Why does a child in a wagon seem to fall backward when you gi 8u:6wy c1jwhu wcnr6g (us(o9ve the wagon a sharp pull forwaro(9 8cucuy(6nw:h wj1uw6g s rd?

A box rests on the (frictionless) bed of a y lu)ti -+k/bl5t;z trtruck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truct5t)u/; kt -rlzib+yl k 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 forces acting on i8p530t 7dxwuk lca3mr t? Explain.

Only one force acts on an object. Can thepvi nm(k.3/rg object have zero acceleration? Can it have zerkr3p( nm/ igv.o velocity? Explain.

When a golf ball is dropped to the pavement, it boj p+sbmy7f y :f c1w9ink6 h0fbo)o3i)unces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exerts thfs)h+ ci7ijobkb9 1 f6)yy30np wofm: e force?

If you walk along a log floating + 07vtk.p0h7do9s4 qlg o qfjkon a lake, why does the log move in the opposite dirgfpkv k+q.l9 7d j4s0o7qho t0ection?

Why might your foot hurt if e3 vp 4 i2vs-w.mwlu7oyou kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quqtl+ /dx qp53iickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using youqq3d5t/ +il pxr own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, i:wljt;z2 (h eand a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If hlzi ;we(t2j: 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 twice as great)a)pwlh 71ibm as that on a 1-kg rock. Why then doesn’t t1w7) a)hp blmihe heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if thrl 5m78drk2om e scale had been calibrated (a) in pounds, or (b) in kilograms?ro k28mm 5ldr7

You pull a box with a constant force across a frictionless table using an/eqt)vp 3t-b n attached rope held hovqt -t/3pn)berizontally. 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? Explain.

When an object falls freely under the influence of gravity +o1t w6nnwle,p+ z e)hthere is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth movz6wl +eth+nw)1en po, e?

Compare the effort (or force) needed to lift a 10-kg object when you are on th*vglk o6n53mg ;xwts)qw7nl0e Moon wi;vlx )7tg6m0 3ws5gqkln*nowth 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 Earth.

According to Newton’s third law, each team in a tug of war (Figi- n -b3mxhdd1. 4–37) pulls with equal force o in13 h-dmd-xbn the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of grocerik5shid : hofc, wuxoje1, / +0bev.x3wes. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted,d , uikhx+c .w:f boeeh1 jw0vx,/o5s3 and (d) by what object it is exerted.

When you stand still on the ground, how large e4s9e+rry gsd/0n: f wa force does the ground exert on you? Why doesn’t this force make you r94/+wr srdgs0: enyfeise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s car is e41si ak7r5dqx +fr:vf.eb u;u/ubk. struck violently from the rear. Expl u+f1be/ .eb;d7:s.rau5kqfk4r i uxv ain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When w(s ukfg.)vv. e4zk1qthe truck accelerates, the crate remains where it is on the tru.k )uvvsk4fw z e.1gq(ck, 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 thejud6l h7( uyw0 block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the asl06w(u7yjd uh cent. Why?

What would your bathroom scale read if you weighed yourselfakh8:,wj5r yu on an inclined plane? Assume the mechanism functions 8j:,ayhr kw5 uproperly, even at an angle.

