Why does a child in a wagon seem to fall backward when you give ths- kgdo2efe4 :e wagon a sharp pull osg ekef 42d:-forward?

A box rests on the (frictionless) bed of a truck. The truck driver starts the t5wia0of8 mw)pruck and accelerates forward. The box a)w08mo fp 5iwimmediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no forces j e38z;:us q2csy+c :z7fytz.sg fk2 aacting on it? Explain.

Only one force acts on an object. Can the object have zero ac0qo8v7 15 na op8kmbesceleration? Can it have zero v1kq e 5oams nvp8o08b7elocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) Is a force k5ijpy/6m22:l g wg cfe oad,-needed to make it bounce back up? (b) If so, what exerts le yg6/-ok : ,jma2wdc2g i5fpthe force?

If you walk along a log floating on a lake, why does the log move in the7hd9 +zrla* i4m kshn(g0jmg( opposite direl9 mggh(a0*hid4+kj nr7m z(sction?

Why might your foot hurt if you kick a heavy desk or7 c 2bow-c 7pd-hu,f6tk6nzfcde 1mu- ucn)0z a wall?

  When you are running and want to stop quickly, you must decelrw gk ql,:c dv9x: i) 8n:epdb7(nlh9yerate quickly. (a) What is the origin of the force that causes you tc7 9l b qw9,rx(kipy: gd:l8d n)nh:veo 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 fine thread from thz(gar,zab 9uj7 y( yb)n9t1qae 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:ybry9 9qz a )augj,a1t(b(z7n below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock ism9:td 7z f)kzw twice as great as that on a 1-kg rock. Why then doesndz7z9fm:w t) k’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results *o2y 83hvg 6el.xfelmif the scale had been calibrated (a) ifev h2 yl8go*lx6.3emn pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table usingkwx 99c /pxr+ ljo6eh3 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) remcr3wl x+/k9h ep 6o9jxain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of g 6* sj0q5 hnrt4/zkyqlravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on stn6hyjr 0q* qkl /54zthe Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-n 9zf1ha3d -l mqf0h,jkg object when you are on the Moon with the force needed to lift it on Eart-a dfmzq1h3jn,h f90lh. 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 w 8 vk l--poybuwto(0t3ar (Fig. 4–37) pulls with equal force on the other team. What, then, determywl-08 3u otto( pb-vkines which team will win?

A person exerts an upward force of 40 N to hold a bag of:-ej v1vsi8 )odmg5sq y6z2dr groceries. Describe the “reaction” force (Newton’s third law) v:ogze86jm)5s 12qs v ydidr- 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, n5x )) eub/pqnhow large a force does the ground exert on you? Why doesn’t this force make you rise up into the airxb)q punn e)5/?

Whiplash sometimes results from an automob 5t6cd ,yb/yh5ryqf3kile accident when the victim’s car is struck6y5h cd5ry/ ,qkf3tyb violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbl hof sw+f)(n0ed truck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes tfo)(+n hl 0sfwhe crate to accelerate?

