In what ways is the word “worzmv5a r/ 3rx.wk” as used in everyday language the same as that defined in physics? In what z.r3 5vm xa/rwways is it different? Give examples of both.

Can a centripetal force ever do work on an object? Explain.u0 cxl. ido*z.

Can the normal force on an object ever do work? Explaitm6bq;xra f:x7wj8 lwe99t ebv: p*o 3n.

A woman swimming upstream is not moving with respect to the shore. Is she doinf:yz49l 8o8n,tqf-3+ei- ntd cuwlq sg -lsduf8e+cn- z: t34 ln8wtfoqiy,9qany work? If she stops swimming and merely floats, is work done on her?

Is the work done by kinedegcc3 x-(ss-; sje 27 cpx,czzh5 5qqtic friction forces always negative? [Hint: Consider what happens to the dishes when yxss7,-c 2 cg3qc5ed(zesq jz5 xhcp -;ou pull a tablecloth out from under them.]

Why is it tiring to push hard against a solid wall even though you are doing nd gkc9w8u 9id9o work 98cdd9wg iu9k?

You have two springs that are identical excepx; .phs2 ub/lv)phl8 ct that spring l is stiffer than spring ulhhv.82 /p slx) bpc;2 $(k_1>k_2).$ On which spring
is more work done $(a)$ if they are stretched using the same force, $(b)$ if they are stretched the same distance?

A hand exerts a constant horizontal force on a block thauzji)m)x h84+ yyxf2at is free to slide on a frictionless surface (Fig.6-30). The block starts from rest at þoint A, and byhix8+2auf 4yzm j))xy the time it has traveled a distance $d$ to point B it is traveling withe bint $o$ point B it is traveling with speed $\nu_\mathrm{B}$.When the block has traveled another distance $d$ to point C, will its speed be greater than, less than, or equal to 2$\nu_\mathrm{B}$? Explain your reasoning

By approximately how much does your gravitational potential energy chaq2 fi u4dbz*3mix bdn/9p7 (pmnge when you jump as high as you cnmbb34(/px7i2 i*z updfm9q dan?

In Fig. 6–31, water balloons are tossed from the roof of a buiz kaq 4nc 48h1b,k0rcuzd4j ;glding, all with the same speed but with different launch angles. Which one has the highest speed on impact? Ignkh41gdzj4nua rkq8, cz4;0b c ore air resistance.

A pendulum is launched from a point that is a height h qye4zo6z5uhhdcu 80; ) cq -cyabove its lowest point in two different ways (Fig. 6–32). During both launches, the pendulum is given an initial speed of 3.0m/s On the first launch, the initial velocity of the pendulum is directed upward along the trajectory, and on the second launch it is directed downward along the trajectory. Which launch will cac eo)0;c6uy4ydq58chu- qz zhuse it to swing the largest angle from the equilibrium position? Explain.

A coil spring of mass m rests upright on a table. If you compress ftwu4x2 bq e38r;0e ujthe spring by pressing down with your hand and tqj2be4ufut ;3x e rw80hen release it, can the spring leave the table? Explain, using the law of conservation of energy.

A bowling ball is hung from the ceiling by a steel wire (Fig. 6–33). The i3 r1ux1w1c.5mpkopca a+egt2 nstructor pulls the ball back and stands against the wall with the ball against his nose. To avoid injury the instructor is supposed to release the ball without pushing it. W5r32cg 111wtkp c a .aumeox+phy?

What happens to the gravitn. 64j4*6n(d r*i5kbef o pzaod ck)joational potential energy when water at the top of a waterfall falls tokrabj 6no5odd6(jz4k i*fep4cn). *o the pool below?

Describe the energy transformations when a child hops around on a pogp-/9+ 6jp0wn usvzfh zo stick.

Describe the energy transformations that take place when a skii vdry5.z27 zber starts skiing dowyir 2bv75d zz.n a hill, but after a time is brought to rest by striking a snowdrift.

A child on a sled (total mas.jlhfzpty(3 0s m) starts from rest at the top of a hill of height h and slides down. Does the velocity at(.0lyj3ztpf h the bottom depend on the angle of the hill if (a) it is icy and there is no friction, and (b) there is friction (deep snow)?

Seasoned hikers prefer to ste6gr,x(j 4gkh lp over a fallen log in their path rather than steppih6 jx(kr4 ,gglng on top and jumping down on the other side. Explain.

Two identical arrows, one with twice th,xuy7xm/en xxh 4wyodf 43 ,ai0;n (zue speed of the other, are fired into a bale of hay. Assuyax/, iyxw7(ne ;f m3 4nxhuo40u,xz dming the hay exerts a constant frictional force on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain.

