Why does a child in a wagon seem to fall backward whenn3-cnf9u/so bhil e ,,lxf,/p you give the wagon a sharp pull forwardbeox c3,-i,uhnslf/p9n/, fl?

A box rests on the (frictionless) bed of a tr08.f9oa rpms huck. The truck driver starts the truck and accelerates forward. The box imm 08os9far .hpmediately 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, aw+q(1vw j4;y4t(rj z x+ xxjifre no forces acting on it? Explain.

Only one force acts on an object. Can the object have zero acceleraf7 1fmg1 izdk*tion? Can it have zero velocity? Expl71igdfz* 1mkf ain.

When a golf ball is dropped to the pavement, it bounces back up. (a) ffo .*zkan jz .bj*c1h3bl/to 81jk0eIs a force needej/b8enatk.k fo0z l1 .ofhcz*bj31* jd to make it bounce back up? (b) If so, what exerts the force?

If you walk along a log floating on a lake, m(+5hr wn68gr,i9am 2wgnlkn why does the log move in the opposite dirn 8+r (9hmmgw, ga wlrn265kinection?

Why might your foot hurt ifcv5mh+ (2q w ldqj0rr8 you kick a heavy desk or a wall?

  When you are running and want to stop quickly, you must decelerate w4ap-e 0 ay2/lq+x6osr8x dwbquickly. (a) What is the origin of the force that causes you to st 6ap q +wre2xasw0 xlboyd4-/8op? (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 a sej1octlb s,0vm*gr/bxixw)/ ; ction 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 answosx/0j*w/1 ;bvt g,c mbxr li)ers.

The force of gravity on a 2ilac3c79kimjv:6 c q:-kg rock is twice as great as that on a 1-kg rock. Why then doesn’t the heavcm37: acqkl i6c: j9viier rock fall faster?

Would a spring scale carried to the Moon give amzd b y7ym3u626 qf-8s;mnzxt psv1 0yccurate results if the scale had been calibrated (a) in pounds, or (b) in kilmm v -b2y68u x npqzd fsy7m603sty1z;ograms?

You pull a box with a constant force across a fricmkm, vo71*5h (n0 nclkx(jjsationless 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),5 xmkmh j(1s,o0k* nc(lnv7 aj does the acceleration of the box (a) remain the same, (b) increase, or (c) decrease? Explain.

When an object falls freely under the influence of gravity there is a net xahsxa+)w5 :pforce mg exerted on it by the Earth. x):x5asp+w ahYet by Newton’s third law the object exerts an equal and opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or fo,+3pwolsyc.u aew3 j 3rce) needed 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 es3a ,+3lpyjc ow3 .wu2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s t tbwlhd: 9*opjl8 k-5.ibr c8chird law, each team in a tug of war (Fig. 4–37) pulls with equal force on 8bcpr5 :d cl*9t8k -.boi ljwhthe other team. What, then, determines which team will win?

A person exerts an upul yu8 iz(p. nik 8)io5e2u.nkward force of 40 N to hold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on58ko.iui n ly u(u.)p28kize n 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 exert (:jm)w dm(;nw )f/dm jylyj j:on you? Why doesn’t this force make you rise up into the air? j(wyd ;/:)wm(mljnjdmj fy:)

Whiplash sometimes results from an automobile accident when the victim’s car i:6 7ms/zok ,ebas b;kj8mkc:t s strucktkkbmbs/:e 7zs ;6k:am8 cj ,o violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a fxu;oxmuw2c n;++.nmtpa 9 x.v latbed truck. When the truck accelerates, the crate remains where it is on the ax+.2 n.w n9uuv;pxm;+t ocmxtruck, so it, too, accelerates. What force causes the crate to accelerate?

A block is given a push so that it slides 1 ;ecyi (eip9zup a ramp. After the block reaches its highest poin y;i (ip9e1zcet, it slides back down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom szasvo dvj .8xy - sqm*4l(o74icale read if you weighed yourself on an inclined plane? Assume the mechanism functions properly,djsolizx48y v ma*7- (s. o4qv even at an angle.

