Why does a child in a wagon seem to fall backward when you given,ggnkrio-k :e,l1 r 9 the wagon a sharp pull forward e,n lrroik,kg1:9 ng-?

A box rests on the (frictionless) bed of a truck. The truck driver startsd:)r km)(ff nd 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:)fd(rk)dnf m ) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting on it? Exxb1; jhkt)n 3b38 w/rt yl3mwyplain.

Only one force acts on an object. Can thglxya8s uww 7v3t: 1u8e object have zero acceleration? Can it have zg7u yt:l8ww1 v sxa3u8ero velocity? Explain.

When a golf ball is dropped to t acluzmg;2( r hz2s,0ipr -r6fhe pavement, it bounces back up. (a) Is a force needed to make it bounce, ;crhz(giua6sp- rl0fz2 m2r back up? (b) If so, what exerts the force?

If you walk along a log;1jo/0tow7o jnz4dvpf d2tw 4 floating on a lake, why does the log move in the opposite direo ;ftjz/7 wdpt1oownj0d 424 vction?

Why might your foot hurt if you kick a heavy desk or a wav . (8ahiwq13 wpt8qxojff)+kll?

  When you are running and want to stop quickly, y;0saw8fe6a u6)pd sns ou must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come8eud n6s asaf ws)0p6; to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the same thg4h i em3*ef;kread 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 thekefei 3 ;m*4hg person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as o+;i; xq 2t -:5mgzixkvos 5bgthat on a 1-kg rock. Why then doesn’t the heavie+gizosm ;v;o2i k5x q:-btg5 xr rock fall faster?

Would a spring scale carrilnv 3v z29 g:rq*m2udted to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (bnl3v29tgrdq2zuv:m* ) in kilograms?

You pull a box with a con zx *b8,d9vog*ox obj mn765zna* xl3pstant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horo*g nb6x,5v*olb9 z8m* jao3n x7x dzpizontal (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 val0h/xd *qsuzd x8, ;* dgjf0freely 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 t8sx;u qd,gz * ldf*jhv/dx00ahe Earth. Why doesn’t the Earth move?

Compare the effort (or force) nex;5btlflvb( kxl* )-xeded 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 object horizontally with a given speed on the) flxk t;( -lx*bxb5vl Moon and on Earth.

According to Newton’s third law, each c(a(7p5 y s2zt )lwvakteam in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, de7tkpza5w2l yc((v) astermines which team will win?

A person exerts an upward force of 40 N toig* t1k4,snk i hold a bag 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 what object it is ,i1k iskn4t* gexerted.

When you stand still on the ground, hovhz m 4*cd6 m (iqdr.pcp b5x,h,cxy09w large a force does the ground exert on you? Why doesn’t this force make y m0hmbyrd,.v pz6 ,5h(pd4i ccxq9 c*xou rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s nm )e09irhc gkla7+tu,af; b- car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it h7 fui;amn9c klbg a)r+-t0 e,really?

A heavy crate rests on the bed of a flatbed tt oqu,mi 6xy3)ruck. When the truck accelerates, they3i)om , uqx6t crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After th/kf k9rzwj;4ekjz5f7. g(snawi8 se8 e block reaches its highest point, it slides back down but the ma9 rkzk7.f e8 8k 4as5;zngijsf/ jw(ewgnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if youn1gm21r4k0+vyktl wx weighed yourself on an inclined plane? Assume the mechanism functions properly, even at an angle.y11 klxmw4tn2kr0g v+

  What force is needed to accelerate a child on a sled at (qxc zhn9*k ln baf.r/b+kg2 4 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider a5ou+z)yeb 4r8 *tb (o aidzi.tt 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 toeb4pfeo5/ a:pij(0p qg; j0l+ fpa 3ob 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 (b -)7lv lfy+7 qs42kzigqvdr$76-\mathrm{kg}$ 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 stodrc)b;7bwn 5r ;audv,p an 1100-kg car in 8.0 s if the car is traveling at 95km/h?wrrd5,v;7 n;a cbu)bd -  

  What average force is needed to accelerate a 7.00-gram pellet from rnsr yx9 s4jz*9 a:4sseest to 125m/s over a distance of 0.800 m along t4*s:99j eazsy4srnxshe barrel of a rifle?   

