In what ways is the word “work” as used in everyday language thf,cn(d qhgq)f0sj,c)m 2s3 8l etq+hre same as that defined in physisq f c8jlsr)qfq3d(eg2,hm +)c,nht0 cs? In what ways is it different? Give examples of both.

Can a centripetal force ever do work on ax ((53rrp::p(hlh ylj pzotl 1n object? Explain.

Can the normal force on an3-i53or 5ihq s)fxgnhla8; ia object ever do work? Explain.

A woman swimming upstream is no-eyb w1 z+bdd31fl sb7t moving with respect to the shore. Is she doing any work? If she stops swimming and merelyelzd+ 1-3bfby s1bdw7 floats, is work done on her?

Is the work done by k5;f1ndczk93 bj:uvnqw6ajg j5h5 (y sinetic friction forces always negative? [Hint: Consider what sdqn( 5zgbv ;ha w55c93f kjj6ynj: u1happens to the dishes when you pull a tablecloth out from under them.]

Why is it tiring to push hard against a solid wall even though you are doinl 9d8a:l*dhghv3 jpo(ckc1+ jg no w1j dkco +d lgj:(c ahhv8p93*lork?

You have two springs that are identical except that spring l is stiffer than 1q xh;cgz/sic8vz +re(v(n f ;sprinr;/ vv ing1schzz(8fec+ ; (qxg 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 freecwtw:. nxq35w6 vs f ;l-jpmi) to slide on a frictionless surface (Fig.6-30). The block starts from rest at þoint A, and 5m3jw:tf )vx.6 p-cqn;wl swi 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 gravitat gm th,1te16 kkrno3q2ional potential energy change when you jump as higho ,nkt6mrqe t3g 1k1h2 as you can?

In Fig. 6–31, water balloons are tossed from the roof of a* ,5o4d rii:ha q yhd+btj z-+qg;hs3c building, all with the same speed but with different launch angles. Which one has the highest speed on impact? Ignore aqc5jt hyz+qd: 4hrh *id+- sg;ao3b,iir resistance.

A pendulum is launched fromek.6r,1mttfjodpso 6 o0 1o+ x a point that is a height h above its lowest point in two different ways (Fig. 6–32). During both launches, the pendulum is given an initial speed of 3.0m/s On the first launch, the initial velocity of the pendulum is 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 position?t x1sme1,r.ofjok6 +t od 6op0 Explain.

A coil spring of mass m rests upright on a tablehu9g ;.tbj-wm-(xf fh. If you compress the spring by pressing down with your hand and then release it, can the spri h.fw;-hfj- 9tm(ugxb ng leave the table? Explain, using the law of conservation of energy.

A bowling ball is hung from the ceiling by a steel wire (Fig. 6–33). The ins-lyns dn)e,4 v(zgyet. z +vt90q and7tructor pulls the ball back and stands ag.0v-,qlgs )7atd+z (e evd ynyt zn9n4ainst 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 w2; zlbd iy*l ok*g.4pwhen water at the top of a waterfall falls to the pool beli2go z *k*.lb ;dply4wow?

Describe the energy transformations when a child hops around on a pogo stic5gek 8 (:dgji4ydahcktjp /c tw0 q+.4k.

Describe the energy transfo yzcz3gipmh0b5 6 yh+*rmations that take place when a skier starts skiing down a hill, but 5bzp*hmy0 z +3h iycg6after a time is brought to rest by striking a snowdrift.

A child on a sled (total mass m) starts from rest at the top of a hill of height:/w vnvr,mnd, h and slides down. Does the velocity at tnv,r/ d: ,mvwnhe bottom depend on the angle of the hill if (a) it is icy and there is no friction, and (b) there is friction (deep snow)?

Seasoned hikers prefer to step over a fallen log in their path rather than s w(m(h:b, p jp t0q92xkpu0fehteppingh0p0m(b 9kpxjpw2( :u, htefq on top and jumping down on the other side. Explain.

Two identical arrows, one with twice the speed of th5b vjxbijm(rrg r*1k3 1,)gf de other, are fired into a bale of hay. Assuming the hay exerts a constant frictional force on the arrows, the faster arrow will penetrate how much farther than the sjr*igg 1(rb5 ,xm3jdkbf 1r v)lower arrow? Explain.

