Why does a child in a wagon seem to fall backward when youu12xt vhuo )+svf)x/l give the wagon a sharp pu) 1x) 2t fuxv+vuols/hll forward?

A box rests on the (frictionless) bed o68)h 1wc gk vn,;dmisyq 2a+gzf a truck. The truck 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 boxd2kg81aq wcgynzvm+ ) ,;h is6, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces acting ewrv zi6*33./iho(cb , s jcz1umsf6qon it? Explain.

Only one force acts on an object. Can the o*3bo7a j/grw object have zero acceleration? Can it have 3w/* jo7 rbgoazero velocity? Explain.

When a golf ball is dropped to the pavement, xg5l5ifnw8a,du;m d1it bounces back up. (a) Is a force needed to make it bounce back up? (b) udgnd5x1i 85wlfm, ; aIf so, what exerts the force?

If you walk along a log flond6 e-9r.x* )mm yd7mazvjv;k ating on a lake, why does the log move in the opposite directi. 7xmvd6)amrk;dnv- j m9* yezon?

Why might your foot hurttu;9qn67fy ;whyp fd: if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, yoeqo3de(v, im+y43w8 bip8lt tu must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using yvm pod( eq8w+yiteb3348 li t,our own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s${}^2$

A stone hangs by a fine thread from ther4:illezir 1- 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 gives a slow anl l-ie4:rri1 zd steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as zjc2*ub4ii0g u8p utr 9s5v( bgreat as that on a 1-kg rock. Why then doesn’t the heavier rock fallic2g tjs8i9vuz4rp bub u*50 ( faster?

Would a spring scale carried to the Mor t.3urb ce;;lpxt+bg8 tw1 c1on give accurate results if the scale had been calibrated (a) in pounds, or (b)1bu8;t;.+xgltrc3bw 1 rpt ec in kilograms?

You pull a box with a constant forcec s*6dq4+ zgjaou q9tzi:g,s5c,6mb k 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 same, (b) increase, or (c) decr9 k+bgu 56 4j6 sgzm,qa:c*i dzc,qotsease? Explain.

When an object falls freely under the influence of gravity there;gg8z ck.o h(c is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Eartz(cg; .chk8o gh. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are o* i8c7e k6waaug.5xi ln the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally w8aiec6a *uw k5li .7gxith a given speed on the Moon and on Earth.

According to Newton’s third yjh: xt: sf3y3law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, fjy3t hx:ys 3:then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe/c*:ua(mpdbx n3m7 gj the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (cg 7p/: n(mma bj*ud3xd) by what object it is exerted.

When you stand still on the grodns: :ifb8 hm6)3kmmmuej6;s:i3kk p und, how large a force does the ground exert on you? Why doesn’t this force make you k: fepmhk6:ui mj kn3msd:;6)m3sb8i rise up into the air?

Whiplash sometimes resul2 -a wxa++4rpgvr4asmts from an automobile accident when the victim’s car is struck violently from the rear. Explain why the heamw4g+v ra+ x4ar2-spa d 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 the truck accet.) au5fb *p/em (4iczakl x+xqv(ki0lerates, the crate remains whtuc(. iep(0 +*vlqkf/imaak )xx45zb ere it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reaches iti1npihh2o r)6;op7iz s highest point, it slides back down but the magnitude of its acceleration is less on o 2 h1r6o7iinz p;hi)pthe descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an incline 0zza eym0/pz. lo.)lvd plane? Assume the mechanism functions properly, even at)p0.e/a.z oz l0lvmz y an angle.

  What force is needed to accelerate zw 3ppu t-x6i2a child on a sled at 1.25m/s${}^2$?   

  A net force of 265 N accelera x:vtxwer ;qw(k4hk.e.+ns3etes 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 accelerate a 9pu9ust)-.-v0 f e/ki agzvrg tykt p9,k br4*-60$-\mathrm{kg}$ car horizontally along a frictionless surface at 1.20 $\mathrm{m}/{\mathrm{s}}^2$ ?   

  What is the weight of 8ifh sb7.b at ;+z)ijya $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $(g=1.7\mathrm{m}/{\mathrm{s}}^2)$ ,   
(c) on Mars $(g=3.7\mathrm{m}/{\mathrm{s}}^2)$,   
(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 i6ve .l0uya)aen 8.0 s if the car is traveling at 95km/h? .a6lueav)e0 y -  

  What average force is needed to accelerate a 7.eypl0auo35rh7*h f8 x 00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel of a rifle 0hfr yx*85heo3laup7 ?   

