Why does a child in a wagon seem to fall backward when you gf-)xlfsha2 )y ive the wagon a sharp pull forwa )2)s-fyflahx rd?

A box rests on the (-skxky4 ;a.ei8yla2 b frictionless) bed of 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 box, in terms of Newik8y- kl eb. 2xasy4;aton’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 on it? Explain.eb 34df t+t;zg

Only one force acts on an object. Can the object have zero apgj;4y nw0c .tqb -wu7cceleration? Can it have zero wj;yc 407-gu qn btwp.velocity? Explain.

When a golf ball is dropped to tj/dodo42l) ph;u r2b/pfsna- he pavement, it bounces back up. (a) Is a force needed to ma fbl ;u/h -2dn /jpdoa4sr)p2oke it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake,)3z7k+p.n 4qiacw9vb j8 ulrz why does the log move in the opposite direcl 9 c3w8u.nb pi 47jq)r+kzzavtion?

Why might your foot hurt if you kick a heavy desk o ku4v c*ui/g:h-o riuh .-a:lqr a wall?

  When you are running and want to std r7 o)vyh;bhw.k -/ l ymeijjt/8+e2oop quickly, you must decelerate quickly. (a) What is the origin of the force that causes you jt y-r bvm d;e/hi.8whok2+jyl7)/eo to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the(fouwfjxd -3 + ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a shf (3 o-uwdx+fjarp 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 onljc:eu a; ,qs: a 1-kg rock. Why then doesn’t the hes;,l:qa :uejc avier rock fall faster?

Would a spring scale carried to the Moon give accurate results if the scalf1 z 0epa7:;d8fy nylwe had been calibrated (a) in pounds, or (b) in kilogra nl7e0:wf1a8ydpfz;y ms?

You pull a box with a constant force across a frictionless tabwgal 334wqm )jle 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), d)q wlmgwa433j oes the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a ne4a(g(rp rs1t sgwnt,3t force mg exerted on it by the E3( srgr4wpg1 na,(st tarth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object whedc ac o8b;l/yj78xz8 :9flneun you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the M9zl8a7l8/xcde:nb jfc ; 8youoon and on Earth.

According to Newton’s third law, each team in a tug of w5fy; x2p, rtf7 w1mhdwar (Fig. 4–37) pulls with equal force on the other team. What, then, determines whitxd,hp;fwfw2r51 y7 mch team will win?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe thg,s+igph cy82dmi 0 8ee “reaction” force (Newton’s third law) by stating (a) its magn+8dcp2 gyhi0egi 8s,mitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does tjif y5:bki6:aug 2ywpl/)ty7 he ground exert on y6iyjyy 2/kli)5p7:gb awf:u tou? Why doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the vit5 + /2kvficw3o47 x u6ccspuglk3ox 8ctim’s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this sit7sipkc8uox2 t/kl43 5xv 36f+ cgoucwuation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When the truck acceleratjtq6,k*q +zs .jo-kss+ a8gtu-9 xf wces, the crate remains where it is on the truck, so it, too, accelerates-otjq*s 9fkz +,-uxca+6 8 sjqt s.gkw. What force causes the crate to accelerate?

A block is given a push g9hy/bf4 v u1cso that it slides up a ramp. After the block reaches its highest point, it slides bv 4/ c1hgfbuy9ack 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 inclined ppl *j28yveb*/h +tro2 4eu :mvsghae8lane? Assume the mechanism functions properlh8*tpelb2:/aeo 4 ru vjs+g*h 82vm eyy, even at an angle.

  What force is needed to accelerate a child 9sjpx:q8c 5hkou(ihft)kg 5*n;bdh8 on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates+sn -ox zzd*9w 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 iigk,n,yu, f- mswtpz x 1/w1 xyx3qc2-f 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 -+dzzpb g3 j0s)bk0jn $76-\mathrm{kg}$ 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 s aa;,m681bqhbr b5q jt,fu3g8.0 s if the car is traveling at 95km/h?fjr 8bq 5 b,6m;,q3aasb1ghut -  

  What average force is needed to accelerate a d,b-3fg zj63y9tlote7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel ott6 gjyed3flb -z 93o,f a rifle?   