  What force is needed to accelerate a chi o5h 5,e7mbbxnld on a sled at 1.25m/s$^2$?   

  A net force of 265 N acv3h f(nhpb43ncelerates a bike and rider at 2.30$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the mass of the bike and rider together?   

  How much tension must a rope withstand if it is used to accelerate a xwar+9w,qw.l,xot7 2 alz( wx 960$-\mathrm{kg} $ car horizontally along a frictionless surface at 1.20 $\mathrm{~m} / \mathrm{s}^{2}$ ?   

  What is the weight of a q6 2 6.nzz;lhe4s ,f;nctgyow $76-\mathrm{kg}$ 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 requi,zt2o6u/)v iyhe ))-mvqbsk ored to stop an 1100-kg car in 8.0 s if the car is traveling at 9svy-t/uhko, 2ve 6zm)q bo)i)5km/h? -  

  What average force is needed to accelerate a 7.00-gram peli c7zxb no)9 w6e35ktclet from rest to 125m/s over a distance of 0.800 m along the barrel of a rifle?o6b 9weic)x 3cn75tkz   

A fisherman yanks a fish vertically out of the water with an acceleration of d5xe 7.xapeac ;ens/3.sxo x(ds3 j 9j2..c93x3ed x(j5/ejpa ;ds7se xxoa. ns5 $\mathrm{~m} / \mathrm{s}^{2}$ 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 qui y:va sh(kpd,db +xk19(- i2dbzjns3arter-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 accelerat43nvv q3do bl)g*p,hj(/ u ivuion is 0.0680 g . What are the maximum and 4h/bljuvnu3 d, *3qvvi)o(gp 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 motio/54avyi .r()beusxsj nless elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the el j5r.ussb()y/a v4ixe evator, and find the direction of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-o8 22hvg;pj wzkg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give hg2 wzv8pj2o;the elevator without breaking?    ( two decimal places)

  (a) What is the acceleration of two falling sky diq4 fx)z h,g-hp45aymovers (mass 132 kg including parachute)-, ph xyf 4ozm)a4qg5h when the upward force of air resistance is equal to one-fourth of their weight?   
(b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?    See Fig. 4–39.

  A person jumps from the roof of a house 3.9-m high. When he strikes the gr(9r(* +coagabci mr9kound below, he bends his knees so that hisrr c(g+aic9a (*9ok bm 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 on a table. A rope3oh8 na3t xcj 0akfb1fa+3j0t 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 tanc30k83jf hoft aaxt0aj+3b 1 ble 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 basketba ntxo9o b(-yg2ll 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 sj-2.r1ft c:8xc twe tit is hit by the bajc:x 1twsc28. fet -rtt, and again (b) after it has left the bat and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 6 ;*fri ac96kkr5jsmdiz 2g:7y50-N force must be exerted in what direction so that the resultant of the two forces points westward? Illustrate your answer with a vector diagramm 2*dk6a5 z irsr;g kyf9:7cji.

  Arlene is to walk acrotz3x 7yfdm) kc-h50bv ss a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is c y 5hdftz 30)b7mkx-v10.0$^{\circ}$ 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 wmzs x+l gg(lvm 807+v3.2$-\mathrm{kg}$ 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 1 fky;fn 0xd pbx7+v(*s4.0$-\mathrm{kg}$ 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 B4usk*jp g;7jbase, Antarctica, as shown in Fig. 4 kjs4g7*pu; jb-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 behind ifo mj5)-u3u bvpc : qtq/bk: t9 gfipa0e2/wg6t, Fig. 4-47 . Determine the ratio of the tension in the coupling betwqju69 f2 a//b-ft0vi5:c te3 kpgmu: qopw gb)een the locomotive and the first car $\left(F_{\mathrm{T} 1}\right)$ , to that between the first car and the second car $\left(F_{\mathrm{T} 2}\right)$ , for any nonzero acceleration of the train.

