Why does a child in a wagmf4id4t -rno-x9y k)cd)ah, us p33oton seem to fall backward when you give the wagon a sharpni-ys)49d43 crtumh, k3xpo )da-otf pull forward?

A box rests on the (frictionless) bed of a truck. The tl4ee5g,gq9 o6ix 8av,8hxdq z 8kgdl.ruck driver starts the truck and accelerates 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) byva8 gx4 dq , ., 58zdoxe8gkgeql9lh6i Chris who is riding on the truck

If the acceleration of an objs,gdgfn7 b)-z0tv kbm n9,z m5ect is zero, are no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleration? /ab)zu) rg5c mCan it have zeg)a zrm5)bc/uro velocity? Explain.

When a golf ball is dropped to the pavement, it bounces back 6gvzp )n.p/0bjg ;rvxup. (a) Is a force needed to make it zb. 60;pjvrgn)vg/pxbounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, why gsg0wzwz0 p/i /ni9tr8ek4;(enb3lg dr:n; n does the log move in the opposite l0 tned i rg/9 eg4ig3z(08 s :knn;p;rw/nbwzdirection?

Why might your foot hurt4m43. h v.(z:pmf moa5xrguj o if you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate quickly. (lq+/let cx9n6hfi 2,ta) What is the origin of the force that causes you to stop? (b) Estimate (using your own experience) the maximum rate of deceleration of a person running at top speed to come to rest. t,96lcxteqfh2+ / in l   m/s$^2$

A stone hangs by a fine thread jq*d1m kfj,ed6pn 8y,from the ceiling, and a 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? Ex, efqjmnk1d8yd,j6 * pplain your answers.

The force of gravity on a 2-kg+xrzbjt*u 4k7 rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavier rock fz*7u j4k+tbrx all faster?

Would a spring scale carried to the Moon give accurate results if the scal 6i vvjrf8v.outwpz ps61ir315tit:4e had been calibrated (a)4 1 8vur .r6ivsttop631jv:iz 5pwf it in pounds, or (b) in kilograms?

You pull a box with a constant force across am0e.o. b8 c*g1lb+gqa2wtufj frictionless table using an attached rope held horizontally. If you now pull the rope with the same force at an angle to the horizontal (with the box remaining flat on the table), does the acceleration of the box (a) rebuq. ga 2o8ft*jm b.+w1e cgl0main the same, (b) increase, or (c) decrease? Explain.

When an object falls freew)gd(bm6hhms017c u4-r r btnly under the 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 Earthtc-nh( rg 0u)mmbbw7r1s6 d 4h move?

Compare the effort (or force) needed to lift a 10-kg objetg* gxubzr eg 0l8.ed1:6)v usct when you are on the Moon with the force needed to lift it on Earth. Compare the force needed to throw a 2-kg objecu6.g)ed*gzu xbg r1te s0:v8lt horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, ea: gj,k ub7gacnb.)b1(xaijn d m,+3e(2ln b bmch team in a tug of war (Fig. 4–37) pulls with equal force on the l(ma1akm:+2b,) jgj.3 nxub ien gcb n(7db,bother team. What, then, determines which team will win?

A person exerts an upward force orhc*o;5*y6jw0vj xxn f 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b 5 h0jnvw*x6*jy cxo;r) 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 the ground eiallm+ 7 ls6-rxert on you? Why doel7a +li6mrl-ssn’t this force make you rise up into the air?

Whiplash sometimes results from an automobile accident when the victim’s car ig+u2e-a *r p o 22al22 paufb4tpajrd:s struck violently from the rear. Explain why the head of the victim seems to be thrown ba+2p a *rplp4oaf -jegb2d2r 2:aau2utckward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truck. liv-+ro01xaa When the truck accelerates, theiolr 0v aa-1x+ crate remains 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 ramp. After the block )fphdg10qs ,w4aitn3 oxq 7w*qo0d 6hreaches its highest point, it slides back down but the magnitude of its acceleration is less on the descent than on th* q6ip7fd1swo 4 qt,x)qo0ag0ndh3whe ascent. Why?

What would your bathroom s rjpbd8e9n--d cale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly,ed-dj8rp-b n9 even at an angle.

  What force is needed tv8m;wa njt).yo accelerate a child on a sled at 1.25m/s$^2$?   

