In what ways is the word “work” as used in everyday language the same as t*znbg7:* r;xet ke9ydb zy*x8 hat defined in physics? In what ways is it differy nbgy9ex **rde;b7xz t:kz8* ent? Give examples of both.

Can a centripetal force ever do work onb m4vsvjd2qiqe:+2zt *;ird ; an object? Explain.

Can the normal force on an ob3) uitv00 dymlject ever do work? Explain.

A woman swimming upstream is not moving with respect a g56w0oesa v6to the shore. Is she doing any work? If she stops swimming and merely floats, i6 5saw gova60es work done on her?

Is the work done by kinetic f.qvl (wzqr v41riction forces always negative? [Hint: Consider what happens to the dishes when you pu q(.zl14rwq vvll a tablecloth out from under them.]

Why is it tiring to push hard against a solid wall even though you are do *7m- 8y*pgka)le neawing no work? geplnk- wa87 *ymae)*

You have two springs that are identicjn 7ip3mtqug0 9u)k r.i85q zm z)pah6al except that spring l is stiffer than sprip p n) im3kiur5)aj.z 0qt8qz7u9hg m6ng 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 constalicipj ppoox 00rz 7*9y h(5n0)oq/zgnt horizontal force on a block that is free to slide on a frictionless surface (Fig.6-30). The block starts from rest at þoint A, and by the time it has t9co5y)7g( /oxji*z00pnpho r0liq pzraveled 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 g6hl o7f1jntb f,s o6* *zrhu(jravitational potential energy change when you jump as highfl61 fsu h*jtbjr*ono(h7 , 6z as you can?

In Fig. 6–31, water balloons are tossed f6rm **a.ursbp1wv/omrom the roof of a building, all with the same speed but with different *b v/mrpmo a. 6wu*1srlaunch angles. Which one has the highest speed on impact? Ignore air resistance.

A pendulum is launched from a point that is a height huz,c ,9/25frrce yvqw above 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 direceyrvqu /w2c5r,zf 9 c,ted upward along the trajectory, and on the second launch it is directed downward along the trajectory. Which launch will cause 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 the sprin+rb n7wsptb3 ,cm x5.ag by pressing down with your hand and then release it, can the spring leave tn+wx.5t 7r pbcm3bs a,he table? Explain, using the law of conservation of energy.

A bowling ball is huagsx(:ggls:0ux ix 86ng from the ceiling by a steel wire (Fig. 6–33). The instructor pulls the ball back and stands against the wall with the ball againstg0gxxs:u 6s a:xl8ig ( his nose. To avoid injury the instructor is supposed to release the ball without pushing it. Why?

What happens to the gravitatlezx-xp4,a 6;n4+i .jysbn xt ional potential energy when water at the top of a waterfall falls to the pool be6py exb ;axn.- ,tin+z4x4sljlow?

Describe the energy transformations when a child hops around iz:b+zs -6l8u* ctodq on a pogo stick.

Describe the energy transfor)nrs*g7zl*cx snwb -2 mations that take place when a skier starts skiing down a hill, but after a time is brocnng -w2zs*b7slx)r * ught to rest by striking a snowdrift.

A child on a sled (total mass m) starts from rest at 2*h0 mmurc:jxthe top of a hill of height h and slides down. Does the velocity at the bottom depend on the angle of the hill if (a) it is icy and there is no friction, and xm*m:02 rjuch (b) there is friction (deep snow)?

Seasoned hikers prefer to step over a fallen lo ko;lpgvi xy (qw*k v b-inf8qz0, xns5w+3:n:g in their path rather than stepping on top and jumping down on the other side. 8:3: x;*0k wybvq5x sp-i(lv ogfiz+k nn w,qnExplain.

