Why does a child in a wagon seem to fall backward when you give *;b /jenzf3nhf gfm ;.the wagon a sharp pug3 ;m.nh /fefbjnzf *;ll forward?

A box rests on the (frict-zo(4zhjoo i (ionless) bed of a truck. The truck 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) bho(oijz-z(o 4y Mary standing on the ground beside the truck and (b) by Chris who is riding on the truck

If the acceleration of an obje ircalh3cm /4.caqb*bvpf0 /;ct is zero, are no forces acting on it? Explain.

Only one force acts on an object. 3q jo5iix;)keCan the object have zero acceleration? Can it have zero velocity? Expl)5eik 3ixj qo;ain.

When a golf ball is dropped to t(b 9/ytfie6pz otk.b(q +v7pshe pavement, it bounces back up. (a) Is a force needed to make it bounce back up? (b) If so, whatzb q9o pf( i/p+tyvk7(ebt6.s exerts the force?

If you walk along a log floati;;k 4yt+gbaylg )hs+q ng on a lake, why does the log move in the opposite direct t;;+hl+yyagk4sg)b qion?

Why might your foot hurt if you n,yo*+r tm h k.uun6sy(fvx +rj35j *2j4k nhckick a heavy desk or a wall?

  When you are running and w6 2/l,)wpl9(xzjclq2g 5ygb3b sfjg iant to stop quickly, you must decelerate quickly. (a) 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 bypl/g2362fj5blig c9 ls wx(z,)j gq to come to rest.    m/s${}^2$

A stone hangs by a fine thread from the ceiling, and a section of e43 r/jx*sbq xley0:zp*ty0 bthe 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 xzeel*pq 4j3y/y 00b :* xrstbto break: below the stone or above it? What if the person gives a slow and steady pull? Explain your answers.

The force of gravity on a 2-kg rock is twice as great as that on a 1-kg ryy az+ *h9iknur fn*6,ock. Why then doesn’t the heavier roc nnyr9*z y+u,*6aihfk k fall faster?

Would a spring scale carried to the Moon give accuratevmd8 luu n.7ws6jl g29 results if the scale had been calibrat 6 lnu97vw.m8sujlg d2ed (a) in pounds, or (b) in kilograms?

You pull a box with a constant fodqi ktln95u66c2m84gagi b t6rce across a 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) remain the same, (b) increase, or (c) decrease? Expik96lbg54qmi86 adut26nc t glain.

When an object falls freely under the influence of gravity there ibx945bz kc /vrs a net force mg exerted on it by the Earth. Yet by Newton’s third law the object exerts an equal an4r bv9bxk5c z/d opposite force on the Earth. Why doesn’t the Earth move?

Compare the effort (or force) needed to lift a 10-kg objecs5:pn1 8k mcg ro+lyi7t when you are on the Moon with the force needed to lift8mgr:5cnkso p1yi7l+ it on Earth. Compare the force needed to throw a 2-kg object horizontally with a given speed on the Moon and on Earth.

According to Newton’s third law, each team in a tug of war (Fig. 4–37) pulls *w7+sjxc66hjomtf :sd)ug, m with equal force on the other team. What, then, d md,6*xjujco 67:+gm)sthws f etermines which team will win?

A person exerts an upward force of 40 N to y6gqjjw;c6 79gwv c 9wz-ul 9ghold a bag of groceries. Describe the “reaction” force (Newton’s third law) by stating (a) its magnitude, (b) its direction, (c) on what o;6wg6cuzlv7 9wjcg9- g wqjy9 bject it is exerted, and (d) by what object it is exerted.

When you stand still on the groun6,xg f1dqwj7y qlh3g8)i-yoqd, how large a force does the ground exert on you? Why doesn’t this force make you rise up into the1g7qqd3y6 qyl8ho) jx w gf-i, air?

Whiplash sometimes results from an ausk u9a xz8d+jcx9:0a ,48 txi5naqhj etomobile accident when the victim’s car is struck violently from the rear. Explain why the head ofaxt0z kh+8:9xc4iea5, ax8u qd9 jsnj the victim seems to be thrown backward in this situation. Is it really?

A heavy crate rests on the bed of a flatbed truc3qia1wd 15 book. When the truck accelerates, the coq bd3i51ow1a rate 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 thatr0 suid,i1k5c 2zaof4 ip5,t-ycqi+e it slides up a ramp. After the block reaches its highest point, it slides ci1+os a5 izfrqy5kti,0u,4c 2-depiback down but the magnitude of its acceleration is less on the descent than on the ascent. Why?

What would your bathroom scacnn)f t(* +y2 p9pbr sppgr;y8le read if you weighed yourself on an inclined plane? Assume therrgn8;9 stc*+ y byn2fp(ppp) mechanism functions properly, even at an angle.

