Why does a child in a wagon seem to fall backwabcr w2rv.;; .mb+ jejard when you give the wagon a sharp pull foew; v a+r.rmj;b.2bcj rward?

A box rests on the (frictionless) bed of a truck. The truck driksi*btltgi55i/x2-ll bbx5 : ver 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 Newt5:*sxgii ilbllb5kt-5x2b t/ on’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 qvj t; rd k.s-ldpy::-g*vgl7an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object hmziy :d (l,56m*zlalohx x,) pave zero acceleration? Can it have zero veloza6p imxh ),,xll :5*lzyd(o mcity? Explain.

When a golf ball is dropped to the pavement, it bouncef r)fg jc+zqup-r 9et ca06/g;s back up. (a) Is a force neeg0)pzcut c /g-a; +ff6erjr9 qded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating t +x7l l355mkg5dbmvm on a lake, why does the log move in the opposite direcx 5tg7kl+mlm 5b3mv5d tion?

Why might your foot hurt if you kick a h7v q/.nv t*ch :lwrc(.sv3 gj).cp4sx ixpb2x eavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate qu h,k7ntpyev7 suq) /kzt.p73 aickly. (a) What is the origin of the force that causesthsnkt)/ap37.,zu7pq evk7 y you to stop? (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 fine thread from the ceiling, and a sectix-k p.memx3 2kon of the same thread dangles from the bottom of the stone (Fipx kxk m3-me2.g. 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 your answers.

The force of gravity on a 2-kg rock is twice as great asx(o +p k5ur/9n8rzqd o that on a 1-kg rock. Why then doesn’t the heavier /rrzx 5op9d(q knu8+o rock fall faster?

Would a spring scale car16spfsk tz1b cv2v,f- yu c;w7ried to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kilowtfuky16v1f svc;7, b s- 2czpgrams?

You pull a box with a k3u42rromtd+7 b.t izconstant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an ano+.zrr47 2dtbki mut3 gle 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 freemc /nkyv p3cy*7v .v:cly under the influence of gravity there 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.3vpc/c* n:ycy7k vvm move?

Compare the effort (or force) nee5diulpb 6 ph58ded to 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 b8pdhup l6i55 object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, eac2x) 3w rk t,b0n3v a)bovd2eueh team in a tug of war (Fig. 4–37) pulls with equal force onxuae wbob0er n3))v,td3v2k2 the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of grocmp-b/qp+2 b bperies. Describe the “reapp qmbb+2-b/ pction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert on pmf4xdeh q (e0c)j mwj,(6d;k, df4hqyou? Why doesn’t this force make you rise up into the ;h(kej4,d0 dme(qhxp) q 4fcwf,dj m6air?

Whiplash sometimes results from an automobile accident when the victim’s car ylpfz2/buag*ht ki2o zg :8-* is struck violently from the rear. Explaii yp-8*labh u:g zfk*o 2z/2tgn 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. Wheum k+16qxpj2q +g8shk n the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to ac 6k sj uh21pxqk8+g+mqcelerate?

A block is given a push so that it slides up a ramp. After ths 2gu14aia.e hdmi+q7e block reaches its highest point, it slides back down but the magnitude of its acceleration is less si d+ .ag4m2e17quiah on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on -xum2p1vko8l53p ur s an inclined plane? Assume the mechanism functions properly, even at an app8rl3v1x2m suk- uo 5ngle.

  What force is needed to accelerate apxb8( eq p8oa0h(3 .y htdiw7k child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider atvg1azz1 9(j))ipwsot 4j c;oz 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 usew272g4tv,e2 yt fbg bld 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 kf:golfk9h smk)i k9. 8ys0 5h-rw:bg$76-\mathrm{kg}$ 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 um1i las;96ui ) gxu5pstop an 1100-kg car in 8.0 s if the car is traveling atum16x)u pu iags;i95l 95km/h? -  

  What average force is needed to accelerate a 7.00-dnp: vs:p 0 mle+*q nf;jfhh3+gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rj:nn*hp fm q;p0l:ev s+3hf+difle?   