Two identical arrows,6r lwy9mq y:c ov:/jb c42dqb yl6af3cr1s)e 8 one with twice the speed of the other, are fired into a bale of hay. Assuming the hay exerts a constant frictional force on the arrows, the faster arrow will penetrate how much f d2ylmqelb6/4jsw8 c9r : cr bv3:1yo)facq6yarther than the slower arrow? Explain.

Analyze the motion of a simple swinging pendulum in terms of energy, (a) d0+7jqz vwmqszt+ e+ *ignoring friction, and (b) taking friction into acz z*++ +tdq7vw0esqmj count. Explain why a grandfather clock has to be wound up.

When a “superball” is drriq 5sn:eymnh-vwf- 1e(pecf6 2 c .2qopped, can it rebound to a height greater than its original height? Explainw 1(n2e qif-6epym5e-cq:fc 2r.sv nh.

Suppose you lift a suitcase from the floor g +(aq9c h+bceto a table. The work you do on the suitcase depends on which of the following: (a) whethecae9+h cbgq( +r you lift it straight up or along 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 nele-,mcwt4. fj n l.da8eded rather than the work.

Why is it easier to climb a m55 tvifqe77:k(pgxlmountain via a zigzag trail than to climb straight uef i7ptxgq7 55:l( kmvp?

Recall from Chapter 4, Exampexm* -4u2 q-g phadixl*/p cu+le 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 a mui-qxd*pe *hl4/pg2+xc-u for every meter the load is raised, how much rope must be pulled up? Account for this, using energy concepts.

  How much work is done by the gravitational force when a 265-kg zs 1),c px2hu( *rzc-ivjf uk 5.kdv2hpile driver falls 2.80rz* 2c2z1usku i, cv(dj- f5h)kh.vxp m?    J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How much work is re0yt.uj kz:cmr6 3 xd 0yhndg44qd3 uzxdy .0k 4j g640nyhm:trcuired?    J

  A 1300-N crate rests on the floor. How much w7c:ge c nepclud-i-t nx8 /*1dork is required to move it at constant speed (a) 4.0 m along the floor against a friction fe nl/nce1x cdu*:7gtd- -pci 8orce of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did the movers do (horizontally) pushing y43h b58sz-bc /sakgaa 160-kg crate 10.3 m z3c48a s by5b/k-ahsgacross a rough floor without acceleration, if the effective coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is accelerated by a 87m- sm ;smccoforce across a floor at a rate of for 7.0 s. Fi7so8cm;c ms m-nd the net work done on the box.   J

  Eight books, each 4.3 cm thick with mass 1.7 kg, lie flat on a t( pw0bzbgeo-cg 0:rg (eny:y,able. How much work is required to stack them (,c be(::wgyo0b z r0 -epgngyone on top of another?    J

A lever such as that shown in Fig. 6-hj6usl7eg n4,pk:cyo1 -s /p2o5y qh lf6.gba35 can be used to liff objects we might not otherwise h6of6u gh7ea5g lj s2boycpl-.ysp:1q 4, n/kbe able to 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 slide6 g//wu:gx(l4ws .ihfnh-nf,m1 vj i rs 3.6 m down a 28° incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 6-3mjv gf/,f i(14sn w:ln-gr .6u/ihw hx6). The effective coefficient 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 required to give a helicopter lr+ ku rui 9f( 5clanj31wf41yof mass M an acceleration of 0.10 g upwr + aufirwky5 41u1 c3(jnl9lfard.    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 axi)wvybh 9m7wd3 am7zk 9s is linear and that $d_{\mathrm{A}}=10.0$ 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 axiizzg2( 2 j8)n ul;umigs, varies as shown in Fig. 6–37. Determine the work done by this force to move the object (a) from x=0 m to x = 1 2;lng iizu(2)ugjzm8 0 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 particle acts izokn*hdf , x 7v(dx8x9n 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, ansx mqrk*f :83d+mc(ko;fl-ydt bx u--1zcg1c oxygen 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 factor has its spe- sj :5fm7jzzcf7g3g. adp /sxed increased? $ \sqrt{a}$ a =    (b) If its speed is doubled, by what factor does its KE increase?   