A fisherman yanks a fish vertically , 8;wy)cdngd oout of the water with an acceleration of 2.5 oc,dwy8 )dng ;$\mathrm{~m} / \mathrm{s}^{2}$ 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-fb4h5y8r7a p0tm 6iu25d,gxwn7hof 7qv- xalmile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

  A 12.0$-\mathrm{kg}$ bucket is lowered vertically by a rope in which there is 163 N of tension at a given instant.
What is the acceleration of the bucket? Is it up or down?     ----待选择----downupward 

  An elevator (mass 4850 kg ) is to be designed so that the maximum )c4gg. wim 02ofru:cyefm;a(h0hq+ cacceleration is 0.0680 g . What are the maximum and minimum forces the motor should exertg4)2.+ e 0cguyhfica(r0fmh; q: ocwm 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 elevatlq0 :7f0oaxqed *u6 p-8wpn2js2; vhfyh wz7nor begins to move, the scale briefly reads only 0.75 of the person’s red -wzhlf 2;e7qonu*8x7h: paw 06sp2y vfn0q jgular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator h70c*uleqac /5 -tjfrxas a maximum strength of 21,750 N. What maximum upward acceleration can it gt7 /5ea rj c-*lcqf0xuive the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sh+(p0xs sdnc9i o9g8dky divers (mass 132 kg including parachute) wh dd8+pogh0xic9ss n(9en 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 roof of a house 3.9-m high. When he str:7es jzc,,d1ko bip cu;:l ls4ikes the ground below, he bends his knees so that his toik s ;sp,celz1uod4jlbc,7:: rso 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 table. A rope tied to the box runs vefj zus/61uou ap. ry+2rtically upward over a pulley and a weight is hung from the o61+oru /f2u .a jupsyzther end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram foa pf+x8 a6.evcr 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 mome7v: w ax40bzpzinzco ++no ,s1nt it is hit by the bat, and again (b) after it has left the bnx70 1:4+zas p+zoo,z wv bincat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N force -h- p :bvman cb4p7i7smust be exerted in what direction so that the resultant of the two forces points westward? Illust iscp7v4-m-hbb a7np: rate your answer with a vector diagram.

  Arlene is to walk across a "h-l v6tgd gcwqot) s853igh wire" strung horizontally between two buildings 10.0 m apart. The scw 36glsq dg-ot5t)v8 ag 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 m jg-+t-8e2iuhtzv*+mzxde9 eassless 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 14.7hr1rd 7;n)hyt zwyp30$-\mathrm{kg}$ 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 to33y5h;ld uv1fl3hf *qim4xjl a new location at McMurdo Base, Antarctica, as shown in4mdl3h *h l1v x3fyqjluif;35 Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pn*mlvm)m2vqr; x a7m6ulling two cars of the same mass behind it, Fig. 4-47 . Determine the ratinvv;2ammqx mrl)76 * mo of 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 pullqz o*nhwfzwf,* w2.5cs herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) How hardzfc, 5wwn*h* . qfwo2z 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 b gf4 j-u;)onqkegan, a 65$-\mathrm{kg}$ sprinter exerted a force of 720 N on the starting block at a 22$^{\circ}$ angle with respect to the ground. (a) What was the horizontal acceleration of the sprinter?    (Keep one decimal place)
(b) If the force was exerted for 0.32 s , with what speed did the sprinter leave the starting block?    (Keep one decimal place)

Figure 4-49 shows a block (ma iw0kzdi7i .t.dxu9(ah v0t+ oss $ 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 frictio1u-uhj(jt)tmk7 )paicea4 :nnless horizontal surface are in contact with each other,1p inu:t)t aja h- kc(7jeu4m) as shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are eac +1 (xq1zfosryh initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is rz(+ofyx sq1 1released? [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 b1rg)e;nza c8v i*try 7y a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. varzniy rcg1);e87*t 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 kinetick 8 qwzw4qf7ma :9y/qr 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 t/t cysxqm2/g+h4ly0m fue 3 i,o 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 acceleraud2 9 )g1mwbgrting at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor wr1 um9g )2bgdif you are not to slide?   

