In what ways is the wysgts(vt 81 wy*jjx6-56q jcyord “work” as used in everyday language the same as that defined in physics? In what ways is it different? sqy8(wtj xvs15 jct6*jy yg-6 Give examples of both.

Can a centripetal force ever do work on an o.uxj+ 32ngk f/4ukp txbject? Explain.

Can the normal force on an object eg3gl h/ +qfp0hver do work? Explain.

A woman swimming upstream is not moving with respect to mx/dqk/ 5qst;2lylfd tn: v(,the shore. Is she doing any work? If she stops swimming and,xvnl5 /fmqlq :kdd tyst;2(/ merely floats, is work done on her?

Is the work done by kinetic friction forces always negative? [Hint:a2qt+))wjwu*wm,* 9yfr.vqqe d )usd Consider what happens to the dishes when you pull a tablecloth outa)uw.+ * 9q ry2msjdtwe f,vwq u)q*)d from under them.]

Why is it tiring to push hard against a solid wall evenvt vhbv0r(m95h vx79s though you are doing no work?9b rt mh7vv(v0s9h5 xv

You have two springs that are identical except that spring l is stiffer than c9a77kfqx-i p)r vcu:et+u9+mqt + obspring 2 +97x cu pq9c-k re+ aoi7b)qvtf tu+:m$(k_1>k_2).$ 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 foaz .4 83qjb*;vmda 8ix+x opktrce on a block that is free to slide on a frictionless surface (Fig av8pz+t3q48kj;. dmax ob* ix.6-30). 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 -:q0 g f*q.b 0unxf.u bqw9xcjchange when you jump as high as yo x q9.nqfcbf0 u.g xj*u0bq-w:u can?

In Fig. 6–31, water balloons are tossv wkw8lrf-08m ed from the roof of a building, all with the same speed but with different launch angles. Which one r-w v8f8lw0m khas the highest speed on impact? Ignore air resistance.

A pendulum is launched from a point that is a height h above its lowest;-t/vg sms*8.t snvsg 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 will8nmvs *gvssstg-;t. / cause it to swing the largest angle from the equilibrium position? Explain.

A coil spring of mass m rests upright on a t;jwh3ep-0gc kn bp7r3able. If you compress the spring by pressing down with your hand and then release it, can the spring leap e k j3h3nc;0prbg-7wve the table? Explain, using the law of conservation of energy.

A bowling ball is hu4w :hjz+apy- 1py: gcs41fm6nrt a(nyng from the ceiling by a steel wire (Fig. 6–33). The instructor pulls the ball back and stands against the wall with th4j-y 1mpaw sy n ( tn1:4f:p6aczygr+he 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 d,ja+sde- kuvd9y5j3er , za )energy when water at the top of a waterfall falls to the 5 jdr,ea )das+ dj9z-vey,uk3pool below?

Describe the energy q xx /i (irlp4yar9+*jtransformations when a child hops around on a pogo stick.

Describe the energy transformations that take place when a skier starts skiing aogu 5u i4n7o-ne(q7ddown a hill, but after a time is brought( 5 o7gn -4nudeauoi7q to rest by striking a snowdrift.

A child on a sled (total mass m) starts from rest at the top of a hill of hefe,da6 ,b:opt4qjfi9 ight 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 b:di o,,t9 6pjqae 4ffis friction (deep snow)?

Seasoned hikers prefer to step over a fallen log in their patblhy)c9 d6c8ckq: 7 sth rather than stepping on top and jumping down on th 6htsc9cl:k7 c)dby8q e other side. Explain.

Two identical arrows, one with twice the speed of the other,.e w ja2ntrnxa,/) gd; are fired into a bale of hay. Assuming the hay exerts a constant frictional force on the arrows, the faster arrow will peg n)a2;wde.n/rjtxa ,netrate how much farther than the slower arrow? Explain.

Analyze the motion of a simple swingit0gy; wl 3*axjng pendulum in terms of energy, (a) ignoring fri3wxag ; y0tlj*ction, 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 than its oaq ;4pn.17q eeuh-.tt fv0vjuriginal heiu0j h4up 7-ft1ea v vqn.et;.qght? Explain.

