Why does a child in a w;isp.tdpo+ t(agon seem to fall backward when you give the wagon a sharp pull forwa otip+(ts ;pd.rd?

A box rests on the (frictionless) bed of a truck. The truck drive-q5s e 8pwp- vmlexj 2+rt50vcr starts the truck and accelerates forward. The box immediately starts to slide toward the rear-p pqt58lxvj2s r-w e+cv05 me 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 cy(t y ;+;whzzp rvgx/v1h4q+ is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can ithcvf jrx gc(aba88+; 6 have zero velocity? Exp +6bjc(c88fga va;hr xlain.

When a golf ball is dropped to the pavement, it bounceswuv cgfx.t)h v.)2wh 3 back up. (a) Is a force nec.th))whux.2v3 gv fw eded to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the o: w62gtol8rdyhtqp- )pposite directiolo6 qdtp :yhr8 gw-t)2n?

Why might your foot hurt if you kick a hebo- mc6o w4-mvavy desk or a wall?

  When you are running and wantapbfu))m8t. on(lh, j to stop quickly, you must decelerate 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 obj ln).8fuhp(a),m t 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 ov7gd . ec 1q;5gcrwz:a section of the same 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 per:oq c;dz7 1gvewg5rc .son gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twip .ylkv4lze*k6y.q7 cug1 u.ice as great as that on a 1-kg rock. Why then doesn’t the heaviere upzc4qk.u71k .v gl.6iyyl * rock fall faster?

Would a spring scale ca.r1 /tf)yquq3jw6bbm*c6 hafrried to the Moon give accurate results if the scale had been calibrated (a) in pounds, or (b) in kil166fbfmt *qcaujr/ hbqy w.3)ograms?

You pull a box with a consv xd5p0/-vsz yi+:xff0tc*y p xs;jw)tant force across a frictionless table using 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 samxw50:ysx *0 /+pfyt p-cdv xfsj)z;vie, (b) increase, or (c) decrease? Explain.

When an object falls freely +ksbr53kehhb11 9vo// xdroqunder the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equ951hh bkqr v k3r+oo1x/d/s ebal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are on tr9nt) ..ihya4hnxh m.he Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object hori yh 4ih)r9.n.ntax.hm zontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team ( ,j/8h w+wyzl wu)hazin a tug of war (Fig. 4–37) pulls with equal fzujl 8+ wz)a hy/,(whworce on the other team. What, then, determines which team will win?

A person exerts an upward forcey j oshs(7/vkdc .w7c5 of 40 N to hold a bag of groceries. Describe the “rea. kwy(s sdh7ocv7/ cj5ction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exert o5lq xc/;6cwef+.py4dc;t ldln you? Why cc 64d+ 5xlflec;q. ;/tldypwdoesn’t this force make you rise up into the air?

Whiplash sometimes results from an automo -/09 . l3p-*pjo0uylizis f2,ym jpllv1czawbile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be thropvj-uyw19pf2-cz0 j pal ./lilz0ymliso3, *wn backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When 9r z:o(fuu a, sd wc9a+r-elk.the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes the crate to accele cf+r wae-9kuou.(: ,d 9raszlrate?

A block is given a push so that it slides up a ramp. After the block reaches its/kqj-x/m)d bw(:tuu vpf yl( (z:a f2g highest point, it slides back down but the magnitude of its acceleration is gt /k)v:u(b-q2 mxdw/jl:za(fu y( fpless on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclinv m1 r:baj.: g+ 7ynh:mhfza:ied plane? Assume tb+h1rg: ::mv z f :h7anma.yijhe mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a sled at q9oe4 gk0q)gk1.25m/s$^2$?   

  A net force of 265 N aht+ h)zf3vq 2vhyc db*x.4nr 5ccelerates 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 accelera dnpp3v*3lml1 rk1w7n/pd h c/te a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight opewc-d9 2vh4yefu3 wo x),3hlf 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 td3yd:j1h/bsv4 y7xvxj5 n j3po stop an 1100-kg car in 8.0 s if the car is traveling atv3d/ 1 y:7 spd34nvxbhj xjyj5 95km/h? -  

  What average force is needed 68up zh+(lhxw to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel ohx( zp+lh8 u6wf a rifle?   