  A window washer pulls herself upward using the bucket-pulley apparatus showf1dq6 ojf u5-yn in Fig. 4-48. (a) How hard must she pull downward to raise herself slowly at constd5fq 6-1ofujy ant 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 b3ni t(zw5wh(l1 0elciq x/1xgegan, 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 foa5j,zyageas944s 6huy.m5 (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 friccblzkh+o,i3d7 cuv : ht g)xi-8tei ,:tionless horizontal surface are in contact with each other, as shown in Fig. 4-51. A force xk:tcvl: c,z-biegu8h+) 7 iodh3t,i $\overrightarrow{\mathbf{F}}$ 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 initiamw.qp p.r b5kahv6l71 lly 1.80 m above the ground, and the massless frictionless pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? [Hint: First determine the acceleration of the lighter mass and then its velocity at the moment th1.prb65k aq p .whvm7le heavier one hits the ground. This is its "launch" speed. Assume it doesn't hit the pulley.]   

Suppose two boxes onciq ,mp/h+0zp9 ahv6b,hgmp6 a frictionless table are connected by a heavy cord of mass 1.0 kg . Calculate the accelerationm,9v 0q,c 6gb p+hzm p/ap6hhi 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 frictio q 8a;cakg01oin between a 35$-\mathrm{kg}$ crate and the floor is 0.30 , what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_{\mathrm{k}}$ is zero?

  A force of 48.0 N is required to start abj,o+b (d1-h*nwcuo,h c aq2g 5.0$-\mathrm{kg}$ box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor?   
(b) If the 48.0$-\mathrm{N}$ force continues, the box accelerates at 0.70$ \mathrm{~m} / \mathrm{s}^{2}$ . What is the coefficient of kinetic friction?   

  Suppose that you are standing on a train accelerating at 0.20g. What minimuto07x,hpi6q yanv+r 3 m coeffi+h6p y,a 30xtn7ivo rqcient of static friction must exist between your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficien 5q.x .ey0arkrt of static friction between the tires and the ground arry0kq.e.x 5 is 0.80?   

  The coefficient of static friction +jplnq,a0 qa:j9le;abetween hard rubber and normal street pavemenalln+ q ,pj0a9:e;j qat is about 0.8. On how steep a hill (maximum angle) can you leave a car parked?   $^{/circ}$

  A 15.0$-\mathrm{kg}$ box is released on a 32$^{\circ}$ incline and accelerates down the incline at 0.30 $\mathrm{~m} / \mathrm{s}^{2}$ . Find the friction force impeding its motion.    What is the coefficient of kinetic friction?   

  A car can decelerate at -4.6tw+yd3b5 (7 gnboc).c bztoz80 $\mathrm{~m} / \mathrm{s}^{2}$ 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 m/b+4qb tcv;r * isdgj2p7ukw+vq .k (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 wwviu)xzfbn ) 2py0 g6;ith an asphalt surface have a very high coefficient of staty bx)g; fvu0iw2)np6z ic 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 friction fo(uw7xsqv 2+qel0 t* thr a $ 22-\mathrm{kg}$ bobsled on a track is 0.10 . What force is required to push it down a $6.0^{\circ}$ incline and achieve a speed of 60 $\mathrm{~km} / \mathrm{h}$ at the end of 75 m ?   

  For the system of Fig. 4-32 (Example 4-20) how large) -jdn-w n(akr a mass would box A have to have to prevent any motion fro) djak nwr-(-nm occurring? Assume $\mu_{\mathrm{s}}=0.30$ .   

  A box is given a push so that it slidesnt 7dlluk8o0 +4dhmi,lbte 2 1 across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 al l7+ie dtdnl8m10b24 otku,hnd the push imparts an initial speed of 4.0 $\mathrm{~m} / \mathrm{s}$ ?   

