Why does a child in a wagon seem to fall backward when you give thzl4n(gz9oky) t q t0qv i,9yt*e wagon a sharp 4ytl(in 90zoqvq z,tt k)y9g* pull forward?

A box rests on the (frictionless) bed of a truck. The ;p vygudawj6k;, /2mn truck driver starts the truck and accelerates forward. The box ;m; 2kv/uwdp6yg,jnaimmediately 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 zeo t+bx6/-kz3 obglst)gqc * +dro, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration ba5b.q:; c1 glgzai i(inl90n? Can it have zero velocity5q1gbanl; (icza9n: glb0 i.i ? Explain.

When a golf ball is droppedh-s;9icqq f+i x1wb),8yygb 3 wxa)rd to the pavement, it bounces back up. (a) Is a force needed to ma8ibc w -) fx3sqd;,qwr+iy)agy19x b hke it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in th 7dh0 dae f)o;cnl9cv9e opposit7l)vn 9oefh 0add9;cc e direction?

Why might your foot hurt if you kick a heavy desk or a walccnkh-8 tvo+ft2 +2iel?

  When you are running and want to stop quickly, you must decewc(/vck*qpi ; yo: 6bdlerate 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 pers dyv(qi c/w*;op: cbk6on running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from daqh d(iub mwyz6u0qku;5 , 16the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person 0q uaudk z,q5dyu ;6(hm6ib w1gives 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-tik4 3, exkq:ukg rock is twice as great as that on a 1-kg rock. Why then 4u:i,ktx ek 3qdoesn’t the heavier rock fall faster?

Would a spring scale carried to the 4n r ht7a9,e nniy p:s0on6r/zMoon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kil:azne,yrih o 0 r7p6n/4ts9nn ograms?

You pull a box with a constants yestlpozyb:o 0(q) dmi;.- ; force across a frictionless table using an attached rope held horizontally. Ifqb; pmsy0o)ltd .iezo ( s;-y: 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, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity t onu 6hf rom(4es7;o0zttm5;phere is a net force mg exerted on it by the Earth. Y( ouzofsm4tt 7rpo06n ; 5me;het 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 c3m3c.xt3mo+ s2au0o p b/vm 0kpao5r the Moon with thes2 p33/oom 5ama r m0b0uv3 cc+tpk.ox 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 and on Earth.

According to Newton’s third law, each tfsam ) g46;i7p 17je7 usijoqaeam in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will wj)uaq is7gi7se 1mo 6p;4f7ja in?

A person exerts an upward force o9b6-o l lwe*p+d7br yq 8ppa+bf 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it b+ p+waqb*-9p6l bydep 87lrois exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert l/pl0u k -rw+qwx2jd3on you? Wh0kwr+ud/w-jq3x lp2l y doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when tpvv3prd+-sc l zi3z9w 5x+o,yhe victim’s car is struck violently from the rear. Explain why the head of the victim seezyp3 5rspxv3w, + -i9c+dlz ovms to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When thvwa)cad:40mj4pq lb 3e truck accelerates, the crate remains where it is on the truck, so it, too, acc)j0aa4v4d:3 q bwp clmelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Afters*kzc+d y,o3x the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Whyo+ykd s*z, 3xc?

What would your bathroom s:j. h rt3g ua/ycf0yz0cale read if you weighed yourself on an inclined plane? Assume the mechanism functi3rg0:fu0zayhy j/.t cons properly, even at an angle.

  What force is needed to accelerate a child osem(nt .bfi:y33 oud e7+1lgtn a sled at 1.25m/s$^2$?   

