Why does a child in a wagon seem to fall backward when you give the wagon a sharakg957kkwz0jfxgc* 7 p pull fo7kzc 7*k9 a0j5wgk fgxrward?

A box rests on the (frictjehcgg+rwb8 2;x/; xf 2aj*g vionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box iv* 2ejc;+g2/8 xxw;ahbjf ggrmmediately 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 t81kqmy4y.hbrw3hq p lqi1:kxh5v48is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acw;3ed .e ckcq*d0 fjt2celeration? Can it have zero velocity? Explain.we.ejd 2*kf;q0 3ccdt

When a golf ball is dropped to the pavement,m2 sudxrnjg m:-in4 c-)o 7lv2 it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, whatg24-v incom:x2l 7rn)-dusjm exerts the force?

If you walk along a log floating on a lake, why does tbg o-/1uwumu bq9*cdiqh:l(o *3 grl+he log move in the opposite directuhq*bwgd:(qb9u 3uci +1l-moo/r* l gion?

Why might your foot hurt if you kick a heavy desk izh l/zwk(l,ba ;1ff/ or a wall?

  When you are running and want to stop quickly, yol4z30afiz-sm u must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using yo0f 4az-zl s3imur 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 t.tgto(bap 0n g:dr+ ;nhe ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36dgao.tbn(: gt + n;rp0). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. b),(tm )scqm5ub4oihWhy then dobh)cs it)54 mmbo(uq,esn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scpw*4awcbc phec tyw2b * d0g)/:do+ z/ale had been calibrated (a) in pounds, or (b) in kiltzw0da 42 cg) c:hwew /poc*+y/pbbd*ograms?

You pull a box with i/mnf :lge:73e n /an4jtqz/ja constant force across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decreae//te 7nj34:nlfq ijg/ amz:n se? Explain.

When an object falls freely un gk,0w+c *uojyder the influence of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposy+0o,kg ju *wcite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object whenyjpb +r1z/swi(* y3 jughp 8y-o cl.*i you are on the Moon with the force needed to lift it on Earth. Compare tsrl*/ib8 wi+ z1uy- jp(p *3hoyy .cjghe 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 f6 )ffietb rci)gl*ze r1:1w4(Fig. 4–37) pulls with equal force on the other team. What, then, det1wc*)f4 tgrbr:)ee 1fi l6izfermines which team will win?

A person exerts an upward force of 40 N to hold ); /m7kn7f esdhai szz +/hi9h3-fjge a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it isz9-mf 7)e/zkfas i/;ihh j+sh7g3 dne exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the ground exeeddz uj )6ar/4rt on you? Wdad/4zeujr 6)hy doesn’t this force make you rise up into the air?

Whiplash sometimes results from an autpzb: .;l3ijzyomobile accident when the victim’s car is struck violently from the rear. Explain why the head oz.pbi zl;3 :jyf 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 . uhveet(hkfl 958vx2 accelerates, the crate remains 9tv(eh 2kfhl58xev u. where 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 rv9 a.l/lpxjze 7kd/: oamp. After the block reaches its highest point, it z9 j/ 7/vxeadl:p. oklslides 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 you weighed yourself on an a b /pd9.-g e7q nhiuk8.gh+oiinclined plane? Assume the mechanism functions properly, even at aiui q-ahgdp.k/e+hg9obn87 .n angle.

  What force is needed to accelerate a child on a sled at 1.k15+y 4gi kt y99xfonfp5zp1x25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider aa ghz0c6m) vt8ypu;b. t 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 u1 o vn2x gm8iqczou-0,sed to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight oqxc ),7ziky6 lf a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s if the car xv(g.-gh 7ozz/ xwv 4vfj/vx4is traoxj/zhx x w-4gvfv g v47/.(zvveling at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pellet xos5bvnt35q ;from rest to 125m/s over a distance of 0.800 qb3x5 vot5s;n m along the barrel of a rifle?   