  Two crates, of mass 75a9 s/*svqjwy3vgtk q2./g*nz kg and 110 kg , are in contact and at rest on a horizontalq*z k*3g j2qvwsg/y anvt9/. s surface (Fig. 4-54). A 620$-\mathrm{N}$ force is exerted on the 75$-\mathrm{kg}$ crate. If the coefficient of kinetic friction is 0.15 , calculate
(a) the acceleration of the system,   
(b) the force that each crate exerts on the other.   
(c) Repeat with the crates reversed.   

  A flatbed truck is carrying a heavy crate. The coefficient of static friq0 *q uq2wgv-zction between the crate and the bed of the truck is 0.75. What is the maximum rate at which the driver can decelerate and still avoid having the crate slide against the cab of the u0wgqzqv2* -qtruck?   

On an icy day, you worry about parking your car in younw* cv hcam-f*eu+ a p:b**a4ur driveway, which has an incline of + fcvpn- a mhe*ucb4a**w* ua: 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 sli;rqwi(ft)jb: s 8z5 dtf y)td:1fzy(sde 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 tilted45 xjgafzpt(o 0rmf,. 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 speed of 3.)0g df 7w apkbr2xz0v.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 hill0 dg yfu/ifa6jz65rr*/smqz , 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 ah4q 3)2efde d4(2gj7fqckwqmgainst a rough wall by someone pushing on it with a force directed upward at(gdhqf32fe4wdm q7 )2j4ek cq 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 roz kwj8 f ioh;zh ;/x3ya5cs+498bwjakofs can become dangerous projectiles as they melt. Consider a chunk of snow at the ridge of a roof kohj4;jcabz 5;wyf wih 8 9/x+k8z3 sawith 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 minimuix ;n4yroa76km stopping distance for an automobile traveling at speed v is equal to a6xrkn 47;ioy $v^{2} / 2 \mu_{\mathrm{s}} g $, where $ \mu_{\mathrm{s}}$ is the coefficient of static friction between the tires and the road, and g is the acceleration of gravity.
(b) What is this distance for a 1200$-\mathrm{kg}$ car traveling 95 $\mathrm{~km} / \mathrm{h}$ if $\mu_{\mathrm{s}}=0.75$ ?

  A coffee cup on the dashboard of a car slides forward on the dash when the drn :tgs0rw cyt-df+*tw(jh5a(iver decelerate-* wt +h(d 5wgcjrfy0(tsnt:as from 45 $\mathrm{~km} / \mathrm{h}$ to rest in 3.5 s or less, but not if he decelerates in a longer time. What is the coefficient of static friction between the cup and the dash?   

A small block of mass m is given an initial+acgln+bdlsl -u( ni52 twz3 8 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 to the packing lt9j 88 yllkhcyw uq)4/ 850nu s9/+p cixyywystation 11.0 m away. The belt is initially stationary and must finish with zero speelxci jp+nuc/k8 thus90 y8 w/lyy5wl y )4yq98d. The most rapid transit is accomplished if the belt accelerates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_{1}$ ) lying on a frictionless inclined plane is connected to a mass $ m_{2}$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $ m_{1}$,$ m_{2}$,$ \theta $ and g . (b) What conditions apply to masses $m_{1}$ and $m_{2}$ for the acceleration to be in one direction (say, $m_{1}$ down the plane), or in the opposite direction?

  Suppose the coefficient ogz0d ku j( qyq*dh8a4apj ;8q7f kinetic 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 (incqpb4t(i 83kk7c y(z5l2,u vaiz;cj wqluding 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 o8w 5 v9kmjvt3) .2vmyejzcj5bm-c q8a mammalian heart, at each pulse approximately 20t mjcm w2mjyq5jo)v98e3bvk . cv5-8z g of blood is accelerated from 0.25 $\mathrm{~m} / \mathrm{s}$ to 0.35 $\mathrm{~m} / \mathrm{s}$ during a period of 0.10 s . What is the magnitude of the force exerted by the heart muscle?   

