Why does a child in a wagon seem tk:t)hid7lwnk;2q pd /o fall backward when you give the wagon a sharp pull forwaw d:) /qn;k tiphkl72drd?

A box rests on the (frictionless) b +;,;xbgio1 z.merm klm .p hnwf.p0c)ed of a truck. The truck driver starts the truck and ap) ;bghwkme xm+l;i.c0m p ,n.zo1f .rccelerates forward. The box immediately starts to slide toward the rear of the truck bed. Discuss the motion of the box, in terms of Newton’s laws, as seen (a) by Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an object is zero, are no for;le m;2jxkl* h uth01xces acting on it? Explain.

Only one force acts on an object. Can the objeho,2boz5ex 8z4 dnz9h ct have zero acceleration? Can it hab9h5z2zxo z84 e,o dhnve zero velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back u8*kqs.mje0dt* wjf 5 op. (a) Is a force needed to make it bounce back up? (b) If so8 sd.k jwjt o*m*fe0q5, what exerts the force?

If you walk along a log floating on a lake, why doeslhi 7ku .vlx,0 the log move in the opposite direch.klul0x v,7i tion?

Why might your foot hurt if you kick a heavy desk xkyl.v0pp+6 for a wall?

  When you are running and wantcxc-j c9lz72f/abds k1cl4 s 0 to stop quickly, you must decelerate quickly. (a) Wha- xjcc dsk9sbfc/ 1zca 2l4l70t 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 running at top speed to come to rest.    m/s$^2$

A stone hangs by a fine thread from the ceiling, and :4sh *wokm p4wk4jd/ua section of the same thread dangles from the bottom of the stone (Fig. 4–36). If a person gives a sharp pull on the dangling thread, where is the thread likely to break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answersd4h s/m4o:*uj p4wkwk.

The force of gravity on a 2-kg rosv, apy0y)m3v/l 09) w g8bm 1bfbkgrgck is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fall fas 30/f,)mmg vwky9p)rla 10b8 sbgvgb yter?

Would a spring scale carried to the Moon give accurate results if the scale had hh4 smw/bfj7* 5ab(dmbeen calibrats 4fwh7 bm/*ah5jb(md ed (a) in pounds, or (b) in kilograms?

You pull a box with a constant force across a frictionless table usino-n qdrs)67fqg an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) remain the same, (b) increase, or (c) decreases)-6rn7fd qoq? Explain.

When an object falls freely under the influence of b.0m frl ,k;se)jhc8c gravity there is a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal andc )chre;jm.0bl,s 8kf opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) nee kldfw-cmi6/y 3+uy(0,qpmry ded to lift a 10-kg object when you are on the Moon with the force needed to lift it on Earth. Compare the force needediyy d + (-u6 ,rqkc/03pmmwfly to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war es mg39ktatx(6p9 ;m rce0os4(Fig. 4–37) pulls with equal force on the other team. What, then, determines which team ;gec ( sms6p9a o4rm9 t0te3kxwill win?

A person exerts an upward force of 40 N to hold ao6x 3s ,dl,izs bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitx,s lo6sd3iz, ude, (b) its direction, (c) on what object it is exerted, and (d) by what object it is exerted.

When you stand still on tj+ 0mt;k*igvky5zjo. fwvy :(he ground, how large a force does the ground exert on you? Why doesn’t this force make you riov0jw5.kjfk:ity y *z(mg v;+se up into the air?

Whiplash sometimes results from an autom brc3mzj( k8(za7hl5v 4(lgmoobile accident when the victim’s car is struck violently from the rear. Explain why the head of ohbla(( zm3vg(j 8cr4m7 zl5 kthe victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. Wherc.jj7 s90h rof1(wrrn the truck accelerates, the crate remains where it is on the truck, so it, too, accelerates. What forj0j .oh1swcfrrr7 r (9ce causes the crate to accelerate?

A block is given a push so that it slides upb sfnb8x,v9 w5 a ramp. After the block reaches its highesvwbf b9 sxn,85t 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 yourself on an inclined plane)n5k wl:q walrffl2dm 9 6 /3llb92jxv? Assume the mechanism functio3)n5mb lkl2w a29f/llx 6jr:wl f9qdvns properly, even at an angle.

  What force is needed to accelerate a child on a sledrb jb,(tg*rrxq + /qib,)u2rr at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bike and ridx wx1)hn 3aikh4w(sk 4ql; .mter 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 if it is used to accs )x c0jvt:ug+elerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight ofau(xi)65 eam,w y,xsw 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 ayu(srdd7+g(mn;.ez *kz nn/if the car is traveling at 95k ;.dszm(e g ykud/zr7n(+a *nnm/h? -  

  What average force is needed to accelerate a 7.00-gram pellet from rest to 125mj7tod ;x1o1nq /s over a distance of 0.800 m along the barrel ofnqtd o1x1 j;7o a rifle?   

