In what ways is the word “work” as used in everyday language the sa2 l 15rlkcor1sme as that defined in physics? In what ways is it different? Give exao11s rrk5ll c2mples of both.

Can a centripetal force ever do workrqxyti48* -7xih t(cu on an object? Explain.

Can the normal force on an obje9 a9 uj27vqswsb9de a7ct ever do work? Explain.

A woman swimming upstream is not moving with respect to the shore. Is she x,mkcnl7eg bhah o8.0y pe(s7 :ot(a,doing any work? If she stops swimming and merely floats, is work dm.alk87ay( oo :7s,egb0ecpnh t xh(,one on her?

Is the work done by kine/nu h3r0*n huutic friction forces always negative? [Hint: Consider what happens to the dishes when you pull a tableclhu 0*ur3uh n/noth out from under them.]

Why is it tiring to push hard against a solid wall even though you ar* x0g7oq,s ktve doing no work?*gxq k07vtso ,

You have two springs that are identical except that spring l is stiffer tx5e+o6n7h )k p-i 4lhlspu:+g7voya x han sprp5 hp 7g:olhivy7xa no4+ kuexl-6+)s ing 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 bg jnu39s 1s kgkixt0+(muw */olock that is free to slide on a frictionless surface (Fig.6-30)uxi 3*wnt sjo +/91smgk(0guk . The block starts from rest at þoint A, and by 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 change whe edv x6+j7 7b(cckr5wmn you jump as high as you can?6rejwbc57d 7 mkcvx(+

In Fig. 6–31, water balloons are tossed from the roof of a building, 30mo5mqwt fjlm;s2y32v p 9gvall with the same speed but with diffeyg2w ptjm2 f9mlsq5v33; 0 omvrent launch angles. Which one has the highest speed on impact? Ignore air resistance.

A pendulum is launched from a point that is a height h above its lowest poiocuf3)va . kwf1cjxi+l 4zp0c j,5w 2knt 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 1jx2z lf5. cfjp430u)v,k+cwawi okc 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 thes+ vphnu5ywf c 9-k/zw.z0;8wbu c7rh spring by pressing down with your hand and then release it, can the spring leave the table? Explain, using the law of conservation of u ww fn.c8b u-ws95 ;7k+yzrh v/hzcp0energy.

A bowling ball is hung from the ceiling by a steel wire (Fig. 6dxtw3u1l kvq3g-by) 0su1ta1q02 lw z –33). The instructor pulls the ball back and standqat3sx-1 z y 0wu2l)u tklqbw31v1dg0s against the wall with the ball against his nose. To avoid injury the instructor is supposed to release the ball without pushing it. Why?

What happens to the gravitational potential energy when water at the mt/otnd(,2 cd top of a watn dmt(2,tcd/o erfall falls to the pool below?

Describe the energy transformatp)zki (3,l c09hieeqtf(-jnk:u6di sions when a child hops around on a pogo stick.

Describe the energy transformations that take place when a skier starer v9.hxz dbf.y -m.0ats skiing down a hill, but after a time is brought to rest by striking a snodz r.09mf. a-yv.eb hxwdrift.

A child on a sled (total mass m) starts from rest at txst)n5 iy 4b:qhe 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 (b) there is frictio :xt 4b5sni)yqn (deep snow)?

Seasoned hikers prefer to step over a fallen log in th ib;9zgyj vgfg/ozkjz; 5h ,+6eir path rather than stepping on top and jumpi 6yb;v /+;j iz9jogg5,k zfghzng down on the other side. Explain.

Two identical arrows, one with twice the speed of the other, arlmlr6bpn65 +- r h3mho bmkkp6g3t)t -e fired into a bale of hay. Assuming the hay exerts a constant frictional force on the arrows, the fagrb) p66 bo-krh tmh6mntm-+ lpl335kster arrow will penetrate how much farther than the slower arrow? Explain.

Analyze the motion o0kaey 67a. rnqf a simple swinging pendulum in terms of energy, (a) ignoring friction, and (b) taking friction into account. Explain why a grandfather clock has to be wound up.a6kqyer a0n7 .

