Why does a child in a wagon seem to fall backward whe esz4lg9 5mu3pn you give the wagon a sharp pull forwar9 e5z ugmspl43d?

A box rests on the (frictionless) bed of bv) :nd8n axr9a truck. The truck driver starts the truckv:)ndrx9abn 8 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

If the acceleration of an ow3 o /xtaj7b.ckzzw+9bject is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accelerati ;mglrqm ;(-xson? Can it have zero velocity? Ex-(x;lmmq gs;rplain.

When a golf ball is dropped to the pavement, it bouncfs f;v9r/+iu5sg*ewa2ob h4b es back up. (a) Is a force nee59rsf+ubgiw ho24v sb/; *ef aded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in ttt;ok;** 0fs(myrgbb9 4rt lwhe opposite directionbs;mrtr*4wktl*0;f(go b ty9?

Why might your foot hurt if you kick a heavy dexfcu. bvm(k: -s*(1.a q.zd y gz,xkvtsk or a wall?

  When you are running and want to stop quickly,9w3. 3zlnvt (jvp kar6 you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own exaktv 6jrvn39l.3w (pzperience) 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 srv4q(o jy2 kirsi-s .-ection of the same thread dangleyrvi -q(ri.4so2-k jss from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as - 8 is delflszoqs1;66 9a6wmlthat on a 1-kg rock. Why then do os 6qz 8wdei1al m9;l6f-s6slesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurq:m v3exdwy(n( lp2t)ate results if the scale had been calibrated (a) in pounds, or (b) in kilogp(x(eln2w 3:m)q vydtrams?

You pull a box with a constant force across a frictionless table; f7(ssn+m+a h g4edgvkc5.no using an attached 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 acceleration of the box (a) re(vses ;fcd47 h++mg5ago.n kn main the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of grawxq3g j3ph +p/m6copwb7 rd,:vity there is a net force mg exerted on it by the Earth. Yet by Newton’s third lgjp dh+/3o w 736b,pq pmrcxw:aw the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) nt*ndqb;n0i w;5j6vfhs5 :c3 d 2uk dkaeeded 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 Moo3;kvnfnh aksqu tcj:5;6wd2b d 5 i0d*n and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls wiahs * qjz v4ma6v,p0)eth equalp6ev q*zas a,40jm )vh force on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Desc 5 oyi1 glgs.d:ee,awp hpzbet9z(c;42tp 76fribe the “reaction” forcew2 bgospp:7t 5,giha .le;ycp4 (edzfze619t (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a forcmqq1)nlgq4c d)5 ld0e 7+ zymce does the ground exert on you? Why doesn’t this forcez ygl0nl4 m+ )q)dc cdeq5m7q1 make you rise up into the air?

Whiplash sometimes results from an automr5w:*vvzm7n kl0 x:ebr9 y 2zaobile accident when the victim’s car is struck violently from the rear. Ex:20 :r 9x*mrayz ez5lwkvb7nv plain 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. Wtschiuc13xc9mv c8pv 8/u0s3 hen the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causpcs3h98 8v/ccuc xu10iv m3stes the crate to accelerate?

A block is given a push sdw2c byr))ymf(bhpskuc5y9 b 9j 245to that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acy bby (spb 4 ym2hccfjdkw9t)2r95u )5celeration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined pldw.x k8z4 y t b-vzb85tk.6gclane? Assume the mechanism functions properly, even .tgx-wylz4k vzdbbc 8.k865tat an angle.

  What force is needed to accelerate a child on a sled at 1.25m/s 4w+sb (yhwgbv 7k-)s*xi wr8l$^2$?   

  A net force of 265 N accelerates a bike and rider at +sr6,bx m t0 eoz8xxk79-yonw 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 acceleratwtnr;z.k dc imbm)xn7t:, )n1e a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a g;4m k6 7yqpdv $76-\mathrm{kg}$ 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 stojvo ns+vbfz2s3 k.k*9;dvj 7rp an 1100-kg car in 8.0 s if the car is traveling at 95km/*.k+b7 3oks; vf2s rzjnvj9dvh? -  