Analyze the motion of a simple swinging pendulum in terms)oc8pj6x umv pldo-,vtb8)m t0qi x,; of energy, (a) ignoring friction, and (b) taking friction into accoulbio8tqv -jmd x,v;68 u)pc0omp) ,xtnt. Explain why a grandfather clock has to be wound up.

When a “superball” is dropped, can it rebop5dc(wthdi, 4und to a height greater than its original he(pi5,cw dthd4 ight? Explain.

Suppose you lift a suitcase from the floor to a table. The work you do 2z;nvfwz v51ton the suitcase depends on which of the following: (a) whether you lift it straight up or along a more complicated path, (w;z5z21 tvvfn 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 t 0c2h0kixwp3zk lf9l 9he work.

Why is it easier to climb a mountain via a zigzag trai1s x bpp.q-yw:l than to climb straight u b-yswp:qx 1.pp?

Recall from Chapter 4, Example 4–14, that you can uyhoplj j,a.,fzf po0g, +a7;rse a pulley 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 rope muf f,; +0za7jop.po yglr,jah,st be pulled up? Account for this, using energy concepts.

  How much work is done by the gravitational force wheg l2uogkx8.)txob 8 (cn a 265-kg pile driver falls 2.k uggxt8x.8oocl2 b)(80 m?    J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How muchio(us/qr*-a3 ifs 5qt work is required? 3qqstasf*i /-o5uir (   J

  A 1300-N crate rests on the floor. How much work is rc 7ab1-k+fjgd equired to move it at constant speed (a) 4.0 bk jc-+1f7dag m along the floor against a friction force of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did the movers do (horizh,qh*ge) k*cluc+ t5gnpa .c618f7rpehac0 z ontally) pushing a 160-kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of frf8kc*e6g,+rt 1zue).0* hc p5cca haqh7 nplgiction was 0.50?    J

  A box of mass 5.0 kg is accelerated by a force across a floor a vbl 6s y8.k,uzqop7e2t a rate of for 7.0 s. Find the net work done on the box. p8,e uz qyl6kb7s2.ov   J

  Eight books, each 4.3 cm thick wc0ja8h/2 kcw.j5d/qd gfkiq ;ith mass 1.7 kg, lie flat on a table. How much work is rej2 c; k0gq dw 5ihk8jcqad/./fquired to stack them one on top of another?    J

A lever such as that shown in Fig. 6-35 can be used to liff objects we mv,az/+i pk /1pi*ma.n nbzn4e ight not otherwise be able to lifn,eb/avz.*innkp ip/a1 +mz4f. 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 from acc -8zj.g 6fauucelerating by a man who is pushing back on it parallel to the incline (Fig. 6-36). Tjc. f uug8a-z6he 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 req 2avqq5cm,kc:uired to give a helicopter of mass M an acceleration of 0.10:qv,c 5a 2cqmk g 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 ;x5tx)k aqyizy3o( 75;ewzpx3 dqdv5 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 shown in Fig. 6–37. p1nv 9n16n c3ett4obn lla.r 8Determine the work done by this forcn1op et36. clvn94bt nl1an8re to move the object (a) from x=0 m to x = 10 m    J
(b) from x = 0 m to x = 15 m    J

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

  The net force exerted on af2wjilh/(i2 q1 v w2 (bb;zb.5qvjgrg particle acts in the $+x$ direction. Its magnitude increases linearly from zero at
$x=0$, to 24.0 N at $x=3.0$ m. It remains constant at 24.0 N from $x=3.0$ m and then decreases
linearly to zero at $x=13.0$m. Determine the work done to move the particle from $x=0$ to $x=13.0$ m
graphically by determining the area under the $F_x$ vs. $x$ graph    J

  At room temperature, an oxygen molecule, xo y9uz*/zmz ;j4 v8ey+f2rxa with mass of $5.31\times10^{-26}$typically has a KE of about$6.12\times10^{-21}$ J .How fast is the molecule moving?    m/s

