Why does a child in a wagon seem to fall backward when you give the wagon an 4z:v2nblems+e(;xf sharp pull forwar:e+xmn nl(e ;v2sz4f bd?

A box rests on the (frictionless) bed of a t9kw2p kh2 9zmw+ts .6pmbscb7ruck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground besi7 2k sm+92wcs t.hmbb9 k6zpwpde the truck and (b) by Chris who is riding on the truck

If the acceleration o3i j00;aqklmnf an object is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have ze (8pc,85 v8p*unilium d(gggdod( sg+ro acceleration? Can it have zero velocity? E,du u + mpg5vsld8(o(pn8gigd(g8 i*cxplain.

When a golf ball is dropped to the oy 9-g2d:o wvnn3*hlbpavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what3 o*vlw:o9dg 2nbn yh- exerts the force?

If you walk along a lvt(,uoc hf,9/o qchn:og floating on a lake, why does the log move in the opposite directi9u(oh , c/ftvo:hqc,n on?

Why might your foot hurt if you kick a heavy desk21un*ajm1 e kk or a wall?

  When you are running and want to stop quickly, you must decelerate qql x,a;:j qk9quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) tq q:ql; axj,k9he 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 section 8nls2cm nit-1 rsltxsp93 ,; nof 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 l -snrmn;c 9pn81 l,2 sl3ittxsikely 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 o s3s eb/wnvgw n8f01v7n a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the hea/e8snws7wbgfvvn 130vier rock fall faster?

Would a spring scale carried to the Moon gjcu5jx 2f+m,aive accurate results if the scale had been calibrated (a) in pof mj+uj,x25acunds, or (b) in kilograms?

You pull a box with a constant force ac:ees62dnm pwt n*m)r .:8nma eross a frictionless table using an attached rope held horizontally. If mnem:6pn )m.2rs d*:wn8 eteayou 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 3aldb;( 4n.o1 wfqkrl0oc:i)nt3ve d of gravity there is a net force mg3.v dnn;k :1l b rfoe 03o)dciq4law(t 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 move?

Compare the effort (or force) needed to lift a 10-kg objectbc,;(sh: xywg when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Mo; :(bwhcx sgy,on and on Earth.

According to Newton’s third law, e9 9lal6ijwlnor.7 /(x cm jgy3ach team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will /l.ng7 a(o9 x 3ilm6crwj9lyj win?

A person exerts an upward force of 40 N to hold a bag j f) oa*0wytv6p4wyj8 of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by whatjawjo pf 8)4tyv*y w60 object it is exerted.

When you stand still on thebr.)o/cex c5hs:d7 n e ground, how large a force does the ground exert on ycs.e7) :5h x or/ebdcnou? Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile acci3*.p pcw4q z8f7qo5wbw6jfz3 f lg vz3dent when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it reallyopf wl *gzj5q4f8bcfz3wqzp.3 v 637w?

A heavy crate rests on the bed 0qe*m *v;u2i qp( ezbkof a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes themk0 puv(qi2* q;zbe*e crate to accelerate?

A block is given a push sok ,wi- /yitmi-bv( h lys2,2gx that it slides up a ramp. After the block reaches its highest point, it slides back down but th 2hy-, i/ykstv (lbii2 wm-xg,e magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourv7ry18aag4rd(a0f81vgn)c pxu 8d id self on an inclined plane? Assume the mechanpivranax gdu84(fd1 g7r vyc)0da 818ism functions properly, even at an angle.