Analyze the motion of a simple swinging pendulum in terms of energy, (a) -k2b m gh2phe1ignorin12 bk2-hge mphg friction, and (b) taking friction into account. Explain why a grandfather clock has to be wound up.

When a “superball” is dropped, can it rebound to a height greater*rwz r1u9m5ua4t0j94i ujn mw than its origina irtuw*w1 4 49jm0a5nu9 zmrujl height? Explain.

Suppose you lift a suitcase from the floor to a ta7 z46ehfz ;hdlble. The work you do on the suitcase depends on which of the following: (a) whether you lift it straight up or alongzfh7zed4;6 lh a more complicated path, (b) the time it takes, (c) the height of the table, and (d) the weight of the suitcase?

Repeat Question 22 for the power needed.8)5t .xy2tfgspbti+b.c q cf rather than the work.

Why is it easier to climb a mountain via a zigzag trail than to climb strair5:i pg8 h.hnoght up?h 5:pgh rno.i8

Recall from Chapter 4,lybl:0* ( hk0ss5fkoqrcu8dq- cyr 2 4 Example 4–14, that you can use a pulley and ropes to decrease the force needed to raise a heavy load (see Fig. 6–34). But for every meter the load iu0 sk loq5c2fr-( rqscy hkl8yd4:* b0s raised, how much rope must be pulled up? Account for this, using energy concepts.

  How much work is done by the gravitationa ee:t,(j *j.nkx++e ilop p4hvzv+p7 dl force when a 265-kg pile driver falls 2.80 mz(pi: lvvkhenp p +*eojejx+.d,+t47?    J

  A 65.0-kg firefighter climbs a flightky y: f)/h g0lrs-gnv) of stairs 20.0 m high. How much work is required? fk ))h/y-:vlgs n 0rgy   J

  A 1300-N crate rests on the floor. How -hvtp r hqbsot,0z+ x(r5fui1k:1b/c much work is required to move it at constant speed (a) 4.0 m along the floor againstshxt1b:r/o5ip h bkf 0+r(utqc ,z1v- a friction force of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did tdqd1w g8eyud. mwy+xx3.. tu3he movers do (horizontally) pushing a 160-kg crate 10.3 m across a rough m u3w. yd.td 1u8+ .gwqxxed3yfloor without acceleration, if the effective coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is accelerated by a force across a floo3zqgkp2 5s8 u7bmb)ktr at a rate of for 7.0 s. Find the net work done on thb 7 zskbt2q5mk3u8pg )e box.   J

  Eight books, each 4.3 cm thick wq z n)fct a7q;ne/o/fg ,j,hv:ith mass 1.7 kg, lie flat on a table. How much work is required to stack them one on top of anoth,:c/t)aeg ,f/v7zfqq; hjnno er?    J

A lever such as that shown in Fig. 6-35 can be udwwctcew 3 h angwb7/h lx 4td5n**o33ja(/z,sed to liff objects we might not otherwise be able twe*4dw/,/ t nda3obh ajg3z n3w7xchc*lt5(wo liff. Show that the ratio of output force, $F_{\mathrm{O}}$, to input force, $F_{\mathrm{I}}$, is related to the lengths $\iota_\mathrm{I}$ and $\iota_\mathrm{o}$ from the pivot point by $F_{\mathrm{O}}/F_{\mathrm{I}}=l_{\mathrm{I}}/l_{\mathrm{O}}$ (ignoring friction and the mass of the lever), given that the work output equals work input.

  A 330-kg piano slides 3.6 m7hvybk v*v w;9u, ok0o down a 28° incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 6-36). The effective coe w; k9bov u0v,oy7*hkvfficient of kinetic friction is 0.40. Calculate:
(a) the force exerted by the man,    N
$(b)$ the work done by the man on the piano,    J
$(c)$ the work done by the friction force,   J
$(d)$ the work done by the force of gravity,   J
$(e)$ the net work done on the piano   J

  (a) Find the force requir fdz*d)od y-b7ed to give a helicopter of mass M an acceleration of 0.10 g db*d- y7of)zd upward.    Mg
(b) Find the work done by this force as the helicopter moves a distance h upward.    Mgh

  $\text{What is the minimum work needed to push a 950-kg car 810 m up along a 9.0$^{\circ} $ incline? }$$(a)\text{ Ignore friction. }$    J
$(b)\\\text{Assume the effective coefficient of friction retarding the car is }0.25.$    J