A fisherman yanks a fish verticals g4,44/cc cg.hgf- (iivj gpt* pii)xly out of the water with an acceleration of 2.5 cg)4 iigp44, ix(-cj*/t.ivgcf hp gs$\mathrm{~m} / \mathrm{s}^{2}$ 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-l m yjr6 4q/(rwz-ad) qvmn0(jmile 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 thac7- *,hd zjl ;y8gpktwd; acw-t the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supp hp8j-c 7d*zal;kcw; d-y,tg worting 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 scnn 6m+vu:a-mtvum5.4o1 ,6ul z erqelevator. 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 direction of accelernvu+ ,mc1 m5lz:mrno.4 uetsa-u6q v6ation.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of oz +etaj.*h,mhg9j.ky;nr *a 21,750 N. What maximum upward acceleration can it give the elehgj*r9m*+j.oeykh a z a,nt. ;vator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling skv qxqf -pq,yoixg *9h2m(ls-6y divers (mass 132 kg including parachute)q*xxsfpq hig2 -( , mvy96qlo- when the 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 ro 03 bs-dxtou4p- zi0cwof of a house 3.9-m high. When he strikes the ground below, he 3buxtwsc4 0p-- do0izbends 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 on a tabl65l /ewtsxl/+f wd20h3ybafn e. 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 hangi06f 3 hn5as w/ly dlf2+t/exbwng 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 plkwz7 l8 cvu9e7ayer
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram oqjlx3s (5ib )of a baseball (a) at the moment it is hit by the bat, and again (b) after it has left the bat and is flyiq5iso bx j3(l)ng toward the outfield.

A 650-N force acts in a northwesterly direction. A secony7 1glejv6(b 6t*dxq9fblg w2g mx-1md 650-N force must be exerted in what direction sogl7b1q(-gx yx1b6* jmg29ltf mw e6vd that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizon+;ug3u9nc 8ftw5dp l etally between two buildings 10.0 m apart. The sag in the rope when she is at td u+t;pcule g89f5n3 whe 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 masslq3bpsr:pqgg34 7q6gh ess 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 14.0d9vjn3*k 5 q l:-lezqu$-\mathrm{kg}$ lawn mower at constant speed with a force of F=88.0 $\mathrm{~N}$ directed along the handle, which is at an angle of 45.0$^{\circ} $ to the horizontal (Fig. 4-45).
(a) Draw the free-body diagram showing all forces acting on the mower. Calculate
(b) the horizontal friction force on the mower,   
(c) the normal force exerted vertically upward on the mower by the ground.   
(d) What force must the person exert on the lawn mower to accelerate it from rest to 1.5 $\mathrm{~m} / \mathrm{s} $ in 2.5 seconds, assuming the same friction force?   

  Two snowcats tow a housing unit to a new location at Mczo(7a b;;lht0kc 3tt sMurdo Base, Antarctica, as shown in Fig. 4-46. Th oh3ta7tkstcz;; 0( ble sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. 4-47 . k.bcy tmk0 b;t.1jbe) Determine the ratio of the tension in the cokec )bk.;m0b t.ytb j1upling 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 hd49e6j vw )smqerself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at9e s vqw)dm46j 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, 4oow37f4u6 oim pqh 6na 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 (ma9+t2auu*mrd-1rxl a1h 0q s nyss $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with each otheu7 riql3*hbz-pq 9 /izr, as shown in Fig. 4-*lzihq9r /p7qz -ub3 i51. 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 1.80 m n. bw6+l+dfqy, :ltwl above the ground, and the massless frictionless pulley is 4.8 m above the grou lndwylfw tqb+.: ,6+lnd. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by9rrf(inm qj cm5m ( fm;,jj,)k a heavy cord of mass 1.0 kg mmr nr5 jcj( , 9(qf,jm)k;imf. Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of kinetic g pw9.dia8um+5 f67yodv;vw,zh s6oc*by v- tfriction 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 5.0)pxhc h/de8 l.$-\mathrm{kg}$ 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 standijj a*sk3hq .3ggv l.q-ng on a train accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor g-l jg3*qa.kj 3h.sqvif you are not to slide?   

  What is the maximum acceleratio4ndj.r2 k ac4zri8d i;n a car can undergo if the coefficient of static friction be4.2r i48n z cjrdaidk;tween the tires and the ground is 0.80?   

  The coefficient of static friction between hard rub2bkm-f ck9(mcf rq0c 6ber and normal street pavement is about 0.8. On how steep a f(m-9cqfkk02cc rm 6bhill (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 atcf4 m 4 (iv3b7 na dhqks29;7eu (zhl;owaer2h -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 a2 3 pap)u0 d, xpj,9-k-snf l)femwrwy rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asp5geme u90-fichalt surface have a very high coefficient of static cfguie 05 e9m-friction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic frikf 96jxqhdjcpwveuyx7 4:2 9kp1:2vjction 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 a mass would b9( 3z/wmh zmseh7tlq5ox A have to have to prevent any motion from o5mwh/e3zthm qslz(7 9 ccurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it 4s3k p*hlaectvnq uw0u2+4a 2slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0q2kuw 4aaustl2np+ 4* e ch3v0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a hoof,k hzx +c48zo.+g0e 8qzh1 k4qe +qthw+zx crizontal surface (Feh zk.wq,t xf +8zcgq4c+ kho z1h++0z48qx eoig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient 61:g(u me -)ekbsmd d/rbfer-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- 6usmer(r :/fed)bemb kg- 1d having the crate slide against the cab of the truck?   