  What force is needed to accelerate a4anf p7*hw2cm child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and r n3x 7doy9-rl+i8 phelider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a h0pk4rhro5b48tiw 3l 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight oefphieoa5 ),vf8 +jx8ndb4 p)f a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to sto4(.kp kmtdl7 d-yp2n2bw xls*1j bv5gp an 1100-kg car in 8.0 s if the car is traveling at 95kk*g-sl bd2lpd12(tx7vwk p j.n y4m b5m/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from do.6tyf,/io)nyii cz6w tn4 b .:h4s orest to 125m/s over a distanw oi.coh n, z4.t/:stnibf y)4iyod66ce of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acch(n .mo wfdhw6 6.4 cx77vpedaeleration of 2.5 m6f h67oh pv4e n.aw7dw(.dcx $\mathrm{~m} / \mathrm{s}^{2}$ 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 tracktkey:8+badrql ;7h( v (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 dex(g8zb9l; koo signed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forceb xgo8lkz; o9(s 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 n7dmxz5 gq:b1a motionless elevator. When the elevator begins to mb1:xq nm5 7gzdove, 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 has a maximum strength (8k tiad*xb(xlm(z/ j of 21,750 N. What maximum upward acceleration can it give the elevator without breakz(bmaxx t l(k8i(/* jding?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 x dvf 7)fsfe*r,b woh: (p1kh(g.3xswkg including parachute) when theop shv*d7( wxr fwx1kb(3 e fh).g,:sf upward force 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 qyx vp;q6am7) of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his to6y) a;mp x7vqqrso (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 q;h/ : yf0rqteto the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. / qqe:h;0ry tf4-40). 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 basketbal 25 foa t1/3eqdxp1ywfl player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body dkh 3iaf9zr/(u o rz6+qiagram of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and i6(zua/ r+i qkf3h 9ozrs flying toward the outfield.

A 650-N force acts in a northwesterly directi88nbh a6efn,(cq n 8hxon. A second 650-N force must be exerted in what direction so that the resultant of the68(8bann,8cn q xhef h two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horrzzx;fyy kvo. toe1+xj i 8*2gzf8-;cizontally between two buildings 10.0 m apart. yyz ;z1ifo r8zx+f c8.2x;o* -gtev kjThe sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucke- 0+ is 1d3tzv;htigyet is hanging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 1ivw kyv)5uh ou5qzi/-9fom2 -4.0$-\mathrm{kg}$ 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 Base, Antarctica, e5:6 ahnb uv:kas shown in Fig. 4h kuav:be5n 6:-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 behind it7 r5e066r xvod :jvaai, Fig. 4-47 . Detedir6 o6rve7 a:x0v5ja rmine the ratio of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus plmx qx4 96oss*qltlqtd / 8t+z1o38yshown in Fig. 4-48. (a) zlyt q+ p81*t9lm os43/8txl6soxqq dHow 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 ,lw q:lf4tdp /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 (mass s4 6bb8k-k7 pqmhyj6 n$ 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 othe 2cwi*uf9.ff ur, as 2 fw*uufi9 fc.shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown ints s x:wz/m93e Fig. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the grom /ewz9s s:tx3und. 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 a frictionlesfr s+xn 0k4mlyh)emx6ib q*.4s table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each bq6 r .yx+)xneh*m044i l kmfbsox and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kip pjxa t (o ut(85leejg-:6yh-uv /al*netic 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 reli,nzv6 . u/e zssxw03quired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What m:om4n mmsi z1zt*9oz 3inimum coefficient of static friction must exist bmz : zo14 smzo*9n3itmetween your feet and the floor if you are not to slide?   

  What is the maximum acceler,si4ft be6-ny,/lhnt ation a car can undergo if the coefficient of static friction between the tires and the ground is 0.,e f-inhb y tn/l4,6ts80?   

  The coefficient of static friction between hard rubberhpjkwx,*emk dod. m3zunc-xo *1n--/ and normal street pavement is about 0.8. On how steep a hill (maximuwd/mu.k,j3 n-k*ocp1d zxn* em xo--hm 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 t05d) rxkyjk2.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 30,8jp a uhh6.gf5 fk+;wlje9 di$^{\circ}$ 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 hi nv2d gndf*e255yqcz x6 3kai9gh coefficient of static frictiodnea9362 zn*5xvf25qi cykgd n.