  How much work is requir2e ypsja ;c2sf *9q4;tk 8qmsfed to stop 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 stop a 1250-kgcar traveling at 105km/hjn q6m)s)nf.x ?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whose strzsz:78:vpep 2n 5zdlking exerts an average force of 110 N on the arrow over a distance of 78 cm. What is zl: :5znsz 7dp2pvke8the speed of the arrow as it leaves the bow?    m/s

  A baseball (m=140kg) traveling 32m/sk i4q5t lh n(-wnm,qe3 moves a fielder’s glove backward 25 cm when the ba li k5,n4 -mte(3hqwnqll is caught. What was the average force exerted by the ball on the glove?    N

If the speed of a car is increased by 50%, by what factor will itr *sa4t3udc;o50fn kwegpq*2 s minimum braking distance be increased, assuming all else is tackn2dq0pt f3* s4*ow;rgue5he same? Ignore the driver’s reaction time.

  At an accident scene on a level road, investigators measure a car’s skid m)m*d8w bm9 :g 7fdl(asitwk,gp -0yckark to be 88 m long. The accident occurred on a rainy day, and the cd0 g-t g(k *bmfiw)pcw87:9ds,kl aymoefficient 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 -d3q3b)n qhxyof 0.25 kg is pitched at By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch, if thed3nbx3-q)hy q distance between the plate and the pitcher is about 15 m.    N

  How high will a 1.85-kg rock go if thrown straight cg /n/sq, j4zlup by someone who does 80.0 J of work on it? Neglect air resistancelq,4z//gs cjn .    m

  A 285-kg load is lifted 22.0 m vertip(54t udaij9f oyr/n t:* ns:clp)h )twy,gr3cally with an acceleration by a single cablds5ton/:9r3 l:))4afryg w c h,tp*( utnyjip e. Determine
(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, of 440N/m How much must this sprit ctvef7 ne4vctj7- -iz/l o; e +9tc9)*khckdng be stretc4zlt9t fve kcve)nt i+h kc7;/jtcec9--7d*ohed to store 25 J of potential energy?    m

  A 7.0-kg monkey swings3:+ bf9kjgknh8 ns 9bb from one branch to another 1.2 m higher. What is the change i3kbk8fgsn: 9h+jn bb9n potential energy?    J

  By how much does the gravitational potential energy of a 6at 4f8e *x 3-5mwqgkfo4-kg pole vaulter change if his center of mass r8fm5w- k*geo aqf3x4 tises about 4.0 m during the jump?    J

  A 1200-kg car rolling on a horizontal surface has speed v = 65 kwa 0fb :vbt5m4m/h when it strikes a horizontal coiled spring and is twa0:5b4m bvfbrought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?    N/m

  A 1.60-m tall person lifts a 2.10- uqr z9gp(+p:rkg book from the ground so it is 2.20 m above the ground. What isprz 9upq+:r (g the potential energy of 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 elevation of 1600 m and climbs to the to ( yxy8xoy*7orww/(kzp of a 3300-m pea*wz y7o(kx (o/wry yx8k.
(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 a ruler. The end of the spring ek: ig2s e-zl;;kobh+s i.jn9is next tozi e2 b9;sk.nh-gelj:iks o;+ the 15-cm mark on the ruler. If a 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 Tarzan, is running atmtp 77kgj9 (an ry1fnfa(hc2 ( top speed (5.3m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high canj7m (gr27a(phncy ka9 1t f(nf she swing upward?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from rest, slides down a frictionless 33 wq(nleue1 x-xa sz6:5.0$^{\circ}$ incline whose vertical height is 185 m. How fast is she going when she reaches the bottom?    m/s