Suppose you lift a suitcase e h9iq6fidf1j:)h 4r afrom the floor to a table. The work you do on the suitcase depends on which of the following: (a) wheth h:aji1 f9if46qh)erder 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 ratheb9vj+ w2k,6me.(ehbf:cthz zsm /qx0r than the work.

Why is it easier to climb a mountain viakn:t7i1gr ; ru a zigzag trail than to climb straight u t7k: ;n1griurp?

Recall from Chapter 4, Example zcv/ y8tw4tc)p/mx 7x4–14, that you can use a pulley and ropes to decrease the force needed to raise a y/m xztp)vxw8/cc74t heavy load (see Fig. 6–34). But 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 gravitatio q46 evz7sl :bbg(eo3znal force when a 265-kg pile driver falls 2.80 m73s:4 (lz bgvqob6eez ?    J

  A 65.0-kg firefighter climbs a fligh 6/7xbjgnen2y*w0ikq t of stairs 20.0 m high. How much work is requirwjie /ngyk0 26n7x*q bed?    J

  A 1300-N crate rests on the floor. How much work i1dyy3 c lr5zc0s required to move it at constant speed (a) 4.0 m along the floor against a frcly 5d0zcr31 yiction force of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did the movers do (horizontally) pushing a 160-kg crate 10fdvxl7n4f3 s2.3 m across a rough floor without accelefxldn43v27 sf ration, if the effective coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is accelerated by a force across a +to:b.abtsz/ic nn c1 hn5)16xgu2g5b:nc pafloor at a rate of for 7.0 s. Fin) cczh2ocapnx/gn1s5nn t ::.t1gi6bua 5b b+ d the net work done on the box.   J

  Eight books, each 4.3 cm thick with mass 1.7 kg, lie flat on a table. H1/r,dp0jqe 1h o9kkwsow much work is required to stack the11/sde j9h k,krwqpo0 m one on top of another?    J

A lever such as that shown in Fig. 6-35 can be used to liff2u,w yeg7r: q f/zw)sy( zy.aq objects we might not otherwise be able ),qw / :z7gruzey q.fw(y2sayto 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 down a 28° incline and is kept fr9m( ngpiekn(+pp +g9aom accelerating by a manp9e++g in( kgm(pan9p who is pushing back on it parallel to the incline (Fig. 6-36). 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 cg8o2mrc)wa+ give a helicopter of mass M an acceleration of 0.10 g upwar w8rg+m2ao)ccd.    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 j3 k3cr.jumycni/0t*axis 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 axis, varies as sho06lok.tplp/ns+dl*u fq; est xe+ )8c wn in Fig. 6–37. Determine the work done by this force to move the object (a) lfs+xtn dlpo0pl )s;6uq.*ee c tk+8/ 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 particle acts in the61s7fv/ vmoto $+x$ 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 oxygeso,w.i+3h4wi ovks7gpi 2 ib7n 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, bjo 6t gj/8he*ry what 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 sty6) -39e4etlbjgzzn n op 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 tra*hlr7gd3/ v 8uopebag8a)2c wveling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whose string extqwul5 -,oigqyhj h). ep -7o9erts an average force of 110 N on the arrow over a distance of 78 cm. What is the speed of the arrow as it 7oeq i.-t9 5pol,- hhguyw)jq leaves the bow?    m/s

  A baseball (m=140kg) traveling 32m/s moves a fielder’s glove backward 25 c,vq6)iuf)ys: ub6b-vn5 pa+lq k 9hs lm when the ball is caught. What was the average force exerts6sklufhiu b 5),yqv+ab -p 9nl qv)6:ed by the ball on the glove?    N

If the speed of a car is increased fyws55 7c8 dru2htsd, by 50%, by what factor will its minimum braki t7 f2hswd8,u5d cysr5ng distance be increased, assuming all else is the same? Ignore the driver’s reaction time.