  What force is needed to accelerate a ck tw t3a6 u2fqj1lp/. 9yjgzmked .1,ahild on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerat9;uz8en+wqwl (dx. eges 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 withstfp mc.w9 6 7fyd0myf4gand if it is 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 of a 7wq,w0 yvo o/p $76-\mathrm{kg}$ 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 the car i r v3(r2rmj)ekfr53q ks traveling at 9vmrfr3 2 ekj) q3kr(5r5km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from res/eu ;qxjqe, 2paulx8+ t to 125m/s over a distance of 0.800 m alongp8qua2qxu,ee /+ jxl; the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration ola3 3em ranf;cxl40n8 f 2.5l4;3m 0nl 8eafx3rnca $\mathrm{~m} / \mathrm{s}^{2}$ 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--t4kr,c 4 j7 u vw0al13qfteiomile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the maximum w a)0tz*e +8xd73o)va k5; ralwbndhaacceleration i8ww3*;n+ azd0h beoax)v5r a)7dalk t s 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the elevatzi xii(1blf 2:q,n(2dfo 5hseor begi(sxi n2iqdoz,b h5fl 2:f(1i ens 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.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has8 5ggjm 5z*oh nso41d loe kuh.*b01su a maximum strength of 21,750 N. What maximum upwarhjd8 .e nmz1g bu5log osh *k0s1u4o*5d acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration ofqz*t1:n sx ,gt two falling sky divers (mass 132 kg including parachute) when the upward ,g tsn: qzx*1tforce of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When vi8ejum-n d4* he strikes the ground below, he bends his knees so that his torso decelerates over an approximate dis dje-mv*8 i4nutance 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 ;fe*syq w.c *btable. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the tabl;b*wqc*y f.es 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 for a basketball player :.*kmt yp8naj
(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 basep5xgm: yii(++s *cyvz ball (a) at the moment it is hit by the bat, and again (b) after it has left the bat 5p (:ziyvx+g+scy m*i and is flying toward the outfield.

A 650-N force acts in a northw/xt z(.(t +oazpf.gv festerly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector di.x.zzt/og(fpfa +vt( agram.

  Arlene is to walk across a "high wire" strung horizontally between two buildva26pzrc0kr4 i 5digp0 r,j6 aings 10.0 m apart. The sag in thejr 04ra pkrd56z2i,60 pgcai v 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 ,g8ca7y 9ga h fwu+*:ta5qumymassless 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 1,o 07p5ml-y0jhxr lf g4.0$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo:zx(pfqe 6 n(p Base, Antarctica, as s6:(xeqzp(nf phown in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass brm(2d.k0tt af5 hhk x-ehind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the rt hk2ka 0hd( x-f.5tmfirst 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 usingy 961e*kvjm5 opsvdq2 the bucket-pulley apparatus shown in Fig. 4-4*e py9156vkvsd qo 2mj8. (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 3e+tqigqe9te4i,izm k (4h: rbegan, 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 h6b (5qfhe:z pblock (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 horizonp2jz w*;jlu7zx z,sy/:wjmpuh.3d 3dtal surface are in contact with each other, as shown in Fig. 4-51wpp; d*z,7ux3/yjdj2 zzwj3lhs u :.m. 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 ini3. t8dy xk3iuutially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the groundd83uy xki3u.t. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cosbgl k*h //5kard of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body *kgks bal//5h 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 k o f+s3(iet vi ) xmsw7+zdlsw2cj71ct()8ryninetic 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 starc s8.2hitvws d :8n4mot 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 as 8j t6z6zpuc6 train accelerating at 0.20g. What minimum coefficient of static friction must exist between youzujt6s 6c8p6z r feet and the floor if you are not to slide?   

  What is the maximum acceler4xs:jb(bc( zw ation a car can undergo if the coefficient of static friction be(b(w 4z cxbs:jtween the tires and the ground is 0.80?   

  The coefficient of static f e.vq(tt4npn+riction between hard rubber and normal street pavement is about 0.8. ev n(+pt4 .qtnOn how steep a hill (maximum 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 -4.89 1uex ep+2rqx0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 roevc*kaa/y 8e0 ugh 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coefficiex0 hs7yovin,(q q;s3h nt of static frisqi,y;hq70 o(vs n x3hction.