When a “superball” is dropped, can it rebouixcf13dn80 xmnd to a height greater than its originc f3dmni1x08xal height? Explain.

Suppose you lift a suitcase from the floor to a table*6ct bc kod5vd. faq* .gut(h6. The work you do on the suitcase depends on whdfk.q 6uctac oth65 b(vg*. d*ich of the following: (a) whether 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 needed rather than the woz1//k rcu2 rimdv 1)7 ycah7bqrk.

Why is it easier to climb a mountaink26gkq5 h6hi i via a zigzag trail than to climb straight up kih iqg65h2k6?

Recall from Chapter 4, Example 4–14, that you can use a g ab-/fsulpro7)41e15lnq p bpulley and ropes to decrease the force needed to raise a heavy load (see Fig. 6–34). But for every meter the load is raised, how much ropep7 a b)puf/n4qoble15g1 ls-r must be pulled up? Account for this, using energy concepts.

  How much work is done by the gravitational force when a 265-k8 ob-gw,0k i4bzgj30agsc m 7zg pile driver falls 2.80aczg4og80bs0m wb-z3 k7j,i g m?    J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How much worhq+ 50eqn6bfj1f :vw*b-bzs g k is require jb1g+*fv h56e:fzqbbqn-s0wd?    J

  A 1300-N crate rests on the floor. 6nbd+ ka3t,spHow much work is required to move it at constant speedp,a3bk +st6nd (a) 4.0 m along the floor against a friction force of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did the*ju3 iwiv9sj (w)rn4:j)yo su8aspm 4 movers do (horizontally) pushing a 160-kg crate 10.3 m across a rough floor without acceleration, if the effectisui y opjs*njv4j wm) :ar)(8w i4u39sve coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is accelerate( kp(o4;jl.1f pochk6h 8;-hiowjmn jz d6kc5d by a force across a floor at a rate of for 7.0 s. Finjch4;j z-po 5ho(6.k o h; (6knfkwjc l81dpmid the net work done on the box.   J

  Eight books, each 4.3 cm thick with mafbdb82rw*8pf*(p i p 3k1sq3udoc+vq ss 1.7 kg, lie flat on a table. How much work is required to stack them one on top of another? qw2*sfd 13d * (3 pvou8f+ipqc8rbkbp   J

A lever such as that shown yq360kj3cg qm in Fig. 6-35 can be used to liff objects we might not otherwise be amy3q0j6g kc3qble 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 slides 3.6 m dov8kts7; 70nui2 zdqs8 yo x-ekwn 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 coefficient of kinetic fric2ky77;sts znoe8 8qivk -0udxtion 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 of 3j8mxaxj. ;ijmass M an acceleration of 0.10 ;m8jx ja.j 3ixg 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 thx2pl .nqe8g853m*c 2acyce pgat $d_{\mathrm{A}}=10.0$ 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 aj6 2feal/ ,aibui+r6x xis, varies as shown in Fig. 6–37. Determine the work done by this force to move the or6/ixbaaluj2e 6i+ ,f bject (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 pa:vwff 7w*lzc kk,)q4wrticle 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 oxyg 5ni4mmb/-zlwmn b3g+en 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 whaq5l 2mo8mtr0ys* y1 pgt factor 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/saam c8 v(3jyzizm 8q7*6qgz 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 trav/o -ec ;1oyxw wh1bjz4eling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whose string e9a qu wv/ 4pobcgqoai qo0,+)2xerts an average force of 110 N on the arrow ove av2)b,0pao4+gucwq9qoi / qor a distance of 78 cm. What is the speed of the arrow as it leaves the bow?    m/s

  A baseball (m=140kg) traveling 32m/s moves a fielder’s glove backward 25gdrrj tldew .f 3.)r )xb5f:j5 cm when the ball is caughtf.jrl:r5 w)rejd.g bd5xft ) 3. 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 its minim- g ik5 x*5k8fpxispy.um braking distance be increased, assuming all else is the same? iyi.k - 8pf5*xskpxg5Ignore the driver’s reaction time.