  At an accident scene a1s g l:m,y*2lbcuo ww-u- ociktg,/3on a level road, investigators measure a car’s skid mark to by toswlg :a w*m-,uu,3i1k- g ccb2l/oe 88 m long. The accident occurred 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 time it reaches thbsqc0, x37.vub a ps+je 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 and the 07sja.,b3 scqxup+vb pitcher is about 15 m.    N

  How high will a 1.85-kg rock go if thrown straight up by someone who does ti 3z w*,1cxnc80.0 J of work on it? Neglect air resistanc ct13i,wz x*nce.    m

  A 285-kg load is lifted 2jene8d ox pker2/ 1b662.0 m vertically with an acceleration by a single cable. Detnedk/x 6eoj pe61r8b2 ermine
(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 Hoj kjkb/ip9xnx+zhz7-0d5 d w4 c+nsz8w much must this spring be stretched to+nk j8nzp 0ih cwdbxxj -7+z59sk 4/dz store 25 J of potential energy?    m

  A 7.0-kg monkey swings from one branch to anotherf wv.ovh4 md*kfh9983*qna 4y ayx,md1gib a1 1.2 m higher. What is the change in potential en ymkbq4 .9wdvvma*d9y8 faxi *3,4fgn hh1ao1ergy?    J

  By how much does the gravitational potential energy of a 64-kg pole vaulter chrm2-dqjzh jo5)k/ z:dx4 */lpbtt*ee ange if his center of mass rises about 4.0 m during the *) ztdjrkpo:d4*x5q- t/l bme2/h jzejump?    J

  A 1200-kg car rolling oputa8a pf 5tn+6x(no.n a horizontal 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 constant ofx5o8taup+( pnt. a6n f the spring?    N/m

  A 1.60-m tall person lifts a 2.10-kg book from the ground so o p+v30dks.42erf bf jit is 2.20 m above the grounso. 30f2vdpjfk b+e 4rd. What is 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 tz x1 mr./wvqm4he top of a 3300-m peq4.xmv/ zmr1w ak.
(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 rul.dnzc 8/f cbh)i+0l mier. The end of the spring is next to the 15-cm mark on the8 )hbil.+i0cmfcd/n z 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 speeedt,v lcms xa5r:2 v0)wpe/ t+d (5.3m/s) and grabs a vine hanging vertically from a tall tree in the v)etmel /w2:avsc0 +tx p5,rdjungle. How high can she swing upward?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from rest, slid blm0m6f ut5r8z v7(ux bwfiul/ pt1f*p,)gt 8es 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 given a shove up a frictionless 28ef+4a(;axw lbxw.,,iflz/c z.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 transfor0z-v*byjc93qa)g vu bmed into gravitational potential energy without the aid of vj 9ucy-b b0*3 vgzq)aa pole. With what minimum 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 froma4k)jd)y j6(yo-*htt 7 nnplo.xukv, the top of a platform with a speed 7au6 nyp,lt-)nydxv )kt*(4.khojjo 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 4cn,f ere4( wxdfza9 /its mass), whose spring stiffness constant is 950N/m is attached to a table and is compressed down,4fwaznfed/ e4 9xc(r 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 looped track shown-s 8w wes;v,zo in Fig. 6–39. If the block is to remain on the track, even a,ewv;s o s8zw-t 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 sp 7 kfubx4/hy0wring (spring stiffness constant k), Fig. 6–40. The w0xyb4uhk7 f/block is 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 cord whosxr:9 kcvfg y,3e unstretchrv :c39kxgy,f ed length is 12 m, and falls a total of 31 m. (a) Calculate the spring stiffness 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 dr2cbdho(mpc8os /hs)9 agged up to point 1 where it is released from rest. Assuming no d mc8ocs( 9s)2p/boh hfriction, calculate the speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown with a speehhlo, o5 xg1pd8 mf-4ytdjx*0,nj9jjd 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 placed at the bottom of an elevator sc:krg a*uuofu :92r(cfmu* 0ehaft. If the elevator cable should break when the elevae :orrcg9u u*2a u*mf(k:0cfutor 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 b3 sul k0yz5kcva:dl(f 5nnr 0q3b-g8cycle 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 traveling 95km/h in opposi r 1il dj1g 78fomd/a*p7k1pdite directions, collide head-on m8 1ppj*lda ki11gd7i/rd7of and come to rest. How 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 andlmrq w;ga-k-s;spl;ci1 l 1 k5 reaches the bottom with a speed of 2.2m/s How much thermal energy due to friction was generated ;gkml lwspc s-q -1l1ia;r5 k;in this process?    J

