In what ways is the word “work” as used in e18sno: 2h ky foe.m3( upkyvu5veryday language the same as that defined in ph 3ok.yyuhkp28 f (:5 onu1evsmysics? In what ways is it different? Give examples of both.

Can a centripetal force ever do ; (eua8 :nl+x wqeqgcv.cbu/: work on an object? Explain.

Can the normal force on an object ever do work? Explaine4y9q4y7 kzpp f s4/dj.

A woman swimming upstream is not moving with respect to 5.pa;k+fp5cmd),* dxpi r xov the shore. Is she doing any work? If she stops swimming and mepvr;ki xp fx+o5dca d5)p.,*m rely floats, is work done on her?

Is the work done by kinf. +fyknq0 -*gt/yik ,cdavh9etic friction forces always negative? [Hint: Consider what happens to the dishes when you pull a tablecloth out from under them.-*i nha+yk9 vtkdcfy0,/f gq .]

Why is it tiring to push hard against a solid wall evz01aw40 hx200mqq y3ymsz n 2d rr:fsren though you are doing no rsh:f042 zwq0d3 yr s0r1a qx0ymnz2mwork?

You have two springs that are identical except that spring l is stiffer than s(vgacb4;v78,vjh g ;ggpmfv rg)d8 r*privgpj(g *7 )g hgr advvr 8,vb;f;8cgm4ng 2 $(k_1>k_2).$ On which spring
is more work done $(a)$ if they are stretched using the same force, $(b)$ if they are stretched the same distance?

A hand exerts a constant horizontal force on a block that is free to sl1o. xleas6 m7kide on a frictionless surface (Fig.6-30). The block ste.kxls a7 o61marts 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 ener 7 :lus,exw4w7r gip9wb/agabl+(bwt. z*4 kogy change when you jblw/9zw(*aw o44,7+7rit b:u gbex w s.pgk alump as high as you can?

In Fig. 6–31, water balloonstm 786y7uwb kvfk6/so3e 7nen are tossed from the roof of a building, all with the same speed but with different launch angles. Which one has the highest speed on ime7ts6ef8b37m7y6 ku /n vk nowpact? Ignore air resistance.

A pendulum is launched from a point that is a height h above its lowe(8i+ uqksa5wc:q vamtjevg/9g, 75o gst point in two different ways (Fig. 6–32). During both launches, the pendulum is given an initial speed of 3.0m/s On the first launch, the initial velocity of the pendulum is directed upward along the trajectory, and on the second launch it is directed downward along the trajectory. Which launch will cause it to swing the largest angle from the equilibrium posga,7 m 5u+5 i(g 9taqgkcq8oev:vsj/wition? Explain.

A coil spring of mass m rests uprigh5r e4palc.6anb)7gu /zis pe) t on a table. If you compress the spring by pressing down with your hand and then release it, can the spbeca5/su4zp7p) )ei.l n 6ag rring leave the table? Explain, using the law of conservation of energy.

A bowling ball is hung from the ce pa66ai epfbw6d)w(; hiling by a steel wire (Fig. 6–33). The instructor pulls the ball back and stands agap6iw p66b;d ha(fw)aeinst 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 potentiaxk967+fmq c+lb o9f qul energy when water at the top of a waterfall falls to the ucf9x+9 +6qkq lm7bfopool below?

Describe the energy transformations whenhp26sk2qqgl:/fy t l 7 a child hops around on a pogo stick.

Describe the energy transformations that take place when a skier startsf ti3(e)u9nlb skiing down a hill, but after a time is b(f3 l)et iub9nrought to rest by striking a snowdrift.

A child on a sled (total mass m) starts from rest at the te*uk/ ax csg:0io(kc aa*s -m:op of a hill of height h and slides down. Does the velocity at the bottom depend on the angle of the hill k*a0 cumx/*iae: o-k(cs a:sg if (a) it is icy and there is no friction, and (b) there is friction (deep snow)?

Seasoned hikers prefer to step over a fallen log in their pat64 .m fdc+n a2spch.r,gsuq o1h rather than stepping on top and jumping down on the other sid s6qur2f pc.an1hdomc+ , 4.sge. Explain.

Two identical arrows, one with twice the speed of the 9a ,bn 0ojtx4pother, are fired into a bale of hay. Assuming the hayxabpt4 9oj,n 0 exerts a constant frictional force on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain.