  A net force of 265 N accelerates a bptr,8x q.wfodmq,sc 83u *m s,ike and rider 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 accfm oyrom0 :/ owvye+.0elerate a 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a.p,m 7z zux dal8 ezapt90n+4f $76-\mathrm{kg}$ 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 s1buk vic khx,,9:wb 2s if the car is travel,bcwu kbs:,9 hv2xk1i ing at 95km/h? -  

  What average force is needed to ajj 1i3er7ad2 accelerate a 7.00-gram pellet from rest to 125m/s over a distance of 0.800 m along the barrel o1 i 7da2ajje3rf a rifle?   

A fisherman yanks a fish vertically out of the water with an accele rkzl9 s ,aww6e93g,hz p0nqf(ration of 2.5 p 9zhge a wfrs,,6z(n3lqk9w0$\mathrm{~m} / \mathrm{s}^{2}$ 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-mikat.o/l y 36qtn0co.y le 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 maxi :rwmxodycimve,4 ,+ds; zfao+n 7*fr q0u5;imum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supportindde5*ivos qf+;mcw;4u:7 ,r + f, amxioz0nyrg 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 el wkc /q*;e,;,fmyj qzaevator begins to move, the scale briefly reads only m ,;f /wc,qyzk *aej;q0.75 of the 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 21,76iwb8f. samh22p6 sfo 50 N. What maximum upward acceleration can it give the elevator without breakbi 2hs.fs68f26o pwm aing?    ( two decimal places)

  (a) What is the acceleration of two falling sky divers (mass 132 kgt a(d10s1p tvqu/jxj / including parachute) when the upward force of air resistance is equal to one-fdq1/t jtxpjusva ( /01ourth 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 he strikes the groun a1lkoa.0vb ,kd below, he bends his knees so that his torso decelerates over an approximate distvk k.0,a1ao lbance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N rests on alkk5ta1 *bkzjaqh9b z4i7x05 table. A rope tied to the box runs vertically upward over a pullek ztql z9ji*bkkax507 b51ah 4y and a weight is hung from the other end (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for l-r+vt fhu* yhe (0d fepz*55va 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 di6bs9e-q n5 nqragram of a baseball (a) at the moment it is hit by the bat, and aganqbsnr 9- 5e6qin (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a,tk2.-fi52vrr c kjis northwesterly direction. A second 650-N force must be exerted in what directio2ks .vj tik-ri5,f c2rn 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" o78 r4tgc j7kcdmj2cht 2mlspy-+ w3z0e-m;d strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is yodjcetm7;mk8w-d-p4 7 rcztc2sm2+gj hl 30 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 s x;jv/ m4x9,ip8sjv ;;e8jyczijd1 y 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 14.0 gpdi4n:dn.y/iu5 vy/ $-\mathrm{kg}$ 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 lo,f3oj kjs3s3a. zxft4cation at McMurdo Base, Antarctica, as shown in Fi,.ox 4jffzs333tjkasg. 4-46. The sum of the forces $\overrightarrow{\mathbf{F}}_{\mathrm{A}}$ and $\overrightarrow{\mathbf{F}}_{\mathrm{B}} $ exerted on the unit by the horizontal cables is parallel to the line L , and $ F_{\mathrm{A}}=4500 \mathrm{~N} $. Determine $ F_{\mathrm{B}}$ and the magnitude of $ \overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ .$F_B$ =    $\overrightarrow{\mathbf{F}}_{\mathrm{A}}+\overrightarrow{\mathbf{F}}_{\mathrm{B}}$ =   

A train locomotive is pulling two cars of the same mass b/ 3jopm7x.z rrk4z45bgxy dj8ehind it, Fig. 4-47 . Determine the ratio of the tension in the coupling between the locomotivb3o8djxg57r4kxj/rz4 yp.m ze and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparh- a vb:kgz9/hatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at conh b/zg-:a9khv stant 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 p0nq b3r,/nfd began, 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 u/ -3gi2k0+ ptb -h+ugqqgdjvblock (mass $ m_{1}$ ) on a smooth horizontal surface, connected by a thin cord that passes over a pulley to a second block $\left(m_{2}\right)$ , which hangs vertically. (a) Draw a free-body diagram for each block, showing the force of gravity on each, the force (tension) exerted by the cord, and any normal force. (b) Apply Newton's second law to find formulas for the acceleration of the system and for the tension in the cord. Ignore friction and the masses of the pulley and cord.