A fisherman yanks a fish vertically out of the water with an d0 8o c) zgk,1hmdfd dr7y.ej3ov )0rpacceleration of 2.5j7d,gz1)kf ) d o3 0yd8d0mh.voprre c $\mathrm{~m} / \mathrm{s}^{2}$ 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 cov. 5+ vukyx-+chsh qf.fer 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 maximum acceleram:8 g uv/-l hd6l9yirktion is 0.0680 g . What are the maximum and minimum forces the motor sm r86 ugvi:h9- ylk/ldhould 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 t*mm1f jqvpk02uaks .lrf/ y. v-h/zp7he elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleajzm q* v02/f p.v1k -p/.hlry7mufskration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevat4x;fzv:uua cotk. ,kk* mwlp*0osr - :or has a maximum strength of 21,750 N. What maximum upward acceleration can it give the e,rcw4* pks.ao;ku*z ol :mxu tk0fv- :levator without breaking?    ( two decimal places)

  (a) What is the acceleration of two fal;/mfp dn8p: c6xs/dp+r;dee kling sky divers (mass 132 kg including parachute) when the upwd;/f k;+pnm6e:crd epsp /dx8ard 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 ty/7tq nluro4hqz.83av2+c 7s2 hn ehu he roof of a house 3.9-m high. When he strikes the ground below, hv scyon .hq2r a7hz+3u nl82e/ qt74uhe bends his knees so that his torso decelerates over an approximate 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 fa:3hkoitede(,r02l0 )fbx z l f2bv58dgd u:on a table. A rope tied 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 other side of the pulley 0:02xhbiod8grevll fab5 u, z 2k3(e :tdd) ffweighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagrao (xboawf +r,/m 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)h1t uw.7/ w (pzhlsvg6 at the moment it is hit by the bat, and ag(g/ pwvl6w. th s1zu7hain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 65.ah 0 u/umy8zk0-N force must be exerted in what direction so that the resultant of the two forces poiu8m.y 0k/azu hnts westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two bp1csw )b2 9 o;q75tw8hdazm 40bihitiuildings 10.0 m apart. The sag in the rope when sh 7omi z4cb )itq9at;81d5wshiw hp0 b2e 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 from another ;kd68,dk 6-mairy fhg8kk bs .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.d-i,wrkp i4z +nbw u:00$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a ho;w+45kglvf(kp4- tg m/qhsjk using unit to a new location at McMurdo Base, Antarctica, as shown in Fig./ - mf+ph (4s5jwqv4 k;kkggtl 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 omw7 e*unme53gvae+.sf4 cr5 kf the same mass behind it, Fig. 4-47 . Determine the ratio of the tension g am57n3wc fvk5se +u*eer4m. 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 lhqpex6nkbca. 7yd0 gj14-2p upward using the bucket-pulley apparatus shown in Fig.42xphak l y601jbcdnp7.geq- 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 beganhosk: h9l r:5d 32cebp, 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 bloc 4s(dt8*f1g+ br whlwtk (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 contbp+vn;eu4 ;nkact with each other, as shown in Fig. 4-51. A force uve np;n4 ;b+k$\overrightarrow{\mathbf{F}}$ 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. 4-5xdp+zymsxw4cyehm -/ ) (c80 i2 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the grou/mec)+dzy 8 cx-(wpmy4hx si0nd. 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 connected by a heavy cord of m reoig*m+7 x9 h s(xkgj (b,n2qdpy39jass 1.0 9ojq ,gn kpbi+7923sx*djrhm((xgey kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic fric: 0i:)sqj;h7i zle.jq5ejc.rrg/l b m tion 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 r) z u(u o(tjmdxld2z::equired to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train acceleratinhyt;t50 bra0 cg at 0.20g. What minimum coeffica0hyr bt;0ct5ient of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coeffdf nw-m -lg8flm0xsc/.,h+wyicient of static friction between the tires,nmhyf wl .fxg -m08-lc/wd +s and the ground is 0.80?   

  The coefficient of static friction between hoc0 twu yg7l 0(oz+i-o8re5puh 8tjk8ard rubber and normal street pavement is about 0.8.j(ur 8cie8 yk0lwo7-ph 8oot zug5+0t 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 atzhv m*9w6a f1b -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a 2 fed+yxh6 xrd-z8:i ikkar4 :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 coefficirvyrk3b z 74)lg p*a y-7bbo,fi8.d tient of b) -y dkbt7,y 7rgp*r.viaf8 3 lizob4static 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 frictio tg- a 5)j0op 5umnmu-rc6ns42p;rvf hn 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. -5i 0/ jpowy;ak6l,y60 o:z ypkn fd moaodd424-32 (Example 4-20) how large a mass would box A have to hav,d/0o4 yoy awiykp -o:ka5pom jzn fdd 0662l;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 will it gobkj+2kx7 ;s4mu ::mwnwo pzc/, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial spwo w7 4k ubm sxzk;n:pcm:2+j/eed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 11.de/ focen,*b 0 kg , are in contact and at rest on a horizontal surface (Figb/fo,ee* d cn.. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static friction bepvox2q k 9h7q lh 6gs40oz49iltween 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 ih7oloq 6094sh94zk qxlv2gphaving the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your drthoz:7 * +owosiveway, which has an incline of o 7ow +s*zth:o12$^{\circ}$ . 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 wi:6,dugryol idor 5x 75th 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. 4-55 li8 nyg 1al u3cwf12s kess181laes 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 initiactg. lw3x u(32gawf3e l speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steep/b4bqx: +cws - o4ci .pf1aito:d(r amest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

