In what ways is the word “work” as used in ev 3o(it9v-pj gaeryday language the same as that defined in physics? In what wa-opi3tj9a (vg ys is it different? Give examples of both.

Can a centripetal force ever p4d6tuzfx lb :5s j4wj:-3dfc do work on an object? Explain.

Can the normal force on an object ever do work? Explxkoli l3i8m9 :ain.

A woman swimming upstream is not moving with respect to the shore. Is she0hj-s ;t-r ohk.w.p2wi**uzy g s1 osk doing any work? If she stops swimyo0 t.;r**gjwi s ph.1-s2 wzkh-ks ouming and merely floats, is work done on her?

Is the work done by k)iveaem (12 c*w hpx5l*qo.o tinetic friction forces always negative? [Hint: Consider what happens to the dishes when you pull a tablecloth hvmq(at el.x1)oecoi ** p5w2out from under them.]

Why is it tiring to push hard against a solid wall evb cm7ubjm.cfap.5 wij,;/1jr en though you are doing no work? ;j,.71imbupf5jcr. camb w/ j

You have two springs that are identical except that spring l is stifsiwlyq+ey qw 6e/c/t (v3 lm;/.ljzr3fer than spring 2 ecsitqv3/r6l w/e/m l .(w+y3 jqlzy;$(k_1>k_2).$ 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 constantsg gm9k2 9*zj xu6sq5i horizontal force on a block that is free to slide on a frictionless surface (Fig.6-30). The blo6 miszkj9 2u9ggs5q* xck 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 doe4ixyw s 94cj:w7 j)*cjcpq* pcs your gravitational potential energy change when you ju4y q7c:j w9*)j4 csxccwp* jipmp as high as you can?

In Fig. 6–31, water balloons arezjurffgq 2x(q ) x 1)5pj.wh o9/pn7rf tossed from the roof of a building, all with the same speed but with different launch angles. Which one has the highest speed on impact? Ignore air resistancep.1x7 fu)jf(o 5nr qxhp gjqf)r9z2w/.

A pendulum is launched from a point that is a height h absjf(ad 8*kn1 xg qj+)o qatfx15t d43pove 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 a*tdjk g sont f4 fxqj1p5)1qa(x+83d along the trajectory, and on the second launch it is directed downward along the trajectory. Which launch will cause it to swing the largest angle from the equilibrium position? Explain.

A coil spring of mass m rests u n ptiu2r+y*q(pright on a table. If you compress the spring by pressing down with your hand and then release it, can the spring leave the table? Explain, using the law of conservation of ene(ty+r pq nu2i*rgy.

A bowling ball is hung from the ceiling by a steel wire (Fig. 6–33)h:3jty1x*zz qtbqa (s 7ohl.6. The instructor pulls the ball back and stands against the wall with the ball against his nose. To avoid injury the instructor is supposed to release the ball without pushing it. Why?qj:bahzy 6t7.z tosq x3*(hl1

What happens to the gravitational potential energy when water at ivypco,mp6 p8l ishldn,5qu t c/.7/.the top of a waterfall fal p p.ocndmpy vsl,7t i5cli.6h,u/ 8q/ls to the pool below?

Describe the energy transformh2o b+: kg9xs4e*he uyations when a child hops around on a pogo stick.

Describe the energy tf;xizkaxed;6w m472 bxzmp -4ransformations that take place when a skier starts skiing down a hill, but after a time is brought to rest by striki42z xam dwk;mxf764x;z b-peing a snowdrift.

A child on a sled (total mass m) starts from rest at the to ls us2-dbj+6op of a hill of height h and slbjo+ luss62- dides down. Does the velocity at the bottom depend on the angle of the hill if (a) it is icy and there is no friction, and (b) there is friction (deep snow)?

Seasoned hikers prefer to step over a fallen log in t/f5 fbtjhb/h /ee4xb 6heir path rather than stepping on top and jumping down on the other f/hf/5be te6bx/ bjh 4side. Explain.