  (a) If the KE of an arrow is doubled, by what factor p 1rqkndb30z9f+ g, lshas 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 an electrak vl:-suc d9*on $\left(m=9.11\times10^{-31}\mathrm{~kg}\right)$ which is moving with a speed of$1. 90\times 10^{6}\mathbf{m/ s}$ ? $\boxed{a\times10^{b} \mathrm{J}}$ a =    b =   

  How much work must be done to stop a 1250-kgcar traveling dsfos1o:1ns btx qt61-9 3 ty(kkcn1y at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whose string exerts an average 3)ezwqj*go*zl do+t;force of 110 N on the arr*owtq+)g3oe z d;jlz*ow over 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 25 cm bga85 tzeak,5bjow ,:when the ball is caughtbkj,aw5,gzt e b8:ao5. 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 wakgv+5.kyksf 5u-ph1r, xp 4 its minimum braki,.u41kvgs+xf kpw5y k5p ha r-ng distance be increased, assuming all else is the same? Ignore the driver’s reaction time.

  At an accident scene on a level road, investigators measure a car’s s e8 *+jio*pc*g3nm inwkid mark to be 88 m long. The accidpgc38 *o*nimwen *i+jent 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 ofen o+g0ip.oi 7 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 bet.g e7oo0+nipiween the plate and the pitcher is about 15 m.    N

  How high will a 1.85-kg rock go if thrown st7u/(*a7 yvb .uo bdalco1hgq:raight up by someone who does 80.0 J of work on it? Neglect air resistance: lh bao.cuva1oqb/7 d(ug7*y .    m

  A 285-kg load is lifted 22.0 m vertically wjlft 1py0h5*h 5 qdu4,l;ijx gysbg++ith an acceleration by a single cable. Determixtj1 yd+l5qu s+big*hl5 ,4g;f0jp yhne
(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 mus wd* 51lw )dbjfxkz4t0t this spring be stretched to store 25 J of potb4d)*fdlk wt5jwz0x1 ential energy?    m

  A 7.0-kg monkey swings from one branch to another 1.2 m higher. W1 +- sy;gcre6sqfzr) zhat is the change in potentialrg)y s1cqefrz+6z-s ; energy?    J

  By how much does the gravitational potential energy of a 64-kg pnep1 x+qoa a 4-tk;-wfole vaulter change if his center of mass rises about 4.0 m during oatqp-4 ;a+1xfk nwe-the jump?    J

  A 1200-kg car rolling on a horizontal surface has speed v = 65 km/h when it stris8te/jg:k /hzy 6.i8l 5pojiv kes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stie6:j/i8 zy jl t5go/8sk.hvpiffness constant of the spring?    N/m

  A 1.60-m tall person lifts a 2.10-kg book from tifk teftk 2863he ground so it is 2.20 m above the ground. Whtk8fe3ft2ik 6 at 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 pg px lbr w*yf63u8c::1600 m and climbs to the top of a 3300-m peak. xb:u 6 crf*pp:g8y w3l
(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.( dus tso-ol5va 9n/g a ruler. The end of the spring is 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 lgtus(dla/ov. 59 - sonine up with the ruler marks?    cm

  Jane, looking for Tarzan, is running at top speed (5.3m/s) and grabshu, 3vo/v jwc jlg++b4 a vine hanging v,3cj 4lvjg h+oub v+/wertically 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 frov ,;1xzgez 6fom rest, slides 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 givf qbs7ak;jqu*5- bh /nen a shove up a frictionless 28.0$^{\circ}$ incline. It reaches a maximum vertical height 1.35 m higher than where it started. What was its initial speed?    m/s

  In the high jump, Fran’s kinetic energy is transformed into gravitation m t+:hyxn4.q o:tl:m0cm3iieal potential energy without the aid of a pole. With what minimum speed must Fran leave the ground in order to3i ht:lin qy0xmo:.e: +c t4mm lift her center of mass 2.10 m and cross the bar with a speed of 0.7m/s.    m/s

