Why does a child in a wagon seem to fall backward when you qk9:p gxrl j,q e-lxzbnc sb)p7a0++;give the wagon a sharpg)b 0;lpqsjae :xqlx, 9kzr7+cb -+pn pull forward?

A box rests on the (frictionless) bed of )mrf0 ts uw9u+;wk ac+a truck. The truck driver starts the truc+a s t0w)kmuf ;9+uwcrk and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no ffu2uqx w jy;:ezg rt1w/4 b1,zorces acting on it? Explain.

Only one force acts on an objenj j4cl ymj0x tlh4nmil*1q*),j1oo6ct. Can the object have zero acceleration? Can it have zero vel * cjtl,njxq o 1mjm14ijn)64*h0olylocity? Explain.

When a golf ball is dropped to the pavement, a5nyn6tuqk3iog /-m1k/h 5.x trf,e cit bounces back up. (a) Is a force needed ,tikcht fq ny-ruo5e//31xk5n.am 6gto make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the logfr 6/ 4vqlfe/n move in the opposite dire4l6 fnvfr// qection?

Why might your foot hurt if you ki6xs5 cpud:g f3ck a heavy desk or a wall?

  When you are runningbc. n e/4k4jefx51lrl and want 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 runningx4 4nkclfr5 lb1.eej/ at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section ofc r t)fxba7n*9 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 th fb cn9*x)rta7read likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a-37l-yrh wvh-m;1* fuyt ot+o.*rlzrm )dhbo 1-kg rock. Why then doesn’t the heavier rock fall fastl 3dom rhty;hf*ov+b-. h1l*zr-oy w t)7m-u rer?

Would a spring scale carried to the Moon give u jwmmi,8w ;,paccurate results if the scale had been calibrated (a) in pounds, or (b) in kil, p8jmwi;,wum ograms?

You pull a box with a constant force acrosh+9uuw k hz q31.lozb5zm)c4 bs a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same,.w3 bh1uzmlkhz 4qc 9o 5bzu)+ (b) increase, or (c) decrease? Explain.

When an object falls freely unde8 ftas3isdf e.c.c2.rr the influence of gravity there is a net force mg exerted on it b2 .rces a.c 3distff.8y 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 d 47kkze*j bn)p:9xgjlift a 10-kg object when you are on the Moon with the force needed to lift it on Earthj*:94 gp) kkd7ne jbxz. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–373k- ez.,/ xyk (oqxdgg) pulls with equal force dgo 3 xz,ykg -(k/qe.xon the other team. What, then, determines which team will win?

A person exerts an upward force of 4i 91mxj1b t:+cbhbzlz;a 1wzvi.f*q+ 0 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stb.qif1*z1zvl+9 cab 1bm+h;t :i jwzxating (a) its magnitude, (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 the grout 1v.+;we:t ) usi3but 8rz2bxj1dshvnd exert on you? Why doesn’t this f1bs;v. 2uduv )htz :rt3e1b8+s witjxorce make you rise up into the air?

Whiplash sometimes results from an automobile 5tv7 y .gotdkj e,b2japy16 -iaccident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown6jt7yyd512gopvbe, ta-i. jk backward in this situation. Is it really?

A heavy crate rests on the bed k+l7gz0 rw /qbthz3y9of 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 accelerate3q/9twl0hryb 7+zk z g?

A block is given a pushhih-wxe5b vh s64-4t ,zbfii- so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is leswhbi-4he fihs ,6z bt5-ix -4vs on the descent than on the ascent. Why?

What would your bathroom scale read if 17j- hxt+ohju arl *20sfre3n you weighed yourself on an inclined plane? Assume the mechanism functi20a3h f esrj7o+jth1-ux*rn lons properly, even at an angle.

  What force is needed to accelerate a child ouzjvc, nc4s2obq1 4a2n a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a b6u ai,jub +8y5rbqmo cwov x40n854faike 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 r*;qrto5w -jo 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 ofjh 7b05f*qxx n 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 car in 8.0 s if t-m5a2 a yfz go1;c+5- uoohrprhe car is travelina55 -zm ar12oc hog +-ypfr;oug at 95km/h? -  