Two identical arrows, one with twic6y/ r 6gnsq3 z a40dkqzx4/utke the speed of the other, are fired into a bale of hay. Assuming the hay exerts a constant frictional force on the arrows, the faster yk3/n0aktzxz4g /sr4q6 uqd6arrow will penetrate how much farther than the slower arrow? Explain.

Analyze the motion of a sim / yyi(gdo(eg zh;v6c1s 0h7 -2waqbwvple swinging pendulum in terms of energy, (a) ignoring friction, and (b) taking friction into account. Explain why a grandfather clock has to bgv1h- (67y/aiv c ( z;gow sbe0whqd2ye wound up.

When a “superball” is dropped, can it rebound to a height greatewf: 8dfazix. .r than its original height :8zi xa.wffd.? Explain.

Suppose you lift a suitcase from the floor to a table. The work you3b t.qg8us7ld do on the suitcase7 uqblg8.dst 3 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 height of the table, and (d) the weight of the suitcase?

Repeat Question 22 for the power ne x0vb6o 3hi +ltcs8um+eded rather than the work.

Why is it easier to climb a tx;x: d4fruth. pemd3jgzl 5q md8o i*n: r510mountain via a zigzag trail than to climb straight up? dxjqo 3; p5*.dmfd4iu: r51xt: relnmzght08

Recall from Chapter 4, Example 4–14, that you can use a pulley and ro 9blyd l,:qbj9kt/widrn : *z.pes to decrease the force needed to raise a heavy load (sy::,9btjldl z wd.n kqr9 b/*iee 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 gravitational force when a 265-k2-kk p..f.9pkfb7hjelaf1y xg pile driver falls fhf p bax l2jpk.-y.. 19k7ekf2.80 m?    J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How much work ibz*o dn)j) 9r2 (kod)nifm2 trs requirez f) rioj )n92()tdonmd*kb 2rd?    J

  A 1300-N crate rests on the floor. How much work is required to move6v 3v ignsd9m3 it at constant speed (a) 4 33d9nvms vg6i.0 m along the floor against a friction force of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did the movers do (horizontally) pushing a 1 o4e jtlsaf.t1w .;rnz4o0 qz*60-kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0.50? r;q40 4a.zl*nowoejtsz.1 tf    J

  A box of mass 5.0 kg is p mu.bw2,1o*melu po x6:g 2xzaccelerated by a force across a floor at a rate of for 7.0 s. Find the net work done on the box.og bu m ppuow6,mz*xl2:xe21.   J

  Eight books, each 4.3 cm thick with mass 1.7 kg, l9je , bl+p+gtkie flat on a table. How much work is required to sgj l t+pbk,e9+tack them one on top of another?    J

A lever such as that shown in Fig. 6-35 can be u9qqd9 7qwl 9rgsed to liff objects we might not otherwise be able to liff. Show that the ratio ofgr7qd q9wq 99l 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 4myki du9z,+h3.6 m down a 28° incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 6-36). The effective coefficientzkd+, ym9iuh4 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/rcw:o :v c8vg3czf 6gdmx a5+ give a helicopter of mass M an acceleration of 0.10 g upv8cd3f:gw ccoxrv5am 6:z+/gward.    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 a4zxsp)z 2 u0x l))pamlinear 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 thq8 - g.lgvkliend*9/ ze x axis, varies as shown in Fig. 6–37. Determine the work done by this force to move the object (a) from x=0 m to x =n/ieqldv-* g.k8g l9z 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 tbj6xws ue0/ 6no2yd 2ehe $+x$ 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 oxyge5y 9s 5tr,clgo4s/swd n molecule, with mass of $5.31\times10^{-26}$typically has a KE of about$6.12\times10^{-21}$ J .How fast is the molecule moving?    m/s