  A 65-kg trampoline artist jumps vertically upward from the topx+3egu47 prbn 2fqou , of a platform with a speed ong37e+4u x2 qp our,bff 5.0 m/s. ($\alpha)$ How fast is he going as he lands on the trampoline, 3.0 m below (Fig. 6-38)?$v_2$ $\approx$    m/s
(b) If the trampoline behaves like a spring with spring stiffness constant 6.2×10$^{4}$ N/m , how far does he depress it? $y_3$ =    m

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

  A vertical spring (ignore its mass), whose spring stiffness constant i:-wx+ dgrm gp.sq (g+bnv6ge(s 950N/m is attached to a table and is cmbex((+pv +wrng.g gg-dq s6:ompressed 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 lgqhz r9yq1sk9 9+:x3ymj7 ca 3idp.rvooped track shown in Fig. 6–39. If the block is to remain on the track, even at the top of the circle (whose radius is r), from what minimum hedyqsazjpm9 v .y+:9qg71ic r3hrk93 x ight h must it be released?    r

A block of mass m is attached to the end of a spring (s0w9hk kre-10xxd: .tgpl:lrnpring stiffness constant k), Fig. 6–40. The blx0h nrk1lpl. x w d-:9tre0:gkock 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 whoxfx t4-(g; hepiq6h.f se unstretched length is 12 m, and falls a total of 31 m. (a) Calculate the springh.h exf 4- 6txipgq;(f 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 wbb):3e q1.jbyndq o,dragged up to point 1 where it is released from rest. Asq ob.j1deqbnb3: w,y)suming no friction, calculate the speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown with a h b16n1cl /-ijwj guf0speed 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 pc 69wh) lw(w;6r8n vp*qrgc oof an elevator shaft. If the elevator cable should break when the elevator is at a height h above thchgorw6c(;p9wp8wn r*qv 6)l e 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 cycle up a 7.8fqk8s6ll7l:69l/h 9qqwft c t $^{\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 opposite v 8,abhq*va(zdirections, collide head-on and come to rest. How much thermal energy is produced in this collisionv,*hz q8v a(ab? $a\times10^b$ J a =    b =   

  A 21.7-kg child descends a slide 3.5 m high and resk)m.d a.3uy-o )dy4fbda/ v m mh.ac)aches the bottom with a speed of 2.2m/s How muc)3asmy/aufc v) ).ybo4k ..adm -d mhdh thermal energy due to friction was generated in this process?    J

  A ski starts from rest anddqsni*6e.yh zpb.0 o(i wu :5t 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+ae.r5w i:s3cy3w m/p o yb;eh from a tree 13.0 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 height o3famnq +ofy;8*vss,go3o+vf tv 1r 8of 1.5 m.sv ntfo+8 yorg vmf1 ;a3 ovs8+q*f,o3
(a) What fraction of its initial energy is lost during the bounce?    %
(b) What is the ball’s speed just as it leaves the ground after the bounce?    m/s
(c) Where did the energy go?

  A 110-kg crate, starting from rest, is pulled across a floor) kzp+9z lw,o3sa ybnp 4vti.) 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. 3)okpwv aist4,blz) 9.zy n+p30. What is the final speed of the crate?    m/s

  Suppose the roller coaster in Fig. 6–41 passes point 1 with a speed of Ifnw/ f an85p7 r/i.agzt the average force of friction is equal to one-fifth of its weight, with what speed will it reach point 2? The distance traveled if. t/ zaigann/7r85wps 45.0 m. $\approx$    m/s

  A skier traveling 12m/s reaches the foot of a stead9i6leiu c l/f6h*di esb1f2.my 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 fi.vsf*d;fc7 nqwdfi. 3rmly 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 the equilibrium position befor*f qncwi3f.d.s;7vf de stopping and turning back. What is the coefficient of kinetic friction between the block and the table?   

