Why does a child in a wagon seem to fall :)g+ 2yum webe- jlgq*backward when you give the wagon a sharp pull f+glu emgy2wb*e:-)jq orward?

A box rests on the (frictionless) bed of a truck. fp/9i ,) cccggar,ik0xi., nv The truck driver starts the truck and accelerates forward. The box immediatelyia,i. fikrvc/ pcgc)x,g90 ,n 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? Explazadgh32 z6s;8 :laffmin.

Only one force acts on an object. Can the object have zerca: a(j (vj7i*ewn7oco acceleration? Can it e :cajj( iac*n7o(7vw have zero velocity? Explain.

When a golf ball is droppedt hz*a28dxxv93 3)klmbw zx.y to the pavement, it bounces back up. (a) Is a force needed tomhxxdy)l 2xzv 3tab* 3 zk89.w make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move i,l9t crvv4 sr. ;s(evbr8sic(n the opposite direc cvs4t(;s, vic r8l .s(9rvrebtion?

Why might your foot hurt if you kickp p. hrp5++l *ein(l,p4tlbkh a heavy desk or a wall?

  When you are running and want to stop quickly, you muoe 7o5gwox lw(zr q,lza3+e9fr brz2ke 43h5)st decelerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person runnqel 7)ok 42, ax9r3o3 e(rze5f5 orzz w+lhbwging at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread f6b 4u,1v ziiqfxt.4 syrom the ceiling, and a section of the same thread dangles from the bott1ybqv z4s.uix6,i4 tfom 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 steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that ok:n, 9*iimz vs+ l f/-hegfp1sn a 1-kg rock. Why then doesn’t thzefi v+-gm,nips* kflhs/19 : e heavier rock fall faster?

Would a spring scale carried toe-2ytmr.t;:dr lw vqs9xc9s37 +jkt2 mx3 wra the Moon give accurate results if the scale had been calibrated (a) in pounds, ot 92st2dc s.3;te-rmkr:ja lrwqwx 73 ymv9 x+r (b) in kilograms?

You pull a box with a constant force across a frictionless table ustx8hw* cf9dv7rwz 14ying an attached rope held horizontally. If you now pull the rope with the same force at an angle to the8 wdt *hc7v wzy914rxf 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 influenceh2mialw -z ++;ldpyxy6 /-jbq of gravity there is a net force mg exerted on it by the Earth. Yet by Ny /wdi+ax-llmh-2jb6y; +q zpewton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to l .3ao5pfw6 8tjnlqi :cift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg object horizont5i.6oc 8p jalq:ntf3wally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–3grv a)eswvmr4 po3n;n 4z fl(71v7ba77) pulls with equal force on the other team. Wmv(1p onzn;4gbew rfr7s)avv7 a4l73hat, then, determines which team will win?

A person exerts an upward forcivs4cmbm4pr9am9-k/4r4 fj b e of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) 9imbf4k4bs/v j9- 44mcrrm apits direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on the ground, how large a force does the gfx7lyea 9l 5pvoh*)f5round exert on you? Why doesn’t this force make you rise up into the aie9ph*l 7yxf )f55 aolvr?

Whiplash sometimes results from an aush) a xq3lk+5ce7i j6rtomobile accident when the victim’s car is struck violently from the rear. Explai3ex k crl75ajihs+6 q)n why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on thef )zh31,y+9ab khv9woui/ qahgwmr+g+ 0 lp*t bed of a flatbed truck. When the truck accelerates, the crate remains where it is on the truck, so iuphvwwthg+mib o kyg *f99) z++1l,/a 3aq0rht, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ramw smmzn29tq3:kkn*)s -jy r t9p. After the block reaches its -2wknm*zt3jk nmqs9rs):9ty highest point, 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 if you weighed yourse70 qquw b3z(mrt sb;b0 vs04mnlf on an inclined plane? A0n7 3bsqm qv;u tbmw40(srbz 0ssume the mechanism functions properly, even at an angle.

  What force is needed to accelerate a chilv2m-3r :umu7aetzu.7:u zf1 7eveb god on a sled at 1.25m/s$^2$?   

  A net force of 265 N alnbflu,kg * 3,,dpx;s1si 0tdccelerates 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 musy/q7 d+2x wdtvd(7 hcet a 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 a k5 8fl9 7wmewj $76-\mathrm{kg}$ 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 sto1 ua 9d5 z*ehli(7zevhp an 1100-kg car in 8.0 s if the car is traveling at 95km/h? h(59 ezlie7 da1 uh*zv-  

  What average force i m0 q0jbqm jm+n.qe7m ;jhx4q7s needed to accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m al+nm 0qm 40qqjbmej;m.qxh7 7jong the barrel of a rifle?   