A fisherman yanks a fish vertically ou6cjcl2x67yevxp3 (pe t of the water with an acceleration of 2.c3vc662px p(yje elx75 $\mathrm{m}/{\mathrm{s}}^2$ 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 canwf2vzj:r()b p6fx wu-en-g5 b cover 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 rrr :6u7 v,d l,wmocco bt-n,+.eb- sdthe maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cable? mat .6vb b:lcnrseco- ,- ru+ drd7m,,owx =    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 motionl;3cpoh7 r77vugdz j4k6d )shfess elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the directi 7zv3r hukdp6d go );7cs4jfh7on of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Whvcfdr7 ,f*/hw,zs )e yat maximum upward acceleration can it give the elevator witrs)f, fe7*,dc zhy/v whout breaking?    ( two decimal places)

  (a) What is the acceleration of tw 7gr:u- qje nq68sj+g,8 wasrv;c- mzmy vx+,bo falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one,e:v ;army +xq8 cgvr7s,+wmbgjq 6-sn8 ju- z-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 housesk3xf,+5z r ikuto r4khl u053 3.9-m high. When he strikes the ground below, k3l05fsz,h5ki utkr+o 3xu4r he 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 of*tgur .*w/ql:- h twtn 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 /wh*u.qt ft:wlrt* g -of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketball playea bi+x(l:nr(-r+hm *ia oj4 z:n.p d,g8 lgxrnr
(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 th6gc5 84/ +wpost ml/7qo m8gijlv.dc5 vs bt;re moment it is hit by the bat, andd t l q/omvm o4lstbs 55g;i+7cwv86gcj8./rp again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly directs*5vs,u:gw 3b +jp mblion. A second 650-N force must be exerted in what direction so that the resulg l:wb umb, jv3sp5*s+tant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between twy o scl) -ms:-qca)a8qo buildings 10.0 m apart. c:mscylo--qa) as 8q) 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 u2.nkm v.q aqg1v6j)vmassless 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 14a od a .rd g46cj;med166x4wqp.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 byok ina t 2u5/foqnyy/)3y mg8(3c;i a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forc8 iyi2ot/y nugyayfmo3kq ;/3) b5(nces ${\overrightarrow{\mathbf{F}}}_{\mathrm{A}}$ and ${\overrightarrow{\mathbf{F}}}_{\mathrm{B}}$ exerted on the unit by the horizontal cables is parallel to the line L , and $F_{\mathrm{A}}=4500\mathrm{N}$. Determine $F_{\mathrm{B}}$ and the magnitude of ${\overrightarrow{\mathbf{F}}}_{\mathrm{A}}+{\overrightarrow{\mathbf{F}}}_{\mathrm{B}}$ .$F_B$ =    ${\overrightarrow{\mathbf{F}}}_{\mathrm{A}}+{\overrightarrow{\mathbf{F}}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behl)-fz q4k t*tfind it, Fig. 4-47 . Determine the ratio ott)4 f -lfqkz*f the tension in the coupling between the locomotive and the first car $\left(F_{\mathrm{T}1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T}2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pull.gp /x oz,b)icey apparatus shown in Fig. 4-48. (a) How h/)., xoi pcgbzard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, ns1,l w pb3*wbn(wwb 1a 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 blocmtft* vv0-l+7to z f0ck (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 +tw55 df uwj6zsurface are in contact with each other, as shown in Fig. 4-51. A fo w utzwj5+f6d5rce $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_1$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_1$, $m_2$ , and $m_3$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_1=m_2=m_3=12.0\mathrm{kg}$ and $F=96.0\mathrm{N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above thecq10,ohgh )j7zg, dvg ground, and the massless frictionless pulley is 4.8 m above the ground. Wh,g o7h) gc0jv1qzd gh,at 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 ypk2onon6z9+fd4wr b 1j6,fsux* sc5a heavy cord of mass 1.0 kg . Cal 2*w4f ,np9ckb6n5 ry od fu1+xzjso6sculate 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 fr8 ;98scbgzadyiction 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 requipydv,3ofuqc*lm3 g 9 .red 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 accelerating at 0.20g. What f(bx y0r bsx)h 211sxyminimum coefficient of st(sx fhbb1x1 0ysy2rx)atic 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 2nj1vcc8m ;x xbco/5 ucoefficient of static friction betwee81xxvnc ;/uj 2c ob5cmn the tires and the ground is 0.80?   

  The coefficient of static friction between ha./wqkl .zv )card rubber and normal street pavement is about 0.8. On how steep a hilll.wvk qz)/ a.c (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 z5ek)1 w*q* nupoitt( -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 rzzc1o /- fw-epbjz8s r1qm. d-ough 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 eite7v : i (bxb-e90icwith an asphalt surface have a very high coefficient of static fr0t ieeecv9bi7:- ixb( iction.