  What average force is needed to accelerate aycg,3kd 9tx9m jxlb 64 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrelb4 3k9lctxjx,y9d m6g of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of vj,xrstz:z s*d0)6 .hrj3 fio 2.5t3)o zjdij.hxr,0 6:zfv srs* $\mathrm{~m} / \mathrm{s}^{2}$ 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 ce rt py+16ig o8)h)gsdan cover a quarter-mile track (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 tfynm4gtq01iz+, c u,xhat the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max nc,,gzt10f+xu4 qmiy =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When the elevator jyckh5;0sd pijamsq tcmq0t-z:+k3n,2. 0nf begins to move, the scale briefly r+ks3ajqc pj. :hit-d;mtsy020, 0ncn qmfk5zeads 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 mb 4x-5w7 ezz u7msj3ewaximum strength of 21,750 N. What maximum upward acceleration can it give the elevator withoujz5 ws7e4m3 uzb7we-x t breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky ) s /gx77agaikv( 9yoljkc 0*;n x.vikdivers (mass 132 kg including payi xnk.gvo a(7vl7 sa)/k k9g0jxi ;*crachute) when the 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 ro5 3 44qhwrqv sa2vs,ggof 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 agvw4 g qrhvqs 53,s420.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box run 691snxj w;as8k1cw 5+sggykq s 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 c9sg s1xw5k 1jn+ ;gy86qkwaspulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram6ktk;xvjys.20 qm,ez v:3 9 q.uunmea 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 mom+be 8w pe lbrz3ye..t:ent it is hit by the bat, and again (b) after it has left the bat and is flyiny b tp+..8bl zrew:ee3g toward the outfield.

A 650-N force acts in a northwesterly direction. A second g2tz lhwp 0w(1b na4i u1cf-b8cp3gp:650-N force must be exerted c1- gn4tiwhub z f0w8 a1:lp3p(gp2cbin what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a tsfymflx 7pu) zgxe.17el *76"high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10.07mt7y1e.e *p6 fxlzl7 uf)sgx $^{\circ}$ 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 at . bsp; h.1fu7ggjxo o/p,ur;nother 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 1* l-j+-t rzq wi)atb/p4.0$-\mathrm{kg}$ 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 McMurd yn5ei0.v .xb q8j gk6/ly)vvho Base, Antarctica, as shown in Fig. vqvvky b 0g.n he5) 6/yj8xli.4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two ca-3p( pkacm0njzt,co89 y+5q1jfla zors of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the fir oz y k53t9cl pf+j01zqocm(n-p,jaa 8st 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-pygo8-5j cs vo4ulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise hersel-o 58soj4v cgyf 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 bt0 kido ;msnydpg*r82,: lte (f2iu +negan, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block ra:xx)x0oqmhna(wx3( z+1if (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 surfacd empg0ng;xgq.7l46me are in contact with each other, as showgmeg7xm60nqdl;p g 4. 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 eacm77.cac6u-q xu z7 dkph 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? [Hint6cz pux 7d7k7u.m cqa-: 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 frictionlesswzi7b :zu12yf table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-57z2f1wuby:iz 3. 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 betwe9ab v10w97bjycia8hee y i 67een 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 staps) 88qep:mx crt 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 accelera(h jr+ /274fiuizahtd vju+ 8bting at 0.20g. What minimum coefficient of static friction must exist bjj/tu8 r4fvu+ bzhih2(ida 7+ etween your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficiemf++iz hc0 0o xu,kce.nt of static friction between the tirx0fh cck+0i,ue. +mzoes and the ground is 0.80?   

  The coefficient of static friction between hard rubber anv yp2ty4;(nm pr ysj.00tck 4kd normal street pavement is about 0.8. On 4(kn 0;vry.2pyttp ys4cj 0kmhow 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 c0b9n+y-wp vchc*/ bt-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 rous ;rser3. u(+fqjmgiic( q2 y.gh 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coefficient x6o8lkz 1we,k of s6o1zw e l,kk8xtatic friction.