  What average force i5h+8i f d d2kj77 hz0hijvaux1s needed to accelerate a 7.00-gram pellet from rest to 125m/s over a distai5uha2+ 0kd71dhxf8j7 j iv zhnce of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish ver pymg++)g4e nenx/gm+ tically out of the water with an acceleration of 2.+mn pe+ / mngye)gx+g45 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mile track (w6y3t2 en 1pfj402 $\mathrm{~m}$) 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 desigaj /d./- zey5yb pojpcgx(99*u: cg dbned so that the maximum acceleration is 0.0680 g . What are the maximum axz g 9cj jg/* /-dyybp(.p5ued obac:9nd 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 elevator. When they*avhuz wz6l 01t3c 4l elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and fiu3vlh 1cza6wzyl04 *t nd the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum str c:j(f 7zd w2 xx, em0qidye;6h.wy ekfq02*xiength of 21,750 N. What maximum upward accjyei 22 xf k:cx6 xze( 0,;fw.eiqqw7 hymd*0deleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 bzi qu)mg 7eqh-qv,- 9kg including parachute) when the upward force of air resistance is eqqgibvu qh)q m-ze79 -,ual 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 housge4-bm 3);fn pvz gn2re 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distanr v)gpz -egm;nb4f2n3ce 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 ys6p g 5oj:a+nruns 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 weig:5ps+ya6jo ng ht 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 pl4q1 ;+lgde9v cnj /yalayer
(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 basebal,8(ms, sbbmho (;( kof q/:oj*zrfic pl (a) at the moment it is hit by the bat, an( mmpqbczshsoob 8ko(/:*rj ,ffi( ;,d again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force must be ,9udzp 4hacm1 g;/ ij;jzgp1 xf*.rhhexerted in what direction so thmir;ugj dgzj9*;f /h 1czph41,hax.p at 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 tfpx tg( a a.).*urm;k)rwiq4 rwo buildings 10.0 m apart. The sa( rrrmp g* 4kqw)ft;uxia a)..g in the 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 h-b 9 ndy-k,qfyly ;68ezt8 rlzanging 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 14.0indm o4n *w08opqbk74$-\mathrm{kg}$ 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 McMurdo Base, Antarctica,o4z-g 4pmvq 4y*lrsi *kv ;bo3 as shown in Fig. 4-46. The sum of the forces q4myvs l3ogpvr z-i ;o44 k*b* $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 cad0o jog4enffrwt8 u 213l6 sr:rs of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and trudsofn w13f420r 6te8l :jgo he 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 bucket-pulley apo,po2;/ge0f(2q n d z kjfv+tm5syth5paratus shown in Fig. 4-f y5,o vf2ds(p nqhj;g02o +m/ktez5t48. (a) How hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race ryre).w;j kr 1k9kxs 7l//azfbegan, 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 id ujr 97wfrvf,c0/-z (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 contact mtraqo9/v l: e,ttb3ny06/xm with each other, as shown in Fig. 4-51.abnxm/et,/tq6yt o: v0rml39 A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above the groacujdiu 88ts;4l 5 f-wund, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" sw cu4uaj-8i5t8s ldf ;peed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictio(isa- -k ty :xfp4rw/knless table are connected by a heavy cord of mass 1.0 kg . Calcu/ kfixwk - :-y4p(satrlate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kiq 3 .- e mdjn;a,xkoz/3rbdl,onetic 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 to start a 5.dd .s:g6kmx1uznl m1.* si4wf0$-\mathrm{kg}$ 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 minimuo)skbf.a-l28 czrl,j m coefficient .l8 js-zkbr 2o)fca,lof static 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 the coefficient of static dg1oy -rz m8s m3e/ev;okq)h7 friction between the tires and the ground kq-d81my v);smzr7og 3 /hoee is 0.80?   

  The coefficient of static friction betweejoaksd 6n, zo5 t94yh*n hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you odok6 hz j,y* sn5t4a9leave a car parked?   $^{/circ}$

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

  A car can decelerate at -47t adk2s/m a6sfz+fv:dg x j/+.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 onc896h; oa kkcgt6( yph a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with j, )rkde)iqvoh+a ;mf ,rzu n ).cee-)an asphalt surface have a very high coefficient of static oan-,kce+)eqmr;u)e r ,.)i jdh)vf zfriction.

