Why does a child in a wagon seem tzkb1hn,h(qxf)voq df 1m c986o fall backward when you give the wagon a sharp pull fb 1hk,8cfm fqh16q) d(ovxn 9zorward?

A box rests on the (frictionless) htw ++o.dmvw)8wh0sg-moza( bed of a truck. The truck driver starts the truck and accelerates d-0. ms(wz+oavww )thmh8g +o forward. The box 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 nowp tiqou22s:ix gf6 ,5 forces acting on it? Explain.

Only one force acts on an object. Can the object have zero accelerati.c.rm7tw ;gzm pp j1:mon? Can it have zero velocityzj:rm mp;.cg m17wpt. ? Explain.

When a golf ball is dropped to the pavement, it bounces back u rhtvi4+yc*y4y; 5pf gsjc+ v1p. (a) Is a force needed to make it bounce back up? (b) If soy sr t+i4phjc5v*y1 4y;v+c fg, what exerts the force?

If you walk along a log floating on a lake, why doe bq .-q*iq1wpfh vzz;8s the log move in the opposite direction?;hv*z.q81q-zp b i wfq

Why might your foot hurt if you kick a ne9.amyyie2 n-c8h8z heavy desk or a wall?

  When you are running and want to stobaat 7/g62(le.v bhej2 , xz izmqfu/6p quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using yuj/ehvg2l /az q76 e6,.xbzi(t bfma2our 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 ceiling, and a section of the safx::mmm 4 q8r3i3ibm-m( 8 xscyv+- 8bvyeso jme thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and stex(ob3: m3e8 sqii +x4 cbym-mjyrvf s88- v:mmady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that7:k/arj5 okp5 821ven1ky tcdpm l )gg on a 1-kg rock. Why then doesn’t th2a/ jym) p5c1tnkk ov kd rl781e5:pgge heavier rock fall faster?

Would a spring scale carried to the Moon give accurate q09 y2squw+kgresults if the scale had been calibrated (a) in pounds, or (b) in kiloq+k0s9 g u2qwygrams?

You pull a box with a constant force across a frictionless table using an attachzrvaj me a wt68(mg: 4n,rbs(9ed rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with theat:(nz8 mj9we r,gb6(m 4v asr 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 gravity4n)eweqxq4(o c:y(f+th my1d there is a net force mg exerted on it by the Earth. Yet by New4my +:qeyntxce(1 4h) w (dqofton’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*tts deky7. - o:522om etbeiw) needed to lift a 10-kg object when you are on the Moon with thie*tskte otdwe72 .yo :2 5-bme force needed to lift it on 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 third law, each team in a tug of war (Fig. 4–37) pullsa j++f tk;i;-hqb nyd, with equal forcj;a f++kh-b,tdqiny;e on the other team. What, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag oeo o2:z( s,wetf groceries. Describe the “reaction” force (Newton’s thirt2e:w(, oose zd law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still ofm52o +7lbu bw+ d o8gt*.rfutn the ground, how large a force does the ground exert on you? Why doesn’t this force make yol*f8 urou.bwtg2+5 7 b+fm odtu rise up into the air?

Whiplash sometimes results fro7z7do(r8u yiicvl:,14 dydy cm an automobile accident when the victim’s car is struck violently from the rear. Explain why the head of the victim seems to be8ry 7idy(dy:c41 ul,odc7 vzi thrown backward in this situation. Is it really?

A heavy crate rests otnh3 lgzc 94of/ti,wa+ )f/,/wkwhu fn the bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truc wcgutl+tho,fwz/ i w) /a4,/3k9ffnhk, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push sk: 2kv suma9 56ffp:yro that it slides up a ramp. After the block reaches its highest point, it slides back down but the magnitude of its acceler mka6 fufpvs 9k:52y:ration is less on the descent than on the ascent. Why?

What would your bathroom scale read if you weighed yourself on an inclined pq n)wut n;4g ovfr1nxt6-s9w,lane? Assume the mechanism functions propesw w f9 t,gxuv;qnr1no46t -)nrly, even at an angle.

  What force is needed to accelerate ahzg 5/qq6g.bc )yvey)l x)gy0;yp yf 6 child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerateiaz+f o a*a)di,6s0 dws 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 ;-,mq vyk9oozwithstand if it is used to accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a lky. b*p/(tag d8lbe -tr kw31$76-\mathrm{kg}$ 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 ilrd/:a nd+ / f7ura1vws required to stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h? 1nl+fwdr ra u7//dv: a-  