  A sled is initially givw2n xpn:7t3 ;gpe;smbx +inv/en 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 is transformed s2fq2cxf a:s2into gravitational potential energy without the aid of a pole. With what minimum speed must Fran leave the ground in order to lift her cenxa2 qfsf2:s2cter 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 of a platfomv;xd i+ym 9x/f+3g2 pxmt f/srm with a speed of 5.0 /+xsi92m mtgfm3x fv/;xd+py 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), whose spring stiffness cont:rcwnb 8z2-i /:m7 be jrvy/cstant is 950N/m is attached to a table and is compressed down 0.150 m. (a) What upward speed can it give to a 0.30-kg ball wh :ce-/i:tb8j/7 z2nc rbvwm yren released?    m/s
(b) How high above its original position (spring compressed) will the ball fly?    m

  A block of mass m slides without frictio- b7rn x.ekfp+6o3 aydn along the looped track shown in Fig. 6–39. If the block is to remain on thedxe-y3a.p 6nf r7kb+o track, even at the top of the circle (whose radius is r), from what minimum height h must it be released?    r

A block of mass m is attached to the engua4 c9frfp6fh tc4)0 d of a spring (spring stiffness constant k), Fig. 6–40. The block pfcr)afg906 4hu4ct fis 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. Shez mr(lv,c/9*. ja pa7 n n,ufmw92pwwv is tied to a bungee cord whose unstretched length is 12 m, and falls a total of 31 m. (a) Calculate the spring stiffness constant k of the buunm,jp2w lc a z7p9a w,* m/v(v.rnwf9ngee 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 to 4b.4ldr u-esis4+gp0a*i mgo point 1 where it is released from rest. Assuming no friction, calculate the speig0 os.l4ip ube-ma 4gd+4s*red at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is throvfvr; o:w8:h3y bw4 eewn with a speed of 12 m/s at 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 plaqgj ruq 1n,gu5 m5fg09ced at the bottom of an elevator shaft. If the elevator cable should break when the elevator is at a height h above the top of the spring, calculatequ ,g0uf15n5 r9 qmgjg 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 elevator and passengers.

  A cyclist intends to cycl zyjn0j7ia q,.mk 2l0be up a 7.8 $^{\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 nu h5;b7runq9dwu)vf bj8di8hs+v(). eg(qo 7650 kg and traveling 95km/h in opposite directions, collide head-on and come to rest. How much 9(hor+dq 5 )ijnfn(dus beuv gwbh.)u78v8 q;thermal energy is produced in this collision? $a\times10^b$ J a =    b =   

  A 21.7-kg child descends a slide 3.5 m high and r g5oy*sglw29 r.kb h3aeaches the bottom with a speed of 2.2m/s How much thermal energy d5yrws hog2bg9a3.l * kue to friction was generated in this process?    J

  A ski starts from rest d9 3xfr9rq7u band 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 13l6,r+mo5hdlk n. ;lod .0 m above the ground.
(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 height of 2.0 m, and it bounce mn8 ze:a(ny;hcp-p v;s back to a height of 1.5 m.e;-p(nhm z:pac nyv ;8
(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, startin,gf7,u;d; :+s m99gteuqr mbv 2wlmivg from rest, is pulled across a floor with a constant horizontal force of 350 N. For the first 15 m the floor is frictionless, and : gir7udvs2q gm, 9levum+;m f,wt b;9for the next 15 m the coefficient of friction is 0.30. What is the final speed of the crate?    m/s

  Suppose the roller coaster in Fig. 6–41 passes point 1 with a speed of Ihathmwbe p bv h.+);.j.o -bg5f the average force of friction is equal to one-fifth of its weight, with what speed will it re;ha.b vohe5 ) h g.jp+wb.bm-tach point 2? The distance traveled is 45.0 m. $\approx$    m/s

