Why does a child in a wagon seem to fall backward when 8zf 0vi 2cpxt*you give the wagon a sharp pull fo*82ptzcix v 0frward?

A box rests on the (frictionless) bed of a truck. The truck driver startk: 9gfoc-g5uc s 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 stu59cgf ok:cg- anding 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? 7 x2q)0rjw :7cwxj vjeExplain.

Only one force acts on an object. Can thzl (hov:(4 cqxe object have zero acceleration? Can it have zero velx:ozv 4qh( (clocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is ac/v) l1 pm/gjk force needed to make it bounce back up? (b) If so, what exerc1kjm l/)g/vp ts the force?

If you walk along a log floating on a lake, why does the log move in the opposq9d1h lii -w q n-59ls7pyf5puite direpui h1qy995w 7-p 5sfqdn- illction?

Why might your foot hurt iffup8-d5g eb q+ u6aww6 you kick a heavy desk or a wall?

  When you are running and want to stop quickly, yc1 n8meg m6;ynou must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own e;6nnm m y81gcexperience) 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 se8( bop*el;8 r:4 vkoxrmmzpe7ction of the same thread dangles from the bottom of the sto z rpvo7lkbpe; m(488omr x*e:ne (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 t1eo lbkpzrc(- ;k9 v4ihat on a 1-kg rock. Why then doik-( 4vezc;rl b1p 9koesn’t the heavier rock fall faster?

Would a spring scale carried to the Mo(d- /zn 4+g(t) xeiz/jrsbqzton give accurate results if the scale had been calibrated (a) in pounds, or n+4s)rzetti(b(gjq/ -z/x zd(b) in kilograms?

You pull a box with a constant force acrossm*(hf4zgefpeq 2eo4- a frictionless table 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) remain the same, (b) increase, or (c) decrease?zqf (*2e g4heef4m-p o Explain.

When an object falls fc0bqe-kutyh;fq l8f. *cgk(jt1 3)r rreely under the influence of gravity there is a net force mg exerted on i)c1j r( tlkt b;gcf fy803 ukqqr.e*-ht by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when y3(t y;vpf;eudjn )g)9on t /prou are on the t)jo; py) nnpf 3(urd/;vegt 9Moon 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 l yr5b7i9s dw6 2i9zyuh tcx1+naw, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which t6hzn59w1y+ur xi72ictsd y 9beam will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe tt n3 x 9-c w41mtrmg3iw-m9ppbhe “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) bytrnt mm93 pw9wc1i bpg-34m- x what object it is exerted.

When you stand still on the ground, how large a force does the ground exer+oyii*6h/ . y nr:),*f ro.vanoa wisst on you? Why doesn’t this force make you rise up ini ooi,r+sn6*n)f.yw : /ai.*ahoyrvs to the air?

Whiplash sometimes results0 x om7j/uy9kftqdu.1oca+ jp y1,a:z from an automobile accident when the victim’s car is struck violently from the r 1+jo1o7j ya,um0 .t9xpfq d /c:ukzayear. 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 thee9nzy ;*agsxflv;0 7w truck accelerates, the crate remains where it is on the truck, so it, too, ac7l*f we0a9xnvgz;sy ; celerates. What force causes the crate to accelerate?

A block is given a push so that it slide au)-d : 5bma3h7 re.zpio9q6w pnsh(bs up a ramp. After the block reaches its highest point, it slides back down but t)wq5rs- .ahnpu 6m 3 a7p: hbbdoie(z9he magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed8co:eokh* gft 8k2g(es6raf - yourself on an inclined plane? Assume the mechanism functionsc(f6-o8atr2o ks: kg*e8ehgf properly, even at an angle.

  What force is needed to djtu(mahnd0d86vpij)ob58, i7xgj .accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accel8zx6f) wbxl;o erates 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 4cy-a9dtfoz:2:o cwm 0 odyq+ withstand 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 (hpdh o9 fd- 4xwa1 2d ups/.pao4)zjpa $76-\mathrm{kg}$ 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 ang4isrc5d+ s c)(tcfy- 1100-kg car in 8.0 s if the car is travelic)-cis r+ 4s(5dgtf ycng at 95km/h? -  

  What average force is needed to accelerate a 70vs3y)rmz re *.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a3r*z)mes0yv r rifle?   