  A net force of 265 N ac-n;jryidoi: wgc6gc9hz -x 0h+ ke.,pcelerates 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 accelerate05t9myp2 ejf v a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a1ja8 yd2vu/)0yaz zo wv7q2tc $76-\mathrm{kg}$ 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 reqs cgb7b5sqt 71bsl8(duired to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h? st51b(b7s 7bqsd cgl8 -  

  What average force is needed to accelerate a 7.0 3ozyow/ +:jjg5m5dp bc2axk 00-gram pellet from rest to 125m/s over a distance of 0.80b3j2ymw z5+5 op ga/0kdocj x:0 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of 2.fg6 x9yr).t va5xy gf9.ar)v6t $\mathrm{~m} / \mathrm{s}^{2}$ 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 trac rdly(xxnpm ky1. /c(0k (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 tha vfh5);b: lqm88l mmkfe0sqv, t the maximum acceleration is 0.0680 g . What are the maximum and minimum for, v)lm 0m em88 ;qb5sqhkffv:lces 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.pw,b2vf*2 sr m 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 direction of acceleration.sb ,*r22pmvfw     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. What7clvx 30:;iup.kqfu+ h hg kb; maximum upward acceleration can it give the elevh3hc k70ivpbg fq+.;uuk; :xlator without breaking?    ( two decimal places)

  (a) What is the acceleration of t xrnt0xw6/4:pq+ m5m ,safsmowo falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-four/f+n,s 6a rm: m 4xqoxps05mwtth 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 v3btd8ah 9h4hxxcr1:hb 38li 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 (excluding legs) is 42 kg, fxi 4hbh1 chrv33dtl bh 8a9x8:ind
(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 )rgejco5f6v0 4hs 9x 8nqso:zbox runs vertically upwar9g rqxh5e n fo46oc0jv:s)zs 8d 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 other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body did 5zsoehejzkdhsi hs39 6a) z6 7*)gh4agram for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagsfngmc 6:zdl ,nt -uhv2ycl9-f.28 anzy sm6 8ram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has le-.s862mzln2nysnhum-y 8fv t c,daglzc69: f ft the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650 cs6m9ukg;v,5qs 5l fu-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustra v,su5 q5sc 9klfmu6;gte your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung u a,zl( jxd/c3horizontally between two buildings 10.0 m apa(,jl a3ucd/x zrt. The sag 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 hankqg*spes* awh,6)g)p ging 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 14.0fb vg/d u*l ,)wxde+wb5a 5qf8$-\mathrm{kg}$ 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 Bvza xf-t(:7 3gaeatbg 3+bvp+ase, Antarctica, as shown in Fig. 4-46. The s(a7-+ ta+3t b:fzgbgavexv3p um 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 3b;v, afrhhpgv4e5(v pulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension (gav v4pr3 ehvf5;hb ,in the coupling between 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 herself upward using the bucket-pulley ap/txzn/ 3sid7jxe4u-u dbn8/u paratus shown in Fig. 4-48e//u834z isbuu dnd tx 7x-j/n. (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 began,/q()8vippu.q hm7. q rvn,nyo 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 block51xxk.t*t xee (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 a bskg( 4eg q,6ujltpey*4/) vdre in contact with each other, as shown in eg,tjdk4yg4sv(b *l6 e/u)p qFig. 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 afbyba+3q jjl6; er )0op)o7uabove 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 thejqa7+eob ojp;yl b ra3)6)0fu ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictiok7xm5:w9l ymy uq*vpud, *vg +nless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each boxv u +*m5xqkm 7:*wudygypl9, v 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 kinetic fricti wb x.:b4c,voa8wag/zon 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 requirk)o-hdbd5ek+v pk35y ed 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 trainqm7sf4jnv ,n: accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you arfsv n q,4j:n7me not to slide?   

  What is the maximum aa:l2h 99t brcz(rdz l*cceleration a car can undergo if the coefficient of static friction between tht* lchd9z zr2rlb(:a9e tires and the ground is 0.80?   

  The coefficient of static friction between hard rubbe0 u8ylgdx ,w,jr and normal street pavement is about 0.8. On how steep a hill (maximum ,xl8 uj g,wy0dangle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4.80 0g2sgq (kay(h $\mathrm{~m} / \mathrm{s}^{2}$ 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 0ojd5oa v 7tq-f8x.gq30$^{\circ}$ 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 verc r4 5qu p5kmig+pu17vy high coefficient of static friction. +i upqr417 mgc v55kpu

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

  The coefficient of kinetic friction f r2(yfr( ia6++c* z)llw wjuajor 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) /: itgyo, cu9lmj, mv;how large a mass would box A have to have to prevent any motiony/,9to:v; lguc j,mmi from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, / 3o7vewr 6in)p/u tmwgiven that the c6pu3o /i vww)m r/7netoefficient 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 c 0k0rq--wpe d 1fv89jm1tpgw gontact and at rest on a horizontal surfamrg p0pdgf- e9q kv1w-0wt1j8ce (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of statitg:z5k mda2t;c 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 slidez gt:;5ka2md t against the cab of the truck?   