A fisherman yanks a fish vertically out of the water wit, ci45lpp aq7fh an acceleration of 2.5cp4qf pal5 ,i7 $\mathrm{~m} / \mathrm{s}^{2}$ 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 caugno8hk*(ys dlzb )vf52e r 1,zu, pa,r can cover a quarter-mile track (402 $\mathrm{~m}$) in 6.40 s starting from a standstill. Assuming the acceleration is constant, how many " g 's" does the driver experience?    If the combined mass of the driver and race car is 485 kg , what horizontal force must the road exert on the tires?   

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

  An elevator (mass 4850 kg ) is to be designed so that the maximum acceleratu-a v-s23b 6ks2gkcht ion is 0.0686k vg su2ska2-bt3- ch0 g . What are 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 in a motionless elevator. When the elev64tijzddp-1i 2, lqy nd a1p(kog9lh,ator begins to move, the scale briefly reads only 0.75 of the person’s regularhtpa, 1-dl(id2z l614 g po9y,nk qdji 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 maximr5 sw6gy:y);fh6difk um strength of 21,750 N. Whatf ;wrsfd:yi6gk5y h6) maximum upward acceleration can it give the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kg including pa 2vlce6:lfoj6nq ..*yzpjz.u 6j b 1oqrachute) when the upward force of air q .l2*66fozz61.cjyo:eujq pb . n jvlresistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When hd5-i)n8abcz 2eztm ij3en2w7 e strikes the ground below, 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)nanzi cim52 ztde7)e3-bwj82 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 rou35vgsz0wiu qh:)s1 r:m 5 rglpe 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 othe5s z g:hqi1uvgr 0w)ml3r:s5ur side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagraqf6r, tplp27cpo j1. kur3 5rdm for a basketball player
(a) just before leaving the ground on a jump, and
(b) while in the air. See Fig. 4–41.

Sketch the free-body diagram of a baseball (a) at the moutowe(ywgq-l -57lu9 r eq49 ament it is hit by the bat, and again (b) after it has left the bat and is flying toward the out( -u tulqoq9 arlyw74w e-9ge5field.

A 650-N force acts in a normz3 qq-50tykathwesterly direction. A second 650-N force must be exerted in what direction so that the r3m5yq tq- a0kzesultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strunvt ctj 50f 5svak2/ v0n7p ew9n;x-xjcg horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpo5 9;nptj jakx7xnv tc0ev-w25cs0 vf/int 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 .n7pzi9 thoseng c.a7 ke1 n(wp5d.q*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 6zatq26 n*hvtrm7i ,l.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 to a new location at McMurdo rjavc 3zg. i21w4*cu uy mpm)je17j7aBase, Antarctica, as shown in Fig. 4-46. The sum of the forcey7 * icpu w3)r1 gcz1 mva.jj4j7ua2ems $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ 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 tg57 erdjt;0i same mass behind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotive and the first ca5dt 0ji;7 tgrer $\left(F_{\mathrm{T} 1}\right)$ , 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 dkf4q):qq lr8 tjp5s6the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at cons qkt58qsfpjl6 d):qr4tant 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 6f wcjmv kfb2w0 9e-zsnw +/4 jla+n4a+5$-\mathrm{kg}$ 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 (mas(oai/wcpgl(e+1.e,1-zk , uixxho p js $ 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 horizontp0 yocfcxqh6w- acwxp/92 o34al surface are in contact with each other, as shown in Fig. 4-51. A f-o6wh2cfa w ypp3 cxc40o/q9xorce $\overrightarrow{\mathbf{F}}$ 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 eaou08 vsb0w,thu4u)s(w fzv)dch initially 1.80 m above the ground, and the massless frictionusof00uvz)u bh tw)vs4d(w , 8less pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table-hms /mc+oux ( 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 diagm(m-cu/h o+xsrams 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 kineticyuz/hxp lw.(6 f/hv t2qyu 7,h 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 reqou),zz0,htv,rxm0dufn x a5xl b ,.jg nu7/a2uired 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 stan (e w3lm5ylarg a*lq,un9,4re ding on a train accelerating at 0.20g. What minimum coefficient of static frictiolyea *mq wre,4 3,5rlgnu( 9aln must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergogw *b6-.phrlq if the coefficient of static friction between t w.*h-l6grpqb he tires and the ground is 0.80?   

  The coefficient of static friction between hard rubber and normal str 2n4gdd xt;t7veet pavement is about 0.8. On how steep d vgxd n2;47tta 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 -4.80 tqvf it3-rb 5a87p+ri w9ae3 k$\mathrm{~m} / \mathrm{s}^{2}$ 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 ro4/dx y8e 1 1eoxnuz+atugh 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 hdz yzcn;l+ k0v 3ynd+0igh coefficient ofzl+z0dydy;nck +3n 0 v static friction.