  What average force is needed to acceleratebml* *c u/agj3 a 7.00-gram pellet from rest to 125m/sga3* jmu/lc b* over a distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out ox .q5e/wp4w ty.d1p zkf the water with an acceleration of 2.55wwpq d1 zp4e.t/k.yx $\mathrm{~m} / \mathrm{s}^{2}$ 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 carb*eejtk6s )t)o 7kd,o can cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maxpi7eve8y50a*v 2z rcfimum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on th*f5zvy2i vp 7eae80rc e 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. iuk .h5al(zedaq/olt )mv(: 4 When the elevator begins to move, the scale briefly readsu4 l (eoq 5.al/tv(mi:azd) kh only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg e2 l1vig r fg:m:roj/l0levator has a maximum strength of 21,750 N. What maximum upward acceleration can igoml 1j r:2:gf0rv/l it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration 8lurw-0kvewk kxv(vt55qahe-) 0 hh +of two falling sky divers (mass 132 kg including parachute) when thwkl (tek08hv qk +-5wheva0x5r v)-uhe 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. W..k imr ,j;nadb u*v)nhen he strikes the ground below, he bends his knees so that his toradi*vrnukm,.)j; n. b so 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 til1 wk7ng0:qq7to.c- jc fte s+ed to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging ok q we1 cs0.q:n7 tf7gtc-o+jln 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 basketbal ca. yxj;p/u0;lni9tul 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 moment it is hit by the bawv sq8hdmd5o00+, d,ah. x4.zcn e gxct, and again (b) after it has lefdd. h xo qd,8 z5ac+n,vwsgcme. 0h4x0t the bat and is flying toward the outfield.

A 650-N force acts is15ueck.n xx;n a northwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer nx1 ukcs e.x;5with a vector diagram.

  Arlene is to walk across a "high wire" strung hor c* v3azswrpq/g6)8z4 g9 tfjcizontally between two buildings 10.0 m apart. The zp4a9*t/ fc s g)vrz8c6w qjg3sag 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 massless cor3qrc*nmnd p 3l*zha85d 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.ha 5w- r7bpo7u ;o5zfs0$-\mathrm{kg}$ 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 housingjxu94haaxew)rb,fi7e.) a k 4 unit to a new location at McMurdo Base, Antarctica, as shown in ))x aa9wkexe4b ,ifh.au47rjFig. 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 pulling two cars ok bn */twfw0g(n2qsxx;y/( va f the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the x 0 (xnf/k t(n/bwy2aw*;vgs qcoupling 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 pullwg)7;lbfj- v :v7f 4 yt5p)huea v;owos herself upward using the bucket-pulley apparatus shown in Fig. 4-48. (a) Ho7v-p;)vub:yf; ot v 7w4e5) awjghl fow hard must she pull downward to raise herself slowly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a 6m)/vyprc r:)yc8mw , z5$-\mathrm{kg}$ 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 5kz+kqu4o+fs (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact withl5ri. *elx(qh2 t2*ura0,t s,yqp jjb each other, as shown in Fig. x5 *.rs2j il20p,tj(, *qeutraqbl y h4-51. 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 i4qi6t b r;qih se94ofg 9g0w:qnitially 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 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 pulleyqgwqe 9iqf 9o0b;t h:4g4 rs6i.]   

Suppose two boxes on a frictionless table are connected.m-bb;5 kvxiv o:e -yl by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the be b;.kl-5myx-vo vi: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 kn zlc:jk)r5 pyuo 2d61inetic friction between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start a*v c knaz9qz9zee)xk9ry1 h9 mz/):xazg*/s a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.24:;monaiwn 5-n sa yy10g. What minimum coefficient of sta4n asni m:y-15wnoa;y tic friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car ca5k5qi, klx5j u/+hir hn undergo if the coefficient of static friction betweel ii5hju,h q+xk5r/k5 n the tires and the ground is 0.80?   

  The coefficient of static friction b:*h/m k 3 mwpv m2*:ydxahbi44k o9sdeetween hard rubber and normal street pavement is about 0.8. On how steep a hivx34i9d m:/dks:4po ew 2 *y*bhmakhmll (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.8 gxp-rbd wp*;qsvr461,n jr +zeqbe2(0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 tp0i wt ga1y.i. sw155a w6neqon 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 ana- b(-f6sb18cq sghzv asphalt surface have a very high coefficient of static frict 1(b--6s h bcs8vgaqzfion.

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 )1,az :urlxrafriction 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 tf;ab0 0u dw(oin/l(c dhh n;7yvx7:wA have to have to prevent 07 cyhdvwlau no; (;dnxb/7(0 f:thiw any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push soia5bj1 01fqysv d c;k, that it slides across the floor. How far will it go, given that the coefi5k1;y, s1 qcva jdb0fficient of kinetic friction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a hori fwde/oi)28c vath97mi4- jht zontal surface (Fig. 4-54)v7 ef-ci8mda2j4 hih)9ttow /. 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 be9m+jy(3 b ou, f;xt.aoi*gic mtween 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 c(ogix+ct*f i ,3mym 9bu;a.ojab of the truck?   