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 friction fori*jjsu5b1 pr4 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) pwqa r c;7r(d(how large a mass would box A have to have to prevent any motion frr dw7p(q ca(;rom occurring? Assume ${\mu }_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the nk ij 9j00i.lu-vviu/iiip g5 :hy*p6 floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and thp6lhu 0vi0 iip-jvuy.5/j9: i*gnk iie push imparts an initial speed of 4.0 $\mathrm{m}/\mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at 2lb+hid2x;bq15jf q.n sa rvj+g+i3l,.m iitrest on a horizontal surface (Fig. 4-54).3l+2 b5 fg.+nt;r1.lj+ hmqxsiv i,iqd2 iaj b 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 hea1 :c. yplnuu7ovy 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 the crate slide against the cab of the trucky nou:plu 7c.1?   

On an icy day, you worry abouq m* ;c/pzpa(zt parking your car in your driveway, which has an incline of /zm(zaqc ;* pp12${}^{\circ }$ . Your neighbor's driveway has an incline of 9.0${}^{\circ }$ , and the driveway across the street is at 6.0${}^{\circ }$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slide with a(*ptx z ml1fub5p./rbmvqsa.s h.;m1 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 lies on a plane tilted at adrl0 il ;h., xg5mbwu0n angle $\theta ={22.0}^{\circ }$ to the horizontal, with ${\mu }_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.0 7mim0a a2df4 k(dot/ m$\mathrm{m}/\mathrm{s}$ up the 22.0${}^{\circ }$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of 6r*)rfih,l ;ktyj u5 2p.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/ fv h;)9u1m h7 dgempq7:qzyk wall by someone pushing on it with a force directed upward a/: zk)h yeum7dgh1m;qq fp97vt 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 projectid f i)x68p(ryct9btx )les as they melt. Consider a chunk of snow 9)6r)8t pb(y xcftxid 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 automob6g(s7 qqfw)ax)9 wdej8 -c nofile traveling at speed v is equal to(fdjwa8n)7 9eq6o q -gscxw) f $v^2/2{\mu }_{\mathrm{s}}g$, 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 carhs scv dl9he*;,; hz.v slides forward on the dash when the driver decelerates fv,;h*zd.;e scs9l hhvrom 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 initial speq:ww nfc0il; 20 uq*gved $v_0$ 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 frod8c5ty7j a -iwm 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 sta-jdiy5a78w c ttic friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_1$ ) lying on a frictionless inclined plane is connected to a mass $m_2$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $m_1$,$m_2$,$\theta$ and g . (b) What conditions apply to masses $m_1$ and $m_2$ for the acceleration to be in one direction (say, $m_1$ down the plane), or in the opposite direction?

  Suppose the coefficient of kin g* dt.ied9o1-6k qh v0w:tmjmetic 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) can coast downq2lca hn-l57p. t 4yqm 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 approximatddy s(hbh, 5v.ely 20 g of blood is accelerated f hd, .5dhyvb(srom 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 3cm+1ytd (hrw surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force o1 r(y mhw3+cdtn 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 earthquage9198bndg l+ wjb c-u2x m1glke is a , and if an object is going to28+jlw1x9 9b be 1mngl udgcg- "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 of an accident involving two carz.v koeamsqbv, bbu1ha)/e/t3w + c)2 s, measure 72-m-long skid marks of one of the cars, which nearly came to a stop bef3/ausqz,+v1/b )tabb oc.ewkv 2h) emore 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 me oc or5*js1 x4d-ly.itans that for each 4 m traveled along the road, the t-*1ojsx4lo5yd ci .r elevation change is 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 the top of the Leaning Tower obleaaz: )( j9h;71nsjy;g fpz f Pisa and falls 55 mnypaa;bsjj:( 79l;1zh)fze g before reaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12mpry78s7zm+cqxt )) mo/s but enters a muddy stretch where the effective coefmt)zsrpx7+ 78)y qocmficient 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 redesign of a hilly ,gu6gll 2qp5y portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hillg g ,lqpy5l2u6s 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, dangsbce.v)v 0tixn7 .x p+les her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. n.0)7e x xv+. btpicsv4-58). She notices that the string makes an angle of 25${}^{\circ }$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket, there are to be several 9vg*j dn i.m1w(srzw7ramps connecting different parts of the j 7n .vmz9wws d(rgi1*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 lrn/jav5pi*-zw/ wq ;wfk*5 n ) using the pulley apparatus sho *n-i/*zrwj5;nkq pvfl/aw 5 wwn 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 :pcl(tmhuiao1o0 1ywz,,sx7$\mathrm{m}/{\mathrm{s}}^2$ 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 ,tyy v -yk:h7uskvu:) considers the following set of conditio)uky:,uv-yy svtk: h7 ns:
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 hasvah sj hekv+ v(8x*eeli /,63n 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?