(rupward 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 34fig7.x4le j0pgmdaroofs can become dangerous projectiles as they melt. Consider a i43mgx4 fj adl0p7ge. 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 v7,g vu.pqob9v /h3+m )dciys3 (iasrdistance for an automobile traveling at speed v is gy, ma i/+ o3vsrhbv(39)dpsivqc.u7equal 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 therudy+ d80n rhc;xt) .q driver decel0trqx)un8+ d.rhd y;c erates 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 speed3go uf)f48p gt rjf**i $ 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 filjx xq*itfr k13r1k:/ cled 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 coefficient of statijct3r1fk: i* /xqkxr1c 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 frictionh9z;ww ev+y *q 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 (including the bicyclxcwx-.yu r; )bj/ ry2pe) 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 u4*lfy6n32 uly tge/k model of a mammalian heart, at each pulse approximately 20 g of bloo6 yfllguy4e*n3 /k2tu d 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 if the dd h98kdj*-py*vfkg e+eceleration is no more than 30 " g 's." Calchek gv d +*9y*-dpjf8kulate 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 produced by 3+ 2b4phsl:n;w 48 r6rhwwfgp*fpnlm an earthquake is a , and if an object is going to "hold its place" on tg84;+mppf :f3r hl *l2nbrw hwpn6sw4he ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident ini )-g. zoxty6z6lyzf+;+ r fzavolving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a levei6fg6yr+lz zfa- ; z.)yozxt+l road.   

  A car starts rolling down a 1-in-4 hill (1-inc2 nir-dqx 0enxd(v3j4 l+:ff-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 55 m? (a) Ignore frix 02lfncqf: xjd3er4nv+i-(dction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped froa . u/)pektcx+m the top of the Leaning Tower of Pisa and falls 55 m before reaching the groundp+)ce ka/xut. with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but ente k,mn0c t yfs-*dp8of 4dzwx5)rs a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the mudmy 8* 5kozf) fw t,0dpn-4dsxcdy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the r,eek-* eyq3 bb.v.ge h- x)msbedesign 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 withou.-y-)eg, e e xbkbeh q.bm3s*vt slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles s* vo*v,( jihuher watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She nojh( oi*,u* vsvtices 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 diffell89b7/ - 0 y jg8jew.g s2fyw3bgpingwr1 .nvrent parts nf9vyw0jl.b3 b w-rp i nge2g 1ygw/g.8s8l7jof the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass nihv7p+t :q)ndr f/bmh2b9u* M ) using the pulley apparh b*f/7nmiv d)2 utqn:r9h pb+atus 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 accel9l wmuzk 7t.+lmz1 .goerating 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-restr,lu0 ,tgw6/e ur ;scxv98hoyhak.xwwf) f:w 7aint chair, an engineer considers the following set okwhh:xtf/,y6f0u s.a8o)e9 vlwwwx cru, ;g7f conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric tons (jz:rdn9lw3 b1 660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of simil, ng;vx l42 e:semxvf4ar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she4fgn ex;,x:4slvve2 m 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 usi jejx1h73hr2 png 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 5ax 98*janv hzbuilding 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 a x(q+g.t)3sxdwagjgt4p ;ah . n ice field inclined at 21.js 4 ;.t xg .(txaq)gwdh3ag+p0$^{\circ}$ 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.