Why does a child in a wagon seem to fall backward when you give tl g asqm-7(1g j+e9izwhe wagon a sharp pull forward?s-+aw jqz1e(9 igl7mg

A box rests on the (frictionless) bed of a truck. Thlx1x7u/z2o jq 5pqm:oih) fa4yt75gd e truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the xg hf/qj o7iy)a5ql5do:up m4x27z1 tmotion 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.q2jvylz -bwafkp yx ex)2)/0 an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zeruatbc1d ;1b s1o acceleration? Can it have zero vel;bus1bctd 11a ocity? Explain.

When a golf ball is dropped to the pavement, it bounces jruv2ej 36 b3lback up. (a) Is a force needed to make it bounce back up? (b) If so, what exertsrjv63bl 2 j3ue the force?

If you walk along a log floating on a lake, why does the log y)tis y:p/ij45; hfd qz(myo9 move in the opposite directij d/:my); sofy5z qih t(p9y4ion?

Why might your foot hurt if you kick a heavy pem /7 8bla+q5u2frpwdesk or a wall?

  When you are running and want to st:i s rxlxu0,)pop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? p0iu,x l:sr x)(b) Estimate (using your 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 fiox,l/ve 3 v5sa nix2p3 nbez+2ne thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain yourpa22exx bz533/nie,nv+ lsv o answers.

The force of gravity3 gfugf7-m:n,aq :zqr7i 9apk on a 2-kg rock is twice as great as that on a 1-kg rock. Why then pza9:, q7qk- 7mggu: irnf3fadoesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the biq .l4ae xi3gie4hq(2gy15 ( kejy6pscale had bee ehi (4j32q gi gbx6.eiqp5k 4al1(yyen calibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force e fuoluy0g)n9oyvz9e90za/.- p v u *lacross a frictionless table using an attached rope held horizon. u/fovpol*g uvuy0 ynzl-z9a)9e0 e 9tally. 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 inflbrq7a2nq -ep 6ypk8*kuence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the obje-ner7qp8byk2k qp6a * ct exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) nee5yemeo0h, n4w ded to lift a 10-kg object when you are on the Moh 4eon5e0w, myon 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 Earth.

According to Newton’s third law, each team in a tug of war (Fi(c/a9c j g p,)ft8twtrg. 4–37) pulls with equal force on the other team. What, the/ rcjt)p(ag 8ttcf w,9n, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of op3pknr1rvm-0j0/h0-gx - lt q e8svugroceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (8rrle0jtvp/q- pguko00n x-1 3mv s-h b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the groun:r 6rohkm d2lug8l;w(d exert on you? Why doesn’t this force make you r u6d:gm2k r(wh ;ll8orise up into the air?

Whiplash sometimes results from an automobile accident w5*jy o6im8p0qu)on r vhen the victim’s car is struck violently from the rear. Explain why the head of the pooj r8 v mni5q6)uy0*victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bemw +dr2 r kz6yz0fpko)8s et5+d of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, k5pz wsrmez)kf0t+ o+y6d 82raccelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Af760vcbp zfia h7zn/: tter the block reaches its highest point, it slides back down but the magnitude of its acceleration is lespn7/6fz i:v7atczhb 0s on the descent than on the ascent. Why?

What would your bathroom scale read ifo o jjk9y3u0a0 you weighed yourself on an inclined plane? Assume the mechanism functions properly, even ayoo 0ua90j3k jt an angle.

  What force is needed to accelevxn,ifl y; ;;krate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates adbm8,lj8 toc v0jrk04 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 ro .gt*4dnti4tipe withstand 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 9wayz -g ti45a $76-\mathrm{kg}$ 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 ucf 5ekp+k 33zin 8.0 s if the car is traveling at kczepfk 3 u35+ 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet fr1 nlco8-qh9uw3e rvvl yx:c+6om rest to 125m/s over a distance of 08o6 nq +u-3 :hv1ewrxccl9lvy.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out t k5nz 0mu56od8)bp3vvb ,zxhof the water with an acceleration of 2.)uo n,vtmhxpzbz 55dk0 bv38 65 $\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