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

  The coefficient of kinetic friction )x 1(mrza e*2:faysds-kzhx, for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how larky3 2tahbad+i 4 irve2k529slge a mass would box A have to have to prevent any motion from occurring? Assum5y e2v sda3+bkhkta9 lr 242iie $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, x kml(0.7cxvegiven that the coefficient of kinetic friction is 0.20 and t07x(cmk. xle vhe push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kgnp*; )juwp ll- and 110 kg , are in contact and at rest on a horizontal surface (Fig. 4-54). u pn;ll )pjw-*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 heavz 6m6bi/wfa8m4r 4 ubey crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still u / 84efaib46zwb6mrmavoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which has ajv0ts+xdzx.hj q 4;7hn incline of 1.sqd7v h+4zx;jjhtx 02$^{\circ}$ . 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 ,z f n vq2xvs 2yb22*4cezcemtom,/6xa slide 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 liesq:1yhj 8ucckbh m )v zt652*xe 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 ang k kgh0ui43),p*ysyp9 l;tpl initial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of 6p im oikhk -)viv)6yb,r/;nv7.0$ \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 pushin5ichx b5r una5/+rv rf6k2:rng on it with a force directr /cik26a r5hunx5b r5:v f+nred 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 hv3* b6pi3 kvcroofs can become dangerous projectiles as they melt. Consider a chunk of snow aci k6vh3vbp *3t 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 7l j(7 wl:w rixw0aw0xautomobile traveling at speed v is equal tlwrix: x 0a0jl(7w7 wwo $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 sli;qge1 -obd h ph0i +c2u)hvx.ndes forward on the dash when the driver che;2+ hug0inqdv)x- .p1hob 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 speedlhacu*5(bs w : $ 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 fx1 8ujiuzf*wc /)ymp e (:5bzfrom 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, t: ufu1ifw8cypz *(j/m)zeb x5hen 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 kineticzg(1 otemt 0 9gkkhf:; 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 bi kff3ws(8l9iacycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approximap 3)0m/ddt5jxoi m7ajtely 20 g of blood is ac i5admxj /poj3dtm70) celerated 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 sur c ,hwyurl*-g7neg72kviving an automobile crash if the deceleration is no more than 30 " g 's." Calculykcg*2e-,7h7 lgwru n ate 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 ac gd/n2;kjqq6js6vd/.xu 8 iji3k ;9vqj gzq o.celeration produced by an earthquake is a , and if an object is going to "hold its place" on2qju9j // gqvkiisdv;6qd6;.z8jkx jg3q no. 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 i05vdni+ utew c 4m(4g2ivy*fp 2 ;mpxsnvolving 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 issn (u4wfvxp y;i mte5mc42 *g+dv 2p0i about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-inz+gmx3*nh-nufp 4w l.-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the.-zp n3+ xwlu* fgmh4n 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 thef ;ry x0m rywi3xb(q*l (l lo8wf)36va top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speedro y8w0l(ivb y; qml r3ax)fw*3lf(x6 of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stre,en6u(. rsniyt6*l pa tch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having t6*lur6.y,np e(nat si o 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 hillyzj+,ozjdixuyd 8: x:6 portion of a city. An important consideration is how steep the roads can be so that even low-powered cars z:j6+d8yu: x zx,ijdocan 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 her watc 3a 8jr49s02oebqhy7 sys9thph from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4 4e2y9b y8q9pr7s3ta hj0osh s-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 acw; avh( w 543urp2yku n(csl(re to be several ramps connecting different parts of the sto(2hv wl(pc4u acynw (ks;5r u3re.
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 ) using d*korbq..,.hep *jc:v, aro nthe pulley apparatus shown in nqk.v* . ,.od:ha*cj breo p,r

Fig. 4-60? (b) Determine the tension in each section of rope: $F_{\mathrm{T} 1}, F_{\mathrm{T} 2}, F_{\mathrm{T} 3} $, and $ F_{\mathrm{T} 4}$ ,

  A jet aircraft is accelerating at 3) imkpzb/k4hbq:l n66.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer consika:jijwu/q6t 8uc j6: ders the folcqt8 kjij :6:a wj/u6ulowing 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 a3as 5 li , ckywd)jp:w52.cfq$\mathrm{~kg}$) . 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'shbknkz/ug qy ;sg3 f2z8ul *,; 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 b; n;kzzqul ,gg 8* ushy3k/2f1.0 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 iuar:ow0c4w7dyu5 uv ,s 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 re;6vp k:w:c(mb7 v/*ziee01feip eg kuach 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 fielf*lq xqv ,sq6,d inclineq,s *,qq6f lvxd at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.