  (a) If the KE of an arrow is doubled, by w( nhd8z-l-o,y4yw q wyi5 vx/lhat 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 tamth feca,4/bq2j ;q4o stop an electron $\left(m=9.11\times10^{-31}\mathrm{~kg}\right)$ which is moving with a speed of$1. 90\times 10^{6}\mathbf{m/ s}$ ? $\boxed{a\times10^{b} \mathrm{J}}$ a =    b =   

  How much work must be done to stop a 125dh0n :v gr,at+0-kgcar traveling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whoa8e;z a gp12bise string exerts an average force of 110 N on the arrow over a distance of 78 cm. What is the speed of the ap2;1eiazgb a 8rrow as it leaves the bow?    m/s

  A baseball (m=140kg) traveling 32m/s moves a fieldeapopyhok79,i+fb rmn9 kg054r’s glove backward 25 cm when the ball is caught. What was the average force exert5g fbp h4kon+r7k0oya i9 9,mped by the ball on the glove?    N

If the speed of a car is increased by 50%, by what fll3g61. nx .z9ok8ofkvfib) tactor will its minimum braking d3gzv 6n 1lko9fk .)ilb.8xfot istance be increased, assuming all else is the same? Ignore the driver’s reaction time.

  At an accident scene on a level road, 6bty2 medyax;qv47u0d( vxf3 investigators measure 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 34qexb 7xvfdy mau y26v 0(t;d0.42. 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 timdt + llxe2+ f;/4kjnprhg- kg9e it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the averag;gn-+fje9hkk/l 2lx +p rdg4t e force of air resistance during a pitch, if the distance between the plate and the pitcher is about 15 m.    N

  How high will a 1.85-kg rock go if thrown straight up by someone who does 80.0 Jbmdyjh vj8)ned k vu90.q-)m , of work on it? Neglecm v.09,v bjjd yu)h -k)dnqme8t air resistance.    m

  A 285-kg load is lifted 22.0 m vertically with an acceleration by a sing9smi )yiq,v1 jekvt (.le cable. Determine ki v 9(e)ys .,vt1mqij
(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 mmxs3zwbq2z2r4 2n nr .ba0)uvuch must this spring be str)a2b2 rxnrzqzun2wm.3s b04vetched to store 25 J of potential energy?    m

  A 7.0-kg monkey swings from one branch to another 1.2 m hi. d;5j. dxy8s nvw928 vsoplbzi/*z kmgher. What is the change in potentiall .d x;s/bpv 5ni .*98ykm vz8j2dozws energy?    J

  By how much does the gravitational potential energy ofinp -0g g9z9ru a 64-kg pole vaulter change if his center9p0g nur-9zi g of mass rises about 4.0 m during the jump?    J

  A 1200-kg car rolling on a w 1lj6x/jt*q3q; hnmktyl szp .-d1s9horizontal surface has speed v = 65 km/h when it strikes a horizontal coiled spring and is brought to rest inht w stl3 kqd/1 9yn.jx;zlpj61sq-* m a distance of 2.2 m. What is the spring stiffness constant of the spring?    N/m

  A 1.60-m tall person lifts a 2.10-kg book from the ground so it l yasbgix3lb.z4;sh69 c;a )w is 2.20 m above the ground. What is the potential energy of the book relative to 9;bx s3)w lgs.b ;alc4izay6h
(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 elevati9b3g::8 gtl6/ 1yakpo tpej rhon of 1600 m and climbs to the top of a 3300-m peak. :jgbp kyr/9e6a81 lth3gp to :
(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 -06l8rvztfp n*qd**- olsvqc vertically next to 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 line up w*r -doqp6qlz-*f vsn c *lvt08ith the ruler marks?    cm