  At an accident scene on a le o /x 7rh5dhhr9naz k bs 3r0o9zi.t4zd5t(r-evel road, investigators measure a car’s skid mark to be 88 m long. The accident thhk30(9xrdsin54zr/ rbz5a 7 eo .thrz- od9occurred 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 ncl(qzsif8wb8d5j+ 7 mass of 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 the distance between the plate an w78jbf(+nzld5sqc 8i d the pitcher is about 15 m.    N

  How high will a 1.85-kg rock go if thrownv/wnz :0,n upx straight up by someone who does 80.0 J of work on it? Neglect air resistancev,/zp xnwnu :0.    m

  A 285-kg load is lifted 22.0 m vertically with an acceleration2 /zt(tf)sv2 b9k5 zrxu-esuda )ie*o by a single cable. Determine d rizk)use5/*vf)eaz oxb-229ts(u t
(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 a-6 vm+)8eik c9h7 6 xvdgviox)enme) spring be stretched to store 26 xvv c-8eeam ki)o6hn e)d9i v+gmx)75 J of potential energy?    m

  A 7.0-kg monkey swings from one branch to another 1.2 m xpz1v(38g u qshigher. What is the change in potential eneup gzx(s8v31qrgy?    J

  By how much does the gravitat54w3dx le ,jggional potential energy of a 64-kg pole vaulter change if his center of ma5dlw j3gg4,e xss rises about 4.0 m during the jump?    J

  A 1200-kg car rolling on a horizontal surfapp6:w2wmnl5 w ce 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. p wnwm26p:wl5 What is the spring stiffness constant of the spring?    N/m

  A 1.60-m tall person lifts a 2.10-kg book from the groun+:ct, (zz ljbid so it is 2.20 m above the ground. What is the potential energy of th ,zl+tjzc (:ibe 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 atpmviq;,rxi 9dp.phmw;ui) t1g/e8n bn g7a3. an elevation of 1600 m and climbs to the top of a 3300-m peak. i.ptm7,mb qih pd/u8 g;19x3vrpgen wn).a i;
(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 vertic wkm- yfh 0je 4(tu.6t-y.lgpially next to a ruler. The end of the spring is next to the 15ulh w tj y06k-4t.-.megipfy(-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 at top speed (5.3m/s) and grabs a vo: +o5qgbd4 e,s/bhy cdq )-pnine hanging vertically from a tall tree in the jungle. How high can sheg :o+ d/q4nchyso, - )5bdbpeq 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 35 79gwc9 glm7qy(2j vwk.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 given a shove up b8c otf 3fbx:-pne--g*cc2.zd/ nmiv 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 trane,f n+2 7wzebpsformed into gravitational potential energy without the aid of a pole. With what minimum speed must Fran leave t e,bz +nf7pw2ehe 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 ynnt(n. ev/bd2j9 sy:s7y l)tjumps vertically upward from the top of a platform with a speed of 5.07bsvl(/tje:ns9 ndyy )n .y t2 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 ma:h s:.fooloh7 o)y cze5nv+dr95p7kqss), whose spring stiffness constant is 950N/m is attached to a table and is compressed down 0.150 9y.o rqhfc l75 dokv:ho)o5 +sen:7pzm. (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 fric; wb4f4,m1 uj3qeg4h kk6hjob tion along the looped track shown in Fig. 6–39. If the bloc3hobe4j ku6m1w jg 4f,4qhb;kk is to remain on the 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 end of a spring (spring stiffness cont.*el2di9 s 4xt:it)j rtwra-stant k), Fig. 6–40. The block iwr:4ri-*jle) ai92 td. ttxst 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. She is tied to a bungee corj 5puo69dxay -d whose unstretched length is 12 m, and falls a total of 31 m. (a) Calculate the spring stiffness constan9o5-y dajp6x ut 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 i az5lk.zojas: -qb 2 axa;h3:mn Fig. 6–41 is dragged up to point 1 where it is released from rest. Assuming no frictioa.qb z2h3s: j5;a-amzo xla:k n, calculate the speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown wsk.l h8j5lbs -0+ 7(eocbjnr aith 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 spri, ) 8qrjouy+o9wotm:l3rgkh.)oa s i9ng to be placed at the bottom of an elevator shaft. If the elevator cable should break when the 9l+orkjmr9qh too)aio,sg8)u. 3 y: w 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 elevator and passengers.

