Why does a child in a w9gw4is xwxzo 8/r/j /wp7-fup +dlzo ;agon seem to fall backward when you give the wagon a sharp oip / /7wdrpx-8olzuzfw9j/g;x +4swpull forward?

A box rests on the (frictionless) bed of a truck. The truck5qu)fixms ,gz t;88ue driver starts the truck and accelerates forward. The box immediately starts to sezfut,)iu8 gs;qx m8 5lide 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 ll*q6,ld u(//8p 4g6n otho+nvhfwxs forces acting on it? Explain.

Only one force acts on an objectk11iqhj9 t r-:e vd2awx,ghy). Can the object have zero acceleration? Can it haw i-11):d,r vkehtgq2 hxj9yave zero velocity? Explain.

When a golf ball is dropped to the pa1gl/l .l1*uwcgo4ifvvement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) 1uvlwfgl*o ./i 41 gclIf so, what exerts the force?

If you walk along a log floating on a lake,jxw/r6,0hx.51v ywk5us r t :gef;w zen9jxo, why does the log move in the oppositjfnkh ewuv,5 ze.0xyjgs61tw/; ro ,wxx:5r9 e direction?

Why might your foot hurt if you kick a heavy desk or a walm zf(,iwn u 2t+bf4p4 u,d5ewdl?

  When you are running and want to stop quickly, you must det;.,j 4h4 xpjkh+n +o-zznjhw celerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest. w tk.+ h4+jxp;ohnnj-z,hzj4    m/s$^2$

A stone hangs by a fine thread from the ceiling, and a section of the samu8kha3 a0go7nl* h8u5cxl) ls e thread dangles 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 pug)*7h8ol83 0k5na l sxu clauhll? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. Whgr uc-; z.g( 3fwns4pm,c.tv py then doesn’t the heavier rock fall fasvupwp s ,;f3.4(tcrn .-gcg mzter?

Would a spring scale carried to the Moon poi-(xj ad964zs;.ubn sr4g ugive accurate results if the scale had been calibr-9 sjd4s bp r(z6nix;guo.4uaated (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a friu 90- p,otadkp2.atrs-ysuf1 z h6p,qctionless table using an attached rope held horizontally. If you nowk,rtuhz- p2p 1 y ,a uf09.d-s6qotaps 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 gravi. e0 dhroxp j.de,-o,fc6xg-mty there is a net force mg exerted p ..,cohxedme- fg x r,o-dj06on 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 Earth move?

Compare the effort (or force) needed to lift a 10-kg object w36 6/wcv(i5sq pz)0a-m:w z9 jlyyqdpat *ogwhen you are on the Moon with the force needed to lift it on Earth. Compar9yq0ioga p3 -6l5d)z/w6:smj avzw w pt *cy(qe 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 e5a4u7(jyp9kco2n ld (Fig. 4–37) pulls with equal force on the other team. What, then, dete5o2d( 7jc kpa4eny9 lurmines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceri*jjc-.qt ebqd1--x woes. Describe the “reaction” forc j.-j*-tqwb-e1qxdo c e (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, ho:zjhw-dw 3*nu w large a force does the ground exert on you? Why doesn’t thishw -nzj:d*u3 w force make you rise up into the air?

Whiplash sometimes results from an automobile accident when thhrg+m1wm0y jlfuxb /yhpufy y1d3fp (e) 5(3*e 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* 0plfyy )fuxh3p(e uy 1hfwjgm1+ r3 yd/(5mb it really?

A heavy crate rests on the bed of a fl 7ixt msncm0;(atbed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force cacm 0;tx im(n7suses the crate to accelerate?

A block is given a push so thahm d4o5oc bx)w/b *(ptt it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of 4oxpo d hc bw5(/bt)m*its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighedl:ly)9jwukjr ra or451k,x: gfq5 kt8 yourself on an inclined plane? Ass)kjrrw5kt5qf oj: k4r:1axl, yl9u g8ume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a chil: s5hgu m-mwc1zk:p .fd on a sled at 1.25m/s$^2$?   