Three blocks on a frictionless horizontal surface are in contact with eac, e)fa/lt* cvgum x94eh other, as shown in Fig. 4-51. Aemct ux9a*lvgf/, e 4) force $\overrightarrow{\mathbf{F}}$ is applied to block 1 (mass .$m_{1}$) .
(a) Draw a free-body diagram for each block. Determine
(b) the acceleration of the system (in terms of $m_{1}$, $m_{2}$ , and $ m_{3}$ ),
(c) the net force on each block,
(d) the force of contact that each block exerts on its neighbor.
(e) If $m_{1}=m_{2}=m_{3}=12.0 \mathrm{~kg}$ and $ F=96.0 \mathrm{~N}$ , give numerical answers to (b),(c) , and (d) . Do your answers make sense intuitively?

  The two masses shown in Fig. 4-52 aki you2tn2;k0re 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 determk2ioun;0 2tk yine the acceleration of the lighter mass and then its velocity at the moment the heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes on a frictionless table are connected by a heav7r4w6 iyqyc ey;2 tw5iy cord of mass 1.0 kg . Calculate thewi4yy 5q6c;wt y72rie acceleration of each box and the tension at each end 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 kinetic friction bq( :e- 0*z 9wkzonafuhetween 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 requiredwy bj6;+xy.kg3 pm ua. 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 0.2hga ,o0z ,lg1:/7)i qlsd tzyl0g. What minimum coefficient of static friction must exist between your feet and the floor if you are not to slide?zatg:i ,yzl1 l,sl0/ )g7ohqd   

  What is the maximum acceleration a car can un0ojs-86c0d2j:xzyk;q gbtmb dergo if the coefficient of static friction between the tires and the grouno: 0 yskj-x08gzbdmj6 tq2b;cd is 0.80?   

  The coefficient of static friction h8,p; . sl3nhgrs n*gwfg(8zxbetween hard rubber and normal street pavement is about 0.8. On how steep a hill (man fgs8 wr,8ph zg.ghslxn *;3(ximum 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 /t mvtznz6-vv/;+e rbl.rv - wat -4.80 $\mathrm{~m} / \mathrm{s}^{2}$ without skidding when coming to rest on a level road. What would its deceleration be if the road were inclined at 13$^{\circ} $ uphill? Assume the same static friction coefficient.   

(a) A box sits at resvjvv-+s 90sfevzwz .7t 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 h-vo bkq(yci.a i3z1y8b; mqml; x :r/oigh coefficient of static f.vzrlbc;q1(aq3:ib mmy;ox y k8-/i oriction.

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 fol s1,v*,i7 t,:ysa7kalxo h ej1xry )riction for a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how largez 0oj l7 dtjxw9:rj.nq6la+: w a mass would box A have to have to prevent any motion from occurring? Assu+:j6tlq07 olajzjr9.x:wndw me $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slides acroad t iwhr h4yd382/3)m b-xoasss the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an in aaddt o2hxh8/ 33brm)wis y4-itial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contac 6q) 6ww*wys 5qjh,ue2akgm/mt and at rest on a horizontal surface (F*yw66he2,kmaq wwmj/s )g q5uig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy czdi o o.9 *;gba(7ugghrate. The coefficient of static friction between the crate and the bed of the truck is 0.75.*b zag dhgouo7(.9 ig; What is the maximum 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 uu6lrl; ij 7w8about parking your car in your driveway, which has an incline i6l7j; r8ulwu 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 with a 28;fapkl2u2 tm6r ry+/ k +hbr:z$^{\circ}$ incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.   

  The carton shown in Fig. 4-55 lies on a plane tilted at an rzlba6zi8 4acg0)4a bangle $\theta=22.0^{\circ}$ to the horizontal, with $\mu_{\mathrm{k}}=0.12$ . (a) Determine the acceleration of the carton as it slides down the plane.   
(b) If the carton starts from rest 9.30 m up the plane from its base, what will be the carton's speed when it reaches the bottom of the incline?   

