Why does a child in a wagon seem to fall backward when you give the way6zz+ fwtb8 2m je:a5bgon a sharp pull forwa8z5a2yzj 6wb+tbe: mf rd?

A box rests on the (frictionless) bed of a trux:e+stbd ta:2mf2 ome)0h/;np,cg h sck. The truck driver starts the truck and accelerates forward. The box immediately st2m0 2pod) esb /+asfe:;,cxnt:hgtmharts 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 f(5n oo1ouzd:y,l/ypgy,)y sd orces acting on it? Explain.

Only one force acts on an object95 -d y9wjo0 ,fr7uhdrncx vv6. Can the object have zero acceleration? Can it h xnh6-5jr90dr 97uwcvd,ov fy ave zero velocity? Explain.

When a golf ball is dropped to the pavementk. 4mngkw0u8s4o+oh x, it bounces back up. (a) Is a force needed to make ios04.+un8hmkow x g k4t bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on acs/v3 -tica60oe0f:fks 9 aol lake, why does the log move in the opposite direc:akc6 i-slaf9 00vscet/o fo3tion?

Why might your foot hurtsfmb;i 8s+2s a*hvg.it tz 4:e if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate zm9y*e h+d(iy y6x1zz8xh nm9quickly. (a) What is the origin of the force that causes you to stop? (b) Esymzn xh6h 8zi9y1 d*(myez9+xtimate (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 thrpw s/:p7cn, r7v ghif.w,qr*njm- v .qead from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person rqr,mpv. :-/jq f, hiv*w n.g7nw7spcgives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock.6.z mcizc seawb8f:6( Why then doesn’t the heavier rock fall fza6 .febi s6:c8 cmzw(aster?

Would a spring scale carried to the Moo lymu1z 0j,tp5n give accurate results if the scale had been calibr5l,j0z t 1umypated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force acrossn lq8r. *z:rlv a frictionless table using an attached rope held horizontally. If y.qz: rnrl8 l*vou 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 therej-7sc)r g2 xxe is a net force mg exerted on it by the Earth. Yet by Newtgce 2 xx-rs7)jon’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 1 +4p)aldxun. c0-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-d4c n+x.lap)ukg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug os 05ud3mbn xfq:t 8.(u igkz-fyp2- 5 ofhfj3pf war (Fig. 4–37) pulls with equal force on the other team. What, then, determines whiim u fn 2uj. t(f-fxg-5fp0bokydps335:qhz8ch team will win?

A person exerts an upward force of 40 N tyfm6 wi-5kwuh 9g8fv:o 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 exerthw ikv5y 8 -9wg:mfuf6ed, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert ont+p78p vi1 3glv f9lzg you? Why doesn’t this force make you rise up izflpv+9 pgitg8v7 13 lnto the air?

Whiplash sometimes results from an automobile accident when the vicp:(mqip6 z tr+z9db2j-xp c1ktim’s car is struck violently frzpp6mtb +kp dq:1i-rz ( jx2c9om the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the mkt-7j a:ssq *9d0ucbbed of a flatbed truck. When the truck accelerates, the crate rsstjaqud9m 7b ck0:-*emains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a pub p0tudejzff6 i77g/3 vy/wf1sh so that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of i03w6e 1g7b7d/ fpfztjyvu fi/ts acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an incli gj5ek7oi texv2 ho 4ni6,js)3ned plane? Assume the mechanism functions k4 oh 3gt52xei7jv6nj,e ios)properly, even at an angle.

  What force is needed to akutn(f i*o (0pz-lxl8 ccelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.30xx- dlqv*x 4 7xat* j.kvi6.fw$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand (aifiz(wis*9v 1c53 yyarbl8 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 awj1f1qliaj**-l qnp )mwj*1bs3 :vl e $76-\mathrm{kg}$ 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 car is -tqs-gwii3 bob a:r-0traveling at qw0--sbt3igr b -iao: 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pelleenk+)ncl(hq tds 0h6*t from rest to 125m/s over a distance of 0.800 m*( q6)scndl eknth+0 h along the barrel of a rifle?   