  What force is needed to accelerate a childv 6bbgfhb32ry drq pmaz+6,. 1 on a sled at 1.25m/s${}^2$?   

  A net force of 265 N accelerates a bikedxv8 qg1qetkiq:7-0kb z s2o fd,0m. m 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 96 .jv0*pk7 izf+) sxian0$-\mathrm{kg}$ car horizontally along a frictionless surface at 1.20 $\mathrm{m}/{\mathrm{s}}^2$ ?   

  What is the weight of a ;dxo7g 8lv6pjy f:ka)3 eyy c; $76-\mathrm{kg}$ astronaut
(a) on Earth,   
(b) on the Moon $(g=1.7\mathrm{m}/{\mathrm{s}}^2)$ ,   
(c) on Mars $(g=3.7\mathrm{m}/{\mathrm{s}}^2)$,   
(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 toh + hpe:-er9 onlhj+i7 stop an 1100-kg car in 8.0 s if the car is traveling at 95km/h? hp 9hh+ije-e : 7n+lor-  

  What average force is needed to accelerate a 7.l6p gkh,w m5e *xu.vt,00-gram pellet from rest to 125m/s over a distance of 0.800 m alonw ,,mul.* 5 pkte6ghxvg the barrel of a rifle?   

A fisherman yanks a fish vertically out of the water with an acceleration of )d8lxp0 jc)a k2.5 jp xl)ad8k0)c $\mathrm{m}/{\mathrm{s}}^2$ 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 can4e5xhafc6 -ymkdus5p;j199t1 sv o mm 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 ) is1z;/id m3hlvck/ kd(s to be designed so that the maximum acceleration is 0.0680 g . What are the maximum and minimum forces the motor should exert on the supporting cadild3 /k/ 1m(k;cvzhsble? 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. Whenxr/)piqi)vp9u7 : *-d of: 9csbxqox n the elevator begins to move, the scale briefly reads only 0.75 of the person’s regular weight. Calculate the acceleration of the elevator, and find the dir::sd r9 /xop)x q i*-fin9co)pubvxq 7ection of acceleration.     ----待选择----downupward 

  The cable supporting a 2125-kg elevator has a ma )l2 ws3-nqupaximum strength of 21,750 N. What maximum upward acceleration can it give the elevator w-l)pn3suqa 2 without breaking?    ( two decimal places)

  (a) What is the acceleration of n uu9 n5oyms7w1h 0wo5two falling sky divers (mass 132 kg including parachute) when the upward force ow7ou0wyn 15 su59hmn 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 grw tvxv 3 (7,yqrmcy; avwf0+v.ound below, he bends his knees sovcy0a.r(7; x vmtvqy+3 fww v, that his torso decelerates over an approximate distance of 0.70 m. If the mass of his torso (excluding legs) is 42 kg, find
(a) his velocity just before his feet strike the ground, and   
(b) the average force exerted on his torso by his legs during deceleration.   

  A box weighing 77.0 N restscj+ c,n3sn l(e on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other csc, +n ln(e3jend (Fig. 4-40). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs
(a) 30.0 N ,   
(b) 60.0 N ,   
(c) 90.0 N .   

Draw the free-body diagram for a baskpobz3q:*8iy7dku1q y etball 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 7wu c102b u4nb6fj8))e/oonfx0jrd p / b mfyithe moment it is hit by the bat, and again (b) after it has left the b8 wfx/b n j)0i )pbfo jrd/1meonyubcf0264u7at and is flying toward the outfield.

A 650-N force acts in a northwesterly direction. A second 650-N fo:;k 0ix rdw5w9z lnf/srce must be exerted in what direction so that the relf 0zix;s: w/5rkd 9nwsultant of the two forces points westward? Illustrate your answer with a vector diagram.

  Arlene is to walk across a "high wire" strung horizontally betwedv:w vv6iv+ /uo dt /jd2n+yg0en two buildings 10.0 m apart. The sag o d/vd:t2 6dj0igv/yu+ v nv+win the rope when she is at the midpoint is 10.0${}^{\circ }$ as shown in Fig. 4-42 . If her mass is 50.0 kg , what is the tension in the rope at this point?   

