Why does a child in a wagon seem to fall backward when you give the wagm o )s4zip.i(gon a shari(. i gzopm4s)p pull forward?

A box rests on the (frictionmxt-g7 d/jtmr*r w0w2lnmz 6,gj,o 7xless) bed of a truck. The truck driver starts the truck 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 st70rml n6gjx*gm x 2t7mwjw,/z -r od,tanding on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an obje. -mrwy6y0eifyaa y+6ct is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zc9fn jx8e; ss/(a rwpdhwb;,1r52sg jero acceleration? Can it have zero ve51ph9,r s2r ;d8fxssga;jjwenb/wc (locity? Explain.

When a golf ball is dropped to thav+ b-q7)7do uau.k5nl iop4se pavement, it bounces back up. (a) Is a force needed to make it bpu7b)u4-7 idn+o5ql akvoas.ounce 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 the om /r:8z+9ia: )dr/ uihf:) 8jumflzp9plrvxmpposite directionl :rrhl8m/id9j) f: /i9xfpzm a)+puuzv :8mr?

Why might your foot hurt if you k lngu-j30 je7bjj9 fx*ick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate 7yov/tl)1e ,6nexp ue quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum r1ueto6,pl ey) 7v/xne ate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a finl/ m7j:w4d rene thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If nrdem /lwj7 4:a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twicralf qz 68m3uxfj*n0/e as great as that on a 1-kg rock. Why then 8z36qu 0rfmn xlja/f*doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give w4 tw7ga,h-0-;q er*1h r8t gkg4 yxzy;pbewlaccurate results if the scale had been calibrated 1,rtw q 8y44g;*ky erglbg- a-wzh0;e7wtxhp(a) in pounds, or (b) in kilograms?

You pull a box with knq r fz,0)ozdhf +9n5a constant force across 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, (b) increase, or (c) decrease? rf+hno ,d 09kfzn5qz )Explain.

When an object falls freely under the influence of gravity thereipka,i0 g(2 yb is a net force mg exerted on it by the Earth. Yet by(p b g2,iki0ay 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 toiapf3c -d.b) d 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 and on .)d cf-adp3biEarth.

According to Newton’s third law cw4up:x9 p+wm u72nr.a*whpf, each team in a tug of war (Fig. 4–37) pulls with equal force onapf x pw9 r4*wn+p.whc7 u:u2m the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceri cm2ue 2b;x9 q3f(qleoff/3mtes. Describe the “reaction” force (Newton’s third law) by stating (a) its magnicxlbq; 9mf3m2f2u/3 ef (toqetude, (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 ao :4+hc5b*w5 vmhfcdl force does the ground exert on you? Why doesn’t this forbv holcc *h:545wdm +fce make you rise up into the air?

Whiplash sometimes results from an automscp842ec x 4xeobile accident when the victim’s car is struck violently from the rear. es4x82cc4pxe Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed kn vid81ui5jl)*a tw4kt j5m:truck. When the truck accelerates, the crate remains where it * 5vwn 1:ilu5 m 8)ktkd4jjitais on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the ; v4; ,karjdisblock reaches its highest point, it slides back down but the magnitude of its acc,;arks ;4jidv eleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if5 g puh0b15xqe you weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an anx1 ubgph055q egle.

  What force is needed to accelerateu /w v,ir(mfmk+maqohs - wv,f )p3(zda1f*h8 a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accea2y:d dm,qiua hbq(pia6:x:+lerates 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 accenggcb e6/ef6am1 )wq/ lerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight os fp 6 op7o-(2a4jgivof 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.w /a va90epxx90 s if the car is traveling at 9 e/0w9xvxpa 9a5km/h? -  

  What average force is needed to accelerate a 7ayfa ztq1+u15on 0 ve5.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a of et5zvn0 +q51ay a1urifle?   