  Jane, looking for Tarzan, is running at top/w5rpk3p9ovx8khz v-rr 7vn0-lkko 9 speed (5.3m/s) and grabs a vine hanging vertically from a tall tree in the kr9kv -vp/kol7h -k9w0r5v3 zpxorn8jungle. 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 dtv*z ji*p*tz0 ,zkzg;own 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 gcrnu i0;e8b83 fh3 sgi t:(han:9gd xpiven 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 gravitational u9 m4sytw5 3h 7ntvs4epotential energy without the aid of a pole. With what minimum n43evs9hsttu7y54 mw 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 fu),ckm ,r r(cfrom the top of a platform with a speed of 5.0 m/s. rf,uccr k) (m,($\alpha)$ 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 950N/e+7uxyfd8 e.msl:: i;xy;e hdm is attached to a table and is compressed down 0.150 m. (adeu ef;:7hd+ 8m.:;yy xselxi) 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 showkmu0x.x mtgiocm1j 7frb, ;;8 n in Fig. 6–39. If the block is to remain on the track, even at the tb,;8k0 i7;.u gc xxmrfj1to mmop of the circle (whose radius is r), from what minimum height h must it be released?    r

A block of mass m is attached to the end of a spring (spring stiffnef7 5t29-k co )g55fc oytiw6bzapo-clss constant k), Fig. 6–40. The block isz69fla)5w g -o c-7ctkfbi5y5 p2 otco 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. Sc)/arhm f4;xshe is tied to a bungee cord whose unstretched length is 12f a 4;rmxh)cs/ 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 8/)vouznj3e*+ h d ygh16leeoin Fig. 6–41 is dragged up to point 1 where it is released from rest. Assuming nln)/hd*1 oeo+u6v3jee8hygzo friction, calculate the speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown/9 1qdk8xrhryv)w(yu with a speed of 12 m/s at an angle of 33 $^{\circ} $. (a) What is its speed at its highest point    m/s
(b) how high does it go? (Use conservation of energy, and ignore air resistance.)   m

An engineer is designing a spring to be placed at the bottom 8*+d+s hfs(u1z/cr hfxk ca .hof an elevator shaft. If the elevator cable should break when the elevator is at a height h above the top of the spring, calculate theu*f+h 8d h+c(.xs r1ks/hafz c 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 uphb: 7o3x .s rrqat3,nv 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 trag3vp+2)ulb c:q uu1dgveling 95km/h in opposite directions, collide head-on and come to rest. How much +)pcbq uul1g :g32vdu thermal energy is produced in this collision? $a\times10^b$ J a =    b =   

  A 21.7-kg child descends a slr2l8ugp ;zn--wtye18zi 5yes ide 3.5 m high and reaches the bottom with a speed of 2ygenliez-u2pw 8yrz; 5ts8-1.2m/s How much thermal energy due to friction was generated in this process?    J

  A ski starts from rest and4zjj* phift.03r5g4 l,gwlv(muob /p slides down a 22 $^{\circ} $ incline 75 m long.
(a) If the coefficient of friction is 0.090, what is the ski’s speed at the base of the incline? $\approx$    m/s
(b) If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level? Use energy methods.$\approx$    m

  A 145-g baseball is dropped from 3s0 ptw+dcfk4(1uhco ze1 o8 jfo*be5a 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 fromoeplhk w6(va 9c:9lo8a:btl - a height of 2.0 m, and it bounces back to a height of 1.5 m. keoa9otl::bch(lpw a9v 8l-6
(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 49xpnl ixfb (e(rn-e)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. Whati)xn4-l e nrf9 pex((b is the final speed of the crate?    m/s

  Suppose the roller coaster in Fig. 6–41 passes point 1 wi edkjy,fs58*t: l gq7 f7qlr9oth a speed of If the average force of friction is equal to one-fifth of its weight, with what speed will it reach point 2? The distance traveled is 45.0 yjflod5l98:77 ft* e,skqrqg m. $\approx$    m/s

  A skier traveling 12m/s reaches the foot of a s2z;5 e-z;4hbuc r xpfgteady upward 18.0 $^{\circ} $ incline and glides 12.2 m up along this slope before coming to rest. What was the average coefficient of friction?   

