Why does a child in a wagon seem to fall backward when you give the wagon a6l5 kezo7gi mb* s0en cbcm(.. sharp pullozm*(0.k7n5.blcge isbc 6em forward?

A box rests on the (frictionless) bed ofmd* f6r9ulc,webkh y(;c i r5- a truck. The truck driver starts the truck and accelerates forwa6c, hd-i9e(w;lku crrm*5 y fbrd. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces actrv hbdi73j +/-hghll-ing on it? Explain.

Only one force acts on an object. Can the objyu2,tec +mizj+.sbize; )vk 6ect have zero acceleration? Can it have zero velocity? Explain.6)seu,; ymb.++tz zecvk iji2

When a golf ball is dropped to the pavement, it bounces back up. (a wxg3r4s3jx.:ru5b nw 2sfn:c) Is a force needed to make it bounce back up? (b) If so, what exerts th3w rf.csx2 snn :g3rbj4:5x uwe force?

If you walk along a log floating on a lake, why doewat rbdr2 z8lej7t 9)2)wv5w q. eskh8s the log move in the opposite direcwz 2r s52kb88e qv9 ra)ww7jt.lhd)tetion?

Why might your foot hurt if you kick a heavy desk owsavx u .rtmaek 2:a*u -k-n35r a wall?

  When you are running and want ts7kg,/b4ti,-r z d.hg0cz svjo stop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (usin.-,gr zs0dzkht, gc/j74 bvisg 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 nv*b7p+h ua,p of the same thread dangles 7h+p,napvbu* from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the 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 thaam,jk q1(. laht on a 1-kg rock. Why then doesn’t the heavier rock fall.j,ah1mkq( al faster?

Would a spring scale carried to theqqk ,4wyp7x.* dfu5 gm Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kx.p5qu*,wk4 qg 7dmyfilograms?

You pull a box with a constant force across a frictionless table us )bmdjex4z urwsn217+ing an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the ssnz421)d7uw+ jrxm eb ame, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence ofh- vs*v3gp(gf:q; rld gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the E3gd-l( rs ;f*gvqpv h:arth move?

Compare the effort (or force) needed to lif76 o rrzq3kzl7t a 10-kg object when you are on the Moon with the force needed to lift it on Eqok lz7 367zrrarth. 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 tug of war (Fig. 4–37) pulls witvaz: u* xqwkn j9,.vw:h equal force on the other team. What, thnvvk 9*jx,azwuq ::w.en, determines which team will win?

A person exerts an upward forc hqbohetxg,)gx21o;(t 24jl re of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is;(t 42bhoxl2qtj g )h,xeo g1r exerted, and (d) by what object it is exerted.

When you stand still on the ground, how loomb5 xcrrb*. 69yds*arge a force does the ground exert on you? Why doesn’t this force make you rise up into thb5r.x b*cyods rm96 o*e air?

Whiplash sometimes results from an automobile accident wbkz -yza:2*j uhen the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it :*-ajzk zu2yb really?

A heavy crate rests on the bed of a flatbed truck. When the truck acb:9 ,gpv5pbt,rqna). q;k bh wcelerates, the crate remains whe;b,rha59g.,bkw qqtbp: pnv )re it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. Afcbl ./,h8wwots0o. h+s-3ogtqu) prdter the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than onq3 ,cstoh0 ph+)so/gt.wuwl8o - b.rd the ascent. Why?

What would your bathroom scale rswsz gzq4bjx79m1 */g ead if you weighed yourself on an inclined plane? Assume the mechanism functions properly, even a4g *1/q9x wgj s7zbszmt an angle.

  What force is needed to acceeeh1 ipah wq+08d 92nb,gk ac4lerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at wimwb;kd.2 4hzv55 20tkg hqm 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 accelerato1flk9q dm)h.e a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of 9411* i snvu2jlf nmora $76-\mathrm{kg}$ 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 i)1o z2wq,p ynzn 8.0 s if the car is traveling at 95k,1np)y 2owqzzm/h? -  

  What average force is needed to accelerate a 8 k:eov*s5vc0j as,sg7.00-gram pellet from rest to 125m/s over a gjvske:5c *s,8vas0 o distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically outu)qj13l vmv 5xz jts2 rziat88x4ny,2 of the water with an acceleration of 2.5 ztvx8 5alvj )q,tj 21isum 3x82 zynr4$\mathrm{~m} / \mathrm{s}^{2}$ 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 covervs5p8b g x bis2rm*9z4 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 maxi f8rf8+ho 7sxtmum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cablf8+oht xsrf 87e? 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 elevatoj)hq tlq9b3)qst n- n,r begins to move, t btqqns lhn93)j-q,t) he scale briefly reads only 0.75 of 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. gji.293 s5zp(+hxakg jj:haq 1wz;v wWhat maximum upward acceleration can it give the elevator without brea gij 59jwjgz q1+h:a.w v;kzsx h(32apking?    ( two decimal places)