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 kinetz e3g m8 n+eh qll96cd1dwjp9;ic 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 (Example 4-20) how my d)j3/ ih,vxlarge a mass would box A have to have to predj)mi, yhx3/v vent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push z;)bjq8sb eqx :u3b y(so that it slides across the floor. How far will it go, given that the coefficient of kinetic bsxb()e3; j qy :uz8qbfriction 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 rest on tpcbvi2 32.wea horizontal surface (Fig. 4-ct2 23epvbi w.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 static frictioazoq b 93q6bjcjm: i6r7k f.3mn between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver .66j mf rmqobk3c :i97azj3bq can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about cup7,r ln f20pmzg;pw)v5j7o parking your car in your driveway, which has an incline of 1nw cup2z)0j; r5,gpfvmp7 lo 72$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a re.7wkp p f045s ee:6punm7 lq28$^{\circ}$ 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 l,pwnpp 9-n8t+zszf .ukcm 4)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 spee r62fu8 ;x s-iuara8n+ w2g+kqn5tc:iqeitm. d of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of )qsihk:k ) fzc1be; 1oucj*8o 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 onu5c-xpnbn xca:k)q bv9e)(; *c x1kds it with a force direc -dc:ekncpbx9a (5xnx*;cs kv bq)1u)ted upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projes+u:cfxwi2, u ctiles as they melt. Consider a cwc+x:2suiu , fhunk 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 sblv-9i j 7-lwnbm+t :qtopping distance for an automobile traveling at speed v-vqtl w7b+ijn 9b:m -l 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 carmpga5ef *9-a8a csxy v:/*ejqfrx 3 g- slides forward on the dash when the driver59 *q8re xx ge:pv*ac -gyajs-/ffm3a decelerates 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 a9c+y ik)4 rae m is 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 where thvb wpgln++kjnt c8**.)dxb v-ey are filled to the packing station 11.0 m away. The belt is initially stationary.jvxnbwg ptb ) *-c*v+n+8l dk 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 coefficiegu n (8a(pg 5prgi,x-mnwarvn0 m+,,xnt of kinetic 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 kpf 3vt0l012juxc :bhxg (including the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of npauq.z ba)7q5:d-. cc0 d3xfh pegv-a mammalian heart, at each pulse approximately 20 g of blood is accelerated fro5na ec h.g)fxq-pvc . pd3:0zuda7 qb-m 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an a2zb*2+q m9 bopbp. fxsutomobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a s2zomxfp9 *bpb2qb.+ 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 , and if a wev*r9nwcb20n object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at lee*2n0w9b w cvrast $\mu_{\mathrm{s}}=a / g$ . (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, examiningr y8y +o(fiz38g5 kktp the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a leve3kz k88rpio(yyt5g+ f l road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each vd5 :mlr05v7-fk ppgxr p i5h;4 m traveled along the road, the elevation change 7-pgrp;v0 vx5hfm5 rpd l ki:5is 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 t*mtbj5dv zt2:bp:y 3oigyh9pi1- /x aop of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average y a *yp93v/bhm2:d1 :izbtg xjp-it5oforce of air resistance?   

  A cyclist is coasting at a steady sp zsfvzsi-( 2p. /qr.34whdl tfeed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretcst.swzf2/ ipd4f -(zq rh.v3l h without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is wo *ms)ys(*(2jfnnw asxrking on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowinaxf(m*(2s ys*ns )njwg down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin piece ofmk5l,0 9aag,a i6drp d string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She n9g m,ar a6dk0ap 5l,idotices 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 c rc0b-lolv f0e)pp3q 9onnecting different parts of 3lrpq v-f b0)p0c9elothe store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) using the y cb6tw 6-c8thpulley apparatus shown inytc68 wt6bhc-

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 acceleratgcmax-w 5b8 1iing 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 fo-hq( x- l0*apyk khhb.z3v +scr a child-restraint chair, an engineer considers the following set of co*-yba0khk( p+z lc. shx-hq3v nditions:
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 Italiass0lg4c/xnl 6n 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 similar len; /v eu,4 9v9p-srz )c4qb i+osatlbsagth. 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 freelyola4bviup,9e;a z /sv-9+)sbcts4qr about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boan)wv7exvqu h .o p,n*4mkz2l 5t is using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed xt dw gkr*q- .h4mrjmb7 i0le*zr5p71 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 areaavu52b( rs,d roped together are ascending an ice field inclined at 21.d5, sar2aub(v 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.