A block is given a push so that it slivdn:x12q,-bg3u kp ltdes up a ramp. After the block reaches its highe2xg3tbp ,ldnqv -k1: ust point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read if (w4 ahq9rr89jtvhvv5 you weighed yourself on an inclined plane?jrah(h94wv8rvvq 9 5t Assume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child of;v w*+ces,+. xsgh8rcw.gi *swlv)gn a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.3 ix+vpi12q/x2jmk fk i. a3y:y0$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope ev fpg zq3.ot0cs71rox839 tpwithstand if it is 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 a )v3hltni6+u5,1 1kd gtkinfb $76-\mathrm{kg}$ 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 wecsawi)an6*2(4 ma i stop an 1100-kg car in 8.0 s if the car is traveling at 9mincaa 4i*w s2(a)6we5km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from r +8r4a7 fgwaz qhct;+west to 125m/s over a dis+z87 +t c;4qaf whagwrtance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the waterr6jx0 y gf6(bmsx:pma2j) g y, with an acceleration of 2.5 fxjg(gpmy,jax ybm)0 :s6r26 $\mathrm{~m} / \mathrm{s}^{2}$ 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-milzy 0wc)+ - ,eirlosib9e 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 48fyp/a)dj bs5-h2j0 ph 50 kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the m5pasf) b20- d/y hpjjhotor 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 elevatoma eqz4u 02450o.z 4qbydhsryed8y5h r beg0yma.ds5yo24yhqh 85z4zqeeb4 dur0ins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. f a7h2tk( tr(m26wn ,h5wsufcs -bv(tWhat m mnhr2hv (-f 2k fwc astt675bw((st,uaximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mav 5.v n0:avaguss 132 kg including parachute) when 5.0unavvg a:vthe upward 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. When hxdr4w1 2lyqx5u hq7k(e strikes the ground below, 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 2xqdlky 1 qwu(47r 5hx
(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 he wd93wonw (ev t/0:wto 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 we:wn w0w(tw /ee vo93hdight 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 dis 2w wh*uzqv ;7s7em:hagram for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the momenth h)7mim-n3v0g t*rct it is hit by the bat, and )*r3t7 ti chn hmvm-0gagain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly dirke40q50gez,)o ,fyi q 8m mmojection. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a v8y4j0f ,qo0gmm )oq ,eze kim5ector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two bu, p8v4xxywa; kildings 10.0 m apart. The sag in the rope when she ;xy,p av8xk w4is 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 ha,ibk9 iz /*qrbnging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{~m} / \mathrm{s}^{2}$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14./zqwc)15ce/ yc1 xpwx0$-\mathrm{kg}$ 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 ay2ljll 9)f-mo new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the forces2l9-lyo)f lj m $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 mnmf 3 w6)qkp,mcca+ooht* z p0)s;2kof the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in t2oo n*m,03pqhcm ; fkmp+6kwc)s )zathe 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-pulley apparatus shown in 9eu(yud+ (gyv Fig. 4-48. (a) How hard must she pull doy(gvd+ uuey (9wnward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 6mqcg (u8r*+ :em cj/mi5$-\mathrm{kg}$ 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 (masy :v81p7lnfi ps $ 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 surfap hd:5r 9/6kkvynk1bu ce are in contact with each other, as shown in Fig. 4-51.9k vpr1kh 65n:/kybdu A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80h28 km sa2 o a3swf4+9yutga/f 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 gm a h+2tas9/ow4ufy2 akfs83hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes onwqzx2z8;y owkv/n7k1zm0(wf a frictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each boxqxfzz1o2w0zkn w8(/ 7ky;mvw 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 kin ,v14+oaegz jvetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to utejbgi;0 :c+xqg2y. 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 accelera85 +tfe(1zmjk )yeuau ting at 0.20g. What minimum coefficient off1am)e8yeuu(5kj+ z t static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a carp, eu1jvv;uc 76rzq- x can undergo if the coefficient of static friction between th; x-7cqj, pre u6vuz1ve tires and the ground is 0.80?   

  The coefficient of static friction between hard rubbea7wx;ir gg5az4kf8v8 xuz *h / l6trx,r and normal street pavement is about 0.8. On how steep a hill (maximum anglelgrx;zfutx 5ai 8xr4gw z 7ak6*v8 ,h/) 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 -4ebu/w550j zbm.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 rom+ gx ch*(fkx j:km9qbhz o4:*ugh 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 cb+ hw9hez;gc b)n f,*roefficient of static gcn+9refzb b),wh h*; 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 kinetic3hves7orue6h2;clgb-; 2o h i friction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large fa,atj- q8k)uo1p gc-a mass would box A have to have to prevent any mfa - gac8jtq1,pou)k-otion 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 gk3 6y3k;jegpe)x-c*kqd: jgqel u3wt,a1 4 oo o, given that the coefftkwok 43x1j6 -; oa c qeqp)gdekg3*,e3luyj:icient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contac:t(ybs3uty c c.m +s9ut and at rest on a horizontal surfacc9: tsmt y+.csuyub(3e (Fig. 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 ad+op;pk(qde iokoo:kv9h6vb ( a008x heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the truc; d(khkv0iooxp0( o:+epv 6kb da8q9ok?   