A fisherman yanks a fish vertically out of the water with an acceleratio;;pwoideuq 20)zd lm1,42lr ajgw kk:n of 2.5;4lw ,1kidkr2 l gu j0:w2mp;zd)eqao $\mathrm{~m} / \mathrm{s}^{2}$ 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 tr)716n aaqo sj-:wr3pww by- p+j4v yjyack (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 ; )e/ wf+xe0 9jjpfnogfi)l ,r) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximumf) )9n fjj;e,+x wl0gip/oref 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 x+(zwk mu 0,vascale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s,mx 0+zkw(ua v regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximu9abd (wtk.rbas/r. 0f m strength of 21,750 N. What maximum upward accelerarwr dbsat.fa/9(0b .ktion can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includinvbp iwu8f1ee420-ai mo us)h1 g parachute) when the upward force of air resistance is equal)m2 vu fi4sepoe8-ub1wa 1 ih0 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 roo7( a3mjq9glfxl5k,p:3 js*qid)3cq)ih f pll f of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates ovef)j3cqj7 gk, a) f:*i3p qldpxll5iml(q39hsr an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertx2xxai ;8er*w50mu fsically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the tablxeasfi0m;x wu8*x2r5 e 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 diagram for8*yn bmgz 3hle/m z9.rffuo, 9 a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) f)q:a+6ja8dlne* 2 jxt iz)pyat the moment it is hit by the bat, and again (b) after it has left the bat and is flying toward the ou)azf6ed2 x:)j pjtn ya* 8ilq+tfield.

A 650-N force acts in a northwesterly direct:viu-dzj pa3 cnna/ e-..uew. ion. A second 650-N force must be exerted in what direction so tha -ej3.i/pawezd c -:. .unvunat 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 twohwks 7t, 9i4rr buildings 10.0 m apart. The saghis 4r9t,7 krw 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 hanging by a massless cord from anot,u-k od9kuq cr;7 .t*ck k g+11yksfkvher 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 14.0fn4 :a++(.m2u+cnpgu lirt e f$-\mathrm{kg}$ 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 housiqyag/+vp39 vz av,5yzng unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces 3aq 9 zv+v,pyv/a5zgy$\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-47-5elavxkr,hkg5im93 . Determine the ratio of - 5kmlk,eh9g3raxv i5the tension 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 uyn/c*i .eeal-mn j;6bsing the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly ae; /alm bec*n y-n6ji.t 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 belk,e of*wc: 5zgan, 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 (m //ek(nisf(qd:nwxe 1ass $ 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 hojn) qd ixrw./-;hr m9irizontal surface are in contact with each other, as shown in Fig. 4-51. A./ 9d rh)xn qi-;mirwj 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 o awqj(y;fco t:m0d pu71( 1hgabove 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 ground. This is its o1a(hgqj0uo (df 1wmp;7y c:t"launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionlei7hiz6q8kw6 bss table are connected by a heavy 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 qb zh 676ki8widiagrams 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 frictionfdda*z-nuhjq sd69 6)gx wn;( 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 as2yq5wi ws xbfq2 x-.) 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating ay8 *4r29effpz xts rd2t 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide? 2rrey t pxdzf82sf94*  

  What is the maximum acceleration a car can underg/b1mne9 *bjd to if the coefficient of static friction between the tires and the ground is e*tj d/nm 1b9b0.80?   