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

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

  A particular race car can cover a quarter-mile track (402 (2/zsm-wmz4 vjmc7yq$\mathrm{~m}$) 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 accelerat pl1l/)j dudx)xn */hjion is 0.0680 g . What are the maximum and minimum forces the motor shu )dp*nxlhdl j/1jx)/ould 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 motionl7ymgyvht /)*u *eejb.ess elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calcub. ve7 yjumegt *y/*h)late the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum streix69zw* ev c7fngth of 21,750 N. What maximum upward acceleec6wvf 79i*z xration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky mv:ie6nt qmo(4i 6r h1divers (mass 132 kg including parachute) when the upward force of air resistance is equarqo4m v:ti66n m(i 1hel 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 roron*zmu2v2by qsptxmvq 6yg671+ 9)njiy+ i: of of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso dece76p:j6zytims*ioyn q1) ngy2vb9qr +u vx2m +lerates over 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 tabg51wqesukt/:xe-hv4 le. A rope tied to the box runs vertically upwardquvk :/1g-xh e 5st4we 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 diagram formwe.e 7*:hy*httyoun/9/ h e p 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) at the moment it is hit by the 8b9kficcq. dz3 o1vzlux( +a /bat, and again (b) after it has lc1(ikc+fdql/z 8ab9v x3o .zu eft the bat and is flying toward the outfield.

A 650-N force acts in a northwesql xot*jkqiz qo+t +1g1ds-;/terly direction. A second 650-N force must be exerted in what direction so that the re ;i+-1qgqsoq *x/jt l+ od1kztsultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" 8 5ebffv kqks.46t24z hb;oli strung horizontally between two buildings 10.0 m apart. The sa4t fh5 k ib.zkb6 42feo8lsvq;g in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces $\overrightarrow{\mathbf{F}}_{1}$ and $\overrightarrow{\mathbf{F}}_{2}$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $ F_{1}=10.2 \mathrm{~N}$ and $ F_{2}=16.0 \mathrm{~N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    $^{\circ}$;(b) a =    at    $^{\circ}$

  One 3.2-kg paint bucket is hanging by a massless cord from ano7pyuo9ke(g 5hther 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 14dj1cj9399o wh uwm wz*.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 hoym1m)6r,ukz g using unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forcezm)u,m 1yrg6ks $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 caf tz m bx).fbi,.:- z2lekn,n jquw7+nrs of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling betweb+xzmnk z n:2qf7b,,ef-lwtu.i jn).en 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.;tp2+yzv- y2g: ixss yd k+nf using the bucket-pulley apparatus shown in Fig. 4-48nd y v;p-t2.yksyz i2+g:xf+s . (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, a 6 v as;ygh4(7ji5$-\mathrm{kg}$ 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 blocf5qc+t h6n6ick (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with each iaevw4*6-qcofax(7 e other, as shown in Fig. 4-51. A fo46 eqcai(7oev w-afx*rce $\overrightarrow{\mathbf{F}}$ 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 eac (/ppm+i zbri ;tl+/sch initially 1.80 m above the ground, and the massless frictionless pulley iss;l(rptb+ipi m/c /+ z 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on mp(2 ;y4g.yk/ca *yjgzsjb5qa frictionless 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 sy 4jy/5.*z 2myk;aq( jcggbpcord, 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 kinecm+:d drg fj;y3a8d 0ptic 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;/kxg;m+,ddapnn bg 4 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 train accelerating at 0.20g. What minimum dr i( 1+2q/tx/nwkfqqcoef+/w2tk q q fxrdq/(i1nficient of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergp//myy )qas9ngrzv y;4q4dg+ o if the coefficient of static friction betwe;sz 4)r gvy9dqynm/g p ya+4/qen the tires and the ground is 0.80?   

  The coefficient of static fg4- zv4mlml qow hy849okn4 iqh+3t 1qriction between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car parkql4w 1gy 4oqh34tnq8i9 +v4h ozlm -mked?   $^{/circ}$