  A person has a reasonable chanc8p,l-lcth8q v e of surviving an automobile crash if the deceleration is no more t q th8c,p-vll8han 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 earthquakefcn,; x-xesm. is a , and if an object is going to "hold its pl-;, xs c.fxnmeace" on the ground, show that the coefficient of static friction with the ground must be at least $\mu_{\mathrm{s}}=a / g$ . (b) The famous Loma Prieta earthquake that stopped the 1989 World Series produced ground accelerations of up to 4.0 $\mathrm{~m} / \mathrm{s}^{2}$ in the San Francisco Bay Area. Would a chair have started to slide on a linoleum floor with coefficient of static friction 0.25 ?

  An 1150$-\mathrm{kg} $ car pulls a $450-\mathrm{kg} $ trailer. The car exerts a horizontal force of 3.8$ \times 10^{3} \mathrm{~N}$ against the ground in order to accelerate. What force does the car exert on the trailer? Assume an effective friction coefficient of 0.15 for the trailer.   

  Police investigators, examining the scene ur lc2-i.j m9gof an accident involving two cars, measure 72-m-long skid marks of one of the carur mjcgl9.-2 is, 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 (1ois 5mt3z ts0--in-4 means that for each 4 m traveled along the road, the elo3sis t- 5mtz0evation 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 thh 4zj82pkgl3w:lu +t3nesl9r1b ay k,e top of the Leaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of air resistance? gy: h,zw enpua1r+843b2 3sl t jklkl9  

  A cyclist is coasting at a steady speedydyl7x etnx+w4 ss;:6 of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the y;67e xdy4x:lnt w+s scyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? If so, what will be the speed upon emerging?   

  A city planner is working on the redesign of a 6br7y/ 9ockoz;rehm5st 2x1l 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, with a mass of 1100 kg , can accel6oscrk2/zh1 9o5 mxlb7yr; e terate 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, danl.8 qhxtz*8ju gles 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 thu*lt8xqj z8h .e 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,xosjw1 kfc28( there are to be several ramps connecting different parts 2w (sf8o jkcx1of 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 forc9 uxzfvt v9)vx,gv :cs -rvn)/e F is needed to lift the piano (mass M ) using the pul :,vvrx-/v9c fnv))xs zv gu9tley 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 ac/c wd9aw wwio644r2;/tf uxmi o)ex:i6dhpw/celerating at 3.5 $\mathrm{~m} / \mathrm{s}^{2}$ at an angle of 45$^{\circ} $ above the horizontal. What is the total force that the cockpit seat exerts on the 75$-\mathrm{kg} $ pilot?    N    $^{\circ} $

  In the design process for a child-restraint chair, an eng6 fbddr)y/n+cou5/m a 6u0iug ineer considers the following set of condit6) +5r uu/did bcy/o6famug 0nions:
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 Italmfiosz6a /+-6aj; kyt r,on:o c sa ;aym89f9zian train has a mass of 660 metric tons (660,000 $\mathrm{~kg}$) . It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum velocity ( 300 $\mathrm{~km} / \mathrm{h}$) , it exerts a force of about 150 kN . Calculate (a) its maximum acceleration   
(b) estimate the force of air resistance at top speed.   

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

Two rock climbers, Bill and Karen, use safety ropes of similar length. Karen a1i6l0uls q ngp 6r7f0tla;sx2t8h3w's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not rea uql sahn2 xr0gptf;s3t8l1l66w7i 0 commended 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 usin mj6qt16cd2cfg 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 tc5,rxyvz0 d -vo reach a maximum speed of 3.5 $\mathrm{~m} / \mathrm{s}$ going down. What must the tension be in the cable to stop this elevator over a distance of 2.6 m if the elevator has a mass of 1300 kg including occupants?   

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

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

  Three mountain climbers who are roped together are ascendi03i dw 5 8:yfu/aa ycldu(9lik- 9wopnng an ice field inclined at 2wauf-:auk y8c9(/3diliw lpoy 5 d 9n01.0$^{\circ}$ 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.