  In Fig. 6-6a, assume the distance axis is linear and thatn bi:zw74, orc $d_{\mathrm{A}}=10.0$ m and $d_{\mathrm{B}}=35.0$m. Estimate the work
done by force $F$ in moving a 2.80-kg object from $d_\mathrm{A}$ to $d_\mathrm{B}$   J

  The force on an object, acting along the x axis, varies as qg8.34toa wt wsbg:hr +mo)(oshown in Fig. 6–37. Determinoq 8+g:tmasbo 3go(4.r )t wwhe the work done by this force to move the object (a) from x=0 m to x = 10 m    J
(b) from x = 0 m to x = 15 m    J

  A spring has $k=88$ N/m. Use a graph to determine the work needed to stretch it from $x=3.8$ cm to
$x=5.8$cm, where $x$ is the displacement from its unstretched length    J

  The net force exerted on a-m-uu ja9 gaw 2qg6dvr9ce w(y;nl1zon 1d/8 t particle acts in the $+x$ direction. Its magnitude increases linearly from zero at
$x=0$, to 24.0 N at $x=3.0$ m. It remains constant at 24.0 N from $x=3.0$ m and then decreases
linearly to zero at $x=13.0$m. Determine the work done to move the particle from $x=0$ to $x=13.0$ m
graphically by determining the area under the $F_x$ vs. $x$ graph    J

  At room temperature, an 7nfplpn1l f5n 4h;o +moxygen molecule, with mass of $5.31\times10^{-26}$typically has a KE of about$6.12\times10^{-21}$ J .How fast is the molecule moving?    m/s

  (a) If the KE of an arrow is doubled, by what fact(d 7 5hgb,w9b,(xqcnbqyha2c.qwj 5oor has its speed increased? $ \sqrt{a}$ a =    (b) If its speed is doubled, by what factor does its KE increase?   

  How much work is required to stop eeiyx :2o bkjop*.a1s(9i cu;an electron $\left(m=9.11\times10^{-31}\mathrm{~kg}\right)$ which is moving with a speed of$1. 90\times 10^{6}\mathbf{m/ s}$ ? $\boxed{a\times10^{b} \mathrm{J}}$ a =    b =   

  How much work must be done to stopa; d4u :u:gnj*cil+pdlg/36 9 nufkd h a 1250-kgcar traveling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bo tqyzq(;ayvs/ q591xy w whose string exerts an average force of 110 N on the arrow over a distance of 78 cm. What is the speed of the arrow as it leavey(x ta q9zyq 1vq5/s;ys the bow?    m/s

  A baseball (m=140kg) traveling 32m/s moves a fielder’s gl5twz0 ,1-q,ne 6uh1qsz dey lmove backward 25 cm when the ball is caught. What was eql6 1 ewq5, td,-h1yus0mzznthe average force exerted by the ball on the glove?    N

If the speed of a car is increased by 50%, byzkx b9g; y8h5s. y*xtj what factor will its minimum braking distance be increased, assuming all else is xz.t xyg k*j58b; hy9sthe same? Ignore the driver’s reaction time.

  At an accident scene on a level road, investigators measure a car’s ski-ml4x pd6 p*hv. dndl+d mark to be 88 m long. The accident od -nldl.hpp4*+ dxvm 6ccurred on a rainy day, and the coefficient of kinetic friction was estimated to be 0.42. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. (Why does the car’s mass not matter?)    m/s

  A softball having a mass of 0.25 kg is pitched at By the lxd i.obk*5gje50,ul time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch, if the distance between the plate andl 05ok lei.*bjd5 xgu, the pitcher is about 15 m.    N

  How high will a 1.85-kg rock go if tb0/5yj* wpd:2y+h zhz y 8rlzchrown straight up by someone who does 80.0 J of work on it? Neglect air resist l8+:hd/hcz yzjr 5zyy20bp *wance.    m

  A 285-kg load is lifted 22.0 m vertically with an acceleratio)0ao, 9 zr/b4nrg kyxen by a single cable. Deterxer a/r yk,0)g obzn49mine
(a) the tension in the cable,    N
(b) the net work done on the load,    J
(c) the work done by the cable on the load,    J
(d) the work done by gravity on the load,    J
(e) the final speed of the load assuming it started from rest.    m/s

  A spring has a spring stiffness constant, k, ofk -. xjr/wjv3hke)h;pk1 x8om 440N/m How much must this spring be stretched to store 25 J of potentialwrphk3-vxhm)k8x1. ; oj e/kj energy?    m