On an icy day, you worry about parking your car in your drivehv .)sz2 x i9xoiz).wiway, which has an inclioi. svi)zx2)zwh i. 9xne of 12$^{\circ}$ . Your neighbor's driveway has an incline of 9.0$^{\circ}$ , and the driveway across the street is at 6.0$^{\circ}$ . The coefficient of static friction between tire rubber and ice is 0.15 . Which driveway(s) will be safe to park in?

  A child slides down a slww;z*vfvdpwm1juj/rqz;:9+ d/ b1d d ide 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 at an ang5e5.sev z( xvjb *tjq+le $\theta=22.0^{\circ}$ 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 init9v.(07lbcn m u 4ytdnkial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed of 9y 5n;rj u:qzw6.0$ \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 in6zxl7sn jr4 *w place against a rough wall by someone pushing on it with an wl47*6 zrjsx force 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 slipp n ngmw; wl0px*g,n)t8vw6yfcm f.(0 oery roofs can become dangerous projectiles as they melt. Conswvnn* tl;f 0y 6m0w w.(xgmpnf8)o c,gider 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 stopping distan;; agpjjb5i- ro46k85xzxuat 4dv em:ce for an automobile traveling at speed v isjr85 gvd utp;aj-xoaeib4 64zkx ;5:m 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 dashboardts/cf ;uud 7w3nz5h-t of a car slides forward on the dash when the driver decelerate/dn - 5w37;chtfutzs us 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 massb aybk-320nun m 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 where they ep m+t;qh5 j*zbnm l93are 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, whaql* j5 m9n+ep hb;3mtzt is the minimum transit time for each box?   

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

  Suppose the coefficient of kinetic m1a1nq3xr* 8x7wjdoo 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 dow9xc3 wc7sh sk8n 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 mrzwn67pk f)4cgc-,yo odel of a mammalian heart, at each pulse approximately 20 g of blood is accelerated from 0.25r -)fnz4o67c cw kgpy, $\mathrm{~m} / \mathrm{s}$ 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 reasonablex7b vh0 ,j5ufo chance of surviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force7 jh0,x 5ufovb 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 producec,bd+cyz3-z ed by an earthquake is a , and if an object is going to "hold its plac-e,3cd+zzcyb e" 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 scenee3 (ul r 8hl(s/k6sjoe of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly cl3(sjku(e/sh6 oer8l ame 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 for7meyl3r+ o ko. each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55.y7eo+3k lrmo m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tower of Pisa axtr mx8cb8 x.wry ces cb(:(39nd falls 55 m before reaching the ground with a speed of What was the average force of air res8mrcw9 xb:b( .txr8s3eyx (c cistance?   

  A cyclist is coasting at a steady speej4e1g:e4yhy03 gwa av+ d 8rlpd of 12m/s but enters a muddy stretch where the effe+p4a:e1 3ljay rygge480h dv wctive 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 emerging?   

  A city planner is working on the redi5 *07r:ew s lenbge6mesign of a hilly 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. A particular small car, with a mass of 1100 kg , can accelerate on a level road from res:0erine bs6eg5w7lm* t 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, dangle: 4 dmjs(tvcn q*w6.bes her watch from a thin piece of string while the jetliner she is in takes off from JFK Airpojb4.:wcv6 qdt(n*em s rt (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 supermark0 * yuja1ac shnd0yu bt)6h6 wsg:20ooet, there are to be several ramps connecting different parts of the )0:oc sjhy0b 6ns2 w 0ha16auoyg*dtu store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is needed to lift the piano (a,e gcsi4 dx2cdj1v- -mass M ) using the pulley apparatus shocj21agdvid,sc 4e- x-wn in

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

  A jet aircraft is accelerating at 3.lqz2 42cx0ar l5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 foekuo,v q,za6( r a child-restraint chair, an engineer considers the followin6,,vuoq e(k zag set of conditions:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

Assume a constant car deceleration during the collision and estimate the net horizontal force F that the straps of the restraint chair must exert on the child in order to keep her fixed to the chair. Treat the child as a particle and state any additional assumptions made during your analysis.   

  A 7650$-\mathrm{kg}$ helicopter accelerates upward at 0.80 $\mathrm{~m} / \mathrm{s}^{2}$ while lifting a 1250$-\mathrm{kg}$ frame at a construction site, Fig. 4-62.
(a) What is the lift force exerted by the air on the helicopter rotors?   
(b) What is the tension in the cable (ignore its mass) that connects the frame to the helicopter?   
(c) What force does the cable exert on the helicopter?   

  A new high-speed 12-car Italian pk)he o4,t vc0train 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 .3ts:na o +iu nian9g8t5yh*ddv:p( sKaren, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro 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 p5ou+d(:tinahd:*st vnag n. 9s 8i3y 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 " ei bgjs07 x+-(+rryvs10-1 $\mathrm{~b}$ 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 reaci3+ta f5iaoet3zmj:. h 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 9f35kxmxtfsl,v;fj aa+ 0 v3bfield inclinvfmf39fx vsb+tx5a;k, 3l j0aed 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.