Why does a child in a wagone4ml*th+ vr 0 16b:go/)6 nrvwndlzpk seem to fall backward when you give the wagon a sharp pull forwn*+bl6ln/ wk41rv:g0mphtderv 6zo ) ard?

A box rests on the (friction9mu2nhay+ *at less) bed of a truck. 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 beside the truck and (b) by Chris who is riding on the truck uta+29ym *han

If the acceleration of an object is zero cxcd4blv3v 2d0 q; y3tbz:c igf():we, are no forces acting on it? Explain.

Only one force acts on an object. Can the objeb;/zgvd7h 4bw ct have zero acceleration? Can it have zero velocity? Expla4 vb; wdz/gbh7in.

When a golf ball is dropped to the pavement, it bounces ba8)/n a s(zxo(rnma7teck up. (a) Is a force needed to make it bounce back up? (b) If san7 m xo) (/a8t(szreno, what exerts the force?

If you walk along a log floating on a lake, why does the log move irj cfmxg,yk,6 y ;4l+dr*g yg1n the opposite directig4, + c6xfj1, y*drlggr;mkyyon?

Why might your foot hurt if you kick a heavy)nmt,y5 z:a4t6cl.ru6*tzw vnhjfs 1 desk or a wall?

  When you are running and want to stop quickly, you must 5asdy bxbg23b9.imqc.uc (.q decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your .iasqbyb.5g ( cqc .u32 x9bmdown 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 section of the same thrm sads;q w igl///ptb3+0fw h0ead dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pul al;+gt0 qp /bfds0h wm3is//wl? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kggbkrhlby7;.: -b 9jqc rock. Why then doesn’t the heavier rockhc 7g;bb9r .jlk qb:-y fall faster?

Would a spring scale carriefsw.3 f fofzdq: x 3ke/1f5e8jd to the Moon give accurate results if the scale had been ca fj8k:z3 / q.ffs3f e1dwxfo5elibrated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table using an attacaz wz wsmh0i0ww-*7 . ennc1i;hed rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the accelerat*hwmw 0n-cwsez 7. 1ni0za; iwion of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net rm9-len6 zvb3 force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the E 39bmnrz-v6el arth. Why doesn’t the Earth move?

Compare the effort (or force) needed to l1mrxi77qgs r8tj wtpts.f.k/ :vdfe:; :htq; ift a 10-kg object when you are on the Mo:sm:t;tqjhrf8 .kt:7 w1s. /p g;r fvxdetiq7on with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each t./m ( kifh(futeam in a tug of war (Fig. 4–37) pulls with equal force on thtm(khf. f/(i ue other team. What, then, determines which team will win?

A person exerts an upward force of 40 Negf+4i 4 aq+zgwdu 74w to hold a bag of groceries. Describe the “reaction” force (Newtu w fdqegwg+4z7i4 +a4on’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 tztegk7l pm( 2 m31o i;o0 q3ax81dguxthe ground, how large a force does the ground exert on you? Why doesn’t this forx82ouigl dg ;mpqt0m33e7 11 tx(oakzce make you rise up into the air?

Whiplash sometimes rdu2 i r 4 i52t,hvlvu wfdeyi8;-y2hp ,lhz.8zesults from an automobile accident when the victim’s car is struck violently from the ref ,h4;eui,whyu 2lyzr8vpl5 8-ih d zdv2.t 2iar. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerak qfdf73njp/)a x78jdtes, the crate remains where it is on the truck, so it, too, acceleratq 387/kaxnd j7)fjdpf es. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. jt 8f 7m5:ftnhuy (8vgAfter the block reaches its highest point, it slides back down but the magnitude o8tjt5f(hnvmyfu78 : gf its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined plane x6k) bahej v:tror5)eurlb(sj-k8 ;nco5: 0h )5kh: rocur(hb)s:aek nt b6 e8 vjl5xr-;oj0? Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled a6qyibxtvc4 (3x6 u.xet 1.25m/s$^2$?   

  A net force of 265 N axe88c hs 77h p/b**jg.yy wbzmccelerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withsta7 osn1g58gvqj sfj5)knd if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a ,qoc9j,c ut)6octmh2s) uq d; $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 11e c6wo6p2 tw.l 8st*o;t/zlth 00-kg car in 8.0 s if the car is traveling t2sctotp/z.ww lh*66o ;tle8at 95km/h? -  

  What average force is neededz2(mgy0q wc ,y vo6s)c to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rif vw,(2qcc g)0ys oy6zmle?   

