Why does a child in a wagon seem to fall backward when you give the wagon a bcw:l,y s 4-e g-s1kpksharc-g:sky4,s-b1 lepwkp pull forward?

A box rests on the (frictionless) bed of a :gs*;8w atj wmf vw.s *tp 10limkc,.qtruck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the t pwm81wqga0s:l.;ism * k, jf.tcwv*truck

If the acceleration of an object is zero, are no forces acting on6a 9iuj8j6ugn it? Explain.

Only one force acts on an objei m eyr;d;o**nsml:qn55l/cs u /0uyect. Can the object have zero acceleration? Can it have0qs eld5/y/uenr*l :oum5s;*i mc ny ; zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a g748up8, qhjomlycaw2 9 :iziforce needed to make it bounce back up? (b) If so, what exerts t8y24uciz7 9,p qi:h8womajglhe force?

If you walk along a log floati 0otfr+m91nw*iw + cmmng on a lake, why does the log move in the opposite directio w+19*i mcm motrf0+wnn?

Why might your foot hurt if you kick a heavy dzdtz 91h3rn(g 7pt3ot esk or a wall?

  When you are running and want to stop quickly, you must decelerate quicbb4q*- hwtdlx0 :dj g41:rl(mh8bcsu kly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speedsgll:- u 4hbmdj:c1rd8xb(bt *w 4h0q to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the sd ze5fs2*:l ba oz1ab+ame thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull feza5osz1*2 : bbad l+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 that on a 1-kg rockq1yple x-n5 ;xluc 4s- 1.ndlw. Why then doesn’t the n x4;xd1yql1 sce5l.n l wp-u-heavier rock fall faster?

Would a spring scale car8imq+ r2hi tll ke;40u gx)uu)ried to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kk8+i0)2 mrx)tl q lue4;giuu hilograms?

You pull a box with a constant force across a frictionless table using an attach3/1auc1ud1,j. fysl x,o r rbyed rope held horizontallyfjrds .b /31cr1ul 1yxoau ,y,. 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? Explain.

When an object falls freely under the influence of gravity tr(qiwm9gwb m7./ bt9 phere is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the w 9(mwtm9gib q.7b/prEarth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when yodjl5/cd -ej uohh8 i.,u are on the Moon with the force needed to lift it on Earth. Compare the force needed to throwd5/hc,8u ho lj-ied.j a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of w38y fesv n3;trar (Fig. 4–37) pulls with equal force on the other team. W ne8vf3tsr;3 yhat, then, determines which team will win?

A person exerts an upward fbbsp00+)8sz2 wbw o nyorce of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (dy0 ws8 )bb2z0+spobwn ) by what object it is exerted.

When you stand still on the ground, how larguow:n ztth)5xq7 l+4ce a force does the ground exert on you? Whyt)h:5ozux74w qtn+ c l doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s t koz 1ixos /)e*7ip)dcar is struck violently from the rear. Explain why the head of the dooise )tx7*/z)pi 1kvictim 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 a.8trsdn(i4+o a 4 ppbwccelerates, the crate remains where it is on the tr. br8 n4ipo wa(4dp+stuck, 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 rfajt*b6 y ),iueaches its highest p ,)y ijuf*6atboint, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an incleyso rc/sa *jf9x ni.; fs*81qined plane? Assume the mechanism functions properly, even at an ang a1*inrs c;yjs9ffq*eox/ . 8sle.

  What force is needed to accelerate a child on kw(d;ra 4az.c a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider xrn -q2rix5) ibq jj7z 18yv:rsw 7eu+at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withs wfze 3dlocl52+y) .hk:idzo*sk4 -fktand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a .2z vz-4judc9 9gln4 :eghphx $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 s if the h(r98- zh ulcm0ut;kr n f0v8scar is traveling at 95km/h? lh 8h0ct 9n8 fmsr z;(ku0ruv--  