  (a) What is the acceleration 6 *tih/)bgtdgxg) tnm- a1z-m of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-fourth of th1a*b/-) gdtiggmmt h)nz x6t-eir 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.3 rx5om dvi*)r When he strikes the ground below, he bends his knees so that his torso decelerates over an approxima 5*3i d)rxovrmte 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 rest/v.tgc.m+ap8/6fqts hiu k2;xp-lc l s on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hun is+ct68qvl- g/c;ft mpp/.klhuxa 2.g 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 of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diag ;qpgu*c dt42yram for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at thek4,tq 9e,kq xp moment it is hit by the bat, and again (b) after it has left the bat and is flying topt4 ,ekqq 9xk,ward the outfield.

A 650-N force acts in a northwesterly- 1ri.a0abqy jims g+- direction. A second 650-N force must be exerted in what direction so that the resultant of --1q.+j iaims0yagr bthe two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "hlqsn3( ,vk /zbj )bg7 ,z*qniyigh wire" strung horizontally between two buildings 10.0 m apart. The sagqvsl, *7b3z nqynb i,zjg(/ k) 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 by a massless cord f :d*pz+7*8icj9aft 6m5 tkwne3otgwhrom 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 1wn6n c b mo+ckrogw:3 t63t2y64.0$-\mathrm{kg}$ 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 unit to a new locart5 ;0n6ojisgtion at McMurdo Base, Antarctica, as shown in Fig. 4-46t;rnis5j g6 0o. 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 behiqdt.u d,7j04r ipcsq +7vcst0 nd it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive dvqcs tq07+spcd7i,0.rut4j 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 fbd zcy wh4 +5m7(saep ho5)htl(7c(,fmjo 9qbucket-pulley apparatus shown in 9z4q7( e + ctd5fhom5bl hwc)fmy (po,(hsj7aFig. 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, a 65x qktlwu0f3 m84k9: iz$-\mathrm{kg}$ 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 ff8dm:. gwamz,tu8 yz:r j2 4j;g4f.9ekzciq$ 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 fri(wrqjr5sk*s;up,l0 a ctionless horizontal surface are in contact with each other, as show;q5lur(ra0s wk, jps* n 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 above the groun4jifcvyl1 q*+d, and the massless frictionless pulley is 4.8 m above the groui1c y4l+*vf qjnd. 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" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are cofw 2h ki.q37s2rich)3*d m lcgqg(yt1nnected by a heavy cord of mass 1.0 kg . Calculate the.r*i d( h3 cg2skfgyqtwcmh37q) 21 il 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 k.d0h8d7 vz blonv9d1 v k(p9dlinetic 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 required to start a 5. y1;pl0 jn,w. m7jep+u4ksbgy0$-\mathrm{kg}$ 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 xcbeli ifwy r;mak:m( 4 9o;9 (3r2vkma train accelerating at 0.20g. What minimum coefficient ofe wm 2:ki;xv(9o( f3bmly9ac ;rmri4k static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can .llgrk qx+ ),veak,.kundergo if the coefficient of static friction between the tire,k.k+ ae l,lxv)rk. qgs and the ground is 0.80?   

  The coefficient of static friction between hard rubt:+e+g (hz ivoc233tprs) aiwber and normal street pavement is about 0.8. On how steep a hill +(its gpcr 2o3ze 3tiw h:v)+a(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 -4.8(e,dn*y vrj7wbftkl ib. -s k7*ok04a 0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 owdojru*u 8py rcq/764n 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 conta v8 ptrhy 7zy:6de93wi7dq yc/ct with an asphalt surface have a very high coefficient ofwdr63:zc 7yy d qi8p79 vheyt/ 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 ksj5z-bz 52 xiiinetic friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large a mass would box A havex t,4sf+o n1a 4zoz8 hprd4vsgw,w1y0 to havwyhszv x 4 1a 4g1nsdzpr f4o8o,wt,0+e to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wiyq ;m;3nysl;yx((u q )e2uta+;focct ll it go, given that the coefficient of kinetic friction is 0.20 and the push impary ;catyql( u;2 ;um(;)tsye+onfcq 3xts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contqmg20rl6d8c5 ko0 o m(mhs rd7act and at rest on a horizontal surface (Fig. 4-54). d0o78(c0 r d6h2g5qk mo rlmmsA 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 7 qjh-++foiyy8 7 ggpgbetween 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 the truck?+gj hqi+ yop7 fgg8y-7   