  A carton is given an initial speed of 3.k04,5pedlj8d5 qitmu,vu ux6 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 spek +12 nhs r;uzj3yli25exz1pied 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 er y,d*.( bsnson it with a force directed upws.eb(nd,*syr ard 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 slipper mud)umw+p a61y roofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge o)wmpm1a6 u+ud f 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 stopp xd2f83icrr/ ving distance for an automobile traveling at speed v is eq3c8x2 frivd/rual 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 a-gwk 77 fbqy)o;pizsj6* nl 6dashboard of a car slides forward on the dash when the driver decelerates from 4z*pbfs-y6l)7;k 7jowa 6gin q5 $\mathrm{~km} / \mathrm{h}$ 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 giv7q. ftf2zo l2ch(* eywen 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 njrqstq7l:a3 k( jk1he*. 2ihconveyor belt from where they are filled to the packing station 11.0 m away. The belt is initially stationary and must finish with zero speed. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coeffiqj(tsh12 qehkrk n il:j.*3a 7cient 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 k(kxvm*:mr4f :aad1o ninetic 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 (inclprg1)u; gn)rl-h 5bf mqp9y(euding the bicycle) can coast down a 6.0$^{\circ} $ hill at a steady speed of 6.0 $\mathrm{~km} / \mathrm{h}$ because of air resistance. How much force must be applied to climb the hill at the same speed and same air resistance?   

  According to a simplified model of a mammalian heart, at each pbndn 6u0 av -*wynvd;qrx(8:wulse approximately 20 g of blood is accnb vq:0 -n v duw;dw(n*rxya68elerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chance of surviving an automobile-q k4 970huf-qynofquytvfg+b,r .. z crash if the deceleration is no more than 30 " g 's." Calculate t.n+4 9. qr y 07hbvquuffgy-o,-z fktqhe 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 zyru 1w4c+ 6eca , and if an object is going to "hold its place" on the ground, show that the coefficient of static friction with the ground must be atcue c4w1y+6rz 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 o p**zk7d (lckvf an accident involving two cars, measure 72-m-long skid marks of od(k*lvp7c* z kne 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 means that for m e75zdng:x8)roo/l)-avr td each 4 m traveled along the road, zxd 8d leao)-r) vn7/tmro:5g the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? (a) Ignore friction.   
(b) Assume an effective coefficient of friction equal to 0.10.   

  A 2.0-kg purse is dropped from the top of the Leaning Tomfnj5ec - ;2zjus(f l;h219 6pumstqhwer of Pisa and falls 55 m before reaching the ground with a speed of What was the hupn 95s-;qm1uf j mls6ecz2(h2ft j;average force of air resistance?   

  A cyclist is coasting at a steady speefsu*yjk 7qy76nx1ktwpl0r/ 2 d 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 without having to pedal if the mud lasts for 11 m? Iffys6x *k7ny lru/j1 2w7qkpt0 so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a hilly portt4+4v9s.m7os 3xrhbgx e +ghi ion of a city. An important consideration is howsgx+i+m9 bg74xo3 th hev4r s. 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 physics expd97 3yuk w/eszeriments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She notices that the string makes an kywd7uz s /39eangle 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 diff kbx 04k6obfurj 83g k949leoherent px hj6r0ooflg bu4k899 be4 k3karts of the store.
Customers will have to push grocery carts up the ramps and it is obviously desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force directed up the ramp is no more than 20 N . Ignoring friction, at what maximum angle $\theta$ should the ramps be built, assuming a full $30-\mathrm{kg}$ grocery cart?    $^{\circ} $

(a) What minimum force F is nee2 sp9:vgm2xu lded to lift the piano (mass M ) using the pulley apparatus shs 29g2 :uvmplxown 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 3.5 jsya jbw31) w1$\mathrm{~m} / \mathrm{s}^{2}$ 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-restraih:dl o2 gizf,ukc s 9sf4l4+3y 2nhj,gnt chair, an engineer considers the following set of cond4j 4d3:hyzlggssun+lf2ic9 ,k, o fh2itions:
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 Italiant;2,1 i/a:ysxx is ati 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 similary8hqud mth 01i ng 9 ,izb17hcv3qt;/q length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope,qi9g7t;n /h v18,tz3cqmh1qdbu iy0 h 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 usinc-j+ f+c twuq oc:)1hrg a " 10-1 $\mathrm{~b}$ test" fishing line. This means that the line can exert a force of 45 N without breaking (1 $\mathrm{lb}=4.45 \mathrm{~N}$) . (a) How heavy a fish can the fisherman land if he pulls the fish up vertically at constant speed? (b) If he accelerates the fish upward at 2.0 $\mathrm{~m} / \mathrm{s}^{2}$ , what maximum weight fish can he land? (c) Is it possible to land a 15-lb trout on 10-1b test line? Why or why not?

  An elevator in a tall building is allowed to r*,3lbo avi:mg6g2p grbo ;9epoc1.nabru+ 9ceach 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 ajfdb02( 0ywzg)kb kafy 4q1q *re roped together are ascending an ice field inclined at *ka 0g1dz0bfqbqkf4y 2j ()wy 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.