Why does a child in a wagon seem to fall bacu el ihoan(o1 ,0i04qqkward when you give the wagon a shari ,a1l0noo( hu4qq0iep pull forward?

A box rests on the (fricti5)baro wpuif,c08eo3 e07fr a5 o0 shponless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediaeaf o7o hpfu3b5)wo5 c,e80p0s0ir ra tely 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 object is zero, are no forces ac8kd l dwza2 ivkpg/byy/do)fh9y7 2 3/ting on it? Explain.

Only one force acts on an object. Can the object have zero accel( zdbmam 2/og81 9iey 7x-iibferation? Can it have zx mb7 zdaimf8/ 1-e b(29iyogiero velocity? Explain.

When a golf ball is dropped m.1yxvoma.eu7d6k 8k to the pavement, it bounces back up. (a) Is a force needed to make it bo .uvm 8a1dmo.7ek6kxyunce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does te24bfss hp f rz)222ik:bx4t g 7do8nhhe log move in the opposite dire ebs8okz)2d bffi:4 rsp7h2t4xh2g2 nction?

Why might your foot hurt if you kick a hea3-sxh j7lv 4y1l *bcypvy desk or a wall?

  When you are running and want to stop quickly, u jv up./o01ox:8x f;l,g hsyqyou must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using yq; ov8fx ,uuy/:jh.0sgpol 1xour own 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 u *au+l(;e m 5nso4o 7nsy)kdaa section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the sto5(;sla uou4omnn7* es a+y)dkne 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 grei9olm4:jgv/ s at as that on a 1-kg rock. Why then doesn’t thl:9ijms4gv / oe heavier rock fall faster?

Would a spring scale carried to the Moon give accur 7qchrbx7d;ne 8kq-mcg1s 87rate results if the scale had been calibrated (a) in pounds, org7rqc ;kr 7-s hmn1bd c88xe7q (b) in kilograms?

You pull a box with axmh-.k1*su fnft tn 68 constant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (withu-xfhn 1 n 6st8ktf.m* the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net fnb4ezr d)om )0a6tj vntg)g,2orce mg exerted on it by the Earth. Yet by Newton’te 6)bg) nnzmjt2a) 40,rvdgos 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 you ar,7aeeo4 azvges(rk: 5e 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 Moa7: oeevs 45rkg,z( eaon and on Earth.

According to Newton’s third law, each teaj tv5(gqoa(t :us0*rmo t;4wa t: in4.pj5tyfm in a tug of war (Fig. 4–37) pulls with equal:*ptm5fta 5a jt q(sgy 4o0i:nv j;u (wotrt4. 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. tx9 0ha.56v dknl 9pteDescribe the “reaction” forca9expdl tv9 k56.t0hne (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 l1(y0r( xubzoeq4ps n( arge a force does the ground exert on you? Why doesn’t tb x1ezu(4 0 q((nsproyhis force make you rise up into the air?

Whiplash sometimes results from d0jf/ k pi,dqhu)w7(bm19e2kub; weh5w x:e tan automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the v2i;:wue wh7dbpk,xb wkq1j( m tuh0 ef)9d/5eictim 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 accelerates, s./e-qmcez cdps2m5i,7du 8*uc1aie the crate remains where it is on the true5/ ,sd. dmuc zs*upqaec1e-7i28mcick, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block j(8wx .7mnqz/wxtsr 5f /9va esm(,f ureaches its highest point, it slides back down but the magnitude of its acceleration is less 5ar8f ,. q/enz(9tw7 (xxmfmw/ u jssvon the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined planxuenz*if10.k e? Assume the mechanism fu*enxu.0ifk 1z nctions properly, even at an angle.

  What force is needed to accelf we4q fu. vhrza46b14r1zfj8 m jxfp/*u9z2terate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N 8ft cbq1+f :cvsw)3ze accelerates 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 withstand if it i*n.ew0d wwm-qj* 4/ /ikymkmws 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 uo;gn b rv075*wwfxb bb 462l)wfb hb1 $76-\mathrm{kg}$ 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 requirott7h agt9nga)4-k t1ed to stop an 1100-kg car in 8.0 s if the car is traveo9t a1th)att4-nk gg7ling at 95km/h? -  

  What average force ifg9uq51wx4 vv s needed to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barreqgwx19 uvf5 4vl of a rifle?   