  A 7.0-kg monkey swings from one branch to ano*u:ky2 xw5 j pltja+yx0a22adther 1.2 m higher. What is the change in potential 2t+a 2 yyj:a0xka5jp*uxldw 2 energy?    J

  By how much does the gravitational potential energy w;jkfz*hggs3h8( -paf2 b .laof a 64-kg pole vaulter change if his cent3s8f w hg l-g2azh*ja;.kf(p ber of mass rises about 4.0 m during the jump?    J

  A 1200-kg car rolling on a ho d/)ksxtxh w .6vg7sb.rizontal surface has speed v = 65 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constwvg/6sbhx.7.k) d xtsant of the spring?    N/m

  A 1.60-m tall person lifts a 2.10-kg book frogd h ;cf:d1m9xm the ground so it is 2.20 m above the ground. What is the potential energy o ;h:mgdfd cx19f the book relative to
(a) the ground,    J
(b) the top of the person’s head?    J
(c) How is the work done by the person related to the answers in parts (a) and (b)?    J

  A 55-kg hiker starts at an elevatilsr:7ia z5i ke 6lxs4x,91dgfon of 1600 m and climbs to the top of a 3300-m peak. i5,es17g96l irzfxl dsk ax:4
(a) What is the hiker’s change in potential energy?    J
(b) What is the minimum work required of the hiker?    J
(c) Can the actual work done be more than this? Explain why. ----待选择----yesno 

  A spring with k = 53N/m hangs vertically next to aw,evv)0 u+ / -j.d6jyixuwqwy ruler. The end of the spring is next to the 15-cm mark on the ruler. If + qevv)dwj6,wyixu/y-0 j. uwa 2.5-kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler marks?    cm

  Jane, looking for Tarzan0, )y*gn:b b(d yf;eid 0l4gz)c mprez, is running at top speed (5.3m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing)*gf dy (z)g: pmirezbd;, l0y4ebcn0 upward?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from rest, svawf2d 7u8as9lides down a frictionless 35.0$^{\circ}$ incline whose vertical height is 185 m. How fast is she going when she reaches the bottom?    m/s

  A sled is initially giv*qmr zeqg8sgf h4c9-tnn+. 3men a shove up a frictionless 28.0$^{\circ}$ incline. It reaches a maximum vertical height 1.35 m higher than where it started. What was its initial speed?    m/s

  In the high jump, Fran’s kinetic energy i6 s)0 ;nzgjq.vaerkk2 s transformed into gravitational potential energy without the aid of a pole. With what miniv ;.2nqzjrkek0asg)6 mum speed must Fran leave the ground in order to lift her center of mass 2.10 m and cross the bar with a speed of 0.7m/s.    m/s

  A 65-kg trampoline artist jumps vertically upward from the top prf xmi, d5hs /,le4bweg c/-)of a platform with -epixdb ),me 5gc/r4 fh,wl/sa speed of 5.0 m/s. ($\alpha)$ How fast is he going as he lands on the trampoline, 3.0 m below (Fig. 6-38)?$v_2$ $\approx$    m/s
(b) If the trampoline behaves like a spring with spring stiffness constant 6.2×10$^{4}$ N/m , how far does he depress it? $y_3$ =    m

  $\text{A projectile is fired at an upward angle of 45.0o from the top of a 265-m cliff with a speed of 185m/s. What will}\\\text{be its speed when it strikes the ground below?(Use conservation of energy.)}$    m/s

  A vertical spring (ignore its mass), whoser* 3s/h3ogxf .8ikhilfhp07+eagw)b+lf i :f spring stiffness constant is 950N/m is attached to a table and is compressed doh*7 :)la30 8+h +3./liifobfphs wrxge fk igfwn 0.150 m. (a) What upward speed can it give to a 0.30-kg ball when released?    m/s
(b) How high above its original position (spring compressed) will the ball fly?    m

  A block of mass m slides without friction along the loua0v+v qc71kkoped track shown in Fig. 6–39. If the block is to remain on the track, even at the top of the circle (whose radius is r), from what minq0+c7a 1 uvkkvimum height h must it be released?    r

A block of mass m is attachxbu91o)9 u h.hy*p9uy :dnqfn ed to the end of a spring (spring stiffness constant k), Fig. 6–40. The block i *ud:.9uyh no9px n)19huqfby s given an initial displacement $x_0$ after which it oscillates back and forth. Write a formula for the total mechanical energy (ignore friction and the mass of the spring) in terms of $x_0$ position x, and speed