  A 280-g wood block is firmly a;r(6j4abf38bmuh jqr ttached to a very light horizontal spring, Fig. 6–40. r86m;jh3 f4qb abu(rj 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 “glider” (massbdv7/4fth s i5 of 980 kg including pi/ dbs7ti f4vh5lot) that was launched horizontally at 500km/h from a height of 3500 m. The glider eventually landed at a speed of 200km/h (a) What would its landing speed have been in the absence of air 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-kgv /f a,( bhxq*m7m4gmd piano to a sixth-story window 16.0 m above? 7,md4f/g vxh mbm(q*a    s

  If a car generates 18 8, eqbddyw8gs7kj) -uhp when traveling at a steady 88km/h what must be the average force exerted on the car due to friction and air resigw)kj7 y-q, s8dd bu8estance?    N

  A 1400-kg sports car accelerates from ref6 8ausgn v99dag +4gdlfpb.4 st to 95km/h in 7.4 s. What is the average poa+4gnlad99.g fu6pgvs 4fdb 8 wer delivered by the engine?$\approx$    hp

  (a) Show that one Britikdusl;4 s4x k,sh horsepower$ \mathrm{ft}\cdot\mathrm{lb/s}$ is equal to 746 W.
(b) What is the horsepower rating of a 75-W light bulb?    hp

  Electric energy units are often expressed in the form of00w:vs bp:7huimmqeb5fk 5nl3 : 5jto “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 in abou1qkezewp: 86.zkr j* mt 6.0 s on the level when it is in neutral. Approximatelye1r8pez.j w mkq6 *z:k what power (watts and hp) is needed to keep the car traveling at a constant 75km/h.    hp

  How much work can a 3.(z igy d5/7xhx0-hp motor do in 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg shot from rest to 14m/s If this motion takx5q/dss n -vf.es 1.5 s, whatn5s/f q vdx.-s average power was developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute through b; xxza 6it8ylhxu(+-a height of 3.60 m. What obu8xx ilh-;zx+a6ty( utput rating (watts) should the pump motor have?    W

  During a workout, the football players at State U. ran up the stadium stairs9 p2; w cwcanjkj4 93u,wwxax1 in 66 s. The stairs are 140 m long and inclined at an angle of 322au jnp3axw19x ,4wwc ;c9kj w $^{\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 cli r*/ yp3pq3baxmb 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 :wvol r hfl.ebf7jli3.y71+/bw.shsa hill can it climb at a constant o7f+/l3lfe br. v wyhs.wis17: b.jlh 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 alo b43ge7l(jr g.b lvmq6ng a level floor at a speed obm74 3gqllvge6r b(j .f 1.2m/s if the coefficient of friction is 0.45?    hp

  A bicyclist coasts down a 7.cra2;8 (nui cv.pgzr-pjnw :v79 k:ur 0 $^{\circ} $ hill at a steady speed of 5m/s Assuming a total mass of 75 kg (bicycle plus rider), what must be the cyclist’s power output to climb the same hill at the same speed?    W

  Designers of today’s cars have built “5mi/h(8km/h) bumpers” thabp zcjq),,j:e pe z90jt 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, wha,cj),ppe9:jbq z 0z ejt 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, h(er4x0y 0 pbhjug8n *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 much work is required to fill all the shelves, assuming the bob *jrhp4g he0nu0(yx8oks are all laying flat on the floor to start? $\approx$    J

  A film of Jesse Owens’s famous long jump (Fig. 6–4dd 3+fn511n8aum cz s1 +cgnpt2) in the 1936 Olympics shows that his center of mass rose 1.1 m from launch point to the top of the arc. What minimum speed did he need at launch if gma8c3n z1+dd5pf+cus1tn1n 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 tracka*h5 v1c 5jaks*/wi hn shown in Fig. 6–39 is to remain on the *1 j5kha /nc 5hsa*viwtrack at all times, even at the very top of the loop of radius r.
(a) In terms of the given quantities, determine the minimum release height h (as in Problem 40). Next, if the actual release height is 2h, calculate    r
(b) the normal force exerted by the track at the bottom of the loop,    mg
(c) the normal force exerted by the track at the top of the loop,   mg
(d) the normal force exerted by the track after the block exits the loop onto the flat section.   mg

