Why does a child in a wagonfp te;d p41pu( seem to fall backward when you give the wagon a sharp pull ftdfp u4;1ep(p orward?

A box rests on the (friv6 r0r -qeeam8yz5b6 actionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to sli bmqa5y6- ae0re8v 6rzde 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 zerhn *ll-u3yl.2z fois;o, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have5(v4:e5 sq vooy k:e4wy7mwve zero acceleration? Can it hwvqo ykv:weos 54 54m 7eyev(:ave zero velocity? Explain.

When a golf ball is d,j)x v:9nx ptdropped to the pavement, it bounces back up. (a) Is a force needed j vx9,:p)d ntxto 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 in thp g85vq16led ne opposite g6n15vdeq lp8 direction?

Why might your foot hurt if you kick nww466r 9p6 laizx 1lqa heavy desk or a wall?

  When you are running and want to stop quickly, you must decef a8iqf+9tangz-x;a8 lerate quickly. (a) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleraz9 gqf-x t aa;a+88fnition of a person running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thre oq z+iwa/:gkhne590 bad from the ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36). ig /+bw k 0eh9z5o:anqIf a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg ), 5,cvdlr:k+qsabfr 9n i r7trock. Why then doeslrr,nb ) 7vrik tf5cs+q9a:d,n’t the heavier rock fall faster?

Would a spring scale carried to the Moon give accurn .rk :x;6ydm um3ns(rate results if the scale had been calibrated (a) in pounds, or (b) s m6 ;:nxr.r(m u3nykdin kilograms?

You pull a box with a constant fv,( t,3veycu-o :4n/-q late yp. wygz vf4.toorce across a frictionless table using an attached rope held horizontally. If you now pull the rope with the same forcne( l4yvfyzv, /wp.q- vtc-u o,t t.eo:4a3yge 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) decrease? Explain.

When an object falls freely under the influence of gravi+cu- )ec h-xij (e,hmlty there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earthc,e+ h)uhjeix c(m -l- move?

Compare the effort (or force) needed to lift a 10-kg object when y sa e5y7 ak6agu0n5y*j(y kv-kou are on the Moon wa*e agjyu(v k6nkyy05 7ka5-s ith 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,wv0l za9.zc jrgy6o;eutd *n8y-+w( q each team in a tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will win(t wgvy c 8-d r l6e0oy;nj*9qwazz.+u?

A person exerts an upward force of 40 N to hold a bag of groceries. Describe tsu4ixg 2jm:x6p7p-bq he “reaction” force (Newton’s third law) byip 2xjmus7 4xqb6-pg: 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 on the ground, how large a force does 7qnx7zcow-p 9 the ground exert on you? Why doesn’t this force make you risow79q n-cpzx7 e up into the air?

Whiplash sometimes resultselu98ulbm; yppxi sdm. 6+2plco 3(5m from an automobile accident when the victim’s car is struck violently from the rear. Explain why the pyus36lom .lpcxme2i +m u bl89;p5d(head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the b/wid,g4nfqvref 4 z5-k3l 2 yr( qw4v.mjvj5 sed of a flatbed truck. When the truck accelerates, the crate rema.w- (vlff/ 3,imq gw5z542r j4ersyk n4dqvv jins where it is on the truck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides up a ravoy1po+ *z9e70v y uznmp. After the block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?9ype o0v +y*uz1 7vonz

What would your bathroom scal;f 1a; r5v p;0(/dowtemq:;s zsexkiue read if you weighed yourself on an inclined plane? Assume i01 k;5met;psd vuz;q o(x ;wesr/fa:the mechanism functions properly, even at an angle.

  What force is needed to accelerate a child on a ( r k.ezs7jjj:sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ribje9j/;z fu7 e8t:k5 p/ pfityder at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if13 e.uciu+m1i jgw:nj 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 y;d ,k kswd- x 2kkqejp:58f8s$76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

  A 20.0-$\mathrm{kg}$ box rests on a table. (a) What is the weight of the box and the normal force acting on it?   
(b) A 10.0-$\mathrm{kg}$ box is placed on top of the 20.0-$\mathrm{kg}$ box, as shown in Fig. 4-38. Determine the normal force that the table exerts on the 20.0-$\mathrm{kg}$ box    and the normal force that the 20.0-$\mathrm{kg}$ box exerts on the 10.0-$\mathrm{kg}$ box.   