  What average force is needed to accelerate a 7.00-gram pellet fpz16qhupa 7c( rom rest to 125m/s o6hz a uqppc(17ver a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with //avvoilh6 1w an acceleration of 2.5 1ol/h/ wavvi 6$\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile track g 0 0z:a:qkzdb(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 de t8sopqqa0x7ok( j2v 6signed so that the maximum acceleration is 0.0680 g . What are the maximum and minim(a soop8t0qqk2 v76xjum forces the motor should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless 8ktffs fbps 7 8- +r9l-vkom-0ignle+elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevators- 8sn fi- rtlfbk++p9gvme 0k-7ol8f, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Whadlu6fu(u8dt0o4 xf)x)nn0 vtt maximum upward acceleration can it give the elevator without breako)4nl t 0ftvu6u(u0d8nfxx)d ing?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg includiya6d *b ,yi*jzng parachute) when the upward force of air resistance is equal to one-fourth of izj6yayb ,d **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 t127 m r bt3icn4q.dtlohe roof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over ant1247 cqndt iom 3rlb. 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 rope tied to thel 3wc( ka5a;pq box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). (wakpa;lq35c 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 a4g tc uau2p-)u 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) aq yptx0bc(qh:6z:2f6f)h edk t the moment it is hit by the bat, and again (b) after it has left qqfe z0(pfcb :k2x)hdy 6t 6:hthe bat and is flying toward the outfield.

A 650-N force acts in a northwesterly soa-.y yb 05mrdirection. A second 650-N force must be exerted in what direction so that the resultant of the two forces porm 50ba sy.oy-ints westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two bui:mnil:jusx i9:oif-3 l i, x+pldings 10.0 m apart. The sag in the rope when she is at tiix3sinji fplo9x +m::u -l,:he midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from another 31*cpnf vmryo9k*0s v23y p-ps.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 1c+ t;1t5 qqkgaeh .:rq wh,:kj4.0$-\mathrm{kg}$ 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 unic*sve.6cy .upaog k c8a(;o8 -qn(qlft to a new location at McMurdo Base, Antarctica, as shown in Fis6co ulna8oq(e (a8g c*yf.pk.c-;q vg. 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 cars of the o h zo/+:u p+)ditxwp2same mass behind it, Fig. 4-47 . Determine the ratio of the tensih ow dxu) pi:p/ot++z2on 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 herself upward using the bucket-pulley apparatrib+ (c.xry 8rus shown in Fig. 4-48. (a) How hard must she pbx+(cr.r ir 8yull downward 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 y*s,:p( ur, e 2vi:jyymh)+iawbek9p 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 (mas.7 s a( fmaoq)b/t-anjs $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with each othwtter6,-4p 6fn 0a oener, as shown-6 4 ,rt6 fntnpoweea0 in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.8)t7wca7/e *m d9xieqq0 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its qtc7q)mwx daie97/ e*"launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless+2q qq sr+k7oo)zj:2 pr 6pv95l rzbyy 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.j6 9sr7voqy:ozzp2rqy+5 ) q kr+ lb2p 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 bhla+f8*vm ga4-hu0vt etween a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a ouxzcn 76)c5c 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 accelerg70g .qetqj; e3wbdnn + evh) 1ecj6o4ating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slidv e0c;d3+bo n )nj1je q .gqghewt46e7e?   

  What is the maximum acceleration a car can undergoe ,il aypkbhf((b d496 if the coefficient of static friction between the tires and the ground is 0.80? k 9ehy(l afipb4d(6,b  

