Why does a child in a wagon seem to fall backward when yoo+ y*n tim/g1lqlo oi3,s3w+m 9hum .ou give the wagon a sharu/onwo1iq y 3+ihlo3gm*9mm.s+tlo ,p pull forward?

A box rests on the (frictionless) bed of a truck. The truck driver startl,dwf(pnwvyx47jkz 1g )1k + es the truck and accelerates forward. The bknzfg,yv(x1)d4+7jl e wpw1k ox immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the 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.ly:) 77cj ej 2)eoiezha -)eyx

Only one force acts on an object. Can the object have zero accelerf h)bsoog (8*kation? Can it have zero velocigohk)of 8(bs *ty? Explain.

When a golf ball is dropped to the pavement, it borp+-lh+uz 5bk3mo gdfmbvwfr ./c)85 unces back up. (a) Is a force needed to make it bounce.wc5-dbmvhlkrg r8 zumpf+/ obf)3 +5 back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log mov ns(ev6fvv 07me in the opposite dir f6vn7evms0(vection?

Why might your foot hurt if you kick a heavy desk or aibmj p8 f,:jr1 wall?

  When you are running and want to stoun -6y4p4 jqqxf9+s ogp quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own expern-j9ug+y4 qs q 4fp6oxience) the maximum rate of deceleration of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fcm5 2i.g fxlx1ine thread from the ceiling, and a section of the same thread dangles from the bottom gmc.fx ilx521of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 8li22t0 wu eddbw *0-anxxg9r1-kg rock. Why thd r-wew*un x9gx2t2l0i 8ab0d en doesn’t the heavier rock fall faster?

Would a spring scale carried to the Moon give zecz7 :ex jn+sm+5pa: accurate results if the scale had been calibrated (a) in pounds, or e:zn5zxm+s + pj:cae7 (b) in kilograms?

You pull a box with a constant fo f fh0f/)zh8ghrce across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angz8 f0 hff/)hhgle 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) decrease? Explain.

When an object falls freely under the influence of gravitp1p6mskuz8 e4g4zsr) y there is a net force mg exerted on it by the Earth. Yet by Newton’s third 6 8purm e41p)4ssgzkzlaw the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg object when you are on th 9wq,m5oj; hske Moon with the force needed to lift it m;wkjs 9h o,q5on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s ;at l40jgoay2s )p8fe third law, each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, t48o;gljpyfs0a2 t) e ahen, determines which team will win?

A person exerts an upward force of 40 N a:dez)vvq vc( ;ya(l2to hold 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 is exerted, and ( v:e;2dlyzav( a(cq)v d) by what object it is exerted.

When you stand still on the ground, how large a force does the grou qsxu o387mx rv9p7o +7rc5zmtnd exert on you? Why doesn’t this force make you 77rops+q3xm 5v9urtmx7cz8orise up into the air?

Whiplash sometimes resu ktrfgv4dh0dnu7/3c .lts from an automobile accident when the victim’s car is struck violently from the rear. Explain why the head n dr.v3 hfg/u dk7t04cof 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 accelerates,)ex. jfumb)c/qwk+wd:k ; -.o6loeh v the crate remains where it is on t.eoh/6;ojw.k) kld):vqf-bc w x eu+mhe truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so th*,p xw:fda,t qat it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is lesqp * ,xd,tfa:ws on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an in8h tsp9fhhsh5s do2. rj8,.d.v) ltuoclined plane? Assume the mechanism functions properly, even at an anghvhr .o8ods,.d)hh 8s2fttlsuj 59.p le.

  What force is needed to accelerate a child on a sled7zuu ;gvw5 xz5 at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at 2.30zxvyc 9r :l1i:$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope0bpb j29 oz9 lniflbj/p5ec(, withstand 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 ofrs eu/ w;.hw 6loe5*bu 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./n7gt8l 7cl (kl/ trp8s2pbur0 s if the car is traveling at 95kr 7t7l/lkg(rspt8bn pu /8lc2m/h? -  

  What average force is8l:+i;d jp pwix kn7d)y/+kkr needed to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m alodyp8;npkl+x /i 7wkj: irk +)dng the barrel of a rifle?   