  What is the maximum acceleration a car can undergo i0rqdyc7(xyp/ 74ep* 7hqyues2 o+d -u2 dd kpuf the coefficient of static frictiod*x/ +edchokq0u 2u qs -7up4yyd yepp72(7rdn between the tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal jzp.o/p d;r(p street pavement is about 0.8. On how steep a hill (maxim;p (jppz.o/rd um 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 -4.80 wk0,y1(,o q oldwsnr) $\mathrm{~m} / \mathrm{s}^{2}$ 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 reek--wax-x*s;obc sacv vxj-8,p /mm )st on a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt sud77,nifrh ux6z +jnx5rface have a very high coefficient of stat5hnud+,6zix n x 7fj7ric 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 friction f9: s+3yrxr wdjf a8+dnor 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 box A g 0pe 71rzsxu 4f1jd7 kufdg3*have to have to prevent any motiongs dd u r14egp0ff z*xjk137u7 from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far 9avkku sg+ --zb6r+qq1ii u4 qwill it go, given that the coefficient of kinetic9kiq 1-bsg+ui6qa k z-vu4r+q 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 contact and at rest on a horizoei)v0 ;tco y fvldvu: :e2w/)rnmp1 +xntal c o):+t1:lvxy r0euf m)e ;npiwd2vv/surface (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 a heavy crate. The coefficient of static friction be;wms(gx3q m,qfl 5n kwc(t n(y, )w2fatween the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate gs(f,(y(q3 ta qn2k 5wm)wl, w mf;cxnand still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your cajk,2rta ;*dkzd+sox- r in your driveway, which has an incline of 1ork jsadk2td*xz+ -;,2$^{\circ}$ . 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 a5mpl1+qtt lv -pai v7 4i5n /jjcsf;g; 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 to78 )up9h)cwuh f 2dcui2,uwlies on a plane tilted at an angle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial s(y9 f6g1uyi gzpeed 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 4r6:ai2imwlxhy-/c n 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in place against a rough wall by someone pushing on itr cxeogoui 0e,9:njg24 9 set2/yqlsa3k32m t with a force dirrx,e04 29sl9q:g je 3at22ntcmg/k3ye osou iected upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectilem8. l:ot. n,lfzb,+y, m qmls1nlp.uo s as they melt. Consider a chunk :mmoqt 1o.l l,z,lbn.nf.8pl,+uysm of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling at sperwhk0l wl( e4 irs:x.:ed v i. k:li0rx:rswe(wh4 ls 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 sj9qq:a8 o ig,5*d 1hdw(cdskj lides forward on the dash when the driver dec5o k,j *wh(9dsq q ciad:jd81gelerates 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 speed j u nitcn;e04tc1jmm06u) 6rd$ 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 films+i;tubp:eysc7c9xb tdkw+7 gj8+7led 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 beltmiy7+9:ku+c7+t8b7db tc; sgwx epj s 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 kinetib4w a 6nxs,yvn ;v(r4pc 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 ws2:k + xz8xog4hjdf1 coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified modes21 w7kgp6v rsl of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 2 wg61 ksv7prs0.25 $\mathrm{~m} / \mathrm{s}$ 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 surkq/h0g)ema 4)qe fl(ac51 intviving an automobile crash if the deceleration is no gfh4/q(na leqi5)1)a mtcek0 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 ants*jap-3hd0w earthquake is a , and if an object is going to "hold its place" on the groun jhpda3 *s-tw0d, 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 gd*q l:72ebuce qe7o4accident involving two cars, measure 72-m-long skid marks of one of the cars, which near7od:ebqeg 2 47q cl*euly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m travelec9lcb3 q6t a3lgb) 3:oxcqab 8d along the road, the elevation change is 1 m). How fast is it going when it reaches l3bo bbg a6q3cl8)9 t3xac:cq 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 To)j3kf; t w:c rntt-z7/(n pldpwer of Pisa and falls 55 m before r:tt ntj3d-ck ;p)wp7 (nz/frleaching the ground with a speed of What was the average force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but enters a muddy stretchjm :j5 :d+uki1*ptxto2 rh;x m where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy strmo :1t tjpk xd rj;+i*h5mu:x2etch 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 swo3(pgie /5p/5uzspymm:b2 8- lhjl a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can-p lu e5bg z85h:pmpmji/ o2(/s lsw3y 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 experimen;zls+ ;4zc mnits, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the szz4c i+;msln;tring 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, s.c ct*w*nw-dthere are to be several ramps connecting different parts of the store. t.sc-w c dw**n
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 ) sa6 39 x8ryoucusing the pulley apparatus shown in or9y6a3xcsu 8

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 1rsvxi0inu,khoh 0.7eh.p.b5e t nc * 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-restra6jzb; bzpy si.ccymjy8 ,9j69int chair, an engineer considers the following set of8zz.y 99,bjim;s pjcc y6y6jb 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 Italidlou*a0m /4 *vmvjfb9k, 4 jxdan train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similarx5cri 7vn-v4g(4kxvc length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, v gkcxx vvn4r7-(ic5 4how 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 a *pb4wp ge6)5)7zpedmy b i1wh " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum uqmzu4 dl n;72speed 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 asce/0hgdw.aiq r a+bae5r ed0 20wx1 tnl)nding an ice field inclined at 21. ln020ab x/hd1e qi)gdre. 5 w0rt+awa0$^{\circ}$ 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.