  An 18.0$-\mathrm{kg}$ box is released on a 37.0$^{\circ}$ incline and accelerates down the incline at 0.270 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    How large is the coefficient of kinetic friction?   

  A small box is held in place aga(k.3 e k-cxdkqinst a rough wall by someone pushing on it with a forck ( k3kqxecd-.e directed 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 slipp(sd xad.1n f(oye6 .opery roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of (x ypofen1o.6(ddas. 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 minimu39gmt3d f)4xb*t bgttm stopping distance for an automobile traveling at speed )mf4ggbtbd x3t 3*tt9 v 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 dashboarp v56 ,trq*nzyd of a car slides forward on the dash when the driver *nt ,65zyrvpq decelerates from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an inv;z /(swg ce7vitial 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 packin:h.7c p4si u1ny,gxzcg station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for eachg:i.zynx7sh,4 1pcu c 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 o0pew0 a:ke(ild* s9ngtpl2 8 hf kinetic friction between $m_{1}$ and the plane in Fig. 4-57 is $ \mu_{\mathrm{k}}=0.15$ , and that $m_{1}=m_{2}=2.7 \mathrm{~kg}$ . As $m_{2}$ moves down, determine the magnitude of the acceleration of $ m_{1}$ and $m_{2}$ , given $\theta=25$ ?   
(b) What smallest value of $\mu_{\mathrm{k}}$ will keep this system from accelerating?   

  A bicyclist of mass 65 kg (inc7kds4; p9p 2d3,arkmduso a/jluding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pulse approximate1fy-)j;h johrly 20 g of blood hjoy jf1r;)h -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 automobile8h g i2 wxa/sb. (bqiyrdy.,9s crash if the deceleration is no more thanya 8 s,/siwbqyh2dbgx. .ri(9 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 prod tsc+x/fj95j+yuz1 uduced by an earthquake is a , and if an object is going to "hold its place" on the ground, shz+fy u/jt1jxcs 9+du 5ow 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 scene of an accident involving two cars,tz1-j(cm 13t4sn yu wf measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficn3fujy( st4c1-t1 zmw ient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that fgx ar7sgg/8i, or each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? ( i7rxgg 8,sag/a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pqcqb +cj)n//uisa and falls 55 m before reaching the ground with a speed of What wabqcu/ jq/n+c )s the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but entewa37 i(in8an jrs a muddy stretch where the effective coen8 i3(wina7ajfficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on th5h: q)p)fzciso0 - zgoe redesign of a hilly portion of a city. An important consideration is how steep the roads can be s0) qfs p)i-5:zh ogoczo 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 hl1fci15;jn()oxpg v cer watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig.1cfcpoj )l(xi5n1 ; gv 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, theuihr,eq h)n 9bod l-;(re are to be several ramps connecting different -),lhd (;uiq nor eb9hparts 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 ) using t-91zyz)i 4lb2v gmtkuhe pulley apparatus-4ivz l)tg z29u1kbym 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 atl2 m;xkz cr5;b 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-restk li-9p x4nsd/*u/b ikraint chair, an engineer considers the follouk-9/k x*bd pinli/s4wing 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 Italian train has a mass of 660 metric tons (660,rk(xz;u7uw6x 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 similbx 7wd-(: b2nzjbbw; :6.i dql wci+fgar 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 wilfcb- 6z: wiiwjbqxn+lb2b;:w(gd7d. l the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using a " /qhbt; f0ex q2 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 allowed to reach a maximum speed of 3.5 ; 7uh0es otkuy8p3 ng;b+. ixe$\mathrm{~m} / \mathrm{s}$ 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 ascendibn 33(he7*,v xpxpsv9su m. lang an ice field inclined at 21.0l3va e.n, hs9(x7pmpu*3 xv sb$^{\circ}$ 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.