Why does a child in a wagotyx 5x9v- ew) 0;xzzjvn seem to fall backward when you give the wagon a sharp 0-vtyze 9jxx;xz5) vw pull forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts x +,cywu2un6: r3rp wgthe 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)+ ,: wcw6pxrr2u nuy3g 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 on it? Explain. z7oip4ev h:oq0nt: 6a

Only one force acts on an object. Can the object have zero acce(8mt2kqtg j1 bleration? Can it have zero velocity? Expb tgqk2mtj8 1(lain.

When a golf ball is dropped toksrn0;; wguy 8 the pavement, it bounces back up. (a) Is a force needed to makeg 0syku ;rwn;8 it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the lohin nqfdj 4 2n 6g:nukm0((a6pg move in the opposite di0fhq(6ugnm(d4ani n k jn2p6: rection?

Why might your foot hurt if you kick a heavy desk or a wallq;5le k.ngv. h95idun?

  When you are running and want to stop quickly, you must decelerate quickly. (a)v2 ewws8) q)0j:ridu-mevky,zl5 z 0k What is the origin of the force that cae , i:)j zykk)ul2d-w00v5vems 8wzqruses you to stop? (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 q/u 1ko0ew --uq yp.msthe ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pule0umy ps-q -k1/qo w.ul 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+tpyk84 v 8 s,lqq3woh:v2y9 s3ugb8omkj: ya -kg rock. Why then doesn’t the +o9 s8 :hqs gy j k8yyvvm4k2,b3uptq: l83owaheavier rock fall faster?

Would a spring scale cag.-i7rie194qmcto oq .mz 8iprried to the Moon give accurate results if the scale had been calibratedim i 4z7.ooqet .m8c1iq9-prg (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a friction4uif4t2 9 :ztyjj3cdrm: v 3cdless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal :4mtv jc34 idrd93t2yu:jzcf (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 theref u t8pc)*:w:1 ghdf4qfjv8s n is a net force mg exerted on it by the Earth. Yet by Ne 81)pj4v8cd* f ufw:shg:nqftwton’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 tfn:(gz as 61e wmba+j+o lift a 10-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-kg object horizontallb 1+ wmfag:+n a(zj6esy with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tuv r0y4ir vkh v*5+dc7zg of war (Fig. 4–37) pulls with equal force on the other team. What, then, determr 7v5rizy 0vh*4dkc+ vines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries.ezt3dhk)d6 0 ;ccpf j8 Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) i c p0;)dtz8hjc d6ef3kts direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the groc)dmg6 v5tvo;und, how large a force does the ground exert on you? Why doesn’t thiscmt;gd)56 o vv force make you rise up into the air?

Whiplash sometimes resqb 0:* i;fmbram7+ stmults from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems tb :;rs+* a7mqi0m mtfbo be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck accelerat hth./n /p6djwv;hl3nes, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to ah.hvl6; /wnh djn /tp3ccelerate?

A block is given a push so that it slides up a ramp. After thb 8hqrra 8fc 4l),f*rp wv0*lce block reaches its hir q4*cp r)ca0*lvw,h f88 frblghest point, 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 /b s+pp 8evgp;ta6g2tread if you weighed yourself on an inclined plane? Assume thes6g;b e2p t8pavptg/ + mechanism functions properly, even at an angle.

  What force is needed to ac q-ujra7e,e; flw3ea ng6:n :ucelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N acceleran3ouh b7+ey tcm)d7p 4tes 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 wi1d+t fu p*.8 jh mtx6qq*nuvo;zj*qx3 thstand 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 o5 4/ke3xz,kcdgjxk -cf a $76-\mathrm{kg}$ 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 if1pp ri.n7+z+ktms76la ptw 8u the car is traveling at pi1r8ta+ k 7mz.p6psutn +w 7l 95km/h? -  

