Why does a child in a wagon seem to fall backward when you /l, . xq9a6wg fc(lku7pnojj: give the wagon a sharp pull forj u p/afjl.k9:7oxn c q,wgl6(ward?

A box rests on the (frictionless) bed of a truck. The tr* l1w;gljoa:3 rt8hbn y:zengw 03d )cuck driver starts the truck and accelerates forward. The box immediatelyd3j:rgbnhwa:wo;81 cln3 *0 tgy z)le 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 acting z 9rf4nh5k)lu on it? Explain.

Only one force acts on an object. Can the object have zero acceleralk -.do4x o-g1 (ulqmction? Can it have zero velocity? Explax1codk-q(ug4 .lo -mlin.

When a golf ball is dropped to the pavemen9ot o q(c-j4wst, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, what exer q49-wo cj(otsts the force?

If you walk along a log floating on a la*cg .gjt fz jof24+/fgke, why does the log move in the oppositejz ffc.gjt 4 */2+oggf direction?

Why might your foot hurt if you kick 1t +*2lnayxmba heavy desk or a wall?

  When you are running and want to .0 9z;eca cgawstop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to ;e. azwa0c9 cgstop? (b) Estimate (using your 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 a section owv-h22q4qdjzu 0*0avg pg,j if the same thread dangles from the ,w2qqujg iag4pdh2 -jvzv*00 bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twic/n9 3kdi.fn ghe as great as that on a 1-kg rock. Why thdnfikhg . 93n/en doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give rplgsi/x;o, 3t .o +mjaccurate results if the scale had been calibrated (a) in pounds, or ,l o3tg x j;+/m.iprso(b) in kilograms?

You pull a box with a constant force across a frictionless table uo 2(hsghjnz3il i., 9atjer*-l8w8 rasing an attached rope held horizontally. If you now pull the rope with the so hwz(an2l i889hr gjij-l.se3 ,a *rtame 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 there is a net forru (,ofxt ea)7ce mg exerted on it x, rut7o(f)a eby 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 forc6kum j.n7ib a 6r-jn:de) needed to lift a 10-kg object when you are on the Moon with the force needed to lift it on Ea6ki . a :unj7n-jbdr6mrth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a 9gw+ut40 su;ghax)co q u qm aj+q:;3otug of war (Fig. 4–37) pulls with equal force on the other team. What, then, detec;;3 t+ux9oujuq mhwq gg a4o0 s):aq+rmines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe th3h;os ; hb99nci5 wu- 9zkdg5pgisz6je “reaction” force knbcohh wdg3z ;6 i 9gu ps9is-jz5;59(Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a 3w 4*+dw+qssak1w;au b zpp ;vforce does the ground exert on youpwb1d+ zwa4sw+*;puqksv;3a ? Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s carap)v4j,t+ f()a fwaqn is struck violently from the rear. Explain whfajq4av +at w(,pn)f) y 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 flatb4l2r8g dfdu 7xed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes7gl durf4 d28x the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block rec wwdt2, k;wkzns/uud303v l2 aches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than onw 2u;0 3/cz t2s, vuwkd3ldknw the ascent. Why?

What would your bathroom scale read if you weighed575q*tk-ssh7 bjszcs te5lf . yourself on an inclined plane? Assume the mechanism functions properly, even at an an7stk5fs7*ss .5t5bjzce q- lh gle.

  What force is needed to accelerate a child o/da28l m)jlo3g -mfxen a sled at 1.25m/s$^2$?   

  A net force of 265 N acceleree93s rh.x+vt 00ggy zates 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 is used to accelerate a , c+ -s bjy0coly43smpz*o3zjy1/qyw 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a;i:b(ygtn9qijs 5 f -k $76-\mathrm{kg}$ 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 requi80pnl nwcslb6 gx:ba.a. p3x)red to stop an 1100-kg car in 8.0 s if the car is travelix.p pg63ns8n bb .0ax cl:)wlang at 95km/h? -  

  What average force is neqq9s2vx q4 2wreded to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rifr2q4wqs qv 2x9le?   