  A 62-kg bungee jumper jumps from a bridge. (iq)ic vwg;ix.)mu- g She is tied to a bungee cord whose unstretched length is 12 m, and falls a total of 31 m. (a) Calculate the spring stifvqii) ;wcu xi)- g.gm(fness constant k of the bungee cord, assuming Hooke’s law applies. $\approx$    N/m
(b) Calculate the maximum acceleration she experiences. $\approx$   m/$s^2$

  The roller-coaster car shown in Fig. 6–41 is dragged up d.so8t9flgv8 b*p;b u1l5m cr0be ib7ot c3/r to point 1 where it is released from res i;m3s.l5fv/p obo10u8r 9eb*cg brldtct b87t. Assuming no friction, calculate the speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown with a speed of 12 m/s aip 2+7gc4xlohv a1nn. t an angle of 33 $^{\circ} $. (a) What is its speed at its highest point    m/s
(b) how high does it go? (Use conservation of energy, and ignore air resistance.)   m

An engineer is designing a spring to be placed at the bb dd+bbu x;cktw5ho z66*+0ooottom of an elevator shaft. If the elevator cable should break when the elevator is at a height h above the top of the spring, calculate the value that the spring stiffness constant k should have so that passengers undergo an acceleration of no more than 5.0 g when brought to rest. Let M be the total mass of the ehob t;x+db56 dk0o*uz+b6 cwolevator and passengers.

  A cyclist intends to cycle up a 7.8 l- bmm 2x;jf (pi/5yet$^{\circ} $ hill whose vertical height is 150 m. Assuming the mass of bicycle plus cyclist is 75 kg,
(a) calculate how much work must be done against gravity.    J
(b) If each complete revolution of the pedals moves the bike 5.1 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses. The pedals turn in a circle of diameter 36 cm.    N

  Two railroad cars, each of mass 7650 kg and tr 6vkvpofvub 1-v zm.y :)n9my-aveling 95km/h in opposite directions, collide head-on and come to rest. How much thermal energvbp:vvm .my 9nfu 1zv- 6ok-)yy is produced in this collision? $a\times10^b$ J a =    b =   

  A 21.7-kg child descends a slide 3.5 m high and reaches the bot3ez94pr ,kesitom with a speed of 2.2m/s How much thermal energy due to friction was generarkepze3 ,i94sted in this process?    J

  A ski starts from rest 5h,i 5-9bzi* ax3ezs*um u*fckam o9dand slides down a 22 $^{\circ} $ incline 75 m long.
(a) If the coefficient of friction is 0.090, what is the ski’s speed at the base of the incline? $\approx$    m/s
(b) If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level? Use energy methods.$\approx$    m

  A 145-g baseball is dropped from a tree 13.0 m above the grjuwj5d-la0i4 1-)gupn2kg puound.
(a) With what speed would it hit the ground if air resistance could be ignored?    m/s
(b) If it actually hits the ground with a speed of 8m/s what is the average force of air resistance exerted on it?    N

  You drop a ball from a heio :xl/-f8qngir *8nj 4z.7( zb3 vfnmxi5hhxv ght of 2.0 m, and it bounces back to a height of 1.5 m. ifjb:ho8/fgnv 5x(73 vniz qhnx4.mr8xz* l -
(a) What fraction of its initial energy is lost during the bounce?    %
(b) What is the ball’s speed just as it leaves the ground after the bounce?    m/s
(c) Where did the energy go?

  A 110-kg crate, starting from rest, is pulled across a floor with gnog7uo y0 +4aa constant horizontal force of 350 N. For the first 15 m the floor is frictionless, and for the next 15 m the coefficient of friction is 0.30. What is the final speed of the u4oyg+og7n0a crate?    m/s

  Suppose the roller coaster in Fig. 6–41 passes po p5ujimogq;+q 07gb2tint 1 with a speed of If the average force of friction is equal to one-fifth of its weight, with what speed will it reach point 2? The distance travelogq50;qugt i m72 +bpjed is 45.0 m. $\approx$    m/s

  A skier traveling 12m/s reaches the fooyp/m. ej4 7ldyp g/(lzt of a steady upward 18.0 $^{\circ} $ incline and glides 12.2 m up along this slope before coming to rest. What was the average coefficient of friction?   

  A 0.620-kg wood block is firmly attached to a very lighhs4sm6u)z igoe*l nj :x3pg :,t horizontal spring (k=180N/m) as shown in6e*o:zjsm ug, :i l pxh34ng)s Fig. 6–40. It is noted that the block–spring system, when compressed 5.0 cm and released, stretches out 2.3 cm beyond the equilibrium position before stopping and turning back. What is the coefficient of kinetic friction between the block and the table?   