  What average force is required to stop an 1100-kg car in 8.0 s if thx2 h6luym+ qx* 2wm3qn+e-rdhe car is travelixy-* q m rnq2xhe+h6uw3lmd2 +ng at 95km/h? -  

  What average force is needed to accelerate a 7.00-gram pell:h4w8r1es fvqet from rest to 125m/s over a 8f 1e4sqvwh r:distance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration o 93wo:knd 6lwl-,kccjf 2.5l:6dc kw-j3nokwc9 l, $\mathrm{~m} / \mathrm{s}^{2}$ 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 trhyq) y+qfq y a3/zz+)back (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 tu.r/w -/j*zl8b vrxsnpky7 6jhat the maximum acceleration is 0.0680 g . What are the maximum and minimum forces .s6*nvu/ x8jzjrw /7by-krp l 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 scale in a mot ,qe g)7bi4wlan,jt 1m/l/ukqionless 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 uw/ke4iq,gbl/ , qnl )j71tmadirection of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength o1a0i *kc0vab ef 21,750 N. What maximum upward acceleration can i cab*iv1kea0 0t give the elevator without breaking?    ( two decimal places)

  (a) What is the acceko1oramohkg j/ 7 8l/mwpq 98)leration of two falling sky divers (mass 132 kg including parachute) when the upward force of air resistance is equal to one-f/78qp rkow)oka mjol hm9g1 8/ourth 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 r wnj;4vdtz8ej5 roq/:oof of a house 3.9-m high. When he strikes the ground below, he bends his knees so that his torj;:we5vd8 tzrj/n o4qso 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 ra ksf/8m71u n8t:llo oests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the 7:l1n foao88 ls/kmt uother side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for1*+jhcgzr *by a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the /htjrcy4 )j-i r*wa,dmoment it is hit by the bat, and again (b) after it has left the bat and is flying toward the outfieldcaw4/i h) -ry d,*rjtj.

A 650-N force acts in a nor4tnbn se-/ 7pwf e9lh s/mf*1tthwesterly direction. A second 650-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustral9s17ne4h-/ mbtp f *w /sefntte your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizonlgrm61 1km (bfdtn/2 itally between two buildings 10.0 m apart. The sag in the rope when she is 1kfnr /(g db ml61tm2iat 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 buckendtv 59vve l-/t is hanging by a massless 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 tb9 kyv,kjba0c7n/ j:a66oic .0$-\mathrm{kg}$ 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 ufc p(,q6u8pc bnit to a new location at McMurdo Base, Antarctica, as shown in Fig. 4-46. The sum of the fo8qppcb,(f cu6 rces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 twok:xcwj8n- ta: cars of the same mass behind it, Fig. 4-47 . Determine the ratio of the tension in kxj-:a:wct8 nthe coupling between the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upxbwv,8)d ow cev-js6 /ward using the bucket-pulley apparatus shown in Fig6s)ov,b8 we-v/dcj w x. 4-48. (a) How 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 65jzg60 dtz(ur ce0xx7 6$-\mathrm{kg}$ 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 blue; sg8mtrw /v 0+k(uoock (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 suru8e4llw/ 5;k jvrub8gt34 ksi+ s(o ptface are in contact with each other, as shown in Fig. 4-51. A /el(s slkwv5;t8pru itk 8+b3g 4oj4uforce $\overrightarrow{\mathbf{F}}$ 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 showng/1 hk-f qdnqxd :e k+z:t2oh*qv+2zl in Fig. 4-52 are each initially 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then it + t 2-+n1fzl* hhoq:q2:dd/ kxeqkvzgs 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 t;jof adq**q9p able are connected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams shown in Fig. 4-53. Assuqd fj;o9q*p*a me $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , 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 betw.3 u h 3orkzpszkl5yy-or aa61/,m 8hmeen 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 require:mtfgpy/zjd.do x6c. d3 -9xz8n1tchd to start a 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What mdw0;x eencp(pu p;v) ki3 ytxk,.;(rginimum coefficient of static friction m(pkn 0.r c;e g)tx piye,xkdu(;;v3wp ust exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of 0 )zofaj et9ki :3j5im*vknoso ,)/y ostatic friction between the tires and the govo9/ost5jje na *:3)yf0 mzi, ) ikokround is 0.80?   

  The coefficient of static friction between hard rubber and normal street pavemm7tfc ,nq;fvyl9z5 a*ent is abyqlmcazv7f* 9tnf5 ,;out 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 -obrbwz25z)beq2f)bdx1/a v 74.80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 restvlee o9ydvd(t-/9 mhld1pb(/ on a rough 30$^{\circ}$ inclined plane. Draw the free-body diagram, showing all the forces acting on the box.
(b) How would the diagram change if the box were sliding down the plane?
(c) How would it change if the box were sliding up the plane after an initial shove?

  Drag-race tires in contact with an asphalt surface have a very high coef2n c t c761:oyq ffv1tw+2mtcwficient of static frtfc 217t6cwn: 2twmoyf1v q c+iction.

Assuming a constant acceleration and no slipping of tires, estimate the coefficient of static friction needed for a drag racer to cover 1.0 km in 12 s , starting from rest.   