On an icy day, you worry about parkingt+jub(-m4o4:fwn)vmsh9l a h your car in your driveway, which has an incline lj)wa-h49s + uomf:mh4( tnbvof 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 withpe 3mp */u9q(jz z9xdl 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 lgs t(uni)p3x .ies 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 initial1m x2 *d9fo7socx3 jll 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 h lt-fl.j2o*thr p5il2 ill 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 x*: 6ecrao -d9si;x erit with a force do-xi r9a:;rcx e e*6dsirected 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 roofszfhj(t +rd8o * can become dangerous projectiles as they melt. Consider a chunk of snow at 8*dr (o+ hzftjthe 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 fvmdurf2g9knd:nx94()es2( ;x fz +)q xg x aoior an automobile traveling at speed v is9i22kg)( f(d9gxv+o )d f4;s:xanqxrn ux zem 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 8z+rzj6w )ti gforward on the dash when the driver deceleratesr)zgz8wti+6 j 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 bvfb3*(6ja/i qr :m7imr7 tj tspeed $ 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 6ce g5usl2)nafilled 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 static friction between a box and the belt is 0.60, whatas6)l en g5u2c is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction betztz/tgonvq 120j 6x8et+zv e8 ween $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) ce.),lcp/g6a av s):ylf v5x rwan 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 modelt7:, hztc7zeoe ak .fpi .n88k of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0.f87khzka78p . iz.tneet: ,oc 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 aqa357xb9 rqz*io k7 ex nc,17iq 0rfqputomobile crash if the deceleration is no more than 30 " g 's." Calculate the force on op1* xq7q5xk0 qi9e,cqnai 7bzr f7 3ra 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 an earthquake is a)r6.3yj:j9i hj n:vjkz (pybs , and if an object is going to "hold its place" on thjjbiy:pszj)9hv k.(ny: r j6 3e 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 jxpwns 4 ,67v0tjmk-q accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before cs, 4j-kp x6vn7tq 0wmjolliding. 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 7noh 0elgb*a3g3ev j8 down a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom afteegjg lo*3a b03v 7enh8r 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 Leaning Tower c ifw2ufi/ytn9cxie )b- ,09c of Pisa and falls 55 m before reaching the gricy92 ife0 t iu9f -xbc,c)/nwound with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s 6a9s- 5 +m56j,jdzah2oud6gsehsv:w nfds u9but enters a muddy stretch where the effective coeff:ws- uhm g5sf 6oe+96 96au sdjan5dv2dzjh,sicient 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 working on the redesign of a hilly portiond6br g,qko;bd(zf;y ct+s;v . of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particul.f;vy b bq+gro 6;zcd;(ks,dt ar 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 3 m1cxq/q1 kwualre45watch from a thin piece of string while the jetliner she is in takes offm1r4lq qak uwx13ec/5 from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several ramps connecting diffm;.-8pkqht.w+zq4ur lz 6roperent parts of the stotkor z 8lq zu.-+rqp4.hw p6m;re.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mb3vc dshi6b xk9zp5:) ass M ) using the pulley apparatus shov: h ip)d5bb 9ks3xzc6wn in

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

  A jet aircraft is accelerating at n. ei87kj wm:t3.5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-restrain, pgiwspu, u-9f)y 3dot chair, an engineer considers the following set of owsid p3f )ugyup,,9- 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 traut3c9d b*k/btin 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,r; pt6i o+un pf/ efq00lhef;/ use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (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 +nf/lof;h q/;r ieuppef 60t0his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is *uku* hudjn 3: rr66bcusing 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 buil zr5: w oibh 9daskk,83(vq9rtding 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 ascend g*;bsb(az *ooing an ice field inclined at osaozb*bg ;*( 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.