Why does a child in a wagon seem to fall sb7wgwfq o3+1dn68vh backward when you give the wagon a sharp pul nsgh dowq+173 8fv6bwl forward?

A box rests on the (frictif y8s uwus5 /v)5m70q0anj.klypx2eoonless) bed of a truck. The truck driver starts the truck and accelerates forward. Th/ym805 ys qpfok e27ujxl vwsan.u50 )e 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 obje :wx a.;ik-0chr6qjkpvca*g8s: c0ow ct is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Canl7s/tpwqo;-g it have zer l7go s-t/pw;qo velocity? Explain.

When a golf ball is dropped to the pavemenj1x p)dx 1y6xri h/b:o+q/yb wt, it bounces back up. (a) Is a force needed to make it :bxy1iho)bxd+r w p6 /j1y/qx bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a laf tkeh1w 70ze8a ;7hzxke, why does the log move in the opposite directi0 ehtzzf kah;wx178e 7on?

Why might your foot hurt if you kick a heav;,2omsb ls1vw)6q l any desk or a wall?

  When you are running and want to stop quickld+ xq8+ci qh,9 b+gc/mx- iyrty, 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 +dxcy/-+r b 9qchi ,xm8qtig+a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine threai.wvg+w 7klskcg2- a; d from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp 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? .gsw lw- cvkak2;i7 g+Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rockklkld(j2gu 8, . Why then do(,2ljkk glu 8desn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate resul4fpe* gzv-01y9 ajss cts if the scale had been 1eav gjsz0c- py *9s4fcalibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table usingu *z/(+i :lcd,6 mtf1zoh6vdzokwwt ; an attached rope held horizontally. If you now pull the rope with the same force at an angle h vitu ( k;lz6 wfo*c/zdwdt,6m:o+1zto 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 under the influence jvq4z(+l*(-/ djb) gxbqqlbq of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law td g-qzvb/* lq+jqql (4)(x bbjhe object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force9ocl(+w8pjcm4p p a d 6qoru2,) needed 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 horizontally with a given speed on the Moon anco2 rmco 9+appujl, 4p6 (d8qwd on Earth.

According to Newton’s third law, each team in a wazy *-dxk3:8rg++dn s iope:tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will win*yk+przs:in o +gx8:d aw3ed -?

A person exerts an upward force of 40 N to hold a bag of groceries. D(3.t4s z2msk mumiw 1oescribe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its directio1sz 24. m(3imutmwkso n, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the glk *u9z ro*a*,esvfj5 round, how large a force does the ground exert on you? Why doesn’t this force m r**lv sok*f5zej,u9 aake you rise up into the air?

Whiplash sometimes resultsn,0huye;id /t from an automobile accident when the victim’s car is struck violently from the rear. Explai;h dun,e/yi t0n 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 4gv*e+dus u. ht8/y p;ttlg:z a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to acce:pg.d8hlvg syt* t 4;+utu z/elerate?

A block is given a push so that it/*ogm)oh)yu k1 )dxnm slides up a ramp. After the block reaches its highest point, i1 dok)n)x/ ) uog*yhmmt 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 weid(u yd1o. m, -cslm-ncno 89ewghed yourself on an inclined plane? Assume the mechanism functions properly, even at an angloeuny-ddm. sc-( 8m,lw1noc 9 e.

  What force is needed to accelerate a child on a sled at 1.2(bu qgn3 mwx 362jz wej3:u90ql0 gqrv5m/s$^2$?   

  A net force of 265 N accelerates a bikerh50k6 0zoo-;uzl awe6tfa y +c2pro 9 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 acceleu ar ns0dw)f0/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 6r3x ybp-34kbygdb4o ,c14r .tukru j $76-\mathrm{kg}$ 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 opc;6. gocfi q7d6b .u3fhi0rin 8.0 s if the car is traveling at 95km/h? fouh7c fqibrg0o;.c pi6d.63-  

  What average force is needed to accelerate a 1;f ba2x )xl-q 9pqbm )zl7xsw7.00-gram pellet from rest to 125m/s over a distance of 0.800 m a2x 7pmb)b1qxs9zl)a wl ;xq-flong the barrel of a rifle?   