  A cyclist intends to n,u5av:(bf4 uvsgy .r cycle 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 7650 kg and travelig cij5o, qhpbk 0 w1tsi0/bn8*ng 95km/h in opposite directions, collide head-on and come to rest. h8*wb5qt s oj p/i0,1k 0ngcbiHow much 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 reaches the bos ur:q8z*xcp +ttom with a speed of u+ q8 rxs:pz*c2.2m/s How much thermal energy due to friction was generated in this process?    J

  A ski starts from resi6hiudp i(d(h3 *mt ga)p:t d2t and 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 grou-*tz7z4 byojdea.6ho ev7l7 knd.
(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 bounces back to a height o1vbgm22x; l)my9e z zu:(nqpxf 1.5 m.zyg; m(2uqlepb12xn)x: m9z v
(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 restqbfm+;q,a; +ii ntr j/, is pulled across a floor with a constant horizonta; iiq/jb,rm;nq+t +fa l 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 crate?    m/s

  Suppose the roller coaster ie) k v)c4o63pow ratmn3 6l7j0ivd te5n Fig. 6–41 passes point 1 with a speed of If the average force of friction is equal to on0m3k)ci7o el)6nr av3jwoe 4tdp65 vte-fifth of its weight, with what speed will it reach point 2? The distance traveled is 45.0 m. $\approx$    m/s

  A skier traveling 12m/s reaches the foot of a steady upward 18.0o1a5g)*1 0u jhpl xa7wny.2fo 4,k.dn uomzcv $^{\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 cr 9hmi+l3;p74hli fd light horizontal spring (k=180N/m) a4d9milhh l r3i+f;c7p s 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 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 horizontalka363sd yjnt, spring, Fig. 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 thynkd3s ,t3j a6e spring is released from this position, how far beyond its equilibrium position will it stretch on its first swing?    m

  Early test flights fore7xjbq ootq0x.s,4u8 o o5*bt the space shuttle used a “glider” (mass of 980 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) Whao.x oqsu,oq*4jo 7x 5t08ebtbt 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 piano to a s43q fvziyno 2gfe. )f4ixth-story window 16.0 m above? fzoi3. fgv2n4fe)q y4   s

  If a car generates 18 hp when traveling at a steady 88km/h what musk/d:n38mlbq zt be the average force exerted on the car due to friction and air r8k b:3mz lnqd/esistance?    N

  A 1400-kg sports car accelerates from rest to 95km/h sr 9xu1p.pve6in 7.4 s. What is the average power delivered by the engine? x16. ursppe9v$\approx$    hp

  (a) Show that one British horsepowev9bbcd5s zf k- th.,/j9(87ebyv yprcr$ \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 fugv5ahc/h 2-+xhbug)/ye7q u orm 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 down from to 65km/h ix0(rx vmr6j9xlpe6 5r23vxmd5c r2v cn about 6.0 s on the level when it is in neutral. Approximately what power (watts and hp) is needed to keep 2rmc6exr jxrxvcv p9 r( 65x3m0lvd52the car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hp motor dovz s-w)rconib0 z 2*ziyu7q-8 in 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg shot from rest to 14m/s Idl//ah; rwx w,f this motion takes 1.5 s, what average power was hwl a x,;wr/d/developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute thr q 8xwrfc10tm1ough a height of 3.60 m. What output rating (watts) should the pump motor h1qf8t1wmc x0r ave?    W

  During a workout, the football players at State U. ran up the stadium;8vp 6uoey*gx4x ;rt r stairs in 66 s. The stairs arru*po; 8yxr6tve4 x;ge 140 m long and inclined 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 a 6.0 tng8/ld7zi ko-k4r ( /h g/tuz$^{\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 ofcgr m3jdzpi(y)aqy451 3k 3 mg 120 hp. How steep a hill can it climb at a constant speed of 75km/h if they)c g5 ajk 33mq1pr4g 3yizm(d frictional forces add up to 650 N?    $^{\circ} $

  What minimum horsepower must a motonk9pc7q+o+y e r 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 fri eo7+c9+n ykpqction is 0.45?    hp