A fisherman yanks a fish vertically outz2j.72oa/o u r1eutvf of the water with an acceleration of 2.5 ot.7zafroe2 u u21j /v$\mathrm{~m} / \mathrm{s}^{2}$ 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-milgd67p4x 1+hcgp y ow2oe 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 m0. wueip dm.s4aximum acceleration is 0.0680 g . What are tus4w.i0pe m .dhe maximum and minimum forces the motor 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 x/ ya7(+q:wf7acrvprscale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate r avxr/+pf(7 qyc 7:awthe acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum stre5w6exhh kqvg3+d p6 g2ngth of 21,750 N. What maximum upward acceleration can it give 5 pq3+gvwg 6ek d6xh2hthe elevator without breaking?    ( two decimal places)

  (a) What is the acceleration gf:fe 7dnk/q-y*j1nuc4w /ktof two falling sky divers (mass 132 kg including parachute) when the upward force of ai 4 un: kqfe-w*/ndykgct/j7f1r 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-mgloi h5acs 6 pr830jc,w.m-z t high. When he 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 (ez3c cig5 6jlsh.o0 r8 ,awt-pmxcluding 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 dt2dj)rf/ cs.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 ts d)r.tdf2jc /he 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 for4urvt,zuz.p vue:d. x r4 u9m2 1uir9u 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) a5i qqrv9a)y7lt the moment it is hit by the bat, and again (b) after it has left the bat and ii75ly 9 rva)qqs flying toward the outfield.

A 650-N force acts in a northwesterl5d5( (w:ry;h okt9k eha8wird y direction. A second 650-N force must be exerted in what direction so that the resultant of i :y5ka9 w dd;hrtek5hw(r8(o the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally between two build p1at89jmr1 + t3yv+zzr5whze ings 10.0 m apart. The sag in the rope when she is at pt+v mh1ya r 138+9ztj5wzerz the midpoint is 10.0$^{\circ}$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

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

  One 3.2-kg paint bucket is hanging by a massless cord from anoth73fx . 0y c.notkamss8er 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.*d o6 mn-nvw.b0$-\mathrm{kg}$ 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 McMurdo Bar.bgwuk.cmtg4 +* s/p:rd e6q se, Antarctica, as shown in Fig. 4-46. .*rmb+/g s gp 6kedrw.q4u: tcThe 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 6 fnq/wl q rbvua6)/)lcars of the same mass behind it, Fig. 4-47 . Determine fnb6)lqr/u l/v q6wa)the ratio 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 pulls herself upward usrfaaw a+ k9)v)ing the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull )wv raf9) +kaadownward 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 bdab 6e gj/i8/p zi5h0regan, 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 (mass i1fqig8 v;nd6$ 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 horizontavphr:yz d p .*d2j3c.cl surface are in contact with each other, as showyc*c:hr.d.3 ppvj2 dzn in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m above the zf4e2j1+b3f onwn, ioground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lightenez fj+n2o3wi14bf , or 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 friction:qvgul2e 1 ac9less table are connected by 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-b91 g v:laecu2qody 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 fviaypa)l ej :rx38 (-7 ubqur5riction 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 start3s(ss(tg0 k 6e4rwnsv 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 train5zys 4z4,atuk accelerating at 0.20g. What minimum coefficient of sta5 zzy 4,utk4satic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acce1visr.0y sq k3g1dmn xp*n:/qleration a car can undergo if the coefficient of static friction between the tires and the grou ys*3:/.xrm gqv1 0nsq pikdn1nd is 0.80?   

  The coefficient of static friction between hard rubber and normal strbt taz.(n g,q.eet pavement is about 0.8. On how steep a hill (maxg (qb atzn..,timum 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 j8f 0nu y,lil0oy1m.k t00lop.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 roug hzwz57), vctjj tj5; ndrb7t/h 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 co7 l d:2g;; *f ,nyfvnds sgc(v:3khsbyefficient of static n;:;vclhs,s2 ngd dyf 7s :f* kgv(yb3friction.

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 kinetid qcg*wch9m-4g8xi8/g wpi.kc 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 a mass would box A hav8isvl nly 18r,e to have to prevent any motion from occurring? Assuy81i8 lln, rsvme $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, ,qms:+;zw jkr7cj 0gc given that the coefficient of kinetic friction is 0.20 and the push impa7mcqgj :wc, +jr;k z0srts 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 horizove y:sh:)h, uf7wtr 3ontal surface (F)y ouvft3:hs:7 ,rwehig. 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 coefficie0cs x mpje4/n8nt 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 pmn 80cx4esj/the truck?   