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 f9 gk7etvi9 o,lor 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 (jav)d1 upxp3pa;idw /ez)ui ) k l;6+eExample 4-20) how large a mass would box A have to have to prevent any motion from occurring? Aje1xv/di;pk)w)u a; ud3 iepazl 6+ )pssume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so y*g3 ikvta:m7that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of gkvt y:a3 *im7 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and g ,/s8jsj+vsu9 p o2 pfor,ht7at rest on a horizontal surface (Fig. 4, j 79r 2sfhop /s8spjotg,vu+-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 fri0l4ska*zl:ja ;soxu7aez / dur2 1 i7cction between the crate and the bed of the truck is 0.75. What is the maximum rate d1/cka*s;z u4:uazj7lx o l0s72eriaat which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you woloe2cyy ,stl6pu/1r(g 1h d.orry about parking your car in your driveway, which has an inclil cp r2 y.l,e/1ohs6(you1 tgdne of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a 2l mz)i; zbe2fw +y e g.*m*r-ldyk(70heb ora)8$^{\circ}$ 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 pla z*(ezt6ig1id3ezzq7ezv3)pr ): fprne tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed otox- n,rus:f+kxm c w10c51il f 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 reac*-wg4v5x1pdw1i y mzbhes the top 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 wall by someone pushing .3swrw)mp+ wxno 65ff on it with a3n x6 .sf+fp rww)wom5 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 sli*hac xp ax1 s5 ro9n.u*tn8hv/ppery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge *h8 s not*u9xx.51avh r/apcnof 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 w a39f7i f d8cn*yft3ustopping distance for an automobile traveling at speed v is98iay73ft df3 wnuf* c equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash jgh.ilc0 zu7n74naakr9 l1j1 when the drive0jijganh7 c1z9. kr14lna7lu r 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 m is given an initial sj)axqej7,2dqscmr 1gzu8 x,3 peed $ 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 convc ,6d kvt: idk2fb-*mjeyor belt from where they are filled to the packing station 11.0 m away. The bel,2 -kcvkdm i :tbjdf*6t is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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 kine 6yuqmryu37,bwq).2,n qturttic 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 1 uiclh9gy 1:+nwecg*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-o3 .l fi0ad9bj/ys66 vg wh;xddjdd/ pulse approximately 20 g of blooh6doay.ivdjg dw3s9f j6/ /l-;0 bdxd d 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 chance of surviving an automobile crash if th38d0jb/ 2q k0dfwgce te decelerac2 q dk300jgetdf/8wb tion is no more than 30 " 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 , and if an objech( fr ;ao)pxoc5bg1h r.cq9/ ut is going to "hold its place" on the ground, show that the coefficient of static fr(cu ;xoorgf5h)b9a.c hprq/1iction 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 sh8( h sq3/upjjcene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which ne3 uj8pj( hq/sharly 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 level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 meansqvtawhp12su k; b+2u x/lb 1w* that for each 4 m traveled along the road, the elevation ch1hbl/vb x2 1sq+twp;wa u ku2*ange is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of8 a9f owvk1b6k Pisa and falls 55 m before reaching the grouvka 9k 61o8fbwnd with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s pgf sq,ng u0ftbim c;s 5 l((/vbzq;:j6k1pz( 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? Ib ff; cig,tqg 5kbu/ssmjv( pq0 1zl6n:p(z(;f so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. A;/d mwimq)/c txsvogc7 u7/f8n 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 cqx u/f/i7d;/gmwvs 8o7m)ctof 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 wat9+zmq) 3fj3*o+9dve vkfq0 j s2hhlgvch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the stringjhsdgkq+m9h *)32lzj v 9ff vqv+o30 e 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 rd.t qu4jk a*8np 7pbw:amps connecting different part:u*a4pt bk.d7p 8qw jns of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M nnv oj2h32-j w ) using the pulley apparatus shown2wohn3- nj2v j 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 accelehpv7.ax (- ;3g116iqt uiqpi dmgwsr7rating 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-restraiepq8x27(7--if 9iff tghky hpnt chair, an engineer considers the following set of2fp-g7kpi 9xt ef hfyi-hq78( 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 Itfay/r1xmfg)-9:hxk 78d u yhxalian 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 K b aiv- ynjt:tj5skd*q0(.94xo-xpl naren, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the res*vjt qi.kx onx4-n dt: j-(byl9 p0s5ault 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 iqth0t.qma6md(q :: yvqp84q 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 b1o1yzt 17vidhu (r wqkw +au-/uilding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice fwx1rvzx( 9ad+j2l v +etrf88gield inclined a+vze1 8fwjt r9 8g2xaldr+x( vt 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.