  What average force is needed to accelerate a 7.00-gram )alewt .oj,h- pellet from rest to 125m/s over a distance of 0.,w . hjel-ot)a800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of 2w*q+22o c.s s59u vojru0ugt a.5 +qotss20ugj2w co* u.95ra uv$\mathrm{~m} / \mathrm{s}^{2}$ 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-mil5e0pf/i( 5jxjylgqz+ 6v 8pjbe 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 bemd5o4q vl1yq, designed so that the maximum acceleration is 0.0680 g . What are the maximum al ydq, 14q5ovmnd 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 eleva4x feykm6mg)i+6 sp k0tor. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration0+sygfm )k x4p 66meki of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximusierj hnhs7a a-wx2l:pfsx;f n81-52m strength of 21,750 N. What maximum upward acceleration can it give the elevator without b8-n s:ahlai s5 xffrxsewpj1 ;72hn- 2reaking?    ( two decimal places)

  (a) What is the acceleratio,q7xj 69qjqi )bmn 4vj,zz6v gn of two falling sky divers (mass 132 kg including parachute) when the upwarqq, igx4)jjn69 b7qz,vz mjv6d force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a houj)cm y)68b3y apj .gbn5g mx:9uqtmw;se 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approxim)6mwj )bu .g:3y m8bmnxpyajq c9;5gtate 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 vego)v1zc y-s9 xrtically 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 they-gv )x1so9 zc weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball pm b. r5d+rqqc5layer
(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 moment it is hit by the 0 rd6r4za.w:xal*q vdbat, and again (b) after it has z:aarx4qd0w6r *.v ld left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly directynx)iokt7)hmq3, 7 bx ion. A second 650-N force must be exer,x q kyn)b7xt37omih)ted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two bu-6h azb mst9+kai (n9j ty6nu)ildings 10.0 a( jhnuk6t6zbyam )s- 99+tinm apart. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging 0 bv4fmbou5ad:c1e fty7 )+fiby 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 14.03*s0fd(qw8 xz ew.wzz$-\mathrm{kg}$ 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 houshf-8smuzbdn d2;:b y- ing unit to a new location at McMurdo Base, Antarctica, as sho sfbzu ym 8b2nd-d;:-hwn in Fig. 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 carsew3hdpf9xb+f kn*+e* d4 -aet of the same mass behind it, Fig. 4-47 . Determine the ratio of thd43fbe*txdh-k9fnpa*e + ew+e tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using thh o)im yift+*amey o ;+:h*7ile bucket-pulley apparatus shown in Fig. 4-48. (a) l:e a **m +fio7;my+hotii)hy 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()yjod(7 hhw9m0owj ysu r o01 began, 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 blockpfk(;9yf8v r7s j. nfj (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with eacrk2gd .mr)m) ii4upsj.6 yms4 h other, as mrkm. 4.4r)su)pg2 m jysd6iishown 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 1.80 m f -7smgmux)6gabove 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.s 6mxugfm)-7 g This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frict.ywjrta-0q 4u1 bgg5 eaqu2o0ionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tens rb.5ae -g twu0jug1q o40a2yqion at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic y;s( usu3zx,t 1) yzzqfriction 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 required tohhl. aak0 2:wj 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 atxo c*s, ujkm,; 0.20g. What minimum coefficient of static friction must exist between your feet and the umx*ks o ,,j;cfloor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffice)91huw+vzef: 4 m mzuient of static friction between the tires and the ground is ) 9 fewz4 :mz+m1euvhu0.80?   

  The coefficient of static frictomx v9+j x90sn8ug k:vtj+:woion between hard rubber and normal street pavement is about 0.8. On how steep a hill (maximum angle) can you lex :m +j:k o+9vvxg9jusnw08o tave a car parked?   $^{/circ}$

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

  A car can decelerate at -4.80x/87 -pkuyetzi.fy -x8 0+s wl8p hdgr $\mathrm{~m} / \mathrm{s}^{2}$ 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 osa kfzl5du1*u kkjdc0nzu0l/4 06is 8n 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 coeywv+6yi /x 6djfficient wy 6/di6+jyxvof 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 frictionyq :px+ ;e 1m8jgduv+l 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 box A havz 5fav3uj 2w,1v6aqv fe to have to prevf,vv35uf 26qazw1 a jvent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slidqzt 1 wp2ea c3pjhy+hu490tz :es across the floor. How far will it go, given that yhqpcz1423 u e0 tjwp:9hza t+the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kglgx ios:8k8j ;p b3y)o92a kkg , are in contact and at rest on a horizontal surface (Fig. 4-54s lx ko 3gkjao: )8k8p2;bigy9). 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 friction be- )mdgto2pk1d tween 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 the crate slide against the cab of 1d-mp )ko2gtdthe truck?   