On an icy day, you worry about parking your car in your driveway, which hashse7kt; r9olnb; m/-g an incline ohgnb-s/o e;tlr9;m k7 f 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 cb(6in79vu,9 gub/b;z zca mq 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 mfuac u1f4jp*b2bvvs ( :p7z1 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 speed * vp-v rb;o(ea4slf( 1qmr0uz 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 *s t rxef*zd nt(6ig03 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 agpe, d) riih, ,gq4w;scainst a rough wall by someone pushing on it with a force,p, ; gscqdhrei4wi), directed 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 dan6,3jtyhld ,misx 3 de0gerous projectiles as they melt. Con3i s mehydx,j63,d 0tlsider a chunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum sb vydxh w9(e3 *eu3b/ofh//ee topping distance for an automobile traveling at speed v is equal by v9 /*e/be/dh3e3 fwehx(outo $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 dasevd1 7h.h klzwsowvs+ 36 -k+chboard of a car slides forward on the dash when the driver kvs wc6+okewv s+z- dh731h .ldecelerates 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 jdzxb,+ 3th pnir 17 l6dwtx/3m is given an initial 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 whe4gb xs, r2 zxvd+lti.2re they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimus 2xlx4z gtrb,+vdi .2m 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 frictio tuzg 2yy2ww*ic2/9yc n 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 down a8/s hkkxdco72io 3ffz i/j(3 l 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 mam:*2p.vp5t hhe0 r:dz;oi wskemalian heart, at each pulse approximately 20 g of blood is accelerated frovo. dph;e: k2tp *: w0zreh5sim 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 automobile cras6+ h:c; s)xtyoyhlbfb 6q6.uqh if the deceleration is no more than 30 " g 's." Calculate tlh+t:y6uhb6. ) 6q;xqfoscybhe 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 produ16h pb; klva*p6 3b a+xbi2zlaced by an earthquake is a , and if an object is going to l zi6 h26k ;ba+*vaapxpblb13 "hold its place" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene of an acciden2o6lprs -a,647c hlhddwe-pf t involving two cars, measure 72-m-long skid marks of one of the cars, whichl-o4-p6 sd d,hrclhwe2 7 6apf 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 6eif*edqp x zv 9 0mf74t-aa)d1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the b4ev 76 )a9imz dfdxa tf0e-*qpottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is droppe tv/d,zb+ns /jm)xa-1g 6kwdo 9zhi6xd from the top of the Leaning Tower of Pisa and falls 55 m before reaching the gr, 9ajv1izmxh-k gt/x6zo)n6 +d/d wbsound 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 stretch whe*zbw o7*3yjcj re the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emyo*jj* w3 zbc7erging?   

  A city planner is working on thek1e+ 9 .f f4rafre9tnj redesign of a hilly portion of a city. An important consideration is how steep the roads can be so nf.4 ej+ra1ek9r9ftf 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 tb :ptv7v,7 : asdmlvj/hin piece of string while the jetliner she is in takes off fvlvtmvp:/7 ,s7:jd a brom JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25$^{\circ}$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

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

  In the design of a supermarket,++ut) gg5(fn lpldwz /jl nk3;((bsmh there are to be several ramps connecting differentmhu 5ldblk /w3f+zpgg l ;nsn )+(j((t parts of the 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 jtj4zeohtx f- d(,4z+the piano (mass M ) using the pulley apparatus zh4zje4,x+ tf(o-j td shown in

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

  A jet aircraft is accelerating akjfl1f9jk q6uqt38 /d t 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-restraex; nn(h i)7cnint chair, an engineer considers the following see nn7incx(h) ;t 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 tr rdq: 8u8qy(xuqwon2 v0r,o 9o(/pyymain 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 similar length. Ka(ytf 9xlh )d f1pyzuh---ll v:ren'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 feed9 l z:t- -hvfl)yyhu1x -p(lfl 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 usf(fod-gei),d oq fs 1+ing a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to reach a maximum s0fn bc8c+(rvqlw 8qw; peed 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 asz 97p s8q.d0z7c teqrfcending an ice field inclined at 21spz87 t0edz.9qcr7 fq .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.