A fisherman yanks a fish verticalq7cp6yqgdbz3 3 h95i9zfw 0ol ly out of the water with an acceleration of 2.5pi zco39d 36097zqqgwyh flb5 $\mathrm{~m} / \mathrm{s}^{2}$ 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-mile track (402 d- ws(c9**2 dpimeogm $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum ajqmwa7(3j9-2m y6 isstl va(scceleration is 0.0680 g . What are the maximum and minimum forces the motomq-6jmy s( 7t3wi9 a va2jssl(r 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 scale in a motionless esrb.;uk,je qr* mp.a +*q1 9wu:kon rflevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the direction of accel p1rj;owf:u *es+q.aq,b k*murn9 .k reration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,7tvj:-tznr/: un5+ow g50 N. What maximum upward acceleration can it give the z +:t/nr ug5to-:vjw nelevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two f)5 )p tj zgq6w+)lfljcalling sky divers (mass 132 kg including parachute) when the upward force j)j5z)c)p+ wl lqf6gt 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 hohqh///xr1z7gfq ku+ puse 3.9-m high. When he strikes the ground below, he bends his knees so that his torso decelerates over an approximate distanhh/qr uq /7x1+g zfkp/ce 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 th qu6f/(f:aq i49m,tmcya yzn, e box runs vertically upward over a pulley and a weight is hung from the other eny6if,qnf9m:mtu ,aa(q cz 4y/d (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a baphth o zf.-*wzs 9*2vjsketball 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 momentt6t:gl r xd6q i 1i4o1jaqs*n2 it is hit by the bat, and again (b) after it has left the bat and is flying toward the ou6 nax :oq6 s1qd1jgtirtli*24 tfield.

A 650-N force acts in a northwesterly direction. A second 650-N forcn.*)szsmuvy . e must be exerted in what direction so that the resultant of the two forces points westwar vmyzu )s.ns*.d? Illustrate your answer with a vector diagram.

  Arlene is to walk ac3r*1n 37fo5bt v.y*ma exsmu*ok5nlb ross a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is bo.35 *5eu y*o3xm slnft mn1a7kv* br10.0$^{\circ}$ 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 masslesscw6x3 12l3zst ,1 w r*;xmbva ram/rsn 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 14.0mkq s w.ql:-s o40m7unu:v rh/$-\mathrm{kg}$ 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 ag7sr4 3:w9h pc;yocxl gri)q6ztv ,z1t McMurdo Base, Antarctica, as shown;r:p ovzlrcgt, y i g1q4sw3h zc96x7) in Fig. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass behint )*s :ke3wzqngy,c. f0 k)vec 1ml7tyd it, Fig. 4-47 . Determine the ratio of the tension in the coupling be* ) s ,fnmt ekygc)tqyl.70zek:1vwc3 tween 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 using the bucket-pulley apparatus shown in rj-mcl)6se 7g 7in6ii Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constant neg)6iic mj677 lrs-ispeed?   
(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 begwg3nh ;mm;ccr yn;8nu x-:ycc+*cuj4 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 eq3c l0*lxn :px83 1t jhz3hvaab6+ho block (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 surt9exhck / *og;face are in contact with each other9*/ extcg;oh k, as shown in Fig. 4-51. A force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 are each initially 1.80 m3c k:-,smpxh.)dwlr n 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) hcdk.nr,xmspwl-3: the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heavy cord of mv)i + 8+z2iilvrcv;vdass 1.0 kg . Calculate the acceleration of each box and the tension at each end of thez+v+v)c id2ivr i;vl8 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 ofui9mb 3brt 5uyy:s-j * kinetic 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 5cr c7,p/6sf ,c.*uwt8 nesuxf.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 trai txi2;ej svm *z8(vln)n accelerating at 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are ns* t8i m;)(zvjvxeln2 ot to slide?   

  What is the maximum ywptb4 i: u5d-o3cb9t pk;y.gacceleration a car can undergo if the coefficient of static friction between the tires anu:db;btwyp5439itp. gk cy-o d the ground is 0.80?   

  The coefficient of static friction between hard rubber andc)9u2 o.ildax normal street pavement is aboa. 9cuo2dxi )lut 0.8. On how steep a hill (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 16jgbj-gu8gdy a-0lda1+c, c nzpnf50 $\mathrm{~m} / \mathrm{s}^{2}$ 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 ron lbgt125lz z/ugh 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 coeffiyv9;.q jkzp+ g1lo hj 2p,a3vmcient of static frictov;g1 ma.3v yjz 9+q2kp,jlphion.