A fisherman yanks a fis vh.k:kn-zc:m h vertically out of the water with an acceleration of 2.5:-. n:vzhkm ck $\mathrm{~m} / \mathrm{s}^{2}$ 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 tz0sr*vy3 yjeq+v.p 5gn ( 3d mw/1ntr0pzvi/drack (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 ddyo /l 3zwlw88esigned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cablewlw8lyoz 83d/ ? 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 o pizsgl o uolq:2;7 ,dg4p6+e;dd:zba motionless elevator. When the elevator begins to move, the scale briodl 27qzo ;;g:ez, bdpl 6+si4pdgou:efly 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-kgb7b2* io(pji kh.q9q z elevator has a maximum strength of 21,750 N. What maximum upj i pq.k9(2hb* o7izbqward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 14g jk8 q/iyr fk+sq82h32 kg including parachute) when the upward force of air resisk/ghs+q iy f28rk48jqtance 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 trrte3 afu(3lnd1e/* nhe ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m.e/1e3 urfa3 *ld (trnn 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. j.05on- dmq ddbi/qlb*li. o7A rope tied to the box runs vertically upward over a pulleqibnlbo * 7. m5-od.i/dq0 jdly and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketbal vx/d-hm5srk 8o5o2qcl player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit by the b15ffupd 7bf zl3 ts,2ok6ntn 9at, an5nzk7o961n ut f3pf ltf s2bd,d again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly directiv3,g 5yreypc e3vy );ke/9ee mon. A second 650-N force must be exerted in what direction so that the;g e9yprmece/3,eyy)vk e3 5v resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between tw-vp4:8onl(d vj9m,o1a jqqf9zqk hy )o buildings 10.0 m aparqhn 4j,dm(-qvo)qo9f y:91 azlp8 vkjt. The 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 bucket is hat:ifn4.yqp v,pl4- uenging 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 14 dk ,r4py17svr,.stom b yne (.fiyd/;.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, Antarc3e)7v5m yxdi5ug qyq: 6w xwo+tica, as shown in Fig. 4-45 omxe)7+yw xguq5d v3:iqw6y6. 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 it, Fig n/ pmo()jyxm)-r7vp5 yt jtm0:dxs; a. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the fir yv;/sjm)(t0)5dyanr mxmpj7: op t-xst 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-pull,.coz/fkj9 h j 3r;mqnu0ge-gey apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at cmq9co,fhg kj3nj r ug-.0/;ez onstant 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 65fl 0,o t2 rn,qvd37fkx$-\mathrm{kg}$ 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 (massngr vep;5g02;4guulg $ 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 otherhd7fnd:; (vj hf)r z/s, as shown )djz: hr(fhdf 7sv/;n 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 in Fig. 4-52 are each initt8ebfz g ).w;zially 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 wgf tb)e;z.8zone hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionl w e9xyyk0zf p0u8)jcg-,-vkgess table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension k ufk w8pz9)g--0,cyy v0xegj 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 kinetic friction between a ggwqnsnp3.5,c 5 zw.cxce./x 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 requir+lbn . vqr4y) y2hph3quuh8k :ed 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. Wha2xnh,6 q/ ph3gstjwr1t minimum coefficient of static friction must exist between your feet and the floor if you at h1xqg6j/n pws23,h rre not to slide?   

  What is the maximum acceleration a iu3 3-(j uze- oi;lkdmcar can undergo if the coefficient of static frictijuil( -m3uk;e3 od-i zon between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal s4df tn -wxxu)y7 4 yc9rzzw3j(treet pavement is about 0.8. On how steep a hill (maximum angle) can you leave a car park f93 y7u4zyw4)xwrz -(xjndcted?   $^{/circ}$

