Why does a child in a wagon seem to fall backward when you give the j3;o ji r2np+uwagon a sharp pu;j+3n oirup2j ll forward?

A box rests on the (frictionless) bed of a tru ,jwpkx 0b n)iclcz289ck. The truck driver starts the truck and accelerates forwar 8b cjci ,zl2xn9kw)p0d. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is64r8yuy:htw9 kaid2 o zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? Can it-xr;n,v9gn r*,qf3 yeno ,ytf have zero vvofqnrx,r-9ng e*y ,,y t;3nf elocity? Explain.

When a golf ball is dropped to the pavement, it bounces back ups7p 92 v1xw2cim(kg gc. (a) Is a force needed to make it bounce back up? 2gw kg7x 9vsc pm2c(1i(b) If so, what exerts the force?

If you walk along a log floating on a lake, why does the log move in the oppw,) )dxx 8+keh6am ouuosite di 8omdwa6) h+ ,x)euukxrection?

Why might your foot hurt if you kick a heavy desk or a wall?n j lk5qn,*o.v

  When you are running and want to sto 4soqigk8wi) 8p quickly, you must decelerate quickly. (a) What is the origin of the force that causes you to stogsi q)i8k4wo8p? (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 fine thread from th uvtw+imh8i 7/e ceiling, and a section of the same thread dangles from the bottom of the stone (Fig. 4–36)8h/ivu tw+mi7 . 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 rq;t 4lfr o ev;bt-6e5sock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fab rtl;tsqov ef4 5-e6;ll faster?

Would a spring scale carried to the Moon give accurate results if qlhse b.g n y7l2/dydp:;47yn the scale had been calibrated (a) in pounds, or (b) in .qy7e4snyl:bl/y dg;2 7dhnp kilograms?

You pull a box with a constant force acr+ it yek r5krmj9my93)oss a frictionless table using an attachek9trymir+3m)9y k5e j d 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) decrease? Explain.

When an object falls freely under theznai9 k sio(o(q,z b6 9.ium/d influence of gravity 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 Earth m./9,9d zsnbamu6zqoi (i(koiove?

Compare the effort (or force) n v5erdi*3u nr.j-iedn;31notu hs * 6teeded to lift 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 horizontally with a given speed on the Moo3n*1nvju dhn6r.o*i- d sue teit;r5 3n and on Earth.

According to Newton’s third law, each team in c3e 4xu5 .mug1zx)pkp, o8:1aekb2ck 5me lqda tug of war (Fig. 4–37) pulls with equal force on the other team. What, then, determines which team will e ck e xm1, m p5g4pculaeko.8bdu35xz) 1:kq2win?

A person exerts an upward force of 40 N *0o.njoxhxd 2to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its moxno2 *0.hdjxagnitude, (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,18)ljzml vwcac .1j- j how large a force does the ground exert on you? Why doesn’t this force make you rise up into thejva.l)czj 8-c11wl mj air?

Whiplash sometimes results from an automobiqshlfj(5wuow 2sbg8b*o2 w6 au::deqa29b *yle accident when the victim’s car is struck violently from the rear. Explain why the head of the victi qf g 6s2:w dos*9huyalw*:j225awo8bebu qb(m seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. When trgj 8 zxv*p9o4he truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What force causes thj zv*ro89p4xge crate to accelerate?

A block is given a push so that it slides up a ramp. After th,qd f kz,tqp/s ; uvnj--wb:r7e block reaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on theks7t w/,q-nf pqj ,u: d-zr;vb ascent. Why?

What would your bathroom scale read if you weigqq c,e, m1ii;jp4st4 ihed yourself on an inclined plane? Assume the mechanism functions p;1 sj,qm,ii qce t4p4iroperly, even at an angle.

  What force is needed to accelerats4k2 b;el-qa oe a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and rider at + 2 gmqn;g2euv2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used tfhya4czs j9/i/0tt 5o o accelerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight opa v9eb1qw*f 6f a $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $\left(g=1.7 \mathrm{~m} / \mathrm{s}^{2}\right)$ ,   
(c) on Mars $\left(g=3.7 \mathrm{~m} / \mathrm{s}^{2}\right)$,   
(d) in outer space traveling with constant velocity?   

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

  What average force is required to stop an 1100-kg car in 8.0 s if the nx-g k(bo:v e *nv8* rqh+)xudnvt (l2car is trave- d(br*vnlevvhx:n*q8g ( oukt+x ) n2ling at 95km/h? -  

  What average force is needed to acceleratee33 dfy c(jk5q a 7.00-gram pellet from rest to 125m/s over a disqckj35e 3(dy ftance of 0.800 m along the barrel of a rifle?   

A fisherman yanks a fish vertically out of the w;qw* f.xfc+z pater with an acceleration of 2.*;cw px +z.qff5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 izo2zpmo k.e7 x5se) 1qgm9q5can cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum acceleratio(oi*xyu5b v,d n is 0.0680 g . What are y vioxd5 *(ub,the maximum and minimum forces the motor should exert on the supporting cable? max =    min =   

A 75$-\mathrm{kg}$ petty thief wants to escape from a third-story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 58 kg . How might the thief use this "rope" to escape? Give a quantitative answer.

