Why does a child in a wagon seem to fall backward when you give the wagon a shl.sw sh.acx00arp pull foa .lh.0c0x wssrward?

A box rests on the (frictionless) bed of a truck. The truc olk4 u2f2bx 6c)x3v9 (1cjepwnyubs.k driver starts the truck and accelerates forward. The box immediately starp2wxb uf9x.4slbokc nue)yj3c ( v261ts 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 force3p;e1a35g tyz ;d98l -w c. ,.naldfi wiuhtycs acting on it? Explain.

Only one force acts on an object. Can the object have zero accelerat4fdmyllt59 lvjw+;; 42 m jtzyion? Can it have zero velltz9y5l wf4jt; 4vy d+m;2mljocity? Explain.

When a golf ball is dropped to the pavement, it bounces back up. (a) 0 ioj0m /elms0eet 2y,Is a force needed to make it bounce back up? (b) If so, w/mjti0m 2o00yse, e lehat exerts the force?

If you walk along a log floating on a lake, why does the log move in u38ke a8c *3zs 1faosks/g1xvthe opposite dizkx1 os us*f c3s8av13ga /ek8rection?

Why might your foot hurt if you kick a heavy desk or r9bsv h bifl9j/923iqf:hu)ca wall?

  When you are running and want to stop quickly, you must decelerate quickl6ute js7. eza:y:v-hpy. (a) What is the origin of the fo:ae-thvs:z je. y67u prce that causes you 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 fin-7p7-bk zmt btr0w* sze thread from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person give-r mw 7k-z tpsb0zt*b7s 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 9p ajzj;8 1x,v ct8saqtwice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall f,18c89sajt v xj;azpqaster?

Would a spring scale carried0yq u/n1n.r mf, h lk2b77xws;a2:bot sx cy8o to the Moon give accurate results if the scale had been calibrated (a) in pounds, orlf nc 7bbmt ,2nquhrs 1kxx.y2o :70o;/s way8 (b) in kilograms?

You pull a box with a constant force across a frictionless qrmon46;*udp ;r8sqf table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease86;qouf * q pds;rmr4n? Explain.

When an object falls freely under the influec)92zxqnn cg :nce of gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerc 9g nq)cnz:x2ts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a ewkhv6o4n(/gqo r(o6;psf:nb7t9r ro np4 z-10-kg object when you are on the Moow(r6 4 /orpbn4e6-nft vn qzo ;(rpg:7oso9khn 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 Moon and on Earth.

According to Newton’s third law, each tea./ djk4/a i1kcm*qbl4mii3cq m in a tug of war (Fig. 4–37) pulls with equal force on the other team. Wd cjb/k i4al/q*kqc im43m1.ihat, then, determines which team will win?

A person exerts an upward force of 40 N to hold a bag of groceuf 8p yhy2o6inqc4 r9/ries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exertedu6pfiro24yc8y9 qnh/ .

When you stand still on the ground, how large ab1:at;fp+eds 77z hgx force does the ground exert on you? Wegtzhd x7 :1f b+;s7aphy doesn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’j4ds+tyq*a(1n2ulcj ,jjb :b u a5y m4s car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. j2 luajay n s+y:u(t4b,jcm 4*qbd j15Is it really?

A heavy crate rests on the bed of a flatbed tru0 jt;c b:/ddelck. When the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What febdjl; :/0cdt orce causes the crate to accelerate?

A block is given a push so that it slides up a ramp. After the block reach0p3wa m85hmrc es its highest pow r0 5hap3mc8mint, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scale read ifn;)kt3 lqcon q*nh +0g/uc1an you weighed yourself on an inclined plane? Assume the mechanism functions properly, even q3 gknht*n1n0u nca; o) lc+/qat an angle.

  What force is needed to accelerate a child onmtvqc8n,a-lu ;j *kj ; a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ride95i85gxxmgn kr at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a nme6,z5n mk 1 wfii6uh j;0na-rope 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 of/j.:sed i 6iyh:s+vm s 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 stoff(+-qdj dxg75tlz 7y6fo;ot p an 1100-kg car in 8.0 s if the car is trav7 tq + t7z6-ojoy fflx(d5gd;feling at 95km/h? -  

  What average force is needed to ayv72on/o*:s7r/ qwehndb a2b( y p)rzccelerate a 7.00-gram pellet from rest to 125m/s over a dista:7/dzyyqb) (hnpa2v * rre2woo7b n/snce of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an accelqihz.ys +7f( xeration of 2.5x7.qz (hsf+iy $\mathrm{~m} / \mathrm{s}^{2}$ 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 au3yiyj1+lvknp5 w:.bkbo9*k 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 4850hmlno:muq -elp/l-466h fh v3 kg ) is to be designed so that the maximum acceleration is 0.0680 g . What are the maxiolhlv/e63u fn--qlh h 6m4p: mmum 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 scaa eoqso)vw9fxv o 57d7s11m.7lpf7w h le in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the directioh71qf o7 s axms7)ev5pofw1wd. 97vl on of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 N. Whap 2- 5b.funghxt maximum upward acceleration can it give the elevator without breakinb2 hp 5f.gxn-ug?    ( two decimal places)