Analyze the motion of a simple w jbn0(gmwd2+ ce4jz5swinging pendulum in terms of energy, (a) ignoring friction, and (b) taking friction into acdj w4w0mc(jegb5 z +2ncount. Explain why a grandfather clock has to be wound up.

When a “superball” is dropped, can r6.xry; it rf k52 xda4gpi8cu 5dxo8/it rebound to a height greater than its original height? Expxy fg84r ritckx8 6 ad2;iu/ 5r.do5pxlain.

Suppose you lift a suitcase from the floor to a tablq9 slu pj544(x (hqlfae. The work you do on the suitcase depends on which of the following: (a) whether you lift it straight up or along a more complicated path, (b) the time it takes, (c) the (4jl9ql4fq5 pxah( s uheight of the table, and (d) the weight of the suitcase?

Repeat Question 22 for the power needed rather t:f h /5hfpz,b;pqne,i. x+jorhan the work.

Why is it easier to climb a mountarv/*ba1b0p gf *uejy-in via a zigzag trail than to climb straight upfpber 1bj* v-*guy/ 0a?

Recall from Chapter 4, Example 4–14, that you can use a ph4waj9 hs:w.xulley and ropes to decrease the force needed to raise a heavy load (see Fig. 6–34). But for every meter the load is raise4:sawxj hhw.9d, how much rope must be pulled up? Account for this, using energy concepts.

  How much work is done by the gravitational force whh(c .q6z0zlcmen a 265-kg pile driver falls 2.80 m0q (lzcm6.hz c?    J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m hpgmi7(9knhubj2a* c 9).apeuigh. How much work is requiredpp9 a*j.n79g2 ubhm e(ku ci)a?    J

  A 1300-N crate rests on the floor. How much work is required to move it at co)2(qfj.7mp4w;ndwjh ulj,*rx h kd g4a/;gjvnstant speed (a) 4.0 m along the floor against a friction forcejln h;rmdjxkf wg/;7h 4w)*. gjv(ap4du q,j2 of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did the movers do (horizontally) pushing jx9o3k zy)al9 a 160-kg crate 10.3 m across a rough floor without acceleration, if the e 9y)zx9l ka3joffective coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is accelerated by a i a kk+5z79cfhforce across a floor at a rate of for 7.0 s. Find the n k9f5ka i7zh+cet work done on the box.   J

  Eight books, each 4.3 cm thick with mass 1.7 kj wopj6p:9;hig, lie flat on a table. How much work is req;hj:6 pwipjo 9uired to stack them one on top of another?    J

A lever such as that shown in Fis85 b31sd;bi7c: folg 3(ov(c vyp srag. 6-35 can be used to liff objects we might not otherwb 7lov (3c:c;srsgva35(y8podb1sifise be 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 slides 3.6 m down a 28° inclij*4a w*do;tl wne 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 friction is w*;wlj4 *dato0.40. 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 *- pp oo j)tss0sc70o3p ijm4cpcy5p* of mass M an acceleration of 0.10 g upws t-mcj5sp0p0j7c4op)p p sio *y*o3card.    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 ax7gapx b:yf,hthm5,krty.7-u is 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 objebmg s6odklg-a ,ow, s+ccq9+* ct, acting along the x axis, varies as shown in Fig. 6–37. Determine the work done by this force to move the object (a) from xoo-c9qa bckm* g+w+ ,6,lg ssd=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 p/cgea26 nrug*article 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 oxygen molbus d;mj +61ruecule, 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 arrowle ccik8*( wrj ib7v.7 is doubled, by 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 stop ica8 t5 0eo/ jhz4o6igan 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 bmlp;ts*;2nhy hftoh:* 8gg z*e done to stop a 1250-kgcar traveling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whosek 2wrb*gyq b,5:h3blt evrba;r325 lq string exerts an average force of 110 N on the arrow over a distance of 78 cm. What is the speed of the arrow as it leaves 5lqq b 3e5rhb,2l2a v;:wrkgyb*t3 rb the bow?    m/s

  A baseball (m=140kg) traveling 32m/s moves a fielder’s glv-;xk+zcr, 3 g2 yuw3x pfpq3hove backward 25 cm when the ball is caught. What was the average force eh x zpvuqf3wk3;r,2 cpygx3+ -xerted by the ball on the glove?    N

If the speed of a car is incv3 x-u;n vkcm1reased by 50%, by what factor will its minimum braking distance be increu3;vck- 1xvnm ased, assuming all else is the same? Ignore the driver’s reaction time.