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 frictiongi2+p j2v txw(:gc9ko 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 oljhf8 f v95x)(Example 4-20) how large a mass would box A have to have to prevent any motion from occu)fv98f hx j5olrring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides across the floor. How far wil7xl+ 9 b3tr w(vcaxgpqhr.*,f l it go, given that the coefficient of kinetic friction is 0.20 and the push impap9l, hvgq(+fxt 7a3bxrr.*cwrts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contxw/,k 2/p;vnrqv 3pe qevew5. act and at rest on a horizontal surq p ,re pwvewe3;qvv5//xn2k.face (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 carryi8vumfi*km j wlt+bwzf ) *d8t70u5 o5ing a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.75. What is the maximum rate at whic+t*)ju7 kv l58w8imf0tb f d5 uz*wiomh the driver can decelerate and still avoid having the crate slide against the cab of the truck?   

On an icy day, you worry abotygzu7h6em 2 -8cqyo3 ut parking your car in your driveway, which has an incliqcgoh3 2u 76myt8e -zyne 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 l6;duz+ski)z e5hqkdn-j a-,with a 28$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tiltee*sol z8w( gy)8ag*vw d 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 ini bnkshwg2 m+.,tial speed of 3.0 $\mathrm{~m} / \mathrm{s}$ up the 22.0$^{\circ}$ plane shown in Fig. 4-55.
(a) How far up the plane will it go?   
(b) How much time elapses before it returns to its starting point? Ignore friction.   

  A roller coaster reaches /lj *oh;tz b-hm-8 y*euydo 0co8ekt *the top 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 pusrmpfqjg+ 7*9dhing on it with f rpm +qjg9*7da force directed upward at 28$^{\circ}$ above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30 , respectively. The box slides down unless the applied force has magnitude 13
N. What is the mass of the box?   

  Piles of snow on slippery roofs can become dangerous projectiles as54stczev( ,dp they melt. Consider a chunk of snow ac,e4dtzp5(s vt 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 an0:a-ws zbo n:-ygx wdznxv4nv*m)1 8u automobile traveling at speed v zv 4-:wsyo* 0 nzmv xx:bauw8)ndgn1- 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 slide w jl zew043h85n)goqps forward on the dash when the driver decelerates 5p8gl04oj hq3znww )efrom 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,w mrm7n:/r,d;mbnemg9 z d5r is given an initial speed $ v_{0} $ up a ramp inclined at angle $\theta $ to the horizontal. It travels a distance d up the ramp and comes to rest. Determine a formula for the coefficient of kinetic friction between block and ramp.

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

  Boxes are moved on a conveyor belt from where they are filled ub veutea*fu qi6; j2o3)t4q3/:imdwto the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient ofijao b32ftq6): e/q3wu ;id4*ute mu v 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 frictio7s(chqm;x +1psn8mh nn 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 bicyc07c m4 mv5(6uyxriglhle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each puawis/xt hp.( k.4yv8ilse approximately 20 g of blood is accelerated hy i(s a. p.4/iwvt8xkfrom 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile crxanl .bx 4jz9 6u+i;wdash if the deceleration is no more ; bawi4x9d6jl.uzx+n 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 earthquake is a , and if aney q0 *w) dran2q m);-gggjy0w object is going to "hold its place" on the gr* j;gw)n-ygqd2mra ey0g )q0 wound, 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,8vs( v7 x urntsy9s3w. measure 72-m-long skid 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 vt u3vwx7 r8y(9sn.ss. 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 ea o*3z gph4afo:ch 4 m traveled along the road, the elevation change is 1 m). How fast is itp34 : fg*hozoa 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 top of the Leaning Tower of Pisa and falls 5zxrfb5ajz/(;hbuf0,u 2im 8w 5 m before reaching the ground with a speed of What was the average force of air resis5(;u,i0zufr/mh f2z wb x8abjtance?   

  A cyclist is coasting at a steady speed of 12m/s butd 9q-*dq3l8elsruhl3ljpx zs0p*7v ; enters a muddy stretch where the effective coefficient of friction is 0.60. Wild* u*zs;3 l8s7pq0rl9dp e3vxlhlj q-l 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 redes ;kz2m5vlq7wyu9kc -,jqq6 el (4bio fign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car,cklkz5y 7 v,iefm j42(ql q;qw-bu96 o 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 from a thin pi s/ ufex+pd5-l)kzmg* ece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an angle of 25lmd/upg sk)5* e zxf+-$^{\circ}$ 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 rampq3 t0lvzwado 2 * mq.1n7bw:hns connecting different parts of the stornl 2.3ndh*wvzb m :oa70 qqtw1e.
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 gz8l m8)juzj)to lift the piano (mass M ) using the pulley app)l m)jz g8zuj8aratus 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 at g-i6mgqev2 25 rj0pi;m-mmvf 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, an engineuf t 26y*dher*er considers the following set of conditit6y* 2*hufedrons:
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 16q)ead71n2wrkgwy 4x7 srku (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 andmsmhv*;b3qyr -7zg )s Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dygvrm sb)qy3;mh7z-* snamic 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 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.aynzwcp,uni) et7 tl-p r 0//-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 allowedv-:ygzlhr2frzx rf/ p 4 j15l4 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 rop, - i3jebiypo8plcb(8wj63 geed together are ascending an ice field inclinedywi(j 36l8e-pbcei ,jpo 8b3 g 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.