A fisherman yanks a fish vertically out of thel3e 11l k7azlt water with an acceleration of 2.5 1kt llz713l ae$\mathrm{~m} / \mathrm{s}^{2}$ 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 covefzxcca4z )*2+ rf/cp xr 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 6 w;xl.uxb:(q 7f tdk-wdey(amaximum acceleration is 0.0680 g . What arxxwf(bw- :dytad67q(; lek.u e 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 au6y jwe6 qka zm m;a)h*rpr91( motionless 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 elevator, and find the direction of accelerationra wr(9 q)haj6uk m1;6zyp*me.     ----待选择----downupward 

  The cable supporting a 2125;/q hs6tofu 9 rit86cvgo q*0z-kg elevator has a maximum strength of 21,750 N. What maximum upward accelerat6 rqoc*vzi goq;0uf 8t9h s6/tion can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceteqfvqxa2( +8 leration of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to t+8qx(qefv 2aone-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. When he strike-bxaba *dc-j f(x j0q7 kb38mas the ground below, he bends his knees so that his torso decelerates over an approximate distance of 0.xa*djk- 7qxmj (fa0bc38ba- b70 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 ruiyy174 b0lg 1v m+jjocns vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side ibg014yymjojl 1 cv+7of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball (a:hn1 j. l78ls hyg nj5t1poct ,:gcfplayer
(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 moment4ejni+(b m 0 6iw8bkwd it is hit by the bat, and again (b) after it has left the bat and is flywdne( ji w60kbi+b m84ing toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N forcc xmzi* .a /vw5y*oy+a7 rwai1e must be exerted in what direction so that the resultant of the two forces points weaywvyr c/5ia7xm+1oz.*a *iwstward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betw(h2ohwprpq f5w v9* (teen two buildings 10.0 m apart. The sag in the rope when she is at thp(qw9*trwo5fph 2 hv(e 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 , r64kdavt *uoby a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 1hu; cgvn,bi0;0z*n ug4.0$-\mathrm{kg}$ 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 unoniu4 452 jvofit to a new location at McMurdo Base, Antarctica, as shown in Fi voij24 o4u5fng. 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 same mass/48;yfv d8 tsfmayh:j behind it, Fig. 4-47 . Determine the ratio of the te4; yh yfa8vd:m sftj8/nsion 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 apparatu)l2 ,m1qxt+.kkhagojv 2zu7as shown in Fig. 4-48. (a) How hard must she pull downward to ajq)ako1mzlkh t 2x2 . v,+gu7raise 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 ht rpno1*z4*t65$-\mathrm{kg}$ 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 (3vq(mm 3(bp 4ykj2cwx e2f.rf qg 5o(imass $ 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 conzv1ym*qz,+l kkc m /;up5z:yr tact with each other, as shown in Fig. 4-kzqupm ky: * lz;m5yv /1z,rc+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 abovb*l/or vyqeq9bpspq3a.i*-9v68/ urv5ucmfe 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 "launch" speue oqc8v5p-rvf 6urb /9 isp3b*qql.9m av*/ yed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a h )x:y 0; ylsitm)3kduheavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the lutimk)ds0h)x3y; y: 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 2infug )(ox.zbetween 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 rev6r/lvmq2 ,r hquired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating a ye1 n9ig/vn6st 0.20g. What minimum coefficient of static friction must exist between your feet and the floor vi n61eny/ 9gsif you are not to slide?   

  What is the maximum ac s0deyf*t x;g,)rqau0 celeration a car can undergo if the coefficient of static friction begfa,y;t qeu*sr0dx)0 tween the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal ao: b;y-i:bt3f n:h kvstreet pavement is about 0.8. On how steep io3vbbk:t:y:nh f;-a 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 atlcnemr 0l552l*v g0g trzg1h,cc 1hf8 -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rx qb6) iajfr7/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 a 7*tbxo2-pjp wc 9fy9q 6:trjgn asphalt surface have a very high coefficient of static friction.*t 9jbf j6:y72ogpcx9rwp-t q

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 frictim sck3st ( yqho,gh9jazz, l2y.g(67pon 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 large a mass would u7.i0qnq ut;j9 ,qt uhbox A have to have to prevent any mj79t h;qquuuq 0.,tniotion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across vk+3ar7(xdm n the floor. How far will it go, given that the coefficient of kinetic fr xadm3( r7vkn+iction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 7/5p .ks-1mgin4c aa0w3jo8ku i9hs bn5 kg and 110 kg , are in contact and at rest on a horizontal na kj4.si1ihsmpn 0go9c a/k5u8-b3 wsurface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coef:w ,-ykmwfbv5 vhq +v+ficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having thhw+y fvv b+ q5wk-v:m,e crate slide against the cab of the truck?   