A fisherman yanks a fish vertically out yb/u 2c4yksj8of the water with an acceleration of 2.5 2c/8kjuy sb y4$\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mile tpbjnstp +36/ 7,nrjst rack (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 that the 5t). fnjzs cu(maximum acceleration is 0.0680 g . Whacz.) 5ufn jt(st 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 bathroom scale in a motionless elevatomix5)m5uzz odc2 da4g20 dy7jr. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the dixudo2dz7gm)imcya452j zd0 5 rection of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum s8 p g/x2y6fhzttrength of 21,750 N. What maximum upwh6/ 82xz gpytfard acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includi*16);zgw l k6etygukg m4 r9zbng para g ztrk1g4);6mb*lz9e w6g ukychute) 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 roof of a house 3.9-m high. When he strikes the ground 4x *m+at-g vkn- tuhx7below, he bends his knees so that his torso decelerates over an approximate distance of 0.74vma k g-xt+ 7htu-n*x0 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 restsm ro ef6 cpzgc50 +:zc93lwk5i on a table. A rope tied to 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 wewl5go m3r+ cpck6 z09i5:cfz eight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball pt6ec(h;fj3 bkh97 myn layer
(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 moment )fc dome5pr4yzafh 6)vlu, g85pw- d2it is hit by the bat, and again (b) after it has fhz2gf,d-vp56mo)cp4)w raled yu 8 5 left the bat and is flying toward the outfield.

A 650-N force acts in a 7mgbc)xra as,+k *po*northwesterly direction. A second 650-N force must be exertgs7,r+*a)*mx ap kocbed in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two 05 f(8 (,tvpg dnhu pypk-qfu0buildings 10.0 m apart. The sag in th tunf(0 ,fvp(-d hg5ky8p0upqe 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 anbczmr3)g n/q, u9*w-1zqvf dzother 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; if wve(eblc8e/ 7qy2.0$-\mathrm{kg}$ 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 Mi,2;rdm5 lwxsb)80kkuq*f p qcMurdo Base, Antarctica, as shown in Fig. 4-46. The sum oklq,xd8*qf5r0 wm)ps ub ik2;f 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 6m uo afni;y3/mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the finf ya3;uim/6orst car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus shown i5,9ipq,l;va tsv3 u(wrk3(x uvt4g aan Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant s w,4saurxp;la9(t5ut qvv i,v( k ga33peed?   
(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 (rldsy(j 8(unofyx 9 +vgogy( 2mze.(began, 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 (masp,ko kip3*s lsp/)izum s /m-7s $ 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 contact with each othe gda/owrrd)ac9(g( .mr, as shown in Fig. (dgda9o)wa. rc rg/m(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 F.sf8ab lv *isu g 138;i(4iwz5wjscyd ig. 4-52 are 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 velocity at the moment the heavier one hits the ayzu(s8*i g;8l wd3vf wc 5 si1jbis4.ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a h+y nn awskan2r j9pj4(e3*l c3eavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig.anpa(29r wc3nsl 4k*jney 3 +j 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 kinetguer r34-y-*.re3 9opvcpj -wxiqv (kic 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 isdw-d *2aio.dc. d34hjb cxo8,9phanj required 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 afctd oyc5h*v e;y*2*,fa. h vm train accelerating at 0.20g. What minimum coefficient of static fric*y d* c52v,y.*ocm th;ffav hetion must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration )a8- b,2 3rrz1x(d ljipm wsvswc1u7b+ w(s bxa car can undergo if the coefficient of static friction between the tires and the groundxbc8w2s3vssj mbdi1z)+awp (u -l b rx(w1r7, is 0.80?   

  The coefficient of static friction between hard rubber and e3+ ne)7z,pjjf f9vvl normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a caj+efvlvn) p,73 zej9fr 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 -4.8o :vcjf9 ib k/uxv.1m85)m ;xf,sscft0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 rough thf.qp p.2u dj x8mu) / 1za.,+iugare 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 coefficient bn.h(wpx)l u1k k( r(q/hcoa;of sta(cp(.aru( ) /1qknh wbl;hkxo tic 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 frictrozi;rfajt ik9q vb0n52/. gk: ))m stion 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. 4wc/x-h/od 3,vle wes*-32 (Example 4-20) how large a mass would box A have to have to prevent any motions elh ,-/odw*vec 3w/x from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so g;:lm 2ryttb1 that it slides across the floor. How far will it go, given that the coeffic;b1 trg2 mtly:ient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg ( okuhtu89x a+and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54)th(8oxu a k9+u. 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 c yoi0hv9 q q4:+bfhld*arrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide againih oqydh bq0 *lf49:+vst the cab of the truck?   