A fisherman yanks a fish vertically aga7t m;9,kk0fr j/e fout of the water with an acceleration of 2.5 /m rkake tfgf7a j;0,9$\mathrm{~m} / \mathrm{s}^{2}$ 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 coverq.9 :vqzo r9lcf0w.f b1 +m2b yeat/st 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 beqxicn/q9, b-fa gu 9q5 designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? max = 99- fin bqxgca/q,qu5   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 elev5cn-zcx l(ead4c9 uszqu/08q9 td n b.ator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, a8 beu n5.qscn9d u(caxczd94z/0-t ql nd find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,jrll)6jf+* oo te1hz(750 N. What maximum upward tl zoe6+ rh1)fol*(jjacceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg e 0 y0zpnssz/ spkm)u)sa7r;9including parachute) when the upward force of aasusr;/z7y)s n)0sem 9pzk0 p ir 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 r wm 2fxxmc 5)tjl3itp s985rj)oof of a house 3.9-m high. When he strikes the ground belowp5 t98x)i mj2l3 cts5mwf)j xr, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A /(bk*ptgq tb6 siqxpml.b8(; rope tied to the box runs vertically upqt(8px b lqtbg;kb *ipms./ 6(ward 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 weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a bas+ogescx6y 1 5 tsaib7-/*wgozketball 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 1f,1 yankopb6 of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is f6y af1k,1o bnplying toward the outfield.

A 650-N force acts in a northwesterly direction. A second g 1jivc8 fane. :oitgq.) x ym9jy2ooqc*x 492650-N force must be exerted in what direction so that the resultant of the two forces pc vq. yoi1.x 8jejy x9g4miag9q2*n)2ocfo:t oints westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung ho1g,hcu 7pzfg;. uiho9rizontally between two buildings 10.0 m apart. The sag in the rop .;7pg9 hui,o1cfzhuge 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 hangin jt( 6yh-sx4nyg 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 1xp 9zncj; z1 d01rojc64.0$-\mathrm{kg}$ 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 housiqq +e*g qgn.v:ng unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4- +q:gqegn .qv*46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of thnx+9e +5nmu*wb lr1t-1kmrnse same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the5 mw19u sm1 r+erbxtn -+*nknl 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-p ufeo --wtzo((ulley apparatus shown in Fig. 4-48. (a) How hard must she pull dow (-wuzo eo(-ftnward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 65bc50o aqv7c z5$-\mathrm{kg}$ 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 (massoii /.khv8*jn 6f wfb ct0rv75- -dxuw $ 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 e// c 76ts9cg vgrb(cfx:orfp5 )yz8rare in contact with each other, as shown in Fig. 4-51. Axrc9rg fry z/g /5eo(b7v)s 8pcf6:tc force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above thec 9smq-spk8pe:gt6ww c s y/z ;2tc-y( ground, and the massl 8cpt2ywsccwpg(-e/y: - zk 9; qtsms6ess 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 it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of ma;xwfjf zugz( :,vf+n 1ss 1.0 kg . Calculate the acceleration of each box and the tension (vzwu f+,1x;:ffn gzj 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 kig :6i:k2m8d, crfor conetic 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 isthctwdfuk 5; x wpz6r-,3+wo4 required 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 a-twq wlqp)yn* w.o2 mkli*:k5t 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to sk p. 2ww:nqoy5l- *mk*qtl iw)lide?   

  What is the maximum acceleration a car can undergo if the coefficient of statis e(milz5mrpd8g- jt373 fnm6c friction between the tires and tfs m(rd37ipl8e-6j35 ztgnm mhe ground is 0.80?   