  The coefficient of static frict e n8egv7km1v da raene(8-c*8ion between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximumemre vdv eae ga nc*88-k(71n8 angle) 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)5x0xoo bfx8k $\mathrm{~m} / \mathrm{s}^{2}$ 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 roug 3re8)ygk r6oqvkw ,b*h 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 vw0 75gsyv2qi aery high coefficient ofaqg y0iv 5w27s static 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 k. uz/qnxplf2drxh ,(: -2osxyinetic friction 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 (Examjl.y uvo 7:h x82osz ow6i6ce/ple 4-20) how large a mass would box A have to have to prevent any motion frovi.ox6eyos7:6h 2o 8/uc zl jwm occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it g wmto3fx 0q14mo, given that the x30 m fqtwom41coefficient 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 , a2 dt3+izg uwn8re in contact and at rest on a horizontal surface (Fig. tuwd nz32 i8+g4-54). 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 coef8mvw 0p;otpm qoa(j d/:slk l74ij49r ficient of static friction between the crate and the bed of the truck is 0.75. What ir ml:mlk8 jaj s woo/9q07vp4;pd4t(is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking ev xbuz53* u-jwb )*vo/ppp/4t5shph your car in your driveway, which has an incline5pjx*3p -u/ 4vhezu5sw*)bto/h p vp b 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 a sliqf7 5u*nc kkf wck;0i8de 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 dj(g*rnld)w, f,( ucpplane 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 initial spe59 ino8l urbq a2w,f7oed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed ogap1ro ,k iy+l +s(j28 u-ywdnf 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 jj8af0+ fwg,x-tdj l 8against a rough wall by someone pushing on it with a force directed upf0jt a gdjlw88,x- +jfward 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 projecyohmt g+ /cfp4 45k1+hmjwed; tiles as they melt. Consider a chuypo4edf1hkthc/w4mj5g +m+ ; nk 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 an b52 uk6 gv2.kx bvrln(automobile traveling at speed v52r. kxvnkl2g b(u v6b is 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 forwarqh re1s eux(,ne9 z19 w7x8/gur-koi.ne c2k bd on the dash when the driver decelerates fr,9okeznc8he1 u7(2r1/s q kbe.x9iw ueg-xn rom 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 b3-fc;5 p;kxl/takia 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 conv, ,:nu7)j voc m/dl5c.arbuipeyor belt from where 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 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? c jmpriv,7ob) 5u ,dn/.u:acl  

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 kinetij 7pvxg.aplz: /e)zo 8c 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 the bicycle) chlc.vtfprq5z ti219k; lu*h 9an 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 mammapb:jyu 84/nd +k5 +f xrbcqop3lian heart, at each pulse approximately 20 g of blood is accelerarq4dypfc++kuoj / bn5 3 8p:xbted 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 su kr,)-1l iielom*vu7 :;szmserviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the1ekmo*l eis, vr-is7m; ):ulz force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an eakah lu+ko.i.(6e: h bg2s:z nvrthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of l :: vn.hgkh2(oa.sk ei+buz6 static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident //vrsy v oo2elu xd/y7.b 32sqinvolving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubberv3xo y/oy.ql2vsbue/ 7 r /2ds 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-kk)a/xga7 hz k46ek0nin-4 hill (1-in-4 means that for each 4 m traveled along the road, the eleva0gah ekk/ 6xn7 kaz)4ktion change is 1 m). How fast 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 the Leaninguy/wk zz823;ghalz1 2 g tk1bo Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air res/g luoy1kh21w2t z83gzak bz;istance?   

  A cyclist is coasting at a st,5 q-nxbz *ihxr* u;oueady speed of 12m/s but enters a muddy stretch where the effective rn x,u - zuqoxh;**b5icoefficient 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 hillypoqh9a4 /kqt kd3y+:o portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , cand:/k9 4ayotoqp+hqk3 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 watch from a t8kba7jc1i gbh akv;f q( v7+4ehin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an anglibc(f;ja7gke+ 87ka 1 qvbvh4e 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 severa gf rewl ewd37l7u5(7ccn3-kd l ramps connecting different parteu3-dwnlfe5(k l7dgcr37w7 c s of 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 l7s a7 cp7)7j6 gmuhjslift the piano (mass M ) using the pulley apparat6a)cl hujjg7 s77ms p7us shown in

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

  A jet aircraft is accelerating at 3.5r5 kaov. p8pf25urb+xm30u o2ti 4wvv $\mathrm{~m} / \mathrm{s}^{2}$ 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 fowv(187k r(ecg zkx2h lr a child-restraint chair, an engineer considers the following set of condilx7v81kkzgce (r(2h wtions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mas6qfwv :hy2f7 ts 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 lengthu3 6+l7mde:lmu krs2yh v0lm 1. 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 resu0h+:lmu mudk ll76evm312r yslt 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 ek)0 )jyf hh2 mr*r *;clsvnd0is 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 fu22ygvzd*, 6if9t l3+a rhn tbuilding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together are ascending an ice field inc;txel un* ;du /p+rw;fyb xo t/n3-ci6lined at o/n-bfuy6iutlx;n / e3x+; r;c t*pwd 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.