  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 -4.80qaz4o;wkq). g,e kyr . $\mathrm{~m} / \mathrm{s}^{2}$ 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 i( uc0dq1/8lz90sm yvwmlv3m on a rough 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 asphaf hurd3la/s) 0lt surface have a very high coefficient off)u/0ds lhr a3 static friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetzp 6 hh5mrb,cslriia3q,0 /w;ic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. zj ag *ohhl l1qx-*;x64-32 (Example 4-20) how large a mass would box A have to have to prevent any motion from occurring?h -q1oh;jlxax**zl 6g Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wil4jvt) -b ipxh*l it go, given that the coefficient o4hjiv)t xb p-*f kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are indndu yq i+m7 h::o47dw contact and at rest on a horizontal surface (Fig. 4-54)ho:4dnqi7+ wd7dy:u m. 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 frictig;t z-s5d tf ;iq/k7quon between the crate and the bed of the truck is 0.7d;fuqttqz7g;5/s k-i 5. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about par:v9jwr b/8 lqf1q:kke king your car in your driveway, which has an inclin1:evk8 rq9kqj:f /l wbe 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 zw r.d csfmgn7*a81 (fslide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted av9z9( u2ij/axe .unly t 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 initiah + 2k35af6k )v7mlispj)lkzr l speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepesq1 s/td1+fpw2z 7yab tt 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 n, .geoj pfew.lo,27 eex8k/cby someone pushing on it with a force directed upward at 288 fk lwjexe7e,o. /,2g pe.noc$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as t7u i n0 ig se* hu7souu5x+15*mscp+kahey melt. Consider a chunk of snow at the ridge of a roof with a pitch o+ mi ouuenxu1cu 5ss7aps h7gk**i+05f $ 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 au v7 jq/xxa;;u*hhuh1ntomobile traveling at speed v i7;/vj;x qhxnhha 1* uus 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 dashboadi8sdjnw 6g9lj :g crls5( zsd6bj. 7,rd of a car slides forward on the dash when the driver decelerates from 45dn5zsll766i9 (jg bwcjdd:8r sj, sg. $\mathrm{~km} / \mathrm{h}$ 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 ru.owo :nf(bjxi:ixxj63 *d6 m is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a (i1 xs*oc3 tqfconveyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the 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*sio t(xfqc 31 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 coefficienz. a /c95yuo/c6gr yaf) ppq;wt of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including 7 lnwz*52lndvt.b- mqthe bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified modelea66ip1mja 3gdihi4oc oe .+3ucp8 .x of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from u c4xip c1j .ap6 og3d.86oeihi3mea+ 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 su knx). iy,ao z.se/sz)rviving an automobile crash if the deceleraa )yn./eos k) x.,zizstion 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 eariwx+oqk/(v 1y*g1 wdj thquake is a , and if an object is g/( giy*o1xkwjq v+1 wdoing 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 two 3+xk e7r msohdykamy(+6dhy;g3p*a * 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*+ydsmkak*h h7emy y+3;d3x6 rog a(p.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling v)w5j1x ci 4ppdown a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevationc wpvj54p1xi ) change 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 qei4j jpetk2)u6-h 2 dLeaning Tower of Pisa and falls 55 m before reaching the ground with e i2 ut6)dqep-jh2kj4 a speed of What was the average force of air resistance?   

  A cyclist is coasting at a sf xgh69 f:tv6cteady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from tth6g9vf f xc:6he 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 hi/ f ;k;l*2 jelprmcmi4lly portion of a city. An important consideration is how sl;p/ejcfim4m; r lk*2 teep 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, dangles hervfqoipzt gd 4w)p7 ) 5z;7flk7 watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the stringlz f; g 7kt4fpziw 5o)pvd)7q7 makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be several ramps connecting diff0w) /u2vidw (4 a cxvl7ouv)cxerent partsx )x 72cu)dwa4cl/0ivv( vu ow 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 tyl 0c54g, ud*d rxk)k y)cf8elo lift the piano (mass M ) using the pulley apparatus show58dyd 0 yk,cxuglrcf)l)e*4 kn 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 acceleratin rjl3 :( 9yyz2v ,n t9,huvbnp)o6nnqyg 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-restraint ch1 ;bym/u+m axbair, an engineer considers the followingmb+x/;a1u ybm set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metric tons (660,000 .2qx+lkj 4 kid$\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar len uex+:(g mob.qp ;ffend(1w8k(tof4a gth. 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 qe ((f fpkea+ f ;1n:4o dxtmgbuo.8w(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 boat is usinyxe(gc76pxc3dwkhkt4 9 km e8(k v)+r g 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 s(g j:7,kk rjfzpeed 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 anxcl/g.gv ik27 ice field inclined atgc 2/.i kxlvg7 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.