Why does a child in a wagon seem to fall backward when you give the wss1 5 bkdd.8pragon a shar1s8ddb 5prk .sp pull forward?

A box rests on the (frictionless) bed of a truck. The t tu 2:hi.:uvmq1s x7lkruck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the tr:v17u x:h u.t2qs lmikuck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acti7t :3zvr+vdydo ypnv2;; wx8png on it? Explain.

Only one force acts on an zkfmq:i1cot) tbmk6*; f b8(dobject. Can the object have zero acceleration? Can it have zero velocity? Explozc (b*ftk:6bk; mtm qd1f8i)ain.

When a golf ball is dropped to the pavement, it bouncb5- ,/dwqbje4xmn - iv5t +jdaes back up. (a) Is a force needed to make it bounce back up? (b) If so, whe-ai4vb-/ x d,jt5w5 mnjqd+bat exerts the force?

If you walk along a log floatingd4 mp+( vol8qy on a lake, why does the log move in the oppositemo 4v lqyd+(8p direction?

Why might your foot hurt if you kick a heax; q59i;tn eheq5wa t;vy desk or a wall?

  When you are running and want to stop quickly, you must decelerate qup:m 2lbpy4uy/nl6w *m -qv;c-mz , idaickly. (a) What is t;4yyp q26uw/lmclbi*vz:man d- p- m,he 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.    m/s$^2$

A stone hangs by a fvbemw-10 yy .uine thread from the ceiling, and 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 person y0 -ue1y.bmwvgives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great a 7j,z u-mlielyzy2dz o7g1q; 2s that on a 1-kg rock. Why then doesn’tilg1umd2;qz,o ez-77ly2zyj the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the sc rm+yso wk53q0ale had been calibrated (a) in pounds, or (b) in w3 ks0ym+qo5 rkilograms?

You pull a box with a constant force across a frictionless tab fro05br8 8nkvle using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizoo0fr5 8vr8bnk ntal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity therhjl6 o/nj ,4dre is a net force mg exerted on it by the Earth. Yet by r4n6 jh/d,jl oNewton’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 when ye* 1y :(v9ob,zcp hijzwdx7o5ou are on the Moon with the force ned ip7h *wo yz(,zcj9v51xb:oeeded to lift it on Earth. 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) pulhl 7,5uf6 7mu;6dtrw frclh vf6um::fls with equal force onf; hd:56utur7,ch6: flvurffm6m7 wl the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hu.0t4bqd nfb. d8vuz 0nsy,1uold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on whu4vsu0.dnzq ybf b n1d08.tu ,at 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 *lmapgpo2k* s7q9 :ei on you? Why doesn’t this fm 9a*ogp:lei *kqp7s 2orce make you rise up into the air?

Whiplash sometimes results from an9vfdxe8 , px u:vz.-ik automobile accident when the victim’s car is struck violently from the rear. Explain why the heae9u8vp, v f x:dx-iz.kd of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the8(ks*-j:hme m5f hi s.5vcrvc truck accelerates, the crate rekr5 hec(c5mvmh.isjsf *v 8 -:mains where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push sz e 3**0dvt4gzfm2zx6 pch 8oskcv 6:4sx h.yyo that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the asceny:8d*zhxz4 e3 mvs yc.*hg2p6 4o s6 0cztvfkxt. Why?

What would your bathroom scale read if you weighed yourself on an ih3*lj :209x5exw l ay1tat; txkvwv7jnclined plane? Assume the mechanism functions properly, evenh3vy7 12alxjxl5 *w ttk xv0jw;:t9ae at an angle.

  What force is needed to accelerate a chimu;.k y;(zo lbld on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bikey/i/brfbf djo+(y 834zo43bgb5w rqg 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 is49z ;yzug( zymw9 hnv0 used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of axr+sn6yb(5ga $76-\mathrm{kg}$ 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 ansb +g58)ahen m;x q1he 1100-kg car in 8.0 s if the car is traveling at sbngem q );8 ha+1xe5h 95km/h? -  

  What average force is needed to accelerate a 7.00-gram peldub)* yr jnhn45j s vu,tf37pt.)9yiclet from rest to 125m/s o3ij5y tu.*nr nyv))uj thcb psf79, 4dver a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish verticallf) rk0js.1 ;s qsypqd(y out of the water with an acceleration of 2.5 r (q0)pksjq.1df;s sy$\mathrm{~m} / \mathrm{s}^{2}$ using very light fishing line that has a breaking strength of 22 N . The fisherman unfortunately loses the fish as the line snaps. What can you say about the mass of the fish?