A fisherman yanks a fish verticallyrbxho9 9re ,7n out of the water with an acceleration of 2.5oh n,r97xr be9 $\mathrm{~m} / \mathrm{s}^{2}$ 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 el j )n7i44bols 6dez3track (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;13r co4 1fhx; oqvllr so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor slfr4qoc1lo 3;rxhv 1 ;hould 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 the0uiyqbou,83 +bv y f9d elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elv,8+309yidubfu yq boevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,7,fui;wklo,xx-1yn b + 50 N. What maximum upward acceleration can it give the elevator wibixw y1fuln; x,+-,kothout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky 2 wuv3o; jl6yhdivers (mass 132 kg including parachute) when the upward force of air resistance is equal tlh u6 o2wjyv3;o 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 he strimfqf lywyk4mo4+5 :s;kes the ground belosm4kl;4f fqmy 5+oy w:w, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, 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 rskkl; 3o0jof a lf0e23uns vertically upward over a pulley and a weight is hung from the other end (Fig. ljaf0ko; 2 slkeo330f 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 for a basketball pla zl+9fgu: rec;yer
(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: hq(brgmv-2k. hnsj sn f)2:z it is hit by the bat, and again (b) after it has left the bat and is flying toward the ou)g h.2q:snjr h(kz: n 2-vsfmbtfield.

A 650-N force acts in a northwesterly direction. Asyeu8ku9 b3)a q4+y fn second 650-N force must be exerted in what direction so that the resultant of theu eykb98f y3qa+s4u n) two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontalxf f8h rjgt+*cqpqxo24: :da0ly between two buildings 10.0 m apart. The sag in the rope wx*gorq2tpahx4:c f8q0f :+jd hen 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 masslep+bx-qhw e8 3d8usm(nt ra d- zt9gp+:ss cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.0mh1ih+*w b ;un,lhq fqnec0n h1-,, u6;c pexm$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at McMurdo Base, An3fof:0gqvk 2x0 *nyestarctica, as shown in Fig.so 0fevxq3g kn2fy0:* 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 t :;l(/mvs*-xp-i en bij;h iofwo cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tensionj- ihiv*n -;xl/ osf(mpi:b;e in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the5 28pxzwuvme 6j+2nyk+ ohr6 t bucket-pulley apparatus shown in Fig. 4-48. (a) How hard m+m p6x2kw5t jeo6 n+zyruh2v 8ust 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 racf+cqg ( xmyx s9oyo ,:40wnm+he began, 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 (mz73c q2hfch za2nbt3 )ass $ 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 sur* m/bewro1 zfl .a.jv3face are in contact with each other, as shown in Fig. fo la3.* jrz.mw/v1eb4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above the grou hn4bep).ce: cnd, 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 then4 pncece:.b )h 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 a frictionless 8jdc nkjnduo9+7 r-+b, zzjac; d.y:atable 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 tzyjn+jdb +judn-9c z .78a,ado:; kcrhe free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic friction between a5jm8 m gkx0bi7 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 strqs2/ k3wphc7w 6xl.rart 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 us p/ 4 vklv,0cbu9y,ycoefficient of static friction must exist between your feet and the floor if you0p /u9v,u,ksyv yc4lb are not to slide?   

  What is the maximum acceleration a car can undergo if(2w2 io- kgg pmbopk7/ the coefficient of static friction between the tires and the ground is 0.80? 7p2/okgg p2(k-bwimo  

  The coefficient of static friction between harvy4tx,g)k66lvi7dit ,7 ms qc vv :m,cd rubber and normal street pavement is about 0.8. On how steep a hv k d,gmqvtv46im6,7 )7xc:y, vls ctiill (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 :yd+4lesfw*zr3jt9kvfte8 ta 285-m-qkem b at -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 rough 30lmnsi6, 29pz yx6jx2x $^{\circ}$ 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 sur1c spz 4q 9qzarrg:(t; 9wa3dfface have a very high coefficient of static friction1aqq4z sprf(at3: rzcwdg9 ;9.