  The coefficient of static friction between hard rubber and nl: oge 8uzg1cs hd:10v5s bi)hormal street pavement is about 0.8. On how steep a hill (maximum angle) can yousc5dl z1 hi08g)s:g:1ebuhvo 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 deceleratef1e0.sjc 5huv at -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 5)k fqo/wg2sccwpt6nu5e 5s w3hx b6(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 coefficienhp2z;p1lk5y n t of staticp1 25kph;nylz 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 kinetim+7ywr0gd/*nk jiy2xe .sex.c friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (t-f7 j:g ypxfw 40emd0Example 4-20) how large a mass would box A have to have to prevent any motion fro:fg47 e0fdmp0twx- jym occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floo 3a,wmo a t6oec *o:mlen+/ah5r. How far will it go, given that the coefficient of kineti cwmtla3h a 5a* +o:eme/,6oonc friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at res * bg*nl ik-ci+h/a9utq0 rhn7t on a horizontal surface (Fig. 4-54)a 7nr9*ibi*- hghqn0ukc/ +lt. 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 frimssefnuo/1 2/ction between the crate and the boem21/f /uns sed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, wq em4).vng:lhf os;:uhich has an inclineu ;e4mo) f:.vsnglhq: of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide (z7 *c lvn,-clsrzv1q with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an angle ka(+o4dh (uz d$\theta=22.0^{\circ}$ 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 sp(9/xw ikup. 5zyz wrkashnh ()95s8 lkeed 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 mvn 0;u z;h5ddof 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing on it with4r jpbqq3o(w0 ov;,a qxp7x(lh+ var - a force directedx (pb aj(qroqh7x3 ov0avw4,lpq r ;-+ upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can bo7i2dmg1y;, - sl5xbi5t o aciecome dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitmg1i li5tx2ib do,sa; 75yc-och 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 fx**0fy wl0erlq f.+mv or an automobile traveling at speed v is eq*myxfll r0w0 +eqfv*.ual to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash whenl1i*5e o+bqcipq( ni /3wa2l-u6 bnjg the driver decelerates from 4bp2g u+i-el lib*1(ncnq w65 io/q3aj5 $\mathrm{~km} / \mathrm{h}$ 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 gip(+wt4 ) gbwonven 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 belt from where they are filled to ;nwr:ben oy:y4n 0c5j +k/kqkthe packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then dece:0e+rjw:ky5 ok4kqc ;nbnyn / lerates 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 kineticjg h) *t7eb.nnn *1pjc 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 ki w 6 kiqt/:rf*qe)nc(g (including 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 mammalian heart,9 qurxf; *x9 xhg,owi7 at each pulse approximately 20 g of blood is accelerate;rxwxh9,u7x* foi gq9d 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 if the decele;r7he9(kq9 x /w toyxpration is no more than 309t qe/yow7 ; xxk(ph9r " 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 accet q.twrrxq)8 *,k 2gzkleration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the groundqkrk ,.tzw82 x*q gtr) 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 of34fiz 5jwmwj61ql)qly vta * 8 an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initj t5qzf8* jy13mi w)vllqaw6 4ial speed of that car assuming a level road.   

  A car starts rolling down y x048yvfc0f)ww24oc lv b7lla 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 w 7 o0v 4x4clfyyl8wcf02l vb)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 th3r+n)5wbgtvm + fo3 hv*hldbfm 30t 7re top of the Leaning Tower of Pisa and falls 55 m before)+0 btf+d5mrotwvg 3n 7rhlf3 mv*b h3 reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but e1o0fmrp ff1g 6nters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having1fgf1 6o0 mpfr 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 portion of a cit p;f50ofjbw m3y. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level rp3bo;5ffjm w0 oad 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 thin piecw9 5a+ fhtyzv-e of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She not-htz+ 59avwy fices 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, z- ;vw+ fzfnhq:9hz- dthere are to be several ramps connecting different-vzfd:n9q w-zzhf h+; 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 F is needed to lift the piano (mass M ) using tn :c r6;m6y+v5wdw8qq :ing1fluh0se he pulley apparatus s l0 ;m6 8ri wne+dh1f:6v:5qu ywqcgnshown 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 8vpnoc+7c-( l7rnoq2c /q pci$\mathrm{~m} / \mathrm{s}^{2}$ 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 consi ok-io4e1 ob*eders the followio4ebo* oe1i- kng 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 Italivp v , 4w0dcwt5hx(wt14v1 xubj+et8can train has a mass 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 ropjov 9syt d3(jjq;(-z3hwh) daes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope,ao wzd -j9)dq(tyjjh(;hv 3s3 not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boag-dwvs tnfdg5b/bkj) x( 0c20ni(bb3npn k16t 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 buildingdhnycvf;z0qqtxwd b +,4s 1;-d nm+ 5s 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 are roped togx7bln jsb+ k0c*aku4ip-/ 9euether are ascending an ice field inclinebbjs*lxcipaen4-+09ku 7uk /d 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.