A fisherman yanks a fish vertically out ofgska y-(,rj cenf45/+ 1ljr bf the water with an acceleration of 2.+ e rks-1fcj 4bjly a/n,grf5(5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 /nctyvy(2eb4f u. l *mcan 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 that the maximum accelera,a9*0 ilh1go nhoyr+bhy x 0o;tion is 0.0680 g . What are the maximum and minimum forces theroh on+i y h1a*0,b0ylogh;x9 motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a m cr m2c:jp56wp vw1e*votionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s reg 1vr5pmpeccv w*2: jw6ular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of z if4e go2(trzjj.l3*. nk-j :sk oh4n21,750 N. What mzj 4.sjgtfo2k ir:eo(nk zn-4*l. j 3haximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleradgplsh6n+wns e 73w 6wg1dh 5(tion of two falling sky divers (mass 132 kg including parachute) when the upward force of+d 3 dgh7wsw1gs n 5e(lwnh66p air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house /v, s wc kz;p vvl4gdsz/36k*hz56vcg3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the d/5 ,lsgvvzpvg kwv6c 4s6cz3;*zh/kmass 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 -ds/5r0r4vkxcvl5 z.u2av by runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40).xv5 k2lcrsv-b uvy/r 0a4zd5. 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 basketball playe2yu,diz:6wbrsqjn 8) r
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the mo)uc5 1-o b t.pa hrp9-wr7fbeqment it is hit by the bat, and again 7. tfpq pe9 ro)w1cr-u-h a5bb(b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly dd,- o vvh-l-bmirection. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustr--o vb,ldvm h-ate your answer with a vector diagram.

  Arlene is to walk across a "hig;:rgq/p+f iznov ub54h wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is fiu zn:5r b4gq ;/ovp+ 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a m1hqswxfo ci :-pn)zqr 14de)7fr/1 c yassless 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 14jvcgrdrjjy 2n ,,tbd / y2);(:rm8q ts.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 h n,yts l +bq6;aotno*hr 9-yej-7i0kt ousing unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-49an k--y0;6 etjq, y onhibol+st7*tr6. 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 5 p-1r (lcr5lusf;za+bjdk* q uc:f: ttwo cars of the same mass behind it, Fig. 4-47 . Determine the rati tal; zfsbrd5:1k-lp*rfc:5( j+uuqco of the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herselz9bju l1gr) jq,wa6)od -xp 8;p myec/f upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise hereg jx8qd9jc-p6r/azwu m1) ) ,yb;o lpself 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, a5e fej8 r9:vf* vj */ine:ugrx 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 bx5+vk: vabco8 lock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface a )7sfdhor+ 3awy:zv5wv6pet1re in contact with each other, as shown in Fig. 4-51. A forszv:7 wt+fro epd)5 6vwh 13ayce $\overrightarrow{\mathbf{F}}$ 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 eaxqpk pic3 (n-.ch initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximkpp 3(qci-nx.um 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 fri7leef cdo1*/cctionless table are connected by a heavy cord of mass 1.*1co/ fdce7l e0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. 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 b unvqys :6 ml5n10 r*ls-ty);ncvw: s35$-\mathrm{kg}$ 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 st*m/ xxf k3.3ba p)4g0jcq s4lqabw;n sart 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 0.2/ .n w6s;yia-j) xfpgy0g. What minimum coefficie-fix. ysg;6pj)wyn / ant of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if2d7a;zs3rz8k l i3(vew v7 t5u 7oadcv the coefficient of static friction between thcivua5 vat33 7rol;7esz872zvw d (d ke tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal st r 6fe i*9a3ksqx) 4bm7bj*kflreet pavement is about 0.8. On how steep a hill (maximum angle) can you leavej* 4i bmke6fkrba f7x *q3)s9l a car parked?   $^{/circ}$

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

  A car can decelerate at -4.80 ka+8,)p itk kpan3 jucnd5923:v zgmc$\mathrm{~m} / \mathrm{s}^{2}$ 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 r7o loec +xh4mlns3b* t. xzz0(ough 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 haveflh zx nv)3,b) a very high coefficient of static friction.n)vlh)3fz , bx