On an icy day, you worry about parkiddj)ups) l4b1xt dy0 ys xpx)67j0wb9 ng your car in your driveway, which has an incline of pu sb7) xw1y9bds jxxdj00 6)lpdty)412$^{\circ}$ . 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 28z-f) t6cdfzg .$^{\circ}$ 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 anglbx)x z- w5ahb+juc63he $\theta=22.0^{\circ}$ 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 spe/w/m er*6r k8snvn:ined 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 of 66 ayf9xe ) zj;aai.yh 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 bj5su-qb un1+ with a force directed upwj+b1u-b nus5qard 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 become dangerous projectiles as the(hd. ipi7vee04,j fygy melt. Consider a chunk of snow at pgvf i 0,7yiej4eh. (dthe ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distaymo (8*q,2 nkq8vpsal +p6nk lnce for an automobile traveling at speed v,pql82kk aop qs8mynvl( 6+n* 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 slides forward on the dash8yj 8ut7, a8krr4k emu when the driver decelerates from kke8u7tr8mu8,y ra4j 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 aalu0nctnjux+ r*rjvl:):-,rn 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 the packing soj n(dp+m-m*n. 2r mlqtation 11.0 m away. The belt is initially+n2-(dnmo*rmpjlm q . 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 the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic friction 7v* uqc3bin+og( pyu ;p/-ci jbetween $m_{1}$ 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 coaf 59,lf*vpl 0:dbhstust 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 simplifiigc+b8p,g *4q cj y0zmed model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated frog0p +,jiq4 bcc*8ygmzm 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 autb0l)rv4 tku0p3n i3t4 f esm8yomobile crash if the deceleration is no more 8uv f0spinye3k 3t)r4m0l b4tthan 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by aulk1om305i ;hgzbz( vn 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 ground must be at hml01bz3(i5 ;og kvzu 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 szwl:a te9ck9 *cene of 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 lc9wk*z:9 ate 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-i7gfk/hlxp 0de4 h2:-u )-w21s2 fnmfj qkd jhfn-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going whe1j mfse)n24 0hu dqhxjh:/2gf2f7k-kdl- wfp n 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 bksgde: + v7v.+ iik 5qqvg(nfjiu3 1:the Leaning Tower of Pisa and falls 55 m before reaching the ground with a spqvdv nkk::s5f7g1.(vu3bji+i eq i g+eed of What was the average force of air resistance?   

  A cyclist is coastinnra2+pla 5+zr0fk8 vaj u9g34zb wma .g at a steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m+nlbr0 4vaa2w aafz 5 pu+.j9k3zgr8m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portion of a city. An imporawkk6 -jr3d(*d-d 5q4/fgpm 2o xzngitant consideration is how steep the roads can be so that even low-powered carko iw(4kmdxq dg 6 g-j5dpa2-3n* zr/fs can get up the hills 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 phy t,*ji n +;tjeimxs4o9sics experiments, dangles her watch from a thin piece of string while the jetliner she is itj;j *soi 4i+9,mntexn 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 connecv 8nhm6cvqoz:4*xh e8/y ry95h*jl uhting different parts orvh * 8y9mxu/h6vl :h8ncz q4*y jho5ef 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 l2:1a wfhpopbz -*) rbwift the piano (mass M ) using the pulley apparb -hwob*p1 )w:pa2zfratus shown in

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

  A jet aircraft is accelerating at 3.5 -6j:ml+r5j6xnnjtq19vabzb $\mathrm{~m} / \mathrm{s}^{2}$ 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 r*b)t q2ch 3yoconsiders the followi3qy*2 )t rcobhng 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 Italiafv- uuwmm-9/2 x1srbz n 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 saf pk9d/lzio5 *xety 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 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 climberki9*ld/zp5o x is more likely to be hurt?

A fisherman in a boat iszsuw)q /2iz 8 t6m/huh using a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is a cnok r5(jys88llowed 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 anne76;tjqhe j 1t +.iyy ice field inclined at 21tjen1tih+7;e j .6y qy.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.