  A 280-g wood block is firmly attached to a very light horizontal spring, Fia)mf )g8hz7a:/k ur2, lrd u12ijwt icg. 6–40. The block can slide along a table where the coefficient of friction isl 2 gt1hd2 raw:izf8jm/c),r i7au)uk 0.30. A force of 22 N compresses the spring 18 cm. If the spring is released from this position, how far beyond its equilibrium position will it stretch on its first swing?    m

  Early test flights for the gw4:l p qj*; xv1t*dpcpz8-nw +timo0space shuttle used a “glider” (mass of 980 kg including pilot) that was launched horizontally at 500k0t* +xipjp p dq8gzwlv*:1mt n- ;o4cwm/h from a height of 3500 m. The glider eventually landed at a speed of 200km/h (a) What would its landing speed have been in the absence of air resistance?$\approx$    km/h
(b) What was the average force of air resistance exerted on it if it came in at a constant glide of 10 $^{\circ} $ to the Earth?$\approx$    N

  How long will it take a 1750-W motor to lift a 315-kg p l9c,:yzs.cvriano to a sixth-story window 16.0 m abov,c v9 sylr:cz.e?    s

  If a car generates 18 hp when traveling at a steady 88km/h what must be the avegbyt 66mk3f*zrage force exerted on the car6btmy *g6z3 kf due to friction and air resistance?    N

  A 1400-kg sports car accelerates from rest to 95km/h in 7.4 s. .zv) gx zahgk:nq81odk 52j5aWhat is the average power delivered by the ek)xg.5k: o 8 51 zhjadvnzga2qngine?$\approx$    hp

  (a) Show that one British horseposkc+ cn4ua 4 :bccl7i(wer$ \mathrm{ft}\cdot\mathrm{lb/s}$ is equal to 746 W.
(b) What is the horsepower rating of a 75-W light bulb?    hp

  Electric energy units are often expressed in the form of “kilowatt-hours.f0-jxz22a5w qg +jiu kcyoe:y, ex 87w”
(a) Show that one kilowatt-hour (kWh) is equal to $3.6\times10^6$J
(b) If a typical family of four uses electric energy at an average rate of 520 W, how many kWh would their electric bill be for one month $\approx$   kW*h
(c) how many joules would this be?$a\times10^b$ J a =    b =   
(d) At a cost of 0.12 dollars per kWh, what would their monthly bill be in dollars? Does the monthly bill depend on the rate at which they use the electric energy?    dollars

  A driver notices that her 1150-kg car slowmn-ap 7*rkb r/s down from to 65km/h in about 6.0 s on the level when it is in neutral. Approximately what power (watts and hp) is needed to keep the car traveling at a copr/ab r-*7n mknstant 75km/h.    hp

  How much work can a 3.0-hp se8p x3 v cvky kb5)rc3u ;t1w7vyxb2;yy1f f;motor do in 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerat5nb,u4 p*vtpjmr-d l:es a 7.3-kg shot from rest to 14m/s If this motion takes 1.5 s, what average power was developed- 4nut,dvpjmr*lb p:5 ?$\approx$    W

  A pump is to lift 18.0 kg-qr p-:75tniqymk(bn of water per minute through a height of 3.60 m. What output rating (watts) should the pump motor have t5- kqn (pyb:rqi-mn7?    W

  During a workout, the football players at Stateims i9dz-)hmv- lj +b2 U. ran up the stadium stairs in 66 s. The stairs are 140 m long and incli)m vlj-szb idm -i+9h2ned at an angle of 32 $^{\circ} $. If a typical player has a mass of 95 kg, estimate the average power output on the way up. Ignore friction and air resistance.    W

  How fast must a cyclist climb ajxo,(/adr a c. 6.0 $^{\circ} $ hill to maintain a power output of 0.25 hp? Neglect work done by friction, and assume the mass of cyclist plus bicycle is 68 kg.   m/s

  A 1200-kg car has a maximum power output of 120 hp4+; w ( op5bhaz:ui:f3tpoe qq. How steep a hill can it climb at a constant speed of 75kmp eoqi+t4p:5 u(3zq h baf;o:w/h if the frictional forces add up to 650 N?    $^{\circ} $

  What minimum horsepower must a mot*l1;x4an112w jy mkul s )linuor have to be able to drag a 310-kg box along a level floor at a speed of 1.2m/s if the coefficient of aun4*1u s; lln w21)ki1lxmjyfriction is 0.45?    hp