  A 0.620-kg wood block is firmly attached to a very light horizontal spring (kcje6hf3g/3pww 9u i/ui;ogg*(g puu *=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 stopping and turning back. What is the coefficient of kinetic friction between tho *i/w3 3p p6 u*h(jcgug9u;giu/wfgee block and the table?   

  A 280-g wood block is firmlkkchz s 2fvezp) ;8*5wy attached to a very light horizontal spring, Fig. 6–40. The block can slide along a table where the coefficientfz2kvh 5 8w*p ;szc)ke 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” (mass of 980 kg i0z+*x38ny vxjd6tstl ncluding pilot) that was launched horizontally at 500km/h fromv3yls8+t* njz6xxtd0 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 piano to a sixth-story winw:mn)p2p b w:xdow 16.)p w:x wn2:pbm0 m above?    s

  If a car generates 18 hp when traveling at a steady 88km/h whatdvtt1d p 6g(r0 must be the average force exertg(dt60rpv dt1ed on the car due to friction and air resistance?    N

  A 1400-kg sports car accelerates from rest to 92, z xok7efk.o5km/h in 7.4 s. What is the average power delivero e.zx2k,7okf ed by the engine?$\approx$    hp

  (a) Show that one British hor+bs f)rg,n3j r di-b-vsepower$ \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 of r :j; lu r,fho33s2 3quk/djtu“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 about 6.0 ngf u 3e(*4hkys on the level when it is in neutral. Approximately what power h4 3(kfu* geyn(watts and hp) is needed to keep the car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hp mo (m.ary9-t.earym +acc7 ,)yt7uhaedi0q u5 btor do in 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg shot from rest ; 23c)j hp ybri/+f,aq4jejfdto 14m/s If this motion takes 1.5 s, what average po)afjbjyef j43hpri 2c/d q+,;wer was developed?$\approx$    W

  A pump is to lift 18.0 kg of wateim 0q/rl7k.f ir per minute through a height of 3.60 m. What outr/mi0i.k flq7 put rating (watts) should the pump motor have?    W

  During a workout, the football players at State U. ran u 5t me;f.ijq1 jjnrdm1+ 4.no63+pc ztn nwti6p the stadium stairs in 66 s. The . cnr.n+4otfdmn1z6 +jjtn163m pjteq iwi;5stairs are 140 m long and inclined at an angle of 32 $^{\circ} $. If a typical player has a mass of 95 kg, estimate the average power output on the way up. Ignore friction and air resistance.    W

  How fast must a cyclist climbjc fw3b5w 0md3 .ck/vb 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 hil*h+jrwxj7 k 7ll can it climb at a constant spe7hlr wx kjj+7*ed of 75km/h if the frictional forces add up to 650 N?    $^{\circ} $

  What minimum horsepower musxch :n39kuftt-bf, f 0t a motor have to be able to drag a 310-kg box along a level floor at afx:0ubfhn tc3f,9k-t speed of 1.2m/s if the coefficient of friction is 0.45?    hp

  A bicyclist coasts d h a)on9nmd8c9own 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 built “5mi/h(8km/h) bumpers” that are designed vj)p tpr 6qv,9ebky:o vt fwe) 0;.s0kto compress and rebound elastically without an v0kj06we.: eov;s fr)bpk vp,yt)qt9y physical damage at speeds below 8km/h If the material of the bumpers permanently deforms after a compression of 1.5 cm, but remains like an elastic spring up to that point, what must the effective spring stiffness constant of the bumper be, 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 firsr318*wkt ua wxt shelf is 10.0 cm off the 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 much work is required to fill all the shelves, assuming the books are all laywt18a3wk* r xuing flat on the floor to start? $\approx$    J