  The two forces ${\overrightarrow{\mathbf{F}}}_1$ and ${\overrightarrow{\mathbf{F}}}_2$ shown in Fig. 4-43 $\mathrm{a}$ and b (looking down) act on a 27.0$-\mathrm{kg}$ object on a frictionless tabletop. If $F_1=10.2\mathrm{N}$ and $F_2=16.0\mathrm{N}$ , find the net force on the object and its acceleration for (a) and (b). (a) a =    at    ${}^{\circ }$;(b) a =    at    ${}^{\circ }$

  One 3.2-kg paint bucket is han.cup ;f;;a4fhu3z xox3l 6gc wging by a massless cord from another 3.2$-\mathrm{kg}$ paint bucket, also hanging by a massless cord, as shown in Fig. 4-44.
(a) If the buckets are at rest, what is the tension in each cord? F1 =    F2 =    (The top rope is F1 and the bottom rope is F2)
(b) If the two buckets are pulled upward with an acceleration of 1.60 $\mathrm{m}/{\mathrm{s}}^2$ by the upper cord, calculate the tension in each cord. F1 =    F2 =   

  A person pushes a 14.pftaj mlgr+l9- 99jk 0 0uw4zb0$-\mathrm{kg}$ 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 McMrsz3-cz ml+7t4upfev8 w3 l;curdo Base, Antarctica, as shown in Fig. 4-46. The sum uz; 7rc3tflwz3 v-+l8c ps4me 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 it, ;)v u)qy3dla2 l gki5gFig. 4-47 . Determine the ratio of the tension in the coupling between t lla)2kuv3q;i gg)5dy he 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 d*u:a g.k 6;hvcl6j vuusing the bucket-pulley apparatus shown in Fig. 4-48. (a) How hard must she pull downward to raise herself slogjd uc. 6lvh *;6:vkuawly at constant speed?   
(b) If she increases this force by 15 % , what will her acceleration be? The mass of the person plus the bucket is 65 kg .   

  At the instant a race began, a lr*95xe+;w xqgcg)yf0fn u5x65$-\mathrm{kg}$ 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 blo+ps1eky +v8xhz3f rz1ryld0 /ck (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 ard2n6. /*u 5cw e*t .oktl (qfa,1dzgku :nhsvze in contact with each other, as /.e(26c :z*h 5nu,u*l t.asndgwvdtk zk 1qfo shown in Fig. 4-51. A 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 are 28vdl4 ty yu9sz8r ;1x:vwnxg each initially 1.80 m above the ground, and the massless frictionless pulley is g18rvyu;s4nvx t2xwly 8zd9 :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 are connectef(usr , gba f )kailf;p-1/y8yd 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 /k) lb8 f(ayr f,;isg-1yfapu 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 between a9g7) ir mny4ov kbp9:vpuv, a5 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 a 53s) nxr9k pn0,-pvpda.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 minimu -v bjvme.kc c04z42m0of8 cucm coefficient of static friction must exist bcc8-2m ke.bo4 umzvvf j0cc04etween your feet and the floor if you are not to slide?   

  What is the maximum acceleration a car can undergo if the coefficient of static j e4a0o/ddb )wfriction between the tires and thb d4wado)je/0e ground is 0.80?   

  The coefficient of spe8 a*8m59gj e)vpm vkzg c*6btatic friction between hard rubber and normal street pavement is about 0.8.e698* 8c pz)ke* vmjmabgvgp5 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 aco(o,ry su:p2 c :aj/pbg g;*st -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 rest on a rough 0b-s g88d- duvn h 5lu:lnwkxbx* h.y330${}^{\circ }$ 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 conwklcna(-a;5a 7yv fh 0tact with an asphalt surface have a very high coefficient o( w afnck;v0ly5a- h7af 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 friction for as ,5kw;v xy8je $22-\mathrm{kg}$ 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 larg irm*lc)ma9 8bvg x 9o5v9g4j0: wqzhae a mass would box A have to have tovim) m9*rcgla 9ag40v8 oq59hxbw zj: prevent any motion from occurring? Assume ${\mu }_{\mathrm{s}}=0.30$ .   

  A box is given a push so that bk 6edjon,pch3m4nrwh j(kvuo) );: :it slides across the floor. How far will it go, given that the coefficient of kinetic friction is 0.20 and the push imparts an initial speed ofon :;)cwkv6 u:njdbk, j4m ) 3ohpe(hr 4.0 $\mathrm{m}/\mathrm{s}$ ?   

  Two crates, of mass 75 kg and 110 kg , are in contact and at rest on a horizontep9 )u c3gf;xfal surface (F c fx9eu;)3fgpig. 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.l6,cs5 z:b * :ejsfppj a*yub 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 which the driver can decelerate and still avoid having the crate slide again pesslzbby5ca:f p u6 jj:.**,st the cab of the truck?   