  A 0.140$-\mathrm{kg}$ baseball traveling 35.0 $\mathrm{~m} / \mathrm{s}$ strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm . What was the average force applied by the ball on the glove? -  

  How much tension musta rope withstand if it is used to accelerate a 1200-kg car vertically upward at0.8m/s$^2 ?   

  A particular race car can cover a quarter-mile+3qj tgs/,3jqc)jy 2rgypft6z n h.* p 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 that2jxxp- . d/nqi the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the m-i2nx ./dqj xpotor 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 the elquy(.++fed lu evator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleratiu.uf+l(e+ yqdon of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elev5*3m 2sqw eu71kxv1y4d*k* pnjtyi ofator has a maximum strength of 21,750 N. What maximum upward accelesi ofk5 14typx*vmkwjn13q*d2e u7*yration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleratgp+ vagy6p d-y of5p+a)a1e/ wion of two falling sky divers (mass 132 kg including parachute) when the upwaryp)wa o5 +gp /fa+g6pe1vdya -d force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. Wm:j9b 8hj9g3kl0o fz;f 8gvp nhen he strikes the ground below, he bends his knees so that his torso decelerates over an appr jvfnl8fz;3j9g8bokm 0 h:p9goximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on a table. A rope tied to the box runs vertcbiv5+5wtq mldi8 et )p8 z2*rically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine t 8tdevp5riw+28i5qlmc z bt)*he 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 diagram for a basketball playe .-waaynjhz02r
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit by the bao: in.k mycwwix4z(fmy2su0 oe,a 06 (t, and again (b) after it has left thef4((ckimn0x iz os,.2:0e yy6owwu ma bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. xw7 ai:6x7 ga 0ychhbt3c,xah.e/1y j A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illusth0by :tigx.w6 7hxax,y3hjc a7/ 1a cerate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betweejmyi (-v3tk6 en two buildings 10.0 m apyvmj3et6k i -(art. The sag in the rope when she is at the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from ackb1in9m7rev36k-e*y 0ap ; :sboc nmnother 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 10cuu8zkk z-pe5 i2xtdl,9h bv 5;tlh4 4.0$-\mathrm{kg}$ 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 loc8hp 6(6gycr3hcr5a mi a /omp:ation at McMurdo Base, Antarctica, as shown in Fig.:r/p8moi rcah(ym5gpa 66c3h 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 pulli0 4kcbd zqr7t/ng two cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomoti/0c47 zkrdbqt ve and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus show p6 )sx3- wjka+x:hi sb+xlft+n in Fig. 4-48. (a) How hard must she pull+-s x aitfbskh lw)+x 3+j:6xp 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 beg w-xgy-jkyn,+ an, 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 (m87cy )m /jm*a7 hgu+5oy nlesbass $ 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 suru o2olz3g r/*g4kh ph0face are in contact with each other, /2 *hpougr40z glh3okas shown 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 fdbv;1xx6)4n yhlj7f33v nt dinitially 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 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 do;fd nb4 vl31vdftxjx)n73 hy6esn't hit the pulley.]   

Suppose two boxes on a frictionless tabvz,hm *al0e3c2x zv v)le are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at zc0 xz vvle)vh*3,m2aeach 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 frict7ju5v .dn ave7 j1060x icajqnion 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 *e,- nk5 -9rsmzvbhtaej*6he 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 53s ,l3qnlusg on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet sg,35ulqsn3 l and the floor if you are not to slide?   

  What is the maximum acceleration a car cangcxqxq1d) g3.zo 0 i: y7ydiw( undergo if the coefficient of static friction between the tir )ci3d(g g01.zqwyxdyx :qi 7oes and the ground is 0.80?   

  The coefficient of static friction betweek m2mud3zul6 :n hard rubber and normal street pavement is about k2uz3du:mml6 0.8. 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 aa :l1t.lj )vw4lcz3e-w 8rx-z t6fkdsai:9 aat -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 rough wtu1 9ejsdi-/ll8/2zm pjd .b 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 hav c f55bsjm 6gh0bw)yd/e a very high coefficient of static frig mws6d c5b0)/bjfy5hction.