  A person stands on a bathroom scale in4nfr:w cs b0hv (4k5inb5ti.q a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the:kin 04(wbbqnf54hci. 5vrts person’s regular weight. Calculate the acceleration of the elevator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a maximum strength of 21,750 9d5z ,jvghc)6t-q*l um/nz kaN. What maximum upward acceleration can it givenzz k-/,) m*q6tvla9 jdg uh5c the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky dis /)mv-j( l:icac1h. wx 1oovavers (mass 132 kg including parachute) when the upward force of air resistance w c11mso jv: a-)iv/lxhc(o .ais equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. u;mc( u0mx.0 hti sy83ax6dkcWhen he strikes the ground belxxi dsyu 8.t(;6mu0hka3m0ccow, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests ong5w hvtvp:ujlt) /-m: a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung pv/u 5g) wh:vl jtt-m: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 the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a basketballvdzwsr 73 gdada(:3+6 he+ ucn player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moment it is hit by the d :tnumkk+ua0v 68*ngbat, and again (b) after it has left the +gu d tv8m*knn:a06ukbat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 65vl8 y5ny.u vt+ 9l.bmp0-N force must be exertetb8 5.pn.yy lv9lvu m+d in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betwe7dphzqyw4 1i-4rrdk2og;zjh 7 cd20 nen two buildings 10. o7 -wg74zidz qd20y21jr;pk hch4rdn0 m apart. The sag 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 cord from another 3 vta;/baw6d*)rnr2o8 /naytk.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 qz:g kzwunlyh gac+*3-: nn8hi 52sd3.0$-\mathrm{kg}$ 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 unit osvxjxgjj ** rb27e* nm.q1 -mto a new location at McMurdo Base, Antarctica, a *xmqmjerjs*7o -2n.xg*b j1vs shown 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 samukc 6edz d7 +ju1u7,vke mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between ,7kv7zc16uek du +djuthe 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 buc 8+v 9ykcs9 igtk)15zcjbx)r cket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constc1))+ xbgk ikv y5t 9zr9sj8ccant 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 b/f jghz1b;+oh+ e/f4v2amfpw egan, 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 (mas3 nnh1o g+h(inzs9p,s5: syx z9ge7u ls $ 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 with7j .c9 q9xmw z*j5 jjdsnct*n2 each other, as shown in Fig. 4-51. A fordj jj99cn*s x75* c tqmznj2.wce $\overrightarrow{\mathbf{F}}$ 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 1.8gn5y d;klku*rx5y3 n rjnx 4-:0 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity j*unyk 4yk lx 55;3nr-rdgx:nat 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 con77ul : 63pid y f(wnpvlnt4o2mnected by a heavy cord of mass 1.0 kg . Calculate the acceleration of each box and the tension at each en tnl6nd wif7(pp3oy:u724m lvd of the cord, using the free-body diagrams shown in Fig. 4-53. Assume $F_{\mathrm{P}}=40.0 \mathrm{~N}$ , and ignore sagging of the cord. Compare your results to Example 4-12 and Fig. 4-22.
(4-53)
(4-22)
(4-12)

If the coefficient of a + t8wcgm8lgb-pq88tkinetic 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 raxmh9jz:; ;y 8iz01j8fat leeequired 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.,d7 rn8e 3ziszkikw8 0.20g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide? re3ikdn8iz s7 ,8wzk .  

  What is the maximum acceleration a car can undergo if the coeffici;vz,9;fl c/tlziu6nb1y l q8lent of static friction between the tires l;8zbtu6f1l; i cl, v/lqn9yzand the ground is 0.80?   

  The coefficient of static friction between hard rur:kmtkkbzx3w ;4/ i0j bber and normal street pavement is about 0.8. On how j t:/mkr4iwxb k03k ;zsteep 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 5ievet;v(.6v +rwujd0 $\mathrm{~m} / \mathrm{s}^{2}$ 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 resd6 wy7zw6 b km8i6wql+t 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 wpx, vog hdbyjkir)pqhc.;rq* .r0*-zm(2xf.ith an asphalt surface have a very high coefficient of static fry*ocq,;zqmh.b( 2 i*fj rv.rd. g)- xprk xph0iction.