On an icy day, you worry aboutc; 8gyei. 3a9fpvy;;/t+/ea s nqiv tx parking your car in your driveway, which has an incline of +a tv;i8f/9y.va;sti y ;xge/qp ce3n12$^{\circ}$ . 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 wit vfb4,(pe 6*zr1sybkx h 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 ftjqq.f2/3zt angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of /jmhu 3+ dvy,c3.0 $\mathrm{~m} / \mathrm{s}$ 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 spz4w3am +ev rlad x 2q/z4qgfc ze.;6p/eed 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 wa)k diz0e92mgb:ph51 hb )5 i h,ib.afecm;bfoll by someone pushing on it with a force.k2oz:hf;5,e9 m d 5bpafhimi)h b i)be c0g1b directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as theyi2q o0a *mx4fm5ltq 7k melt. Consider a chunk of snow at the ridge of a roo7 a q4lio t0*5kmqxfm2f 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 forki7ai1m/ws .s*-rq er an automobile traveling at speed v s*.mw-s ark71 /iri eqis equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides ww gnnn7+/q;t forward on the dash when the driver decelerates from 7ngw+ n;/t nwq45 $\mathrm{~km} / \mathrm{h}$ 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 give+o+coqm/q vi u8wlq4 5n 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 conveyor belt from whe.;nv,h4da wy(ric6 j wre they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplis(jrc aw4v6 . nwhidy,;hed 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 kineti2rx*ws-9; /eol snnffc friction 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 (inc)cw - fua2g7 5x .xbw7tkroxeg83m2khf 1ld2gluding 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 wl /w1v2yh; vomammalian heart, at each pulse approximately 20 g of blood is a;/o w y2v1whvlccelerated 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 automobiwl()dz8.swej,u9z a vle crash if the deceleration is no more than 30 " g ewu.d8s (zazlj),9wv's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleratir 2acnidzda,e 8f (l.:rj/7nmon produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of snaa 8d dfiejlm/ c:72.r n,zr(tatic friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving two twf 9;rd)bnza e.q0-rcars, 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 r0z rb-;t9n)d.fwqe athat car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each wx/p4gao1ntw4*ioxs t1 ( +wi4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the botn*swxo4(p w g+iixw t /a141ottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaningx: p;z6eht/x+xfbr3h Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force3h ;hb:zxpefrx/+t x6 of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but ent.) lirabkcu,m/3eh+ vna r.g25t( dzaers a muddy stretch wherect5m+(k3 a ,hdinl)z.grer/a .2vbau 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 emerging?   

  A city planner is workinre( njh m9xvz(mg*3s6( a9a omg on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowih(x6(9agzv *nj(r m emmas9o 3ng 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 her watcplwc iz-+n(, bh from a thin piece of string while the jetlizl -ip w(b+cn,ner 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 rampfxq(x2 9ard u o.:hjo 04mb)qts connecting different parts ) mfbx0raqh:tdj(o.ux q 924oof 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 M ) usinvr3:o 5n1a2 badpuv 1sg the pulley apparrsa1:bd2u5a pv1v3o n 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 acceleqr*voa ew9w 2+rating 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 consik*m 0 amz4ux;bders the following sexz bu*k4ma;m0t 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 trai 15qiqxr/ru5bu.p ex;so t)i1n has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar 0cx ni mnz ;z(f0m/a0+w-zvm hlength. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a statv zzh-0m ;(izfn n0wxmc/am 0+ic rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat in ofzqpi7:d7y x04cg71 t uz 1o+u8fuhs using 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 reach a maximum spe2ji*gtbh2 )k:bf7bmy ed 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 ascen3csat 0jmt6(9c7nv we ding an ice field inclined tm6 0vsc(e93 njwca7t at 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.