  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 f43mau,onwe( -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a n,vi l-xks*(b ct+t3rrough 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 coefwoj9f- uvckf x)n:59 nficient wv9n5-:on9 f ukf) xcjof 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 kinetic friction for a +n4wjmp pvn tr5z:y71$ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a w-ogvbec8sxi-0cw56 mass would box A have to have to prevent any motion from occurring?ccosw-ivw05b g x-e68 Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the f8 cj mfpy-:vn p)9.pcgloor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial spvp9p8ny -pjm. c:c)g feed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg a sw58b- devh;igt(-o zejz0xo71 (ao dnd 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). Agi(ae od ezv75(;th bj -wzo8 xso0d1- 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.rq.z 80s6nvnyxe)r7o The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at yoq xsevz)nnr6.7 80 rwhich the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parki;cdd4 ifa. j3wj.ux. t.eq .vvng your car in your driveway, which has an incline of 4.3.ej;ic vf. x tujad.qvdw.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 slidh,q-h ul c3uvasw,/v6u9s.b(4olkmh e with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at a7 e ag;cgch.0gn 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 initia)u8t 8g4 dbnxqezl1o7 l 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 hill with a speed of phg5+5 8 fsxc4boa;ak6.0$ \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 by2/xst*ggz.b1 3f b+df 9vho*i5 u lhyz someone pushing on it with a force *xf 9vlf/hbsz2*5ggod1 3hy+tuz .bidirected 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 projectz83 8w bp vczyk.9uwe4iles as they melt. Consider a chunk3vczb8w.p8zy9 4e ukw 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 automobilhjtw .h: iwfqln( 3/m2(yorv :e traveling at speed v is equayr3nvj:(woil / h: hw2 tfm.q(l 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 forward on the dash when tho6f oq e.io 1 +f;-2j z5b/mk.xejgrvpe driver decelerates f r6oefok. b -f zqej1+p/x52.omvigj;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 speedh0aew e/;flmnmm029x 3td3vwn 0ag 3s $ 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 whk.w/ z; v ; 1b7c064g z fmgusp73opvne9ocapqere 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 div7 c0ne;pgmq k6zcu aow4p 1/ b9sov3p;.7 zgfstance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic frictior3z puyx6)x;b,rzv;un 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 (d;nr9 /mw m,a:gbb z i11js7yyincluding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approxidnxy ;v6/ k3v-0f mek6ljck7 u6q-lsg6 8peucmately 20 g of blood is accelerated from 0p7sdv 38e u fm6 kk--vle66nc0l/g cxky6;jqu.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 automobile crash if tfe,a r81yy:lnlm2m: uhe deceleration is no more than 30 " g 's." Calculate the forc am m 8rnueylfy:l:21,e 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 prvn4 9lk ue )y0g9q8tieoduced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with eqi k eg8)uv094nytl9the 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, examini:6c-fdzbmm7 yx cf u4.ng 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 dm 4 mcy-f6uc:7bfzx.and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-w :hsmeloasv p1v 7.wnypvk:( 83u yd9w(a12m 4 means that for each 4 m traveled along the road, the elevation change is 1 m)wlm:hopy k1(puv (a 8ssw 2dy 1w:m .v7nae93v. 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 droodv( r+3 emr/ppped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air residremo/+vr( p3 stance?   

  A cyclist is coastingslgua; .s8b1 +vnyu+g at a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the spgysanug; v+ .ub+1l s8eed upon emerging?   

  A city planner is working on the r c6ms5eb9p5 v;vsq x/nedesign 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 slowing down. A particular small car, with a mass of 1100 kg , can acceleesv 55v ms/bnp69 ;cxqrate 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 piece3f 4m6 m b1yqmh*4bdoo of string while the jetliner she is in takes off*yf44b mdbqm o3mo 1h6 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 ;w(z wpa ug);hto be several ramps connecting different par)z; gpa; uhw(wts 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/g:86spv mp.y v nfv.l to lift the piano (mass M ) using the pulley apparaspv8v..f n6vm /yl:gptus 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 accelerattw*ce)i 82 5dyk ,wthbing at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-rhs*jr cf1s 7i7ieb7z0estraint chair, an engineer considers the followingbsz frc7js 70ih1 *i7e set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Ital xl,mzqfnr snk,brap0o3: 6 /d7nz:t ,ian 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 Karjb(rvhw;s d +2ow0 cn0en, 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(hdbs 0vnc0;o2 ww+j r the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using arh :tna q*w:n6 " 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 5q lw/a ,by.sc40:v zy b;ifgsreach 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 togethuj60hflu)qz0 x d5 -pver are ascending an ice field inclinezqfu0vl 6 hpx)d5u 0-jd at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.