A fisherman yanks a fish ver4jsy/.hy +( cnu( g3yssjtw1h tically out of the water with an acceleration of 2.5 y tcs/(yn wgyjj+ .1huhss43( $\mathrm{~m} / \mathrm{s}^{2}$ 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 tu )ho3 bjex*h sh9l2:arack (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the v4un lioes+:s91w8d o maximum acceleration is 0.0680 g . What ar 8woso1send4uli v9:+e the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bath)pjm f ;r/z8axroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the apz )ar f;8/xmjcceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg pvc uo. oc/7vy jde3r:x;0*sh elevator has a maximum strength of 21,750 N. What maximum upwar:3oode 7u/ycvx vcp0* .sr;hjd acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fk;jzg 98 i8 cso*aucw3alling sky divers (mass 132 kg including parachute) when the upward force of air resistanc3wugkzsc9*i8o c8 j ;ae is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the groupi k933fsk .h pzep2-qnd below, he bends his knees so that.3sp3z2k9e fkhp q i-p 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 ai5kh)d;rbc)1 fg.om t table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley ck)5)g .mdr b;o1ti hfweighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body dierk75*d r1 kixagram for 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 mo* (ipp mo1*aylment it is hit by the bat, a(m*pli*1o pya nd again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly dat n8 )jt +:ydxzqu7o4irection. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagramj4odat)8 +zuqx tn y7:.

  Arlene is to walk across a "high wire"s c5ezoq wnsq.)y 4h 4v,skr+2nn;j7v strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at t;eyzv2. o4h nc 5nvsj ),n 7qs4q+kwrshe 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 another 3.2 67h. ooto;9iy9x ytn o;;drpw$-\mathrm{kg}$ 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 p*2/0ile ;ohvc2lz/ . qzdqjg.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.n iplj)jm +v9z2zt;s new location at McMurdo Base, Antarctica, as shown in Fig. vlj+;)pz z 9ijmn ts.24-46. 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 pullii+ fe7r/2xja jng two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling /7 xi+ ejra2fjbetween 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 fkc2 tj u;3 (gu/cu hf;g+)ybgapparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself s)+c jgy 2/ gkg;;fuhubf(tc3ulowly 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, edj5tz;l4u. 4hr-ce 8).jqvq zwqvk5 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 bwfmqt4 /1 au/kem8hg-lock (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 other mjtqlcjno 4j91 *cstx48 8ul7, as shown in 1on78x49mc 84jqsjctl *jutlFig. 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 shown05m ixdzjx)/v in Fig. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume jxz )dv xim5/0it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cunq )3a46vbcq:vgzc*ord of mass 1.0 kg . Calculate the acceleration of each box and t3zvavnq: qb c 4)6cu*ghe 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 kinkq( e*z8a+i wvk6w ra8etic 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 start a 5. h.gjh2o(gk5/cch b 3yw6hd4r0$-\mathrm{kg}$ 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 ackp2g -dh 9uyx+celerating at 0.20g. What minimum coefficient of stk+ gdu y29x-hpatic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergodbg.c)f i. 2xf if the coefficient of static friction between the tires and the ground d)fbxgci ..f2 is 0.80?   

  The coefficient of static fric(uy+unx;,tlsfho j4v8yz(k,d pa, u 6tion between hard rubber and normal street pavementz8ny;u,,(tsfl a+pvj,(udkx uyh4o6 is about 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at yy3zn58 1gfb-gw3vs9ify-jz -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 roug)njmm- v u+rxs)*a ,gch 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 sur;m+852qse lorpht.c7n d x-t* rc(qctface have a very high coefficient of stats 8xce5rq.; prdm7ln+c oq2tct-ht(*ic 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 kinet-kez : o67s;)n c:1ezp qixyrn sx.ep4)v*mrwic 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 )b0cbn,-xt jm4-20) how large a mass would box A have to have to prevent any motion from occurring? A,bc -xbmjtn )0ssume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it3cwf0tyaa6bfq x3 7c: go, given that the coefficient of kinetic friction is 0.2cxaqfwtf ya3637bc:0 0 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 73,tm ukn o,qo:5 kg and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). A :kuoqnmt o, 3, 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 cratefd6p /7ky 5w56dqet 7+xfullx . 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 and still avoid having the crkwp+t l7 udef6 6l55xdf qyx/7ate slide against the cab of the truck?   