  (a) What is the acceleration of twow*43c ynwhel a/6kl;t falling sky divers (mass 132 kg including par;ea*l/6yk tlw4w3 chnachute) when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m q+bf-pu8-3w 75 yjv queukp2lhigh. When he strikes the ground below, he bends his knees so that his torso decelerates over an a wyq-b fpk73 8u u2pqu5+j-elvpproximate 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 ver6jc8ovg,r(9skd (p mxu z8qp;tically 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 on the other side of tk;8 m x,gv8(pc9 6pz dsujo(qrhe pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagr 94ufufhul,6 fam for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body o.nj4 wy(9ol ji c8f7idiagram of a baseball (a) at the moment it is hit by the bat, and o.i7j 4(o8wl9yjn ifcagain (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwestefu-2kl)8 h.lvn: tz. 5nkky dmrly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces .8mfl:d2y l5u zvt-nhnkk)k . points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high l t0sgg6zd7* xwire" strung horizontally between two buildings 10.0 m apart. The sag dt0 gxls*z76g 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 f,fb 5jy1qwem qr7j,/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. *y2 )itsjp.eo. 1bit/sfe2xl0$-\mathrm{kg}$ 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 locatnh8u c65;;ni-5. srkq q whrlcion at McMurdo Base, Antarctica, as shown in Fig. 4-46. The.l6sruc;n8riq5 k- 5chq;wn h sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behind it, Fig. yofo.6 sa 5wx,lg 29sx 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first car ylox.29g,5 s f6aowxs $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulbkk2 zp3j8ytf(m0( vvley apparatus shown in Fig. 4-48. (a) How hard must she pull downward (b(2j m3 v8zpyvfk0tkto 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 begzr ix m.6oejj8uety -;itsd/8l)w2fo79m i, p an, 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 xpi6.g dgnv .7(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 with each -50,c,udb vdeo*h o)dn5m, *d gmhjfil h5z2aother, as shown in Fig. 4-51. A 5)mgh -52b lminod*d,odf*,ha cdu5e 0 vz,hjforce $\overrightarrow{\mathbf{F}}$ 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 jti/irk8z:jg) 9uvu2 the ground, and the massless frictionless pulley is 4.8 m above the ground. Wh :k/ 8 i2jjugtrzuv9)iat maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are con k2 b6.noaebm);zy 4gtnected 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-body diagrams shown in Fig. 4-5 )ygbk;n4.o ae62tm bz3. 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 friction between a 35dqxpitezk/xxd 9 ly 6;,g+9g* jn3bv5$-\mathrm{kg}$ 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 starh*gsxu)8ifp5n j0a( a t 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 i (/e9r cyvhic)f5 ysp6y5f d.at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor id/9pc5yeiyh y6s(vi c. rf5)f f you are not to slide?   

  What is the maximum acceleration a car x s4a7 gbafz(01y oz+pcan undergo if the coefficient of static friction between the tires(xaoa yz1psf z gb+074 and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal street 2vf ll0vl;q6 bpavement is about 0.8. On how steep a hill (maximum anq6vl;02llv b fgle) 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 t d*c;d2lmr/2/aheup at -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at rest on a rough 30r/jt ezni.f/yi9,oh 9$^{\circ}$ 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 cone+ s+9m1qd*pvp /fjb8kkwd.ey 6q f(ktact with an asphalt surface have a very high coefficient of static frictio k+ykdqq6+eb9 k(ev 8*f1fds/.jp mpwn.

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 fricti+e.sh7 k zt2ukon 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 hgoq+g r)9,tsfok7c 7 have to have to prevent any motion from occur, ogqr9sh k+ocg77f) tring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it sleea h+mg1r b) xok0h th49/b;k6nq1sxides across the floor. How far will it go, given that the coefficient 4x 1gbthmh)91/b6nkxqkr; e0o+a sheof 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 ono oi0zpg 2usho 0oj1,-0p1kae a horizontal suro k oo1gh00isjp-a 2 0z,1peuoface (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 coes))rfmhbi: ;yx 9s)jzfficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate bi js)y)hf :;rsmz)x9at which the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry about parking your car in your driveway, which 8km(b 8 9d0o0chz ixpvhas an inclinhc89 k vo00pb 8x(dmzie 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 sl;2x71kgm+1+ewt kapwp cz*vn 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 )5yhnx6afr i qha)0n-Fig. 4-55 lies 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 s6- ixhjt 7bwr6peed 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 stee ka1f9hmj9w4o.xim2u pest hill with a speed of 6.0$ \mathrm{~km} / \mathrm{h}$ . It then descends the hill, which is at an average angle of 45$^{\circ}$ and is 45.0 m long. What will its speed be when it reaches the bottom? Assume $\mu_{\mathrm{k}}$=0.18    km/h