  A ski starts from rest and slides down a 22 e av6u ,-iuda rm )ugcdf-- ax34(+tpa$^{\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 grl1*q*ybad8c2qx 6 e mjound.
(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 heigyi 93hc2kc bv5ht of 2.0 m, and it bounces back to a height of 1.5 myk b5cv2 c9ih3.
(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 acrosf+xc45eq9o s)294 xddzwd/ utkfyf :b s a floor with a 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. What9ffey5 w4udcdtksxx+z :)29bdf/oq4 is the final speed of the crate?    m/s

  Suppose the roller coaster in Fig. 6–cv 0l3k9y)c(uki-mqd wny*z;t3m ;z1 p hw)xw41 passes point 1 with a speed of If the average force of friction is equal to one-mylucd1czpqkk 3) yx*h wi(tw;; )vnzm03w9- 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 oi;tggu5 jy8 /27,t. pjilmimgm*z /lmf 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 f( q(dt5oqg 5tr4o .zi2s9 iyryirmly attached to 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 ty4iqys5t( oidorr. z q259tg( he 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 horiuf,pmra;-q p8jqzf0 ( zontal spring, Fig. 6–40. The block can slide along a table where the coefficient of fri -ma0f;q,rjfp zuq(p 8ction is 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 space shuttle used a “gli -5kpj5v9 dcsdder” (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) What would its landing speed have been in thcd5 d sjv9k5-pe 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 08hk (7lqgumrb9 sf.oiano to a sixth-story window 1m rg b0hs98o (lfu7.kq6.0 m above?    s

  If a car generates 18 hp when traveling at a steady 88km/h what mustv y/+rsfqv. f7s ;caz p8xe*+k be the average force exerted on the car due to friction syvv*8.7z+x/qf+fpe ;acsr kand air resistance?    N

  A 1400-kg sports car accelerates from rest to 95km/h 7tt *lnfs+ j::trj0agin 7.4 s. What is the average power delivered t +ts0 jla*:tf rn:j7gby the engine?$\approx$    hp

  (a) Show that one British horsepowvsg./(rbsv1( h8sh jser$ \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 .yg5 m; cx/go-m*yet qs;x c+eof “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 slowsu nu nzl5ymz 68hq.w)wv+e5 6o 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 kwnwe) m56lzoyqz8hu 6u.v+ n 5eep the car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hp mot7goj00lm(2hkk: ojfzor do in 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg shot from rest tyh3us1a m5r4epe 4r z,o 14m/s If this motion takes 1e rrhzeu m 1a4y4p3s,5.5 s, what average power was developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute thvb)u)pt(tvz ogd;y 0j)gr 2j,rough a height of 3.60 m. What output rating (watts) should the pum;y(dt)jt2j g 0)grb,p vou)z vp motor have?    W

  During a workout, the football players at State U. ran up the stadium9f *tt 9tilgbh5 9:ftx stairs in 66 s. The stairs are 140 m long and incifh9t9:5 gl tfb9*t txlined 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 cuc;jbcxnl ;h w)4jy-cna (50nlimb a 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 hi, d3uvw,h)hq3+ s qfclz7 8+d8fnefi sll can it climb at a8hwds 7f lq++ dzfv,hq)8 fi cu,3sn3e constant speed of 75km/h if the frictional forces add up to 650 N?    $^{\circ} $

  What minimum horsepower must a motor have to be able to drag a 310-kg box along+5dzr:3t06j osd ig *wqivx/p a level floor at a speedsrtd3wpd+0vz* i6/5 qg ji:xo of 1.2m/s if the coefficient of friction is 0.45?    hp