On an icy day, you worry about parking your car jlw+i nmjy4k,8u1) wp in your driveway, which has an inclineji8 l ,)wmynjw4u1k+ p 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 slik; *z y;rtop ji)c)7izde 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 tilted at an anglezzqee/yaqnb zm5 * 275 $\theta ={22.0}^{\circ }$ 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 ivqz;i8y ju op h;h2+pxj d)l,+nitial 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 reachm.oykt+ / io;jes 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 bp1e tf/zmjs /hx,;o0lj +vws4y someone pushing on it with a force directed upward at j4tmlhses0w,1zj+/vo ;p /fx 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 dange.3dwq s y4/owakiq m12rous projectiles as they melt. Consider a chunk of snow at the ridge of a roof withom1y3s/ q kw2w.4daiq 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 dir em1wdviriwad;kmz 1g1/2bq(/)x ,rstance for an automobile traveling at speed v is)/(11 ermkmwgr d qa,r;z biid12w/vx 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 slides forward on the dash p0be642a+z fvzy .smtwhen the driver decelerates from 44y+m 02aez 6fptz.s bv5 $\mathrm{km}/\mathrm{h}$ 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 speed v*p;8k6 hinoj$v_0$ 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 packinsf j*2agt uk7sugel) cp*,0vd7 u8n x+g 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 accelere2 07uud,nsf8)ks a7*jup cvg*gl+txates for half the distance, then decelerates for the final half of the trip. If the coefficient of static friction between a box and the belt is 0.60, what is the minimum transit time for each box?   

A block (mass $m_1$ ) lying on a frictionless inclined plane is connected to a mass $m_2$ by a massless cord passing over a pulley, as shown in Fig. 4-57. (a) Determine a formula for the acceleration of the system of the two blocks in terms of $m_1$,$m_2$,$\theta$ and g . (b) What conditions apply to masses $m_1$ and $m_2$ for the acceleration to be in one direction (say, $m_1$ down the plane), or in the opposite direction?

  Suppose the coefficient of ki) mmw7l da8a3pnetic 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 a6u/ kw(fs9 +msb1k e,fid a7bp/yl l8kg (including 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::y tim,w nfq 8 rhv:*tv9:ioq pulse approximately 20 g of w: f9ri :,qn*8vyq:ithvtmo :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 chance of surviving an automobile crash ift52r(;d3 p ewbotya4 h the deceleration is no more than 3;(owh 4 pab3y5dte2t r0 " 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 an objecmoznkbyf02oh 4 o6xy8; )v l5ct is going to "hold its place" on the ground, show that the coefficient of so oyf4vh5; zockxlnmy)82 0b6tatic 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 invol sti p yd96l7yjqnq-zs0st c5:h f8t/3ving two cars, 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 s70qn t-pz:ij5cydf/9htslys 386 qt.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 f*dzx9vdenzt/jm +f 7xpd++6l or each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after travevpt+6*xzfl9 d+/dj nm+x ez7d ling 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 L0 /) a,niyoak/xdyj b8eaning Tower of Pisa and falls 55 m before reaching the ground with a speed of What was the average force of aidnbx) kya 0,/aj8i/yor resistance?   

  A cyclist is coasting at eua:ptm 8)f,,iuw3sv jk3 (tfa steady speed of 12m/s but enters a muddy stretch where the effective coefficient of friction is 0.60. Will the cyclist emerge from the muddy stretch without having to pedal if the mud lasts for 11 m? Iittm:)j fu3 8u,ks3vfw ,(e paf so, what will be the speed upon emerging?   

  A city planner is working o .6khqyjie,zb zv0 5;tn the redesign 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 slv;j.,0z zqk6hti bye5owing 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 experi-gl xh3t.)y qm ovr-b*q+tua,ments, dangles her watch from a thin piece of string while the jetliner she is in takes off from JFK Airport (Fig. 4-58). She no*mbat-+, .)h3rqquyv- olx tgtices that the string makes an angle of 25${}^{\circ }$ with respect to the vertical as the aircraft accelerates for takeoff, which takes about 18 s . Estimate the takeoff speed of the aircraft.   

  A 28.0$-\mathrm{kg}$ block is connected to an empty 1.35$-\mathrm{kg}$ bucket by a cord running over a frictionless pulley
(Fig. 4-59). The coefficient of static friction between the table and the block is 0.450 and the coefficient of kinetic friction between the table and the block is 0.320 . Sand is gradually added to the bucket until the system just begins to move. (a) Calculate the mass of sand added to the bucket.   
(b) Calculate the acceleration of the system.   

  In the design of a supermarket, there are to be 23ww gwk+ /jeqseveral ramps connecting differentwq ke 3w/2gwj+ parts 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 needed to lift the piano (mass M ) ugns68z f g:w1qwe/p -:aq;vbrsing the pulley apparatus she; qagq1 gf6vn8z: s pwb/w:-rown 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 accelera7 :,mq,kanhye ting 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-reny8e4g9x9 t ljstraint chair, an engineer considers the following set of conditi n jy489etlxg9ons:
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 6,ii9bt ; 5wvbl60 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?