On an icy day, you worry about parking your car in your 6:t)3roi :oo/qw 1isqlm0pp mdriveway, which has an incline soqrwi6 m/pom:tpl31qi 0):oof 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 sli0g56ww y xnkeff08(gy de with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig.)-+fpag6 xlhs-3 nad s 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 initial speed of 3.e 9; ytdng4d-r w2o1st0 $\mathrm{~m} / \mathrm{s}$ 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 jh ,f864b:ib:cto sxhy bqtxi831i ,lhill 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 xhubd4on*5ynki*r 87 on it with a force directe n8**d7kuo r h5inxb4yd 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 become dangerous n4)v2 2c b9z7qhecyvh projectiles as they melt. Consider a chunk of snow at the ridge of a roof v) 792c zhy b4nceqv2hwith a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile7iu-z o xooe81 traveling at speed v is ex- z 7eoo1uoi8qual 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 h qio9-yx(pz m:+qafou(kan15f2,la slides forward on the dash when the driver decel+ fzonam-(qyo,a52l9 a1hpx(q: u fikerates 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 givenm bwhgcnjo49) ;a5p ub7vb1u 7 an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to the packing st45a gy3c /9crhhikkr6cx8q+ ;lm/ h wlation 11.0 m away. The belt is initially stationary and must finish wit a l8rmcl 59h;yh+ r4/gx3kckiwcq/6hh 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 betweenz*p,d*)js(uvy(4ca x( knb dv5mh -ea $m_{1}$ 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 coaso6lj ze9c6 e0ejq5ca 1t 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 simplic6k yu+ 3h:ac,at t-rdfied model of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from + utha36:t crady -kc,0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crash if b1.z0tbb,2tg wmdc3uthe deceleration is no more than 30 " 0m3 b.tdtgbubc,2 1zwg '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 an earthquake is a , and if an os ;kjjps w:mo1iyw )z: .;0r5ah1glk ubject is going to "hold its place" on the ground, shoz:w0o1r:k) s5;ukw.im1ps a j gh;yljw that the 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, examining the scep w1kcw7v /u;vne 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 of kinetic friction between rubber and the pavement is about 0.80. Estimate the iw1 7vp;cuwk/v nitial speed of that car assuming a level road.   

  A car starts rolling down a 1- e39uhsq40ics- z6e rain-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). Hoq4rcs 90h- se36 azueiw 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 theu u uvj1oycw6*au7v 5( top of the Leaning Tower of Pisa and falls 55 m before reaching the grau6 y ucjuvw 7ov15(*uound with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy s,ek ip+sgrsr0yp-o9 k3 (8qogtretch 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? If so, what will be the speed upon emergiqgop s or,i-r8+gkp ys(ke093ng?   

  A city planner is working on the redesign of a hilly portion of ahe y;80h3uz;y8x l hlt city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small etl h08u38hzlh; y; xycar, 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 experimex4 dg0 5gw0v:bdo+qc cnts, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She noticesg 0b0wdq +d5v4:cc gox 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 tkjrq,,ycou .n/hp. )oo be several ramps connecting different parh n.,oc/)j.r,q koy puts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (mass M ) usjqkqhv6e vgip1++t,1 8t 9dpz / lma7ming the pulley apparatus shown in gm6ahm7p1qkt/lj q1+9 z t+d8p,i vv e

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 acceleratingkh oo 9(5sox3s at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer considers the fom;ge6e7x), d e-i krpyllowing segeied -6k,ryx7em ) ;pt of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian train has a mass of 660 metric tonn k;t )jrq1y rgx7f0 3e2 cz slvf0q1+w(.wjgxs (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of simila1nhlk)7qg:0v9iuw k z r 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 falllh nw 07qzk1ki 9v:)gu, 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 us zbbahfhbh2;:e76o; d :lmj )wing 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 allowe c l;3zb3)hmff*mcqs 2d 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 i/kzq - uqjgnq8 rd u5,qca,-sw z16r+ace field inclined -+kqwuza5zj6s,ac8 q rgqu,r n-/dq 1 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.