  At an accident scene on a level road, investigators meas 3cclemw12o9 xure a car’s skid mark to be 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 notocw 9cm x21le3 matter?)    m/s

  A softball having a mass of 0.25 kw;n idr*z4 6w5fzwkau2 :lj c4g 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 platenwc4 j:aiw 4 2z65rw;l*u dkfz and the pitcher is about 15 m.    N

  How high will a 1.85-kg rock go if thrown straighfw jgqufo f6 2:/wg)j,t up by someone who does 80.0 J of work on it? Neglect air resi/,):jfggfqfowj2 6wustance.    m

  A 285-kg load is lifted 22.0 m vertically with an acceleru0heyk- 8.rsem t+ pn:f/q*dhf2,sm mation by a single cable. Determ.r fmm umneqyhhpde2*f0+ 8ts-:,sk /ine
(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 440Nxfx.w/ tlq,.y/m How much must this spring be stretched to store 25 J of potential energy?ltfy..qw/ xx,    m

  A 7.0-kg monkey swings from one branch to another 1.2 ,n4avb.ejdk+6: 0spx (pqbx zm higher. What is the change kp+dp4a( vs ,jebxz nbxq0:.6 in potential energy?    J

  By how much does the gravitational potential energy of a 64-kg pole vaulter c 6wfe cwuvp;7;hange if his center of mass rises about 4.0 m dur6ev7;p;wcf uw ing the jump?    J

  A 1200-kg car rolling on a horizontal surface has speed v = 65 kmvem+ rc3/rlr 9xeo780ph rb6 h/h when it strikes a horizontal coiled spring and is brought to rest in a distanc rl 9prcr60hmhe7o bx+3 8/vree of 2.2 m. What is the spring stiffness constant of the spring?    N/m

  A 1.60-m tall person lifts a 2.1z1s9j57 fse cl0-kg book from the ground so it is 2.20 m above the ground. What is the potential energy of the book relative to 9fj 1z5secls 7
(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 th6pibf0 *hf 6 n35m rr0a.bmcoje top of a 3300-m peak. pbbomr3r afh0*5f0 c n6j.i m6
(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 thevyz1) kzuzs-u kct034 spring iszvu3kt4u kc10sz ) zy- next to 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 at thyby8i8;m,b pjx f *o( f5u4bpop speed (5.3m/s) and grabs a vine hangi*py 8ij5 boy;hfu4, xbb8m(pfng vertically from a tall tree in the jungle. 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, slides down a frictionless 35.uu io (fcld :01ip7g-h0$^{\circ}$ 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 frictionlebh+gv( x g-l4kss 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 i+dvu ,q) i oqxmgbt7v6v s0zn;l(9c2bnto gravitational potential energy without thm6,cbvtl)20od7 ( b;+nv gqvsi9uxzqe aid of a 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 jump;r boi-kcp-)bs vertically upward from the top of a platform with a speed of 5.0 m/s. ()bc ko-bi; pr-$\alpha)$ 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 constant is 95p*pc 6 z eco;d3g6qb4e0N/m is attached to a table and i;6pb3*q6c c ezgoep d4s compressed down 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 l 7 3genar5jq1vooped track shown in Fig. 6–39. If the block is to remain on the track, even at the top of the circ 7agjq v15nre3le (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 (spri2irn 0mnfky(de 72ky,l rp2pl7l;m g: ng stiffness constant k),0d2ge;yf nl: yi(ml lr7k2p2, pn7krm Fig. 6–40. The 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 whose ugpn4 rn 9(rbx /o56deo70x sfinstretched r6e 4po(figob7x95 nd rn0s/xlength 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 dragged up to point 1 w(elb9pjw upy-cij,pa527 k3yhere it is released from resc2 yp(pj 3w5y -a7kp9j ,biuelt. Assuming no friction, calculate the speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown with narf-)sw. )sba 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 placed at the bj.dxnm 0 95u qgy2q b fn+jw)xjw*gkl41tb+1jottom of an elevator shaft. If the elevator cable should break when the elevator is at a height h above the top of the spring, calculate the value that the spring stiffness constant k should have so that passengers undergo an acceleration of no more than 5.0 g when brought to rest. Let M be the total mass of the elevator and p01lf+xj9+1qt4bxggjw5jnq*n. u w) ybmjd2k assengers.