A fisherman yanks a fish vertically out of the 8 l.(z/ 0 ostoprgb)sawater with an acceleration of 2.5gtplr/sos8(b a.)0o z $\mathrm{~m} / \mathrm{s}^{2}$ 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 (40z +a r00 ge3g5 mw9l8tx3qykva2 $\mathrm{~m}$) 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 qv o37f65kzunlppx8cz2w0 5ethat the maximum acceleration is 0.0680 g . What 2pn7 l56cwz0u5 fp8qzkxe v3oare the maximum and minimum 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 elevator. When the epf; r nbx/ s*u3k ,eq-m;tiys(levator begins to move, the scale briefly reads only 0.75 om b,nx p-3uessfqty;*k r/i ;(f the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Whl6qqs 22i9zggo7 6u(d q)w epqat maximum upward acceleration can it give the elevator wiqoldw2z7)i es 69qgqg6 2u(p qthout breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky czlhl:lw i 0j*fk:k54divers (mass 132 kg including parachute) when the upward force of air resistancew4klihf50:cz k*j: ll is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. Wuv q ncj bkm)zb/q3891hen he strikes the ground below, he bends his knees so that his torso decelerates over an appro9bnkbu8q) 1/mzcjq v3ximate 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 the box runs vertiitbqccp41e w-z2gw3 5cally upward over a pulley and a weight is hung from ccbi w1 e3t52pw 4g-zqthe 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 basketbaf6b mci: +hvp3ll 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 bap56k; /tfn)y8dfi c qjseball (a) at the moment it is hit by the bat, and again (b) adif/)t 58qp6fc nkyj ;fter it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N fbmxem)e/3 g w3orce must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your anxbwg)ee 33 /mmswer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between cv9j z)oz/tji46 whwh g(ei rtv)8;6qtwo buildings 10.0 m apart. The sag in the rope when she is at the mhz)vr86ww;eio(t g 6jt /zc 9h4vjiq)idpoint 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 anothej82m ut)-,jv5ps gusu r 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 14ba5u,h6pkeix3 20ytht ye9s 9jfv- c2.0$-\mathrm{kg}$ 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 ho.ri ld98lsviapkerwv..+i8*using unit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forclir.+l d ewp.s vair8v 9*ki.8es $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 xpat2 cr868nc same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling bep xr8826nc atctween 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 up9 whvnh51wlf 3ward using the bucket-pulley apparatus shown in F9 hlfh51wwvn3ig. 4-48. (a) How hard must she pull 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, dseu -3q6z,vrnrgci5 hw:/ -z a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (mass g8cx 8aa 0yd-geoc(k+$ 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 othe 9qsi;.g cxq07k8aro wr, as shown in Fi.7kco0 ;8 qriwxqsa9gg. 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 1.80 m above the ground,:s5ef 8e pmp3w 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 thews5pp 8f: mee3 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 b3h-v.wg/aaa-raq- e ch*q )c of mass 1hbqg-aa- ceha w*a/3)vq-rc. .0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. 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 ki9)i xg2+a;ui/oz bjlnnetic 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 is requirez8f.f.g/j n,jiez6e h d to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What k; lscsnbm91h1p,1z n1 i4 x+8jv yazuminimum coefficient of static fric1 4s19 mu zj8znihpy,s+bxn;k1l 1avc tion must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo my48ei +rl4aq;dj8p hif the coefficient of static fmiylrdj h;p44 8eq+8a riction between the tires and the ground is 0.80?   