  The coefficient of static fricm;x8 ac ,xa3j kdom5iqkmkv ly(3q,8-tion between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum ai x o-x3,yvq3;da( km8l,5mjm 8aqck kngle) 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 ynhn0a2*v ;t ux(oor;tg +g7y -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 res:tv1*8mihus6( hd ul*gpm s*at 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 asphalt surface have a very high coefficie-ncx3q ;o d dd)6ajpg3ypts+.6z n8q znt ozdxdd)q-pqo p+ ;z3 836js6tn .c gnayf 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 kinetic friction for adp, t6,kvzz1 m $ 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) howf4/l*/k*ibaw v rnww4 large a mass would box A have to / rlkfw*b iwa44/nvw* have to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across9yi 9ii t6lgb3y4s,+a lw(s wu the floor. How far will it go, given that the coeww t +i34ui9lay6si(sy glb9,fficient of 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 tzt -o o)f:x3l110 kg , are in contact and at rest on a horizontal surfac ltzt:oof- x)3e (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static fri;b g- -c2 a3vsko,;oavfkrwf. ction 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 avo2agw ca r,kofsk. f -3vvo;b;-id having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which yga suc n9iioq7j/e +6s;yya)d)o ecu+g/31shas an incline of i7 ayc9 yggej/dns)oauseics6qu o1++ ; y/)312$^{\circ}$ . 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 slidapbclk6 0 o3ekko**2w e 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-wrk3 fja;p:x m(-c9u6ff z zt955 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 in. 2b v7dhupsv5zy81f kitial 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 reac166nwy je0ktmb6(nw thes the top of the steepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place kjs4j1 * qfn 4iaib4cgyb6,c,against a rough wall by someone pushing on it with a force directed upward at fyck1 44,bn bcs 6,i4j*aqjgi28$^{\circ}$ 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 becomoi s:2 ,d0mvda8odwm 75v0g aee dangerous projectiles as they melt. Consider a chunk of snow at the rvmvodwd 5:eos7ad0i ,20ag m 8idge 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 traveling guwql*sq o el rv,x;+*-*jg1dat speed v isqx-wolu,j*q r+ 1g; lg *edv*s 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 das3w u 5c0gvbf2)iy gs e1ux5.l0 ua2ntthboard of a car slides forward on the dash when the driver devut nwg5y20t0fcxu.)352ag eilub s1celerates 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, 6v53e vmoqnl 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 conveyvd(. ow umb-1 ba8 /la02we 1lciknj)cor 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. va2 81 cn.0-d/wleijwa(mokb1 lbc u) The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction betwhb1hb(afn;ul5 5 -pcqeen $m_{1}$ 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 (includg g1/6ynfp:yl):m ii ving the 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 model of a mammab4,*ztm.rv5 5 fgu h uem3 ihue7y(p-glian heart, at each pulse approximately 20 g of blood is accelerated from 0.2u 4g u.3v*z(r mht5ygbe,h-5fpeui 7m5 $\mathrm{~m} / \mathrm{s}$ 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 automobhhzw+2uto dnr+er.: ;ile crash if the deceleration is no more than 30 " g 's.;n+tor uwzh rh:d.+2e" Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake isgvj38kial w.)p 3 / lddse/au8,:hoz elt *cw( 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 as*l.gd3c k/( hwa al) oeztp/3u jw,d:l8i8vet 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 inc soc 6kl86cb8 b7ws7 f;l5gfyvolving 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 iss lf cfywsc8oc bk76b65lg;78 about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling do. ) vxkmy5u8,hdw35vfp r9 qwf*k;qw q hb9c;xwn a 1-in-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 bottom rx, qwcbkf* p;59y8wkxu 9)hd.h ; 3qwvqmv5fafter traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower ofohdg0 a:5 q/uq Pisa and falls 55 m before reaching the gr 5q0a:g/qd uhoound with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a :+ q(pa,a9 tl (t;0vqix 89vgohr0g*sgyk inimuddy stretch where the effective coefficient of friction is 0.60. tg(yo+rqx9qh9pl 08,i;s a kg(iv*tnv : ga0iWill the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hil 1 t-ivu7v8dinly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hillst 8dvivun-71 i 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 watch from a tv r c0fd7q7w -34pegokhin piece of string while the jetrveq k73o w47pd0fcg- liner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several rampsx3mau)qg+/et)z)wj i0dd 5 0t pgc+ vh connecting differentvc0ijtg0 pu3+gw zdd) 5ax )etmqh/+) parts 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 0 26eo p2hm3c lrsbj5vF is needed to lift the piano (mass M ) using the pulley appar2s2o mjpecb63 v5lrh0atus shown in

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

  A jet aircraft is accelerating at 3.5 ;a caux1 xo/.n$\mathrm{~m} / \mathrm{s}^{2}$ 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 considers the fol2zrtbgy td/ s/rl(/a)c6jgf5*n rfd 6lowing set of condtbag( dszn/c/y2rl6trjf* gd/6r5)fitions:
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 mugo6 0skm4 ggb5m n77r1i d-bbass 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 lengt6vu e4ad5k ;swh. 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 45w kasdv;6 uethe 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 boatyj8c3 gdrqr-041imh v m:i6r ulr: ch7 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 mb3gvs71z; w4 ghf 0j(q gs7boe:b7kqlaximum 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 togethe p 6.q5kl5vfshr are ascending an ice field inclinedk6vf .ql hsp55 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.