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 kinetv.je3vg* h l8fx34h4lxc l5vhic 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 large a mass wo fg9tma;n2txjr 1yd1/uld box A have to have to prevent any motion from occur t;jrf9 xgm ad/ynt211ring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acro cqnbzbs5vzhic2) 3 -,ss the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the pucchz3v2 n -)zb,bqis5sh imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contall*(o/r:jbos :j lix ;ct and at rest on a horizontal surface (Fisbx ;oo:rjlj l:*(/ ilg. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a +o ,wlr u hx4*5it;njppjmr21heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate an *p hj1w pmrt+o2ur,;xjn54ild still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your drive 6tzo.iluo. 8tway, which has an incline of oi .tu.lz 6to812$^{\circ}$ . 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 28iyr -y5u cjk)6$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an angle j-9v)izei2hsnktf8z+c vf 8;* ntf 2g $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of lxkd*bn7f9yyn ,4p :b 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 40:pukp mjxn ck;ek(gilg20/ z:;gvttop of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough waly ay0ef/p -wi32 +qikmm4thum y13-dal by someone pushing on it with q4i- hd+-mu2te ka/a3 iy1p fw0 yymm3a force directed 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 bec1/lfd 6i hdf2jome dangerous projectiles as they melt. Consider a chunk of snow at the rid h/ildf1f 2j6dge 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 stoppingoqi (vef8rlz20 o v//s distance for an automobile traveling at speed v is equal to sq v 0ve2r o(ofi/lz8/ $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 8kuy jyazj8h 7 79zso-dashboard of a car slides forward on the dash when the driver deceler7y7 z-a9jk8hjuo ysz8ates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m ip2ifye/,*qvxfh d eu+x:+9 kwnm l85 us 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 they are filled to the packsqa*x . 0sn+ading station 11.0 m away. The belt is initially stationary and must finish withq d+sx 0*sn.aa zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kic;hbp(w / ss ;hvy(1wtaijn- )netic 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) can coast dow 59nzvhidct( (n 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 approximat5mh ;dho /:4voxilc 4ny7z c98;vu iblely 20 g io 8 dhlv9 l;5c4c /;xzbh 7nu:y4vimoof blood is accelerated 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 t7-mz: v 6 40 wjnbwyiuffb4j2chance of surviving an automobile crash if the deceleration is no more than 3bwj t6 vbnwi4mj4-fuy2 :0fz7 0 " g 's." Calculate the 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 earthquake is a , an7l(q*vry:m*u 4h a jxrd if an object is going v4r u m q(ya:*xj7rlh*to "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident involving tqqt lx.e3qcng*6-c 46jdqje7 wo 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 assumigd 6-x3entj q.*c4q jle6cq7qng a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m - j7tlo1,7d4wrylc t itraveled along the road, the elevation change is 1 m). How ricyd,tjt4l o71w7 l -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 )3 *:c(1xke6wdc bxpj -hoqtnthe Leaning Tower of Pisa and falls 55 mdq6hbok -j)*:c 3en(c wpxt1x before reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady dphf-+he; jlnnx-00pspeed of 12m/s but enters a muddy stretch where the effective coeffic;pf0-d hn ehnlp+ -xj0ient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly po+;4 k2* bpece+h cckjzrtion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hillzec4e*c+ 2 bcjkh+ k;ps without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiment n 8aal0y*a 8mvtra)/ms, dangles her watch from a thin piece of string while the jetliner she is in takes off 08mya)l*8mrva tan/a 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 supermar*85lzht xgo7 yket, there are to be several ramps connecting different parts olx7*8gyz to 5hf 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 lift the piano (massf:ahih0z t yg x-3zs1ch6zmx5m) jx-/ M ) using the pulley apparatus showhy50fj xzs-mhtg/x)a1-:ic3z hmx 6zn 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 afm+s*7 gkfih7 sb(u(st 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer consr fgyh*)9a:hss9y nj13 wd/f oiders the following set of conditionfh dgy9s: w*af/hr9j3o) y1s ns:
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-car6 0p8rh yuga+s Italian 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 s*h2v:j (x4jv *sya m6tdrpwame;h. /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 distanc*(amphw/*2s;jyvjer hd 4:vx ma6s. te 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 boat is using a i55qx; vp g7ow" 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 allowejyjr5f762uohti vs/iar2 h2 :d 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 whs02uddw ex+/ cqgz1()qz wny* o are roped together are ascending an ice field inclined2e wz1wx* (s/quzyq dn0)gcd+ 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.