On an icy day, you worry about parking your c 1s(gs,l(b lztar in your driveway, which has an incline of 12gl zs,(b stl1($^{\circ}$ . 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 wit g t/,v+*l:dnlsa. kpoh 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. 4nh16b xj3e/ 3f9xerkb-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 initial speed oeg f0.x +vsb;y2+sinjx 6jds;f 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 steepeor3c91 , v 4w0oobr0qsi js3 +drj2udmst 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 against a rough wall by someone pushing on itu7upo 1m,j* sp with a force dirpsp,7uju*1 mo ected 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 becomexm (p3so0 5x8*axd cey dangerous projectiles as they melt. Consider a chunk of ( a8yxcx3mp0d*5x e ossnow 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 stopq8n*(x 1d-f8kjegxzrping distance for an automobile traveling at speed v is equal r 8 zd*fxx 8egjnq(1k-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 when the 1v3x7hn kjnif . ;vomu9+o4 utdriver den;1ujk m7nvvh+t.fi oo9u 4x3 celerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial 9q bw/)ro 3jh)e ty7f/mmfy l(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 conve (j5enl/wu z7iyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and /lwien5j7(uz 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 +awgxv0)rhee 9qr p ex+utjr*4c67(i of kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (inclu 8 ktz,bipeie. d.s81 wp6km a+ykcf04ding 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 azt q)hr+ u4se39bw0xof a mammalian heart, at each pulse approximately 20 g of blood sz)ewuqt3b9axr + h40is 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 o+n ,hn-b0 ut;nleaxj/i7/wg64 ijaiif surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the forceji0-bn x6i;,j7+ge a/iwnahinl4/ut on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an ea:9kz q,6q)nljdsz phdogf5 */sa1 /birthquake is a , and if an object is going to "hold its place" on the ground, show that thenah/qsl 1 5,bzzdoq*gk9 6j/f)dip s: coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, exami3 grph*ex.qsj0x5z j5ning the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a sto 0exp53*5z .hjxg qsrjp 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-i.3cj4k37 y;gvh es uzun-4 means that for each 4 m traveled along the road, the elevation change is 1 m).e;jc. zgv73 y 4hus3uk 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 the Leaning Tower of Pisa an00j43i xia3. zyllaub0ij)y dd falls 55 m before reaching the ground with a speed of What was the average fouliy b3xada)liz0.3 yji4j00 rce of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddyrln*ms vb1y ;/ stretch where the effective coefficient of fr;yn1lr sv m/*biction 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 py38rukdmtz,8l) vtnrco -4q9ortion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hillydc3qv z8,- 8 trnul9)kmrto4s without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles6w tz8ive1n csi2w5nzna/0:f her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string 8sez6ci:wwnnf01avtz5i2n /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 ra ofvj*-))n ka: )bet*js:dsjh mps connecting different parts of the sto-hb:*ef))os *k:sjadvt j )njre.
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 tv wtbt6 ut/h0mb 5mo1xpr)4)zhe piano (mass M ) using the pulley apparatus shown in u/tx ow0bvmh61 4rtz m)5)t pb

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 2jq48vq 7k(jdcmf qwwj+j (-8 -glfxn 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-restpgi v)(; rl b): 7orjivti/nm4raint chair, an engineer considers the following set of conditn))ilmi(br/ tvvog i: 7r; 4jpions:
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/t l. c7x,icler89c sk,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes o7-gl au nac77df similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has -lc gu7n7a7ad 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 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 using a " 1c upd-1g9zy+ o0-1 $\mathrm{~b}$ 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 talljtk/k4 w1 2ro j o7igsevbqg:xk6,)7z 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 field :rm 3x1mumjpdr06qm qi49v4 d inclined at x 93 m rj1qpmiddmmv064r:4qu 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.