  The coefficient of kinetic friction for am7-en /-0u;g/d nu jhp*rw qwue9ku2t $ 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)wd,w zao33 o( ;jzv x.gz4.oah how large a mass would box A have to have to prevent any mota(a3.jw4 xhzdooo. zw; gz ,v3ion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a pusokw//eyab): eh so that it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speeoeyk bw :/e)/ad of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a homs;wg b+xrd- +n:rc6dl t2:uzrizontal surface (Fig. 4-5l:ubr 6 r-+d m +2cnzd:;xgswt4). 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 cr ca1nqe,gl1uo 560w7t crh5te ate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at which thctql5 w1eoc6ga0eu7 t1rn h 5,e 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, whi ztj/* +a+xkkylv(mhj*:9bwvch has an incv+hx+twv* k(ka:zj lb m9*/j yline 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 withp *rrgu agoa1(rral2df3up,3 ::zg1wnv 7bp) 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 :i.t+v 0c04cs7 k g fmzuwu5kylies 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 spe 6ix.1gfbt u6nn (afp9ed 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 steepe )rzmzsv) h8 9f5i3abkst 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 pushing on it zl sp bjg,m/0a-4w3 1nq l+ 7teuptlu*with a force directed upwardpup ,+la0q4bzug*- l17et3t j/nls wm 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 aoji1hmb* qguh;54dsb 73s :gdangerous projectiles as they melt. Consider a chunk of snow atd bm*73a1hbu q4sisjhg; o5:g the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for ane w,lc.18dj(0t h yrck automobile traveling at speed v is equal tok0dy jrt81c ,(ew l.ch $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 onj ansxosirb *vc g7/,+4g s45k the dash when the driver decelerg,kg4cj 5r/sixa nsobv7s4*+ ates 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 speedl b3i:3qij//,8 q q-pxpcyfle $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

  The $75-\mathrm{kg}$ climber in Fig. 4-56 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.80 and 0.60 , respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum. Ignore his grip on the rope.   

  Boxes are moved on a conveyor belt from where they are filled to the pacdoji3m3r +t; )nn/h qqking 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 fina/ nq3thqjo;+m r)id3nl 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 kinetiac7f; x d3l.iuc 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 do0y n9 0 wd07l9jtopf2hmsqa z9wn 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 approximat evy 05a/w5/u4xfxykz+7 hz beely 20 g of bhuz/ f4zbye50/7xw5e v+akyxlood 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 su6n:w(s8xn3pq ./bk j j-nehou rviving an automobile crash if the deceleration is no more than 30 " g 's." Calculate the force e 8q/s:36j-wnnnubo xj h(kp.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 accelerahfb9 l /ye8ng7bfk.8 )cqwj6 dtion produced by an earthquake is a , and if an object is going to "hold its place" on the grounf6wjfdcb) bkgq9 ./8yn lhe78d, 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 two cars, mfyohw92r/c z+yu,okz dn z e z),7c(h2easure 72-m-long skid marks of one of the cars, whichye/z,uzhc+hw9rc o7o2k2ny zf z(, )d nearly came to a stop before colliding. The coefficient of kinetic friction between rubber and the pavement is about 0.80. Estimate the initial speed of that car assuming a level road.   

  A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m travela,b gj,.xypx4 2 s:yuv4par)jed along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignoy4usgpj. xx,ajr y :4)a2p,vbre 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 Pixvv to(1e+v*3 ni fhu, fw +id(; e15hk/iopqpsa and falls 55 m before reaching the ground with a speed of What was the ave ieo5,vv3hk/wq+ i n1df (+i o;p tpfux*(h1evrage force of air resistance?   

  A cyclist is coasting at a steady speed of 12m/s but eo w:kqa i sx- -zv8u*wdga5(2enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge frdaqo se*- 8xu5(zk ag-w2wv:iom 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/u yb7wo3) vrp a hilly portion of a city. An important conu 7)wv3y/borp sideration 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 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 physicz fhcc eptv8:(1rwt:4s experiments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFvzwrf4hpe :8 ct :(1ctK 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 ramps connecting mnjf;xg* -lt1different parts of the store.f;m*-1lx j tgn
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 pmr)p(ou -/ik mi 6q2sviano (mass M ) using the pulley apparatus sh(s6m/p2k mvu-ro)qiiown 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 acceleratj86rzek4 0aw f pk*v7/yzu d9v k7)oguing 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 chair, amhtv yfm86 tq.6 2zz0vn engineer considers the following se hqm8v6zmz 2tv0 tf6.yt 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 ma es6x0 ;fga)Italian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar le:r ky/bt bc,8hngth. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro cliyhc,/k8tr b: bmbing. 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 using a ",6 npv0blqr(w 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 maxiv y -v(mu;irv(mum 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 way/q f 5 7pxxp65vqeh30;qcawho are roped together are ascending an ice field inclined 06y vqwp5/pc qaa3;fehxx 5q7 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.