  A cyclist intends to cycle up x4r);8vjg5gy )gajvb j.ixi3 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 oppo1 djbr6r8o g3zsite directions, collide head-on and come to rest. H8r z6j3brgo1 dow 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 bota -hy+ gmcw7: : u6ivsw/mm+attom with a speed of 2.2m/s How much thermal energy due to friction was genera+wu: s+6 hvyi/mc m:a7 t-gmwated in this process?    J

  A ski starts from rest and slides d7lotqh vp7i/h+8 sc4ee/o 3vftca ;.y 7wxv-vown 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 13so. 8i8kh+fd z.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 bounces back to a heif 43ud- 9uhhchght of 1.5 mfh hc9 u3dh-u4.
(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 acrossb keccts80r93yy/n0s4- ozyn+bj8 4 sgci1d q a floor with a constant horizontal force of 350 N. For the first 15 m the floor is fibbs40jtc qyk1rzy s go/ s+e8nc8n cdy9-034rictionless, 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 in Fig. 6–d cosj6v7:s h+d ;qmh *1gs;vh41 passes point 1 with a speed of If the average force of friction is equal to one-fifth of its weight, with what speed wi do:s16v +h q;7 dvjgmhhss;*cll 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 upw7 kx.l+iq8so ay 8s8szard 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 attach l8ug1h/ s+r3y,its71lybgs z5- mjcxed 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 the equilibrium position before stgsmglh 83+-/l1isu,xytbr5 y1 c7 sjzopping 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 mq,n* blr2z*o -u:wfg spring, Fig. 6–40. gz*nl*muw f-q, ob2r: 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 position, how far beyond its equilibrium position will it stretch on its first swing?    m

  Early test flights for the space shuttle used a *aiho 2s: bxp h 4h8hu-pd)-9+hvjjiw “glider” (mass of 980 kg including pilot) d2)hjphbp:4-hvi x8a w *hj +-io uhs9that 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 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 ftp*25bpvy0qclnhh/ ;lm7*ugn.jm 3 iano to a sixth-story window 16.0 m above? ;mlutlbnfm yjh7pc025. n3h*/ gqvp*   s

  If a car generates 18 hp when traveling at a steady 88km/h wh iyx*uv*jt+foe/*cpy(z x /t,at must be the average forceit f e/ xco(zpj**vy,*yt/xu + exerted on the car due to friction and air resistance?    N

  A 1400-kg sports car accelerates tad)0 u4 +mwjrq(9iqt from rest to 95km/h in 7.4 s. What is the average power delivereqj4utw(d t+m) q9r0 aid by the engine?$\approx$    hp

  (a) Show that one Britk; : jf5jdi6gq3+juit ish 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 expre :7zntl(o,ez mssed in the form 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 qcs+ /ce7 0h8o +yqjfw; c ky2cvtaw(ner4y8)her 1150-kg car slows down from to 65km/h in about 6.0 s on the level when it is in neutral. Approximately what power (watts and hp) is needed to keep the car traveling at a constah;c s+fye4t ocv ew/qkcncy(q07ay8 8+2w)j r nt 75km/h.    hp

  How much work can a 3.0-hp motor do in 1.0 h?x9y* jkhz) cc(; 53glc.prdfm $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg s ro*ykbzq z y.p3hi-7rw1rt2/b bk+) dhot from rest to 14m/s If this motion takes 1.5 s,kp2-b7z3q1 zrh r)i*.d/o+wk rbyb yt what average power was developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute through a heigt2t pd21tyj -mht of 3.60 m. What output rating (wa2jdpm tty-2t1tts) should the pump motor have?    W

  During a workout, the football players at State U. ran up the stadiujmco*zb+ 2im8m stairs in 66 s. The stairs are 140 m long and inclined at an anglmcbj *8o+2mz ie 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 clit /pox ub bw .s;xa7*:43nms-zxy7lsl mb 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 pola dakz( y5j+:wer output of 120 hp. How steep a hill can it climb atz(j5 +:ady alk a 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 a4 hqh)5p khj(h1vpsvk v3hr 4.q5 hqi1long a level floor at a speed of 1.2m/s if the coefficient of frictr(1 v4kvi pv3hhkh h qqhh.j 5pq14)5sion is 0.45?    hp