  A bicyclist coasts dowpgkh rt 64w64r t0/h ub-nyxy(n a 7.0 $^{\circ} $ hill at a steady speed of 5m/s Assuming a total mass of 75 kg (bicycle plus rider), what must be the cyclist’s power output to climb the same hill at the same speed?    W

  Designers of today’s cars have built “5mi/h(8km/h) b48 sxi :k.i /cwki y(j3idk:h4pls,qcumpers” that are designed to compress and rebound elastically without any physical damage at speeds below 8km/h If the material of the bumpers permanently deforms after a .dk4jhyi4(clix: 3p, /i:sk qi8c kswcompression of 1.5 cm, but remains like an elastic spring up to that point, what must the effective spring stiffness constant of the bumper be, assuming the car has a mass of 1300 kg and is tested by ramming into a solid wall? $a\times10^b$ N/m a =    b =   

  In a certain library the first shelf is 10.0 cm off the/e)awob 96ap* f2tzrp ground, and the remaining four shelves are each spaced 30.0 cm above the previous6ftb* a) or/e2wzppa9 one. If the average book has a mass of 1.5 kg with a height of 21 cm, and an average shelf holds 25 books, how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start? $\approx$    J

  A film of Jesse Owens’s famous lons7 ;3cmuy d 8sx).nl vqt;rh,og jump (Fig. 6–42) in the 1936 Olympics shows that his center of mass rose 1.1 m from launch point to the top of the arc. What minimum speed did he need at laun qro8tcu3ynsh; d vxslm.,); 7ch if he was traveling at 6.5m/s at the top of the arc?   m/s

  The block of mass m sliding without friction along the lehz5wd9 kz; y6z s,/hmx4 pb*iooped track shown in Fig. 6–39 is to remain on the track at all time*m;sw b p6/ihzzyzx,k 94deh5s, even at the very top of the loop of radius r.
(a) In terms of the given quantities, determine the minimum release height h (as in Problem 40). Next, if the actual release height is 2h, calculate    r
(b) the normal force exerted by the track at the bottom of the loop,    mg
(c) the normal force exerted by the track at the top of the loop,   mg
(d) the normal force exerted by the track after the block exits the loop onto the flat section.   mg

  An airplane pilot fell 370 m after jumpicx;m8j/ 4)bdasep ea,ng from an aircraft without his parachute opening. He landed in a snowbanp/edb ;,x 8s)mja4ecak, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the pilot’s mass was 78 kg and his terminal velocity was 35m/s estimate
(a) the work done by the snow in bringing him to rest; $\approx$    J
(b) the average force exerted on him by the snow to stop him;$\approx$    N
(c) the work done on him by air resistance as he fell.$\approx$    J

A ball is attached to a horizontal cork5:z(*y vz f) 8mknd)jzyax13z,xgrtd of length L whose other end is fixed (Fixngzv8 r5k1,: jzy3)d mytaz)kx *(fzg. 6–43).
(a) If the ball is released, what will be its speed at the lowest point of its path?
(b) A peg is located a distance h directly below the point of attachment of the cord. If h=0.8L what will be the speed of the ball when it reaches the top of its circular path about the peg?

  A 65-kg hiker climbs to the top of a 3700-m-high mountain. The climb is made in jxbzox8 9e)muek0* 0s 5.0 h starting at an elevation of 2300 m. Calculate ebxs 0mje) 0z*89uoxk
(a) the work done by the hiker against gravity,   
(b) the average power output in watts and in horsepower,   W    hp
(c) assuming the body is 15% efficient, what rate of energy input was required.    hp

  An elevator cable breaks when a 920-kg elevator is 28 m above a huge spri- npkn;lj00;9kbju ds /m9kepng ($k=2.2\times10^{5} \mathrm{N/m}$) at the bottom of the shaft. Calculate
(a) the work done by gravity on the elevator before it hits the spring,$\approx$    j
(b) the speed of the elevator just before striking the spring,$\approx$    m/s
(c) the amount the spring compresses (note that work is done by both the spring and gravity in this part).    m

  Squaw Valley ski area in California claims that its lifts can move 47,0kblm +4edm-v p, w9z;k00 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the power needed.v-k lzb; 4mmd+ 9,kewp$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and fapndy6-q ++f e4bkbd7flls vertically 81 m before striking the turbine blades. Calculate pkb6dq-y+ 74bne+f df
(a) the speed of the water just before striking the turbine blades (neglect air resistance), $\approx$    m/s
(b) the rate at which mechanical energy is transferred to the turbine blades, assuming 58% efficiency.    W