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 frictiolp53,f::edr o r* twdln 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 4*jdth rl vv:-j h58z8g)tcaza mass would box A have to have to tzrt5valhc *8 )zhd-v8jj :g4prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wil fif 0z9md u)-v 303ahp7ihwyyl it go, given that the coefw9 d7hi0vu3fhp -f y m0yi)3zaficient 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 and 110 kg , are in contact and at ryyu und 8x bxj*1)d0g5est on a horizontal surface (Fig. 4-54). juxn80* ydudy15 xbg)A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefnovbp0s419yv3k*zuj0ur0 f t ficient 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 dec09y14ju ro3* pf 0svbt0zknuvelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parbv;r(:sq4mn v6mm7 z bking your car in your driveway, which has an inclinzsb 7n vr(q 4bm;6mvm:e of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down aowm( i1 0mt5pw slide with 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 angl5gg25 6gu7y a cjj amh;v7:pzie $\theta=22.0^{\circ}$ 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 356ar.o0,hx4mahub 7v q( ql rh.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 reachz7l4uazw+ y1mya rw5.es the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing on it 2n1c rft48x2tfe fw x+;-dyer with a force directed upward at 28e - dtt 2y xf;82crw+4er1xfnf$^{\circ}$ 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 5-nz2ivrqo:bi(d.w rfy zu*6 projectiles as they melt. Consider a ch:onv.b( zqrz*62iuyr 5 -wdifunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for a-iowo2 w(ajt ,n automobile traveling at speed v is w j,2ta(oi-ow 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 forhnvt9xv4 5 vi2,kx wn.ward on the dash when the driver decelerate 5vn2wn xhtvi .9xk4v,s 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 ie2 0v*bi2ikero7vd y) s given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from whsapzbc6y. i :,ere they are filled to the packing station 11.0 m away. The belt is initially stationa ip,sb .yzc6a:ry and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of ki4q tp9/-ow 71kchu yq( zla,tbnetic 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 (including evlto8mq apnm2+**+/j cx 3gg l /jw-ithe 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 ecm 3+u:t,oozq5l.vt uwkw x.k*p g6*o ach pulse approximately 20 g of blood is acce*ploxo *q5 t6ou3vzg c..wk +,utw:kmlerated 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 l 0r; 0du09.:bxr5fa0pr egvby s.dcjof surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a ay00v:px rj9r b0d5lg0re.f bcsd.u; 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 hcs7n9;l7rtg bpcgm+s7v ge)* pnd* ( produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at leasg*t * e;(vc7l7d)bhpcrm7gpng ns 9+st $\mu_{\mathrm{s}}=a / g$ . (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 7 7tj.6)hk6ldfi* bi 4dzgafx8osvz*of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop b d 8 gzz*.vt )i6jlk*hfisa77 dfbo4x6efore colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for qil*+uffj p.f1gvi*6 each 4 m traveled along the road, the elevation change is 1 m). How fastpulvif* *f f1j6qi.g+ is it going when it reaches the bottom 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 5jt awt/c 6n8vthe Leaning Tower of Pisa and falls 55 m befo5ntv a j86/wctre reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a strq v6 o3ak:)uceady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emecquv6): 3arokrging?   

  A city planner is working on the redesign of a hillyf 5d0x4v oym.ke+u nbs7q v(:xheq/v1 portion of a city. An important consideration is how steep the roads can be so that even lo exf54 bm7ysv(/01 hou. xv :dkqeqn+vw-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road 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 eilqu(am l9 6x3tqv(4her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string make4 mxi(lv9tuq3q 6(le as 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 diffe,6v dr*k ,v dra2d7/gmx2toefrent parts of trgo,f k7e*/x2dv d2 a, mvrd6the 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 2s(0hofglr:w/e qg7n.p zv*i v 8 ysx1qsw;o3the piano (mass M ) using the pulley apparatus rw3pwosgqislqzy1.o g e8sv*0(hnx/f2 7 : v;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 acceleratifovib/ 87li2( a ku1bxhj3qa8 ng 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 considers t-.puvzt 3bv* l d8u55bbutrr .he following set of cond5*vz835v.brt uudr- bptblu . itions:
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 p.gs 3uie5syoo 1-t z*train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of siib7x0/ oi+gqbmilar 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 she will feel from the rope. (Express the result in multiples of her weight.) (b) In/iob xb7ig0q+ 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 usz.fq 9 n7su:goetb y4ve9ew4+ ing 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 alb.g7yta-w02ykme 14 kawv/cw( b y :uplowed 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 fielw(cuf2nswfjm+u /c3.moc4k8d inclined a j3n( uwcf u8k/ms2o m4fc+.cwt 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.