  A net force of 265 N accel.7e anj/8,ng7 zyf dajq6g ua:erates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to s/ muteb62:3awcq wmj c4y 5i8accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ofhgj1p gd0b3n2 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 ip d*04mpdvkq + z3 fgc,;-ergin 8.0 s if the car is traveling at 95krgvm d0d*,3 zi ep;4 +pck-gqfm/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125mw4zdjz,wd f wux +m/;)/s over a distance of 0.800 m along the barz,/f+wzmw )xdwjud;4 rel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of 2hy/al-qc/yn5eud yhq q,lg43;: d a8l.5 ;l/u3lq84 la eg, yq5dan :qcyh-h/yd$\mathrm{~m} / \mathrm{s}^{2}$ 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 (3/jbzedfah 0o; ;1alcdi l0jquarter-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 dexne,hfwtf+upm zy7n/*6 i-z j 1qd4:fsigned so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motqz76/jmf tfpnhxz dwi,4:f-+ 1 uyne *or should exert on the supporting cable? max =    min =   

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

  A person stands on a bathroom scale in a motionless elevator. When thet scu r u/tvi*dp7 (+0f-vexp- elevator begins to move, the scale briefly reads onitdu-c*( +vx/vse 7p -0p tfurly 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 max h-wm- lxd+gz,imum strength of 21,750 N. What maximum upward acceleration ca-z+dm -xh wlg,n it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 pz i7ws20cqof8voqm3blr 6-( kg including parachute) when the upward force of air resistance is equal to one-fourth of their-p2 o6m qz0li r vbow(7qfc8s3 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 strikes the grobvoc rf4/38sy-)zdxksfl2c qzvy: 2/e+*w k ound below, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso:*2cs c-bx32wlero+d zk/f of8kz qyysv)v/ 4 (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 tie7 oxq+jpapq8dw-: gr 3d to the box runs 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 o:-8pgaq rxqpoj 3 +7wdther side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram f . erwrl+uev.3or 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 the moment it is h5zpi1 a8p ooo8it by the bat, and again (b) after it has left tp58p1o z8ooaihe bat and is flying toward the outfield.

A 650-N force acts in a northwesterly - f ; d)3anxrcuw3i2ayo53rgo1cxqb+c wcl6 :direction. A second 650-N force must be exerted in whndarfb w2u-3lq; :1r3cc5i 36xcoo g+)ya wcx at 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 veh- 79 b/xpyowire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is/y- he7b pv9ox 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 hang hc15co:9 bsuictf2b8ing by 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 1470ptqd ldz8tiw u3 ,t+h;wxx. .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 location at McMurdo Base, Antarcticadv -)h-+fuixr0diej 3, as sh 0-h+id) xf-ei3 djruvown 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 cars of the same -pa,j9l.gjb1*3v rxovxirv3a09 vw cmass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling betweev 9* 9 0ac-3jxaroxvgb1ivwl rj 3.pv,n 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-pjz,69hjg6 4,wua9 ku rf /t4+brjj iqculley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constat cwzju uf,+jh4ra6rk6 bqg/j9,94i jnt 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 racfzc9lt+dgw x n 4*gr29e 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 block (masgtk n;6nbh* 9ns $ 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;+sezjj 2ilt9 3 t.7dn8 tla2ju7 dkip are in contact with each other, as shown in Fig. 4-72s tpl+ iknudeajtj27dj.8l; t3 9i z51. 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 ea5 oo2li*r 6 (7xtxn0sxv, 1i stpkjx(vch initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the accelerat(t*0 5 17vix2(,6 nspixxv otslkrx ojion 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 fa se.3 5:wlczarictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53.zl ws:a53. cea 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 -w+ r wcx17hr hh51oxzbetween 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 1/s 7tksndag45.0$-\mathrm{kg}$ 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 o4ik/ 01 imurepn a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet andiir u km/p1e40 the floor if you are not to slide?   

  What is the maximum acceler6mp cd 2o;n0rd/djfp7ation a car can undergo if the coefficient of static friction between the tires and the gp/d 02mf jp;cdn7dr6oround is 0.80?   