  An airplane pilot fell 370 m afts4q2y6mae7jk k: w u4per jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assumingjw42 k sp6eyk47u aq:m 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 whos7ygz9dc4l/zu2o5 nate other end is fixed (Fig. 6–43).g /5 uc 27otzazn49yld
(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 mountainsd2k6.z 0dwxvgb+ fy3. The climb is made in 5.0 h starting at an elev6.0f bd gz +xvsky2d3wation 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 elevator is 2 jbk y./;ba8ky5 gw1wt8 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 Califorbfk 4z76z+5 l hbhm0u5z ta9exnia claims that its lifts can move 47,000 people per hour. If thaxfuzz ehhl5kb645 0+79 z mtbe average lift carries people about 200 m (vertically) higher, estimate the power needed.$a\times10^b$ W a =    b =   

  Water flows over a daa b(/;4x,6 9)wupccr r-h;tddmjmjimm at the rate of 650kg/s and falls vertically 81 m before striking the turbine blad9pr-x (dh j wmu; c m)a4,r6im/dctbj;es. 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 cebs2;sc muud gyomsf3: a5hu+4c.(s 4ircular 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 minimum needed, this answer doesn’t depend md3s;e+sb:5o2sy c4huu su4a mc.gf( 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 in3t .bvixepi4o-l*p0a+ x ys;t to work, how high could an 82-kg man climb a 4lx .*tpio;0 3+aytbvs xipe -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 ebv1)tna.6rejys /7i an upward angle of 45.0$^{\circ} $ from the top of a 165-m cliff with a speed of 175m/s What will be its speed when it strikes the ground below? (Use conservation of energy and neglect air resistance.)    m/s

  If you stand on a bathroom scale, the spring inside the scall6:uv;ya0 1cryhuf i .e 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 : i;a0uuyl f.vhy6cr1the scale read at its peak?    N

  A 65-kg student runs at 5m/s grabs a rope, and swings out o4pd 6jf5sn0 kazmtjx,-e (t5qver a lake (Fig. 6–45). dmf 0z5p(45kq,tj nasxt e-j6He releases 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 w6e3juyf j+l6fe-9 /m lxkq1q athlete climbs a vertical distance of 5.0 m in 9.0 s. What minimum power ou3lj+1 qem-/yeq6jwk flx f96utput was used to accomplish this feat?    W

  Some electric-power companies use water to store energy. Water is p7 l 8cl2caxrg,umped by reversible turbine pumps from a low to a high reservoir. To store the energy produced in 1.0 hour b,x ag 7r8c2lcly 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 7qea*a*aux(obca w 5m*y;rnohp :p 8*cut in half. What is the spring stiffa7*uh r**c(p ym;:8nbpaoo*a5 wqaxeness constant for each of the two resulting springs?   k

  A 6.0-kg block is puw(5um .b9lk yjukwa9uk8d ,o n-0a1yvshed 8.0 m up a rough 37 $^{\circ} $ inclined plane by a horizontal force of 75 N. If the initial speed of the block is 2.2m/s up the plane and a constant kinetic friction force of 25 N opposes the motion, calculate
(a) the initial kinetic energy of the block; $\approx$    J
(b) the work done by the 75-N force; $\approx$    J
(c) the work done by the friction force;    J
(d) the work done by gravity;$\approx$    J
(e) the work done by the normal force;    J
(f) the final kinetic energy of the block.$\approx$    J

  If a 1500-kg car can accelerate zrd.6(fydtoflp i5,7uf//gkrn 4 i6hfrom 35km/h to 55km/h in 3.2 s, how long will it take to accelerate from 55km/h to 75km/h Assume the p4tnd(56 uizyf7g frpdh k/l./fro6 , iower stays the same, and neglect frictional losses.    s

  In a common test for cardiac function (the “stress test”), the patient walks or*rdx w fkbv6;j5k 4n;n an inclined treadmill (F*;nr;6fwd4 k vj xkb5rig. 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 vertically upward a dvs:+h24 :r ubtk7oexvub i/,jistance of 500 m, what was its velocit2/+o u4e,7ibrujx sv bh :k:vty when it left the volcano? $\approx$    m/s
(b) If the volcano spews the equivalent of 1000 rocks of this size every minute, what is its power output? $\approx$ $a\times10^b$ W a =    b =   

  Water falls onto a water wjba + )v(-ceqql n7e,bheel from a height of 2.0 m at a rate of 95kg/s (a) If this water wheel is set up to provide elecvqb (j +l7e),qaecb n-tricity output, what is its maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s