  A skier traveling 12m/s reaches the foot of a stu)4k n3,fji/m- lmjr /l (ognaeady 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 t.ifd jq )n f28p1v5kixo a very light horizontal spring (k=180N/m) as shown in 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 equ) ikxpj8dq25 nf.i f1vilibrium 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, Fig.it+9z0oiff (-0ndcnr 6–40. The block can slide along a table where the coefficient of friction is 0.30. A force of 22 N compresses the spring 18 cm. If the spring is released from this posi dntif+oi9z ( 0rn-fc0tion, how far beyond its equilibrium position will it stretch on its first swing?    m

  Early test flights for the space shuttle used a “glider” (mass of 9 7)yro 9peo0 ,1:qczyak:4e p-ds mywg80 kg including pilot) that was launched horizontally at 500km/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 res::ode-p9mkzow y7r4 eay0 ypg1,q)scistance?$\approx$    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 piano+jvtcy,e ld87q9 pox5 to a sixth-story window 16.0 m ab897vxjeo+tp5 ycdq,love?    s

  If a car generates 18 hp when traveling at 9yme;omfjr af4s-z68 a steady 88km/h what must be the average force exerted on the car due to frictio;r smmj6f-fez4o8 9ya n and air resistance?    N

  A 1400-kg sports car accelerates from rest to 95km/h in 7.4 ,4ryz rymv0k1s. What is the average power delivered by the engizm r4,yykv 10rne?$\approx$    hp

  (a) Show that one British+g lqt9/ a(hcm horsepower$ \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 gfg/urdw4 ;*mform of “kilowatt-hours.”
(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 slows drv mwhs;r ++3 q6c7vypown from to 65km/h in about 6.0 s on the level when it is in neutral. Approximately what powh7 wpc+vsv3ry q ;m6r+er (watts and hp) is needed to keep the car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hp motor do in 1.0 wgw5p(.kuedpws6r- . (ck5m zh? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg st0 /*yfxy0 ugahot from rest to 14m/s If this motion takes 1.5 s, what average power was developed?tuyy0/ ax* 0fg$\approx$    W

  A pump is to lift 18.0 kg of water per minute through a height of 3.60 m. Wlz*,vii;h,vk8pja djel* +y .hat output rating (watts) should the pump motor hj8zva*kij*pllei,d +v y;,h. ave?    W

  During a workout, the footba xxo-8qyjm 7a/ll players at State U. ran up the stadium stairs in 66 s. The stairs are 140 m long and inclined at an angle of 3/m xy7oxj-aq8 2 $^{\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 as*7mw wivgjvo2 . a8tkrt5m6 / 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 hp. How steep a hill can i+l;*7vra i/7 xapz0eya y+jppt climb at a constant speed of 75km/h if the frictional forces ada+*0;ar+j7ippav/xz y lep y7d up to 650 N?    $^{\circ} $

  What minimum horsepower must a motor have to be able to drag a 310-kg box axly;) ct8 u*bx:/qnx8qzu l5tlong a level floor at a speed of 1.2m/8*n 8tqxltlx;5 y/b: zxu)qucs if the coefficient of friction is 0.45?    hp

  A bicyclist coasts down a 7.0 :f(ex whq)ozy2 ,k8sv $^{\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) bumpers” that are des wt:aqixaa1.yi:(sx ; igned to compress and rebound elastically without any physical damage at speeds below 8km/h If the material of the bumpers permanently deforms after a compression of 1.5 cm, but remains like an elastic spring up to that point, what must the effective spring stif w;ataiaxi: sqx(. y:1fness 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 ground, and the remai4txer1xx e28qning four shelves are each spaced 30.0 cm above the previous one. If the average book hxx1r4t q2x e8eas 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 long jump (Fig. 6)g dgj;)jtd-ze f9d/vqwea)-–42) in the 1936 Olympics shows that his center of mass rose 1.1)e;gj)edf-v-awt dq g9)/dzj m from launch point to the top of the arc. What minimum speed did he need at launch if he was traveling at 6.5m/s at the top of the arc?   m/s