On an icy day, you worry about parking you9ya8k0+ (migo 2iz azlr car in your driveway, which has an incline oy( +z98g i0a2limkazof 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 ozvgjgv-4( e: 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. 4-5xbdv m h 1322wq.p vbpa,d0u3p5 lies on a plane 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 of 3qjra5 (i cynqadg )+f inz,mk:.;y0 :v.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 withtinp7-,ap. wc 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 pun5avp4l j h3x6shing on it with a force directed3hajvn5p 4x 6l 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 i4ahs p:3,/hv x*ooyudangerous projectiles as they melt. Consider,/x3uyihs4 : ahpvo* o a chunk 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 automobile oc69nd9kze;dd ero2( traveling at speed v id zoce; rno9e2d9d (6ks 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 tnq zm5 pu-//n6j*ppq-svyff50ul o2 phe dash when the driver decelerates from psu/j5fm2pfqpl0 * z-vn 6 p/nuo5-yq 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 in+4s2 u c w*zbd3bae* r*j 9hlf,izzc6aitial 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 toi /w+ d95diyep)tu7v p the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of s +i /e w)dpd5vpt7u9yitatic 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 friction betwe)k1,tlhu( idr en $m_{1}$ 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 down a (qyc;sb :a.we) epkn . 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 mammalianmto74u h+7ack i dgg,0 heart, at each pulse approximately 20 g of blood is acceleri0 o+gm7a4td hk ,u7cgated 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 a2nm213 wmda ,2p qv fajp2r ubuiay:1:utomobile crash if the deceleration is no more than 30 " g 's." Calculate the force on a 70m 2r bd1i2vy p:3au mapj wnu:a,22fq1$-\mathrm{kg}$ 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 acceleratiohtikr mcy3 4:,n produced 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 the ground must be at:mk,hyi4ct 3r 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 involvinr2 r-1mn l+fmy)xcfw2g two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car +rf 2w1ml-y rfxcn2m )assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m fmblu 7pt(zv/5* 6mid ep ze6 zmlv+v3/n*s: jtraveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 5f5m3(s7vv /bljm6t+lz:i6en m uzpz dpe*/*v 5 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 of Pisa and faos.r z7 my2xxc,8qryjm.r+ l(q 8zc(ulls 55 m before reaching the ground with a speed of What w zulryq,z8m+(scrj x2qycr. .7m x8(o as the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/l3vc*85c (kmo,rlc-a iqdxg 6s 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, wha(q, rx o83m c-ll6 ckdc5a*vgit will be the speed upon emerging?   

  A city planner is working on the redeseii9vu( v*yv8c f-g3h , 9fy6a+ iwgavign of a hilly portion of a city. An important consideration is howi9(-fv+6a i3e8fihy , *av 9uyvwgcvg 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 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, dang,pa*-kz jmyvcx j(*2rles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4pk czy- (ar x2m,v**jj-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 to biq 6q6k g)giudc;;d/de several ramps connecting different parts of the st;)kc6qiq/ didg ;du g6ore.
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 )h m7.stad8hp) f6ab (p using the pulley apparatus shown in ) 8ads7 .a(thm6fpb ph

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 ac(vol.lcgif 12c i iv0xp8 +g8p8nd .otcelerating 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-restra+e d71mcd44w k/i ectrint chair, an engineer considers the following set/ 4emrec dw4i1ckdt7+ 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 Italian train has a of0 bqpd/ -m:dmass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

  A 65$-\mathrm{kg}$ ice skater coasts with no effort for 75 m until she stops. If the coefficient of kinetic friction between her skates and the ice is $\mu_{\mathrm{k}}=0.10$ , how fast was she moving at the start of her coast?   

Two rock climbers, Bill and Karen, use safety ropes of similar length. Karen's kne h8b1uvbd4vu *)9 vt4 wfl3rope is more elastic, called a8n14wvbvd *4f u3bv 9the)luk 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 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 boag 9;kg+* rnwhk88gytik 64r oet is using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum speed of 3.5 h:kg/m an15 h yk3n6sasql/- m$\mathrm{~m} / \mathrm{s}$ 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 ascen476a:sj5r7f ffpn qq mding an ice field inclined at 2fs47jfqf :q n5p rm6a71.0$^{\circ}$ 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.