  A film of Jesse Owens’s famou )s:issb e;pb.s long jump (Fig. 6–42) in the 1936 Olympics shows that his center of mass rose 1.1 m from launch point to pi.ssbeb ;)s: 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 slidieh7gzz 8n 36cpng without friction along the looped track shown in Fig 83cehn7 gpz6z. 6–39 is to remain on the track 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 after jumping from an aircraft without hig k99z4q 5cwa zd6v0qcs 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 tw9cvg qac z5 zd4k9q06erminal 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 other end o;a6s 3rk k tm/t:v7oois fixed (Figtt3 vm/oo k;76okasr: . 6–43).
(a) If the ball is released, what will be its speed at the lowest point of its path?
(b) A peg is located a distance h directly below the point of attachment of the cord. If h=0.8L what will be the speed of the ball when it reaches the top of its circular path about the peg?

  A 65-kg hiker climbs to thda .3( q5qxzzue top of a 3700-m-high mountain. The climb is made in 5.0 h stauzq x.(5zdaq 3rting at an elevation 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 28 m nulc8 8)*/h7i u8a1prxxvi loabove 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 lifts canet*govu5;n up j uc0q),fo-+v move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the power cog ,v0-nf);qt u e uj*5+ovpuneeded.$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and falls ve ;txn3f6:v qqdrtically 81 m before striking the turbine blades. Cat: 6;nd3q qfvxlculate
(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 -b.gunpqbl t0d / ,4fkvertical loop (Fig. 6–44), the difference in your apparent weight at the top of the circ, 0p-. 4utgbf/dbqknlular 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 on the size of the loop or how fast you go through it.    mg

  (a) If the human body could convert a candy bar directly into work, how higm 8ycy4k*ef +hh could an 82-kg man climb a ladder if he were fueled8c+kyhm4yf e* 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;(20p egtqkf ;fd/qxn at an upward angle of 45.0$^{\circ} $ from the top of a 165-m cliff with a speed of 175m/s What will be its speed when it strikes the ground below? (Use conservation of energy and neglect air resistance.)    m/s

  If you stand on a bathroom scale, the spring inside the scale compresses 0.60 m b 2 dp6y itutf7u(h.)ubq*1ipm, andi .tpu ht) b67*qpbdui2yf1( u 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 its peak?    N

  A 65-kg student runs at 5m/s grabs a rope, and swingst7uuc5.c7 59rzpegn f out over a lake (Fig. 6–45). He releases the 7cnpzrgcf 5t u9.eu57rope 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 72n 7w q..cq+vz 0r9ynce-kg athlete climbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used to accomplish t.n znqv.+079q wcc reyhis feat?    W

  Some electric-power companies use water to store energy. Waacnj6i18ge,7p4 k*ytqb p/ h)at:h pater is pumped by reversible turbin4)p/ tae :g q6c1hai aj hbpt8pn*,7kye pumps from 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 const i5jj.x1n szb*4rv12. stfecu ant k is cut in half. What is the spring stiffness constant for each of2u14zjenj1vx.c*5 si tbrfs . the two resulting springs?   k

  A 6.0-kg block is pushed 8.0 jmjtxl*;lwnkx 39 0b 3m 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 from 35km/h) f 3uond/om+a to 55km/h in 3.2 s, how long will it take to accelerate from 55km/f d /anu+o3mo)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 patqod;3ka6)m ot y 7d)sr9v:vaaeq88azient walks on an inclined treadmill (Fig. 6–46). Estimate the power required from a 75-kg patie 8 rv7m6)z;o8ea ts )aoak9daqvqd y:3nt 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 verti3ljv6n/r uel4 cally upward a distance of 500 m, what was its velocity when l3ju/64e vnrl it left the volcano? $\approx$    m/s
(b) If the volcano spews the equivalent of 1000 rocks of this size every minute, what is its power output? $\approx$ $a\times10^b$ W a =    b =   

  Water falls onto a water wheel from a height of 2kus0 6(jw4ljl rmg/ a..0 m at a rate of 95kg/s (a) If this water wheel is set up to provide k.4a06m(/l uswrjjg lelectricity output, what is its maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s