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 fgoyf hikj;1am0*(opb bfrp y5t6.d:-riction 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 db-a 4:/ew76rbvfdqv6/z zu mbox A have to have to prevent any motion from r/m b:zqzwu ddb/476v ef v-a6occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far will it go, s-w3 -j-febfjgiven that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed 3sfwf- j-bje-of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass f55k( bwzxz h875 kg and 110 kg , are in contact and at rest on a horizontal sw558zz hk(b xfurface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static frictio l (bg7uw*w 9nyekp,1wn 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 blwy u9ek,(7n *1pwgw the cab of the truck?   

On an icy day, you worry abxarzv;yt)mc3(l4;*kfa j-3p.z gh +n;es tocout parking your car in your driveway, which has an i;ma hnxs 3f rk3(tc; g p)atoez;v-j 4.y+clz*ncline 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 slide wp,4nzk.hd f (kith 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 ang 2/h usrwurnw 3a1q7p: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 initial speed of 3.0ri t-f ,/edzfx524tfd $\mathrm{~m} / \mathrm{s}$ 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 th bs1xizwi4,s28rpmr0 .* alq op of the steepest 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 place against a rough wall by someone pushiltnz/6v2 oxl6rkij 06ng on it with a force direz jnolr60i lv66 /k2xtcted 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 bek3iuj v95 5oph1xoap ;come dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof with p31oauoxv;k55 9ip jha pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an automobile traveling at 5ar 67zugxhsl n *ic42w 7n6kjspeed 7krj 5nz 2x66lgsc*uinaw4 h7 v is equal to $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when the drivev(k9elpot*k t( +a ff3r decelerates fklt9pk*at+3( (fovef rom 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 infbb -+qjw9 i9lwt4gc8itial 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 conveyopw kpbgqv1 f z9g54-q5,ed,adr belt from where they are filled to the packing station 11.0 m away. The belt is i vk59 5w1-f, bp,ed dpz4qgqagnitially 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 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 friction bew,w6 ,cvpcv;i(zo; ce0ht3 sfk 6l/p dtween $m_{1}$ 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 dor.kiwvhp8(h2b* mdy 5,wbk g6wn 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 each pulse approximr+oj4g2r,mufov 6f/ 3 yc9c,pq y.saaately 20 g of .fpm2r,j qovc4asfco/3ayu 96g+r ,yblood is 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 survivi7kl*8fz qnlr 5ng an automobile crash if the deceleration is no more than 30 " g 's."k 7*n58zlrl qf 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 9 2cjaubsg .zq5t,:ria , and if an object is cr5zg.qiub: ,9j2 stagoing to "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 accident involving tw1vs6gzvxh pf h5h98zi12 - rkvo cars, measure 72-m-long skid marks of one of the cars, which nearly came to a stop before colliding. The coefficient of kinetic friction bhifx86z2p z 1-vgh vkrs9h15vetween 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 kl* m8 2xf,1riyf ru-maq1:zzm traveled along the road, the elevation change is 1 m). How1*r y z:i,k1afm-uqr2l xz m8f 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 drq-ajr4l0n gum7y1 :7lpd4y hyzbk5xkr ) b/x1opped from the top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of 5k:d /upnhymr17yxl- g l)4ba r bqkz0y71 j4x What was the average force of air resistance?   

  A cyclist is coasting at a steady s).2 hl r/m*ns.gyb wl-.jrnwvpeed of 12m/s but enters a muddy stretch where the effective wb.l2.y lw-h.ng*/nmsj )vr r 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 redesign of a hilly portion of a city. n w7;o0a xf1eeAn important consideration is how steep the roads can be7 0exfn;wa 1oe 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 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 fr13bhpqy/ab*m om a thin piece of s hbyp3a* 1qmb/tring while the jetliner she is in takes off from 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, there are to be several ramllyqin+)6o z 3ps connecting different py)z +nlo 6qi3larts 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 the piano (- r3vl0k q)ceumass M ) using the pulley apparatus sho-3c)lv ku0rq ewn 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 ycbb u *zs26 5q4nfwi: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-restraint;()rbh)he fn x chair, an engineer considers the following set of condit(n;x)f heh) brions:
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 an/ xm wjq0n6e/ 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 ropnitv 9), sy;4ir.3zgux-a1k+b r3 0dubyg ynbes 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 weight.) (b) In a similar fall, Bill's rope stretchyid+ny-r bgrg9ib3t.u4 0y z 1k3u,;sxb na )ves 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 " 4uvkteei/h8kpzcqp/h: +k, fs(3va x: k3 9pg 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 adre8 ,hgh efcs 8)6npjjmp:54d/u hz-llowed to reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together arep r1.lkfq5i87f1 :wdav) n 1qkejr 6nt ascending an ice field inclined at 7 ldqf1t6np5.k11)rr je8afqi wvnk: 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.