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 ;91dt a.xsknnon 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 4-20f 29x0-qcau20p eivlo) how large a mass would box A have to havefu2 90v0qpaie2-oc lx to prevent any motion from occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that itu zf-v9vp fc2-he5c ici: 42zyvuw;p8 slides across the floor. How far will it go, given that the coefficient of kinetic fri -2zfy:wc;vfu i4ev- pc p9z5 2ci8huvction is 0.20 and the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a htbjr ur)b,w- jbaq+x6,n *nd:orizontal surface (Fig. rj)tn6d b x, j-n,a:rbw*+qbu4-54). 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 heavybzb*+/qr o1o)uo (rb- yhas7 m crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the max(rbb yo)a/ 1o+rhzus m* b-q7oimum rate at 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 paowk z m(nx11avdat4 4 hs1-tn+rking your car in your driveway, which has an incline of 1td knnot h4 v1s+ax-zma41w(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 slidwyd3a**t:aij ub+ a-d e 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 Figc yzvwlt2-1 k4. 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 s3t4x:imgkdxozw*y q38j*v 3speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches the top of the steepest hill with a speed4 lb xb8bfk-9 zfi9gn/7mss ;pdipa,91 agu7h 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 someonezkx8h:tm /4)a+a.pcx 1z i,.sz8/pwr xoflnd pushing on it with a forcel8f8,wznp h4to x1i ./p/ra .c zm:+sazkxxd) directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dumqq6j qi r*-1angerous projectiles as they melt. Consider a cq6 u-jmr qi1*qhunk of snow at the ridge of a roof with a pitch of $ 30^{\circ}$ .
(a) What is the minimum value of the coefficient of static friction that will keep the snow from sliding down?   
(b) As the snow begins to melt, the coefficient of static friction decreases and the snow eventually slips. Assuming that the distance from the chunk to the edge of the roof is 5.0 m and the coefficient of kinetic friction is 0.20 , calculate the speed of the snow chunk when it slides off the roof.   
(c) If the edge of the roof is 10.0 m above ground, what is the speed of the snow when it hits the ground?   

(a) Show that the minimum stopping distance for an auto kq*arpy.p(p:2fc qd1vk7n bt,9fk v5 mobile traveling at speed v5q:t.9pa1y, f 2pk*v(qpdkbvfnk7c r 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 dashboardlbm+ 3jt5rm.d of a car slides forward on the dash when the driver decb+3rlt.5 mm djelerates 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 any9ftz u fl:(s c;i,ca4ql1pid-1r e4m initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where ak5m*e5rkhe-; yn0eslp 8 8lzh;h3hpthey 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 h l reha3ekz- ;e*h58s0 5p mh8yk;plnthe 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 fr4yqlfs6 s9+d2iap :v t3oel 4eiction 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 (inclu4 lh1m nacvcx8,rv4,fding 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 p b50ggv. mgxw1)x3 ubmammalian heart, at each pulse approximately 20 g of blood is accelerated from 0.25 35gux.v0)m pb x 1bgwg$\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile fbc.: dhfh s35xxq- h/7nzc 8s5xk+i5eaw. l zcrash if the deceleration is nonswcd .x hzc5.i bf-+xkf583hh:7sqa 5e /lxz more than 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 ear f 7hy(yctnbk i4q*w5;x n22hdthquake is a , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground muf2;ti(hwyb47x25n yc *qkndh st 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 ofd7z(21pu68w) rz ynzjw)ps 9k0p jzaw an accident involving two cars, measure 72-m-long skiw89d j)1z 7uw6 spjykz nz)0rp a2wz(pd marks of one of the cars, which 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 meansiz:d +c oms;1s that for each 4 m traveled along the road, the elevation cha:1 si+do;mcsznge 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 from the tm/hvh9fmip /*op of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of a/*m i hm9hf/pvir resistance?   

  A cyclist is coasting at a steafj t ui9 xhmf1))w /o0x5zdm4ody speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch withoxoiu01f/ 9m)mxoh ) 4fjw d5tzut 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 c,0d0m6 p c n 2(aygj2shfomdh8ity. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 1100 kg , can (dy,6cp2 0dmfg an2sj 8hm 0hoaccelerate on a level road from rest to 21$ \mathrm{~m} / \mathrm{s}(75 \mathrm{~km} / \mathrm{h})$ in 14.0 s . Using these data, calculate the maximum steepness of a hill.    $^{\circ}$

  Francesca, who likes physics experiments, dangles her watch from a th zci2.0:2 epk;u aht:x um+sdbin piece of string while the jetliner she is in takes off from JFK Airport (Fi+up t k: abeu2;:dczh m2.xs0ig. 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 dwfm4et.6n6 w 8 mebj)lifferent parts of the st4t eemwmwfb66) lj.n 8ore.
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 thqla+s3y, e4ti* z ua-1c/k4 tkge :ubce piano (mass M ) using the pulley ileugq t1c be*y4z-k4 ua3+:/cs ,kta apparatus shown in

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

  A jet aircraft is accelerating as/(9ve 3s r gvv;hjt d7/1 .xxzlwadq+t 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restrainjv8g ibkwcvgt 44t( z-j/ i./dt chair, an engineer considers the following set of conditionj/ziwv.jc - b v4/tt8 g4gik(ds:
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 metric tons (660,000 : ae f)s) nj(pok)/rhy$\mathrm{~kg}$) . 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 simizoffg: +llh u86z+6ppgxw1e:lar 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, Bil :zh6fppgz8lfg :+ +x6uewlo1l'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 " 10-1 qltb,: yk+rpxs(yxj( ::fw4ge-e7 dt $\mathrm{~b}$ 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 speexqlox 7kh 1 79izd+(ysd 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 ascendi4mcv2zzzbars( 9m g8: ng an ice field inclined at 21r2m:mz4avb sz 8c(g z9.0$^{\circ}$ 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.