  Show that on a roller coaster with a circular vertical loop (Fig. 6–4 y3mo6i d b/x v(pv98aliajzxl6f, vjkp561y;4), the difference in your apparent weight at the top of the circular loop and the bottom of the circular loop is 6 g’s — that is, six times your weight. Ignore friction. Show also that as long as your speed is above the minimum needed, this answezvyl;( j fjli/i 5666koxay,1 xdpv a3p9bv8 mr doesn’t depend on the size of the loop or how fast you go through it.    mg

  (a) If the human body could convert a candy bar directo ln16l xi4,z7a czw 1z/f/lcyly into work, how high could an 82-kg man climb a ladder if he were fueled z4a11zcl f,xzo7li c6ly// wnby one bar (=1000kJ)    m
(b) If the man then jumped off the ladder, what will be his speed when he reaches the bottom?    m/s

  A projectile is fired at an upward angle oyq3-mrvf yv:0 f 45.0$^{\circ} $ from the top of a 165-m cliff with a speed of 175m/s What will be its speed when it strikes the ground below? (Use conservation of energy and neglect air resistance.)    m/s

  If you stand on a bathrooa ha2+wkbh8t q;vn b*9m scale, the spring inside the scale compresses 0.60 mm, and it tells*q+9 na 28khh;avbbwt you your weight is 710 N. Now if you jump on the scale from a height of 1.0 m, what does the scale read at its peak?    N

  A 65-kg student runs at 5m/s g0h.xyzv19f uy rabs a rope, and swings out over a lake (Fig. 6–45). He releases the rope when his velocity is z hf vy0u.x91yzero.
(a) What is the angle when he releases the rope?    $^{\circ} $
(b) What is the tension in the rope just before he releases it?    N
(c) What is the maximum tension in the rope?    N

  In the rope climb, a 72-kg atheqgo n0( 7tgs47s ibv,lete climbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used to agb,47son tevg0s (qi7ccomplish this feat?    W

  Some electric-power companies use water to store energy. Water is puhl waj,i5 pf*q9i0bpi/ u 9)gvmped by reversible turbine pumps from a low to a high reservoir. To store the energy produced in 1.0 houvi0j g/a lu) b*5 h,99iifwppqr by a 120-MW ($120\times10^{6}$W) electric-power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Assume the upper reservoir is 520 m above the lower and we can neglect the small change in depths within each. Water has a mass of 1000 kg for every 1$m^3$.    $m^3$

  A spring with spring stiffness constant k vy gxcxj664ql -yt 0c*is cut in half. What is the spring stiffness cgt q6 vxy4y cl6*x0j-constant for each of the two resulting springs?   k

  A 6.0-kg block is pushed 8.qrw5b.o8bin cod4 .-g2tw :sf0 m up a rough 37 $^{\circ} $ inclined plane by a horizontal force of 75 N. If the initial speed of the block is 2.2m/s up the plane and a constant kinetic friction force of 25 N opposes the motion, calculate
(a) the initial kinetic energy of the block; $\approx$    J
(b) the work done by the 75-N force; $\approx$    J
(c) the work done by the friction force;    J
(d) the work done by gravity;$\approx$    J
(e) the work done by the normal force;    J
(f) the final kinetic energy of the block.$\approx$    J

  If a 1500-kg car can accelerate from 35km/h to 55km/h in 3.2 s, h3wioe* pf-hx +ow long will it take to accelerate from 55km/h to 75km3x*h +poi-wef/h Assume the power stays the same, and neglect frictional losses.    s

  In a common test for cardiac function (the “stress test”), the patient walks,*/ evrr onz/w: wx)u/bykz*t on an inclined treadmill (Fig. 6–46). Estimate t/y*ot*w n :/rz ewuk/rzb)xv,he power required from a 75-kg patient when the treadmill is sloping at an angle of 15 $^{\circ} $ and the velocity is 3.3km/h (How does this power compare to the power rating of a light bulb?)$\approx$    W

  (a) If a volcano spews a 500-kg rock vertically upward a distance of 500 t,8 4vd )upk ,hifsch,a:kwx(m, what was its velocity when it left u,sw ,4cxh )t(:hiv 8f k,kpdathe volcano? $\approx$    m/s
(b) If the volcano spews the equivalent of 1000 rocks of this size every minute, what is its power output? $\approx$ $a\times10^b$ W a =    b =   

  Water falls onto a water wheel xfc5 ju4(d-wf from a height of 2.0 m at a rate of 95kg/s (a) If this uc5wjf( 4-fx dwater wheel is set up to provide electricity output, what is its maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s