  The block of mass m sliding without friction fqd lp+znpo c:8d+i-(along the looped track shown in Fig. 6–39 is to remain on the track at all times, even at the very topo- cdl+pz f i8pd(:+nq 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 jumping from an aircraft withok : .75jut7+xvaige/pep yn j7ut his parachute opening. He landed in a snowbank, creating a crater 1.1 m u5+n7tj epx7./yjekv a 7pgi: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 zthv050ov0fed r .ih(a horizontal cord of length L whose other end is fixed (Fig. 6–43v r5ho( 0 zvdfit00.eh).
(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 mo1,s epf/lzhhyy 7i*do2 ws9yp)4 .vipuntain. The climb is made in 5.0 h starting at an elevation of )zpsy*pwfp4 dih1oly,2 v.s/ 9h 7iye2300 m. Calculate
(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 v acr* (.cg 6ufz2vv)gvc2kba1u+sp4qu (;da28 m above a huge spring ($k=2.2\times10^{5} \mathrm{N/m}$) 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 tbnk9(i -h m mc,2 crrdh22jc00ex6tep hat its lifts can move 47,000 people per hour. If the average lift carries peotec - ec0b,p6n29mh0cj kr(2dxir2hmple about 200 m (vertically) higher, estimate the power needed.$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and fallzsnba x;*w-1 ,0wyy*b4 og tods vertically 81 m before striking the turbine y;obdwxbazo1t, 0-wgs4*n*y blades. Calculate
(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.lrnev)6ee4 3ov5r 5f 3zo twr/ 6–44), 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 ti eow /elevzof335rrn) v64 tr5mes your weight. Ignore friction. Show also that as long as your speed is above the minimum needed, this answer 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 directly into work, vusu+-bf c 3)show high could an 82-kg man climb a ladder if he were fuecss+3u-fb u)v led by 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 hpk (n;sa+-ho:tz8ed at an upward angle of 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 bathroom scale, the spring inside the scalhg:ye-s u 9gq:e compresses 0.60 mm, and it tells you your weight is 710 N. Now if you juhg9:ges :uyq -mp 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 grabs a rope, and swingsb3p7k q gfx.n( out over a lake (Fig. 6–45). He releases tbxq.3g7f kn(p he rope when his velocity is zero.
(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 athletez0-1 j- hwzklb climbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used to accomplish -zjzb w0k-l1h this feat?    W

  Some electric-power companies use watp psi1a z guo2*:7g(nqer to store energy. Water is pumped by reversible turbine pumps from a low to a h(pa21nq: s7*ggi upoz igh reservoir. To store the energy produced in 1.0 hour 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 consp1 e ywhq 7qcd-a2e-/ 3wk/qfvtant k is cut in half. What is the spring stiffness constant for each of the two res/3 p1/ v e7wqf qkhdc2ye--aqwulting springs?   k

  A 6.0-kg block is pushed vhgnp1t)09yj4w 1b dhuh-ma*8.0 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 acbyt m*zh -+)gkcelerate from 35km/h to 55km/h in 3.2 s, how long will it take to accelerate from 55km/h to 75km/h Ass+ythmkzb -*g) ume the power stays the same, and neglect frictional losses.    s

  In a common test for car q s+ty;.ui0shdiac function (the “stress test”), the patient walks on an inclined treadmill (Fig. 6–46). Estimate the power required from a 75-kg patient when the treadmill is sloping at an angle ofs.;i+u 0stqyh 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 500ly2;n*uhkdtpg) (mi, m, what was its velocity w;t2un d lyg,)i kp(mh*hen it left the 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 from a height of8fk6 6clixbh- tm4 l jb0j1n,r 2.0 m at a rate of 95kg/s (a) If this water wheel is set up to provide electricity output, what is its maximum power t-hbmnj 160lbl8jk i6r f,c4xoutput?    W
(b) What is the speed of the water as it hits the wheel?    m/s