  The coefficient of si f3 a4 sqv.mj3wz2/ruti/r*etatic friction between hard rubber and normal street pavement is about 0.8. jwq4 ei /23i avz3*must/.fr rOn how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -5c fr1l0 7pv;udbqggayc.8 q*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 re - pn:rpl -8 j4op.qhuwo7j4gy+nrmjq8 q0b9ust 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 coeffici 6*gjyw ez*q8nent o j8*y*6qg zewnf 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 f e/e1 0l6jio a:vv vt1,;oaakeriction 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 i+o0isfev+m3) how large a mass would box A have to have to prevent any motion from occurrii3imvs ++feo0ng? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acr o tp79pwk6kz 9)b1dmuoss the floor. How far will it go, given that the coefficient of kinetic friction is bu7 mzk9dpo9wt 1 k)6p0.20 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 andi.t at5i3xry 2-hwb)g at rest on a horizontal surface (Fig. 4-54). A 6y5ihwb2 -.t3targ i) x20$-\mathrm{N}$ 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. Theu5z8n i . rsi9*k6ux ibsw+j)n coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can dec)j.unix n 6i5 ks8z i*+9rwbuselerate 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 drivew+h; fm2k 0xzna3sd 9cvay, which has an inclin hz2fx;+v mas3cdn k09e 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 with a tpu9/:0 0gd eaou(( +1g gfcpjs,tlci 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 ; sc3qvluz8 4g9-gga+iz.3 qv, l nehjFig. 4-55 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;k 8z;f(( 5ncmuz kmwkitial 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 reach eeml (gwam*:29i cc6oes 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 placey5r:iofmf 04cun/ u0c+h- yk t against a rough wall by someone pushing on it with a force directed upward at 2804r-chyi0u5 nmk+f yu/ co:tf$^{\circ}$ 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 r x)oe)hca)p o.oofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with a pitca .eco)x)o h)ph 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 distancpv/ksg. --lmhw2yy :d+l su-fe for an automobile traveling at speed v kywsu p/+-vh:y2-lf. l s-mgd is 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 dashboard of a car slid*w a-b1lk ob,bes forward on the dash when the driver *1 w, k-lobabbdecelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given k ibf0u 1lyx1gl ;h/zj2 pi2n*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 fi6v l0jm w1p)nki1y:tc-+wg vqlled 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 distan06 n-i1kpc)y +vm1lg wwtv:qjce, 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 f urc)p)-z/( qdx9kjzvriction 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 bicycle) can coastiy+w: v(6 7xs8ynjkuh;cuwi; down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at ea 5.pl* sd.sxpach pulse approximately 20 g of bloos*p5 a.dsx p.ld 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 automob8iu dh-i gipno+5/xj4ile crash if the deceler4j/i5ou+id inh -x8pgation is no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal accelegu:-b98cv9 p vqrf vu.8kxo 9jsosx.6ration produced by an earthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient :pv oqxs j8obf9 crvu8 6-s.k9xg v.u9of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an accinfvqj)qv. o,0 ;rigky3a 0y 7(apivt 7dent involving two cars, measure 72-ma. a,q kvpr) iytv0(o0gij37nyqv; f7-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 initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m travele /tr;r/mo:7hgun* c-lu: p uiwd along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after travru 7m;nul g*w o:upr-//tc :hieling 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 To;q(o j vya0 jxv84uwe:kw. :pfwer of Pisa and falls 55 m before reaching the ground with a speed of W.j xuv( fewj:kyvq08;o wp: a4hat was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12yu*.s/ w qkpg1wysz,) )pg,kzlb 0,mem/s but enters a muddy stretch where the effective coefficien0,yzwgq z, up )l.skbk 1gy) p,w/*mset of friction is 0.60. Will 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 portion of a city. Anhod-)n 2 vmta: 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 road fron:votd2)am h -m 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, dangle3qdh7 t3 bmjg9al:(d ys her watch from a thin piece of string while the jetliner she isl d 3:3m t7ah9djgbqy( 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 ramps conne0pz9d3 tlfpz( bf),xv cting different pa0t3 ,ffpvbdz xlpz)9(rts 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 force0 ass/drt:*b llh9 o2o F is needed to lift the piano (mass M ) using the pulley apparat*t2ohl 0d 9/lsr:obasus 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. d/f0yz.q h: y,fog(*un:b gcw5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 fs slv 1qp0 ijyec r(t. .o3rh;r./gil4or a child-restraint chair, an engineer considers the following set of cotg1y..s slo4 r3ejv/ pil.;qhr(i0rcnditions:
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 trx5 +k eyw gf+)ha5nhg2ain 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 safe.y9hryyyqdu .7d x-;kty ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel fryy 9.d y-rx7d kyq.h;uom 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 using a " 10-1 6 3r bpk8ausn5ru f5u2$\mathrm{~b}$ 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 talz4bo/1 u 2elmnqdq6i1 qn8kj1 l building 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 together are ascending an ice r9k v06:agpr wtw)n0efield inclined wnk9 6 regtap0v 0)wr: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.