  The coefficient of static frwb)5 sxwr 6k0tiction between hard rubber and normal street pavement is about rsw0w k6t) xb50.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

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

  A car can decelerate at -4.bqwny hxlme*2*w1 r8;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 rougqfnq6/:7wim*it; i ox- mxl 3mh 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 coeffm6nbh1wg, rg: 2u:g 4na(0 mo)gkexpticient of static friction. mr (10ap)u ,w4o2h6:b gnn gg xe:ktmg

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 fric. )xe4m3rnpkgvw,s: wtion 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 (Exami f4z802x7p/pzppvaoxfn). yple 4-20) how large a mass would box A have to have to pre2/nip0p4 7z afxyppx.f)8 ozv vent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slpqcz)yp+e f3vskrs 4 1)26nr wides across the floor. How far will it go, give 3)qyc) f krzp6vpewr+ s41sn2n that 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 kg , are in contaen7 wq9g+/47m/i cr btl+ gufyct and at rest on a horizontal surface (Fig.n7 +7gmu9/fqgcbl wy4ti+/ r e 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 ceaox1 qeb +psl1z/9/g arrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having th gx+19/e q o/e1lbazspe crate slide against the cab of the truck?   

On an icy day, you worry aboe:7wql y xm2*fi7v +ocut parking your car in your driveway, which has an incline ofvo* +:melfcwy2 iq77 x 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 ;e r 9 zsjcd+i,bewtr(4m/ll+slide 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 as:4h z n,0-pzh bfye9Fig. 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 oh(p;, wfkv hfly(ns1 z m+x*4rf 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 .jyk6te( mu0ca 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 z2, evg8ns6* qnff 6gsin place against a rough wall by someone pushing on it with a force directed up ne8sg6* 6g,fszn2fq vward 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 4s 1mn2 fg 2r.p4xpjmrbecome dangerous projectiles as they melt. Consider2pf x4mnm4gj.sp21r r a chunk of snow 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 stopping distance for an automobile qh- 25ao1g,urh7fnch traveling at speed v is equal1q-,7ahgu2hon rcfh 5 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 for+4s/ be*: x qeg(mo cxumc5a.jward on the dash when the driver decumx cjso*4 gqe(mb5/+ae.:xcelerates 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 mc l;9uoko,t m:sssd5 4.+jkh v is given 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 co 6 t v6n aop44c wa9/cin3ih)ug3sl;cqnveyor 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 a/iui t ;ov 96s 43cq)cgaahlpncw46n3 nd the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic f fnw2(5(ed vmy) mvbf*riction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (including the bicycle) can coast down a 6.0k26 td 3xws-cu$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approxtgan,z6 - dyof-k x)8ximately 20 g -k- x8gfdzo)xay, tn6 of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobilew6 h3p csf9he/ crash if the deceleration is no more than 30 " g 's." Ch3 9 cew6fsp/halculate 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 s 2l4y ;;w,gw/+pabp3 xy qbz6;vkaxb is a , and if an object is going to "hold its place" on the ground, show that the coefficient of stati; y34 kw2+zv;aasl q b/g6,;ypxwpx bbc friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

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

  Police investigators, examining the scene of an accident invol-ug ,-w6fsegxtk9j i ;ving 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. Estimattxw9ig eks--f6u,j; ge the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that fon7m0um6e avz9 c8s3vsr each 4 m traveled along the road, the elevation change 9smvucenv3 6ms0z7a 8is 1 m). 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 thhe ptfgbyrc ;bpwa81. is(.t0 ydx*:3e top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the bfh1p0c3tg: y*(tp..axe;r8 sbid w y average force of air resistance?   

  A cyclist is coasting at a stenw:rl;n., c :os gptz2ady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the m,sorlg : ncnt:2.;zwpuddy 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 p8p7y f/ q)j5plo kmwq/emk( b)ortion of a city. An important consideration is how k/)qb( wkmopeylp/ 57 jf )m8qsteep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her wat.;nm(e ;zeg5(h w*+5l hiip1p jpqd oech 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 makes an angle of 25plzmpo;e. nh*;qe h j1ew +5gpi(di5( $^{\circ}$ 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 seve8w3; uhwuxl b x6:.hderal ramps connecting differe6.83luwhd x;bue: xhwnt parts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano ita8gx* zi9c5(mass M ) using the pulley apparatus xz c5tg8* i9iashown 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 acceleratiu :gwc)a+ga3t ng 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, g( vu8:e tes1rqat6m:an engineer considers the following set of co: t18et6mg(qev: rsaunditions:
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,i-a tc z:y)cj Italian 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, Bi.8)fe b2tcjhsll and Karen, use safety 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)cj8th 2be.fs rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is 93jb: dz n5stlusing 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 allos 0a4 jhyb;9+ov- frjnwed 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 inclscy)fo54;iue+adl c0u 3fly6 ined 4 5ly60loicu3 dsy f;)+aufecat 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.