  A bicyclist coasts down a 7.jgsn7hkmb):(*+ 6 iiq sb ff-b0 $^{\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/hho0 k4 uzmux1b/a17 hb) bumpers” 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 compression 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, 1oub xu/m40zb 7a1khhassuming 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 t 98oybj/0b(e,asnexq he ground, and the remaining four shelves are each spaced 30.0 cm above the previous one. If the average book has a mass of 1.5 kg we8syb e /j09ob( n,aqxith 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.( i+ w7i/u;8ti vtkebs 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. Wkbi st it+8wue;i7v(/hat 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 fria :eol izjj ne)iz75 wpf2 po;24r,xy1ction along the looped track shown in Fig. 6–39 is to remain on the track at all times, even at the very top of the loop 5n7o)rzil izw4oe ; j2:ye2f pjx,1paof 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 withovh w s,ep3-.myut his parachute opening. He landed in a snowbank, 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 3-vehymwp., swas 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 cord of length L whose other endx)y ,xo; :qg- pyvc:d -;tkbwo is fixed (Fig. o -tx;xky,dwqg)cvop ;- b y::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 i .*uk:5uy)g swaij+gvn 5.0 h starting at an elevation of 2300 kggj.5u +v ay iuw*)s: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 28 m above a huge sprinumuwsry8d 7+d+psr) 0g ($k=2.2\times10^{5} \mathrm{N/m}$) 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 47,000 people+ukkzt: 0mu, awj+ 5kk per hour. If the average lift carries people about 200 m (vertically) higher, estimate the power +zm tuak5:j+wku0,k k needed.$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and faec2 r: h1a wmwwc0g4.s 1vwpd vvc7*2wlls vertically 81 m before striking the turbine bladmvc2v.0 ae:w*r 21 cw1h4sw7 dvwwgcpes. 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. 6–44)-ei rjp2p by3/15v weo, 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 ise o /pwj-bv 21e5rpyi3 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*ry* 8qb pim: wy1vq(p work, how high could an 82-kg man climb a ladder if he were fueled by one bar (b8pp:vy* wry(* qm1i q=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 upwu*/pm ibcy :4kef+sg q.3 p6wuard 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 0w9ke 4 pxn 2;wlps8mnl0 l7tyscale compresses 0.60 mm, and i0tml y47kpn2nxls wwpl0 8e9; t tells 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 grabs a rop4xht c,:pgi:b : b:xmfe, and swings out over a lake (Fig. 6–45). He rb:pxc :h gfti::m,xb4 eleases the 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-kg72 qnhtorq.ekc2 (kzz.1 d(zf athlete climbs a vertical distance of 5.0 m in 9.0 s. What minimu1 ke nz(2q.d2.r(o z7 tfzcqhkm power output was used to accomplish this feat?    W

  Some electric-power companies use watci +pgl ,t8wqe9br18d er to store energy. Water is pumped by reversible turbine pumps from a low to a high reservoir. To storepbl gdwiqt88r +e9,1c 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 constuffh fo9 b*x)ko:a-m.ant k is cut in half. What is the spring stiffnesf-fh):9f*ubx km oo. as constant for each of the two resulting springs?   k

  A 6.0-kg block is pushed 8.0 mg*tryab8t2 r+- oa7lc 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 jadu9amx 7c1n(cr8 (a ,ff f :2dikf9daccelerate from 35km/h to 55km/h in 3.2 s, how long will it take to accelerate f 8j 1fd,dni(2ff:x k9c(adm7f9ar ucarom 55km/h to 75km/h Assume the power stays the same, and neglect frictional losses.    s

  In a common test for cardiac function (the “stress test”), i.ddrzzho07ml:+9ne ghon ) 4 the patient walks on an inclinl ngor9mhon7 :d +i0ed.zh)4 zed treadmill (Fig. 6–46). Estimate the 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 verksvfd38 ze, i*tically upward a distance of 500 m, what was its velocity when it left the voz3kdisv,*e 8flcano? $\approx$    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 heighb+k sn2-9tz b4 l/zirct of 2.0 m at a rate of 95kg/s (a) If this water wheel is set up to provide electricity output, what is 2s9- /cbnil+krz4 ztb its maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s