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 kgj-t r(rw pa.9inetic 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 lvewps 58 ne3/(t,mzyvn t69b0g)yu xb arge a mass would box A have to havevt6 xvt(nb), bwyzup yms0n 38/ 5gee9 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 go 1i ig1x x4mzv*lr2+g3z 3ecdt, given that the coefficient of kinetic friction is 0.20 and the push imparts an i2rcxxgvzm3t41 e g *+idzi1 3lnitial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on(ypj+or7yj adgc/t*mx y:t15ls r t52 a horizontal surface (Fig. 4-54)t c+a :2r 1 jy7syx/jp5tdt(gor*5myl . 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 carryix hevx3 rk+ e.c8.nvn3ng 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 hhkrnc3 nve8vx x.+ 3.eaving the crate slide against the cab of the truck?   

On an icy day, you worry about parking youre; w*ro*e erofp)zk8jt98 i4n car in your driveway, which has an incline e8e i;9r )pj 4wnez o8o*rt*kfof 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 slide withxgd-y:v 7ya)pu2zyg s(2 6 xtq 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. 4-552vh gbycja :/; 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 ini/f6sb 3 m2zh ++npttaxdr041zg)woh rtial 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 sterti-nva vti i;z-*cs;;fn. 4bepest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone 22nbb7ddus53dx.u dxpushing on it with a force directed upw22x bddb .sdu53xnd7uard 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 projectil* t :3x*i) prujyp:csyes as they melt. Consid)u**tpj3ciy rxp:: yser 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 travelin)l q2a-p2 lmv0bsx 9npg at speed v is equ)xsl90p-q va2 bp nm2lal 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+o be,7uni ;d okq.nd.+ we9tx of a car slides forward on the dash when the driver ixqn+t7 +wek .,eodn o.u;9dbdecelerates 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 inx3*: cys3aktdp6v5 sq itial 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 u*d8. drdykh**pqk2 1n*k sm cto the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time formdnyrkc*8k d*u2 *1qks.pd*h 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 kipd: 2lfub- m-3oj+1ojq4u )yj+xpni enetic 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 (including the bicycle) n,r c; ahtu22otl3 fa(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 simplifieje,t f rr 5)wy)dk)h* :rpwio5d model of a mammalian heart, at each pulse approximately 20 g of blood is acceler ) 5)idkhy ):wwf jeo,pt*r5rrated 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 b7/ dlo/lpi 93uum 7ztof surviving an automobile crash if the deceleration isudu/ilp77 m /tlo3b 9z no more than 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquakes r2lpjw9a)(p g- 5cec is a , and if an object is going to()ea2gp-jl crs5wp c9 "hold its place" on the ground, show 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;mc iuuk6z)8m of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nm8 u c;6kmz)iuearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m trkb52-9y epezo-x yc q9egd;q+ aveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore xd 5-pyock99zqey qe g+;eb2- friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa and fa zrg. tl7q.ooka,,7umt0u(lmi1p naih82o*l lls 55 m before reaching the ground with a speed of What wast(zokai2om hiug tqra78n l *1mpu07.l,,lo. the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretch wjob a:y6-h ydkp.*5(qoe z(ojhere the effective coef((*j6. j qobd -ooy:k5zeha pyficient 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 the redesi4uf5ud*-g tx1kv)ul.9njb tjgn of a hilly portion of a 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 -f4ujd)ltxgj*b t1 u .5uk nv9particular 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 watch from a thin1lg2z9ucv wh1 piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). gl2zvh1c91wuShe notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be several ramps coe a 4z:6bkdv47w wmb4onnecting different parts of tm4avoze : 46dkw wbb74he 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 piu e kehig+/t :8l2n;brano (mass M ) using the pulleyg ee/2;hn+ lbu8k:itr apparatus shown in

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

  A jet aircraft is accelerating at 3.5 v*k3fudl 1)ed $\mathrm{~m} / \mathrm{s}^{2}$ 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 consideya +wx6j mr;fznx,ck ,b 5hs.*rs the following set oy,. 5bx6js*kc; whz+ nafr m,xf 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 jnij n; 8sehq63h+3zq has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, , fjos+; hio;xuse 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 fhox;; sj ,+iothat the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is us/abd(e 4g yea7ing 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 allowed to reach a maximum speeyanhfq49 *zd )w4 hl;jcrqb3 ;z;az.vd 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 togethe;b ;qoxlg v,q-r are ascending an ice field inclined atq lgvxqb;,; -o 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.