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

  A small box is held in ,fb:qkg(p y6k place against a rough wall by someone pushing on it with a force directed up kf(q bg:pk6y,ward 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 projectixhfhg;; bl)0sles as they melt. Consider a chunk of snow at the ridg;x bh0glf;h) se 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 am z - ):izt:5k,t-ibbs;kuti lt speed v t5z, s: bi-:-t;ktmiuiz)lb kis 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 szmez b2qzo*, :zc8t.o lides forward on the dash when the driver dec,:obm *ze zq zt28.zocelerates 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 h5 doer04aqt/j-wj+g4t36 dvcl-vjdspeed $ 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 convwbm r:) )qjc0)n1qhd x3 rsd 3zas:ce7eyor belt from where 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 focns1q 7a0)x smezh r3:c :)rwd3q)jdbr 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 coefficisdusnqsh7.q ;8g 05l0(jqis zent of kinetic 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 (inclivn1dv 8s u1/5ah;m uu l+xdc4uding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at*9 wb/7huhrmq 5q v6ya each pulse approximately 20 g of blood iar y /*hqh9657qbvwum s accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an+l):;hc.k a h.ddbs pn(qbq+g automobile crash if the deceleration is no more sbdq+(g n;h.:hpc ad)q+kb.lthan 30 " g 's." Calculate the force on a 70$-\mathrm{kg}$ person undergoing this acceleration. What distance is traveled if the person is brought to rest at this rate from 100 $\mathrm{~km} / \mathrm{h}$ ?   

If the horizontal acceleration produced by an earthquake is a , and if auwq,vs)t1hciz0htd e2i13(snb+20 0 ejxb hyn object is going to "hold its place" on the ground, show that the coefficient of static friction with t3d0is0 ytnbzte c(21hi+ 10 2wjq xesbh,)hvuhe 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,9*i;vd2oyqs93 *tjymu03 xmyomghz6 examining the scene of an accident involving two cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before collidi;06y*mohg 2 mxujv3tosq9 *iz9 myy d3ng. 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 travqz1m3zsp6x79tfi* jp9gro i 54:luzaeled along the road, the ele zizg6rizl:ou 1ptf5x3p9m jqs9 7a*4vation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped froqjx -voogo,h3yc (6:bm the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force o3bvjox,-o6yq:h(g c of air resistance?   

  A cyclist is coasting at a steady speed of zdpwqv*krgj6 y *i(e*u- -uh,12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having tu-(ekj** qg*p6w d,urhyz i-vo pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is workjinl;,,ymom7uds )6b ing on the redesign 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 wit;sbn7ijlu 6yd,mom), hout 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 ph7d1z at 5okb-wr 55oshnz js5 x(7jv0hysics experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She no5770(-nbxztho1raj5o5s5 swkd vj hz tices 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, there are to be several ramps c 9c ayum,o/ 8bv5e )sgpi;l*vhg2cb9ronnecting different parts of the ac 8rcvmel95*h )pg 9 y/ibosuv;g,2bstore.
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 thpk:/ hmixaf )4k7 s7c.yxj-hge piano (mass M ) using the pulley apparatus shown in c-:7fj)skmihph x7ga4x/y .k

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 accec+fg/mf 47 e 8cc7 v4wtfdpp,rlerating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-resowm;,91jcw:nri + 3 hfvx re-uyu6d*ttraint chair, an engineer considers the following set of conditions3hew i 1+tf-c* rw jnmo9vd6rx,u:; uy:
A 12$-\mathrm{kg}$ child is riding in the chair, which is securely fastened to the seat of an automobile (Fig. 4-
61). Assume the automobile is involved in a head-on collision with another vehicle. The initial speed $v_{0}$ of the car is 45$ \mathrm{~km} / \mathrm{h}$ , and this speed is reduced to zero during the collision time of 0.20 s .

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

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

  A new high-speed 12-car Italian train has a mass of 660 metrirj:qt w jdl :r7ff4wc 2z761fbc 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-1-sk7d qjjszkgsa , 1, 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 g7a,1d- ksssjz1-qk jpro climbing. Karen falls freely about 2.0 m and then the rope stops her over a distance of 1.0 m (Fig. 463). (a) Estimate, assuming that the force is constant, how large a force she will feel from the rope. (Express the result in multiples of her weight.) (b) In a similar fall, Bill's rope stretches by 30 cm only. How many times his weight will the rope pull on him? Which climber is more likely to be hurt?

A fisherman in a boat is us-bc4*mvo3j yi tz un/y4z66kp5ekjo5ing 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 speedy eoq-9t1cnw5(tt0bme1+i t kt. gw k: of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascending an ice field incly46 1 xwiy8munined at 21.n164xw8 ymyi u0$^{\circ}$ 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.