  A bicyclist coasts down d2qladnl,x* 94k:g cn a 7.0 $^{\circ} $ hill at a steady speed of 5m/s Assuming a total mass of 75 kg (bicycle plus rider), what must be the cyclist’s power output to climb the same hill at the same speed?    W

  Designers of today’s cars have -jr)r ,o fm(ud/*fdg;qn iuh 1built “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, but remains like an elastic spring up to that point, what must the effective spring stiffness constant of und miq ju;1- df(/ *h,grr)fothe 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 th m:l6+* qhdgmclf4h3onq w7w 3e 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 with a height of 21 cm, and an average shelf holds 25 books, how mu34 f:n wqd hgq mwll7mc*63+hoch 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 1936 Olympics pp8vezv5by2/g+ c b k+shows that his center of mass rose 1.1 m from launch poi 5b/c+y+kpv2pbg ev8 znt 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 along the looped track shyqmh99zw *l6 rown in Fig. 6–39 is to remain on the track at all times, even at the very top oml99*zhy rwq6f 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 without hdcm4t:/:zt4exqfvc x / +t l;bis 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 was 35m/s estima4/;t4lfxqte : cb ct+d mv/zx:te
(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 qc r*whr8t k-0,nh/lmcord of length L whose other end is fixed (Fig. 6–wqck0*lhn , 8/r-hrtm 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 nlpklx+y 46*d y b,cgvu99p-htop of a 3700-m-high mountain. The climb is made in 5.0 h starting at an elevation 9c9pg*uylpbx +6l ynv, d4hk- of 2300 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 elevatodyz, :* .vuomlr 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 0nki 5i7mgon n +j j:iquyq+9)in California claims that its lifts can move 47,000 people per hour. If the average lift carrie9jqu)goj7q: km +in0in ni +y5s people 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 falls vertically 81 (jp0 lp97nh kcm before striking the turbine blades. Cal 9kh70cpn(ljpculate
(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 coas- orbw /p hqppsg58e*d2t:3ekter with a circular vertical loop (Fig. 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 times your weight. Ignore friction. Show also that as long as your speed is above the mbrp3qpsg*p e 2/ d- 8ohe:w5tkinimum 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 directlyo+ (qslo3- byt into work, how high could an 82-kg man cli+ts-o bq(lo3y mb a ladder if 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 upward angle of 45.l2 t*ia qi+nb/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 ins(mr.m, a ht,1-wbij2q dprs exc+w5n6ide the scale compresses 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 itwmcmri pa.(q e ,-1stwxhrd, b+ n562js peak?    N

  A 65-kg student runs at 5m/s grabs a rope, and swings out over a lake (Fig. 6–)mjeekm i 6i;rzx:*.f 45). He releam)j: ex.e*i ;fmik6 rzses 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-kg ath d 9 0 9q4yaip(ib/rz3zk +xd0xy+hvrqlete climbs a vertical distance of 5.0 m in 9.0 s. What minimum power out a qr kx0xiz03+vh(byd+ 4y9 dpriz9q/put was used to accomplish this feat?    W

  Some electric-power companies use w qd.aup22l i *w.(uymsater to store energy. Water is pumped by reversible turbine pumps fromm*(. 2a dl iwu2yupq.s a low to a high 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 constant k is cut in hal7 4ak riw 3;5iczshox/f. What is the spring stiffness constant for each of the two resulting sprinhzr;ics i/4wx7ao35k gs?   k

  A 6.0-kg block is pushed 8.0 m up a roug1r:mo(1uhsg o h*nyob;pu0osm)zy *0h 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, 5h+)zl*z /o3yqnny t,qn2xxz how long will it takezz qhyx nzl y),o*2+qn3n/5xt to accelerate from 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”), the patient walks onz(u l(u2c 8weon)8l eu an inclined treadmill (Fig. 6–46). Estimate the power required fcwe)zeu88un o 2ll(u( 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 vertically upward a dis 1h rbfc7 echd**9+hnftance of 500 m, what was its velocity when it left the volcano? r*e9f1bc n *hfh+hcd 7$\approx$    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 wheelz );n f*lfuhf* from a height of 2.0 m at a rate of 95kg/s (a) If this water wheel is set up to providehfu)z*ff n*;l electricity output, what is its maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s