On an icy day, you wr y z8 7t 4fl2,19jalljjqh+kxuy+f(aorry about parking your car in your driveway, which has an incline of 1ajfh97+z+qfljy8tyk4lr u , (x2alj 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 wi3ewfsk:1us sblj, hp l::fn .q05fv8tth 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 .nk9n vfaj n(/o( r(latilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speukjo f+o w :bc.782euped 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 steepest hill with a speed of 6.0yhx:j-lfa-2zqh(5 7j j;qt ez $ \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 2d ud;nqand8: a rough wall by someone pushing on it with a force directed upward at 28n8;d du :qd2an$^{\circ}$ 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 dangerousfu;r2 u*tm1jbc5c f /(n8r lwp projectiles as they melt. Consider a chunk of snow at the5 (ftf wjpun *luc2/r8;bm1r c 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 fx -ilom nzp3+0gs7m0 z cp)ge3or an automobile traveling at speed v is -m7 nmpg3+z0se)0xipczg o3l 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 on the dash9lnil sxm/3 kois jw:b/s(, -t when the driver deceleras:ji m, sionbt(lwl-3sx9 /k/tes 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 init(2piw.cyt; pwial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to the packiqr;)msp tn3m2ng station 11.0 m away. The belt is initially stationary and must finish with zero speed. The mp2 mm)trqn s;3ost rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for 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 k0,jkbl .wr:c .0wjlr 2seha2linetic 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 dow t+jx 8vxpc8+ rpm7k7bqokw-;n 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 77,s*yeu yugp xvy-(heach pulse approximately 20 g of blood is accelerated from 0,esv(*7gyh7y upxyu- .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 an92t-j r*iqm5 /oub .5v gwk ah6x)tgfc automobile crash if the deceleration is no more troa gcbk-/x hw)5f m*v.gtq29u56ijthan 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 earthq 65hymle(xs 2o t4-+ehypr2jzuake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static y2hoeyh er t6sx 2j45(l-pz+mfriction 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, examina ; cyb:-73ifh+o(znw6ub hpring the scene of an accident involving two cars, measure 72-m-long skiu:ow h- zf (arbcpn;i+hby736d marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (18vik 0se,q*hnxpksbi 7 3h(bhf xw (8/-in-4 means that for each 4 m traveleds v8kehbx83pb 7s0q i*,wkix h/h(f(n 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 friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped, ic /pi9dcid1 from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air p9ci,/d 1icidresistance?   

  A cyclist is coasting at a steady or*m4n+zqvo 9 speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the+no4q vm*9rz o 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/4e4ar7lxf poq2ebm9qz* b;q 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. Albq e 94r zq42;/efxaqpmb *7o 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 tqa4pkb2nw d2q3i x,c*hin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angd qpk3q2c 4bnaiw *x2,le 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 ar782d p 3ovpsdye to be several ramps connecting different parts of the sd7 yd8opv s2p3tore.
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 pia mye7 /5v aao5qxga(*rbu0 g6bno (mass M ) using the pulley apparatus shown in 5gm*x 0y7 aver65q ug/oaab(b

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*sws a5cqi7uv(.ti 5g at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a 1 k 2wshgv6t yez13g2*gejva1child-restraint chair, an engineer considers the following set of conditiv ys*1egg weh1z jvk gta22163ons:
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 hasp1qxe-77niv ,bwe o:m 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, use safety ropes of similar length. Kar7taekit3 h+yr bt (eq: a13o5ben's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to a: tqeo3rkib7tyb5 et(1 3ah+be hurt?

A fisherman in a boat i9x v7stp*sej1s using 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 buildins*z. lmi+ b8o9pz k2cpg is allowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice field*i lqi*6kgne 0j0,p gqasg0bw:q e2 j7 inclinedls0e6bqk* pi 0 a*jeg 7ggin:0wq, 2jq 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.