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 frictionu jgkb;hd7c 0v9i8 q*of:-esv 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 largwkuw-uimode+ (.h9j4e a mass would box A have to have to prevent any ewd +4kmhjw9ou-.u (i motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How fark:dre0rq0gz 9vu r. s- will it go, given that the coefficient of kinetic friuqzrv9sd ker-g.0r0: ction 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 in contact and at rehrkc r2 -*f3fn;.ni gtst on a horizontal surface (t.*rnik; gr2f-nf3ch 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 crkffvd7- vg: 7 (2fdsegate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate 7 dff gd(:72gvfk sve-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 parking d 7f5kfr/wi)yf r+x 7dyour car in your driveway, which has an incline of w7yid/ff f7xk dr+) 5r12$^{\circ}$ . 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 slid bj49jk4gr ; jlwn+q2 uw)fhb-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. 4-55 lies on b9y: og:y0 qdwa plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed ofcv-)5su(e 4n b ew:sdh 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 reauu5pqw jm ;5)sches 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 agaii6in th unaw67zkf2rw s8-8*gnst a rough wall by someone pushing on it with a force directed upward at 28 i tizkgs7n2h86 wn*wfr-6au8$^{\circ}$ 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 prtzlpmb-0g0 7vojectiles as they melt. Consider a z0vgp70 -lmbt chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance a5wxvfjl1r05 for an automobile traveling at speed v is equal t15 falrxw5 vj0o $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward ow ba)yy9zxg+ y:np *4dn the dash when the driver deceleratesyg+ 4*pazwbynd 9x)y: 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 t l4av 3fxt59ugiven 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 conveyor n6kuti3s/ 3/o1qjosgm7gs jf1j (3psbelt 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 distancs3f /n ogts1 g/163o73kjup ijqj(msse, 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 fq3pkqm jn.m u704ucx7riction 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 tree:n jadi,r-g75o 5 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 modvfbq3t3 k1ky +(gn0wsb74m y zel of a mammalian heart, at each pulse approximately 20 g of bloodmzq fbtbk3n+yyg 7s1wkv3 (04 is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if2q f7 4+ag4a o*8ffqrasee n/b the deceleration is no more t r2 4age/8qs*ffn4 afa+bo7q ehan 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 bfh1 9. /5r;exu) rdocrt5lsbsy an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static fursehr.;9bxfc5 s5/r)td o1lriction 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 accidb/h+v0kse 4igent involving two cars, measure 72-m-long skid marks of one of the cars, ige+ b0svk h4/which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-98c c)ek f 3rr6rxgpa;1rhgj.4 means that for each 4 m traveled along the road, thc x;g3j6r9gerkr 8 1pfcr.h)ae elevation 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 th-pru4i gawsvn-k01 8m e Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average forc8r--g a kv0wm14sinup e of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch l3dp l ;f-l7tvwhere the effective coefficient of friction is 0.60. vdlpf ll7; t-3Will 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 hilly portp5 sjc.46so bfion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without sljbf4.cos 56spowing 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 experimeg8lmkzf 7yv;bgkj ;3ayb .4y1nts, dangles her watch from a thin piece of string while the jetlym;3g.fa kv1yy kg7; jl 8zb4biner 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 b:c459 g/)ly fwzkftp ia:d0+lza dok3 e several ramps connecting different parts of the sto f+ 5yztkfwdc3)iop0 ga:9ld/: kazl 4re.
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 5ee x:2. zwdieneeded to lift the piano (mass M ) using the pul5e:dex .2 iwezley apparatus 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 acceler/c3pl(r sv x/uating 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 chair, an engineer considersm:qa5z e.3m ag the following se3q.eamzmg5:a t 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 (660,000h7 6dern gdwg 20d.fz3 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length. Karen's relw2qsq+ 4;dh ope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purpo+sw;qe h24dl qses in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is usi ,y.e-pszee l6ng 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 n8rgls6 gu7+i q d6h(lbuilding is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who 1cxe+5/c pm nvare roped together are ascending an ice field inclined at p5/envcmx1+c 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.