  A bicyclist coasts down a 7.0 p 4 +zyde/m5dh$^{\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 b2; 1 9jwgfnzy“5mi/h(8km/h) 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, j;n9 2gy1fw zbbut 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 ground, and th 7x t i:a(j(-v+tpvltme remaining four she: +j pm(tta(t vi7lvx-lves are each spaced 30.0 cm above the previous 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 long jump (Fig. 6–42) in the+4jrfif 2kb9 6fta4ge 1936 Olympics shows that his center of mass rose 1.1 m from launch point to the top of the arc. What min4gtf+f 9f b4k aji6r2eimum 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 along the looped track s/m nw3 *bwjblp )00cvdhown in Fig. 6–39 is to remain on the track at all times, even at the v m *d)ncb w0wpjb/30vlery 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 jumping from an aip oq 1h+q-s-aj( ja6lurcraft without his parachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injojqpus-1 (-q h6 laa+juries. 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 cord of length L whose otk 9f 5v7 z5rc/fkiaay)her end is fixed (Fig. 6–43).ca7fk)yai zk955v /f r
(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 ihooe/3 o hj(yi2m ;t9f;xx5sof a 3700-m-high mountain. The climb is made in 5.0 h starting at an elevation of 2 5(xoe3fh 2hoxti;iyjos/m;9 300 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 920q7x xnkzi/8d+, dm+sy+hqg *n -kg elevator is 28 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 that its liftsh)xqk a7h (5tl n;pnu2 can move 47,000 people per hour. If the average lift carries people abou;nhpnl7(a 5uhqx2t k)t 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 falls ver 3 k5q 5*e8cfvl;,hei icrk(dxtically 81 m before striking *; ciexi3 , vkhr fkq(5edcl58the turbine 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. 6–44), the mf* :-2sgxypl8;ed nm 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 2pm8*-mydf:; s x nlgeas 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 bc 7mu /q1(a: c)epb sc*ymk*qpar directly into work, how high could an 82-kg man climb a ladder ifapus mmcq (y**7bk:1p) ecc/q he were fueled 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 at an upwb x+fzg5828;dx t fxw*v b2qt .9hcz.-iijj gjard 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 scale c .j.kkcd nr,*wijzg x:8yji7;ompresses 0.60 mm, and it 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 w cjd*ni,.zgj;k.ir j :y 7xk8its peak?    N

  A 65-kg student runs at 5m/s grabs +pbw+qnp+z,d;41 nberb luj9 a rope, and swings out over a lake (Fig. 6–45). He releases the rope ++wn9ljqnd1ez b,4+; pb rpbu 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 athlete climbs a vertical disa7qm85x+ng koxy 89px tance of 5.0 m in 9.0 s. What minimum power output was used to accomplish tx+858n k yampgo7qxx9his feat?    W

  Some electric-power companies use water to store energy. Water is pumped by rewkorz2 qrd6 xc:+6xe,versible turbine pumps from a low to a high reservoir. To store 6:6rr+ keco q d2,xwxzthe 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 constant k is cut in half. What is the spri es w5lm,a*qqa.jna/* ng stiffness constant for eacq *a,w5elaj/ amqn.s *h of the two resulting springs?   k

  A 6.0-kg block is pushed 8.0 m up a z6 gl+t7ao4m nrough 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, how long wbeo z t+*2:7v2euthlfill it take to accelerate from 55km/h to 75km/h Assume the power stays the same, and nego2tv fbth:e 2*7el+zu lect frictional losses.    s

  In a common test for cardiac function (the “stress test”), tyjvai( 87q- mbhe patient walks on an inclined treadmill (Fig. 6–46). Estimate the power required f7-jyqamv i8b (rom 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 vertica+00ozn sk3db5v /yp4up (vrvmlly upward a distance of 500 m, what was its velocity when it left the vol +vudp4o3 b0/z5nyvr0(mks v pcano? $\approx$    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 was .wpp+(,q)y 5) yrlhvhk:ibheel from a height of 2.0 m at a rate of 95kg/s (a) If this water wheel is set up to provide electricity output, what is it))p(,hs.k+h:lv iq yyrb5 wp as maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s