On an icy day, you worry aboute,wy0e muej1 *bztk0, parking your car in your driveway, which has an incli0e1k *eet ,uj mwz0yb,ne of 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 y7uk9lj1n6sb a slide with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted 5-3- dm a.6: kxghgqzq5/ll + ply*wc4qommnvat 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 in;ebewm- 0 up7x5tvc,n4t: ntwitial 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 7pm /;ie5aj/(caglgqthe top of the steepest 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 rou y se.6wma,9:c igual9gh wall by someone pushing on it with a force directed upward s6ygc9. ue,m:iawa l9at 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 projectiles as they melt1..1jg lcad*o,g9pkln ;,j sc 2rkafd . Consider a chunk of snow at the ridge of a rog,d1r.jk9pfn sl .a;k a* o1cl2d,gjcof 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 minimumbp l1cn x)--i8b -rmcy stopping distance for an automobile traveling at speed v isy-81)cibmp rc --nbxl 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 dashboard of a car slides forward+ke r-ejy5 eme tjbs+vk9/+( p on the dash when the drivert/ry5j( es+evpemk9+k- jb+ e 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 initial n6lrhb3jqk2o.sy.)a 4 tv m0 aspeed $ 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 p* 54qqkxopne qqwf(7lh 0 x(u0acking 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 q 4 wqqxx ol0*p7n(qe(f5 ku0hcoefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic 6am3; tvf5d 3x+,jalcsvcxu3friction 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 (includi6 ie:62tfiypq ng 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 simplified5gs2wu g 3/uxf model of a mammalian heart, at each pulse approximately 20 g of f us5gw/32xgublood 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 automoy1 n ( sd4yq.a6tjue8s8q0vmv bile crash if the deceleration enq1qyy8vtj s08(4umv . d6asis 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 earthquake is a , and if an obj -h.)8aumyze6)q.ojnp a iq*d ect is going to "hold its place" on the ground, show that the coefficient oih . a68zm -*e.nuyp)d qj)aqof 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 suf-zv (c/zdlso42k*of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pau4scf- (zdzs*v/k2ol vement 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 tr iuwxq2q: owgex) zns0/kgx le65 0z-hj:)f r;aveled along the road, the elevation change is 1 m).)20qxzkf qw ei0o:xz-wns : e5hgr6x)u l ;/jg 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 Towe( -y svzh4ok0z./smk2h 5 yvdlr of Pisa and falls 55 m before reaching the ground with a speed of What w 20 s/kdvzh 4lkos5yz(-.hym vas the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/l3q8ynkf8f34m x( nx ps but enters a muddy stretch where the effective coefficient of friction is 0.60. Wi8f3n4xx 3y8mqknp(lf ll 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 redesi xp7u oub(qq+5gn of a hilly portion of a city. An important consideration is how steep the roads cano 5+7xqpubuq( be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can accelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a thin pia;e4:1 ce ox2 o jp.kk:au1dgvece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices tvjue11 xk ca4oe;2g.ado:k :p hat 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 seg:ypwg i wg-a- 62e7gsveral ramps connecting different parts of tswep7-g:ag2g w g6i y-he 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 the puo28evj d b6 ka4d85bswg(gg 1klley apparatus sgevdo1 ka5dgwk2bg 8 bj( 6s48hown 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 vc db3h3kv4 sd1 6yv4r 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an engineer considers the 8axvx cy7wu ,j t8*ert. +y(wafollatyjxyr( 8t8. wacv7uw ex*+,owing 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 meta:gdrsyn; gvk2 i*-k 3ric 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 2ra2hw// j fkixatwt95 v,5beKaren, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro clixbr5a/2ti 2 v wk h9jt/e,5afwmbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is using as (zt0e1/ w/eq wb(ztf " 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 maxim0ufd 8pigw n:4um speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

  Two boxes, $m_{1}$=1.0 $\mathrm{~kg}$ with a coefficient of kinetic friction of 0.10 , and $m_{2}=2.0 \mathrm{~kg}$ with a coefficient of 0.20 , are placed on a plane inclined at $ \theta=30$ ?
(a) What acceleration does each box experience? $a_1$ =    $a_2$ =   
(b) If a taut string is connected to the boxes (Fig. 4-64), with $ m_{2}$ initially farther down the slope, what is the acceleration of each box?
(c) If the initial configuration is reversed with $m_{1}$ starting lower with a taut string, what is the acceleration of each box?   

  A 75.0$-\mathrm{kg}$ person stands on a scale in an elevator. What does the scale read (in N and in kg ) when the elevator is
(a) at rest,   
(b) ascending at a constant speed of 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(c) falling at 3.0 $\mathrm{~m} / \mathrm{s}$ ,   
(d) accelerating upward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ,   
(e) accelerating downward at 3.0 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  Three mountain climbers who are roped together gyp9 /rt :gyvo:qgikz9p5.t 4are ascending an ice field inclinedv4 5ry9q k/g:t . zogi9:pytgp at 21.0$^{\circ}$ to the horizontal. The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg , calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.