In what ways is the word “work” ()ny 3xj(.2sgjhd6tzlah7d pjcu 3q* as used in everyday language the same as that defined in physics? In what ways is it different? Give examples of bochdy )u*(3g7qjsnl j(2 pzdj3 ht.a6x th.

Can a centripetal force ever ;n7d3 yun87cymk p2+v v* kgaddo work on an object? Explain.

Can the normal force on an object 3 j1l 61 sg)wdf 5qip2whwypi;ever do work? Explain.

A woman swimming upstre;xk3 6hiz4gfk am is not moving with respect to the shore. Is she doing any wixg346 kk hf;zork? If she stops swimming and merely floats, is work done on her?

Is the work done by kinetic friction forces always negative? [Hint: Con p.;:pwuyuqi 0hxm 8rdk78u5 nhh8i(i sider what happens to the dishesiqkpi n iu8mpu h rdu.hh:887;x(5wy0 when you pull a tablecloth out from under them.]

Why is it tiring to push hard against a solid wall even tho,/avmvdsz 4.zm qm n*1,tg,s dugh you are doing no mmsv,gmz,n /a.zdtds ,4* 1qvwork?

You have two springs t +0r2gj j6d v,is.h gmd6rjo iez*iy xz.2uw+)hat are identical except that spring l is stiffer than springwg6 di6d).m z+2sixyv+roije2j0g, rzu*jh. 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 slide on alj ;+k ssf 5(,xddt eii(b9l(a frictionless surface (Fig.6-3bijflai((d e9+;l s5sd (tkx,0). The block starts from rest at þoint A, and by the time it has traveled a distance $d$ to point B it is traveling withe bint $o$ point B it is traveling with speed $\nu_\mathrm{B}$.When the block has traveled another distance $d$ to point C, will its speed be greater than, less than, or equal to 2$\nu_\mathrm{B}$? Explain your reasoning

By approximately how much does your gravitational(y6l12lxzeiz nboa35 potential energy change when you jump as high as bzizly1xo n3a6l(e 25you can?

In Fig. 6–31, water balloons are tossed from the roof of a building, all wlb fdr/h9:z39f00 v au6 fk6k/ipdebbith the same speed kz:avb bbdf6 93if/d9fr0hk6elup/0but with different launch angles. Which one has the highest speed on impact? Ignore air resistance.

A pendulum is launched from a point thb/ hct.tkh6f )at 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 initia)thbk.h c/6ftl 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? Explain.

A coil spring of mass m rest+ej+p.5+sj 5 gtua xxks upright on a table. If you compress the spring by pressing down with your hand and then release it, can j5.tg ue+k5x p+jxas+ the spring leave the table? Explain, using the law of conservation of energy.

A bowling ball is hung( ,by .et(r ml+bndq,o from the ceiling by a steel wire (Fig. 6–33). The instructor pulls the ball back and stands against the wall with the ball against his nose. Toy (,tre,(b+d lqm. obn avoid injury the instructor is supposed to release the ball without pushing it. Why?

What happens to the gravitational potential energy when water az solw,:9iq j/t the top of a waterfall falls to the pool bel :w9l,joi zqs/ow?

Describe the energy transformations when a child hopss0vmwp adm+m: e-/w0(:l ycee around on a pogo stick.

Describe the energy transformations t aab,*0a nfv(gvt gr:4hat take place when a skier starts skiing down a hill, but after a time is brought to rest by strivf*g vn:4 aarb,t0( agking a snowdrift.

A child on a sled (total mass m) starts from rest at the tonc2iyrq+9ixfaab cd6c r4 s88a63g (c p of a hill of height h and slides down. Does the velocity at the bottom depend on the angle of the hill if (a) it is asr8gq 4ic i+3fyn(r6a 9x d cc68cb2aicy and there is no friction, and (b) there is friction (deep snow)?

Seasoned hikers prefer to step8f4 zzi r7o-uk over a fallen log in their path rather than stepping on top and 8f7ukoz -zi4r jumping down on the other side. Explain.

Two identical arrows zlrhl4hx egh +jjs3p8l1o ,,/ v+cpt0, one with twice the speed of the other, are fired into a bale of hay. Assuming the hay exerts a constant frictional forc+1l elszhjx lhrhv3 ,p4go t80 cp/j+,e on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain.

Analyze the motion of a psq4tfp1x 5. 3s6mzl q.y/bginqq3:bsimple swinging pendulum in terms of energy, (a) ignoring friction, and (b) taking fri4/ :qt q.q61m qp.i33 snxg5bpzsfyblction into account. Explain why a grandfather clock has to be wound up.

When a “superball” is dropped, can it rebound 71bqq3l wzmm0 5/xxe oto a height greater than its original heighm01b/z 7x5xq3 owlem qt? Explain.

Suppose you lift a suitcase from the floor to a table. The work you do on th21p;xup qkn c7e suitcase depends on which of the following: (a) whetherpu17 k xqcp2;n 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 efutd0l4z6q.y 54zhuneeded rather than the work.

Why is it easier to climb a mountain via a zigzag trail than to climb straiua(kq1g v i5h0ght upk(i50 v1gahqu?

Recall from Chapter 4, Example 4–14, that 3gw8dh*u 2unryou can use a pulley and ropes to decrease the force needed tu8n2hwr*u3gd o raise a heavy load (see Fig. 6–34). But for every meter the load is raised, how much rope must be pulled up? Account for this, using energy concepts.

  How much work is done by the gravitational force when a 265-kg pile driver fa n-:s; u:raqwllls 2.;lwq: - n:rasu80 m?    J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How much work is rews4yguex9++z +5gax nce *;uzquired? gwz*g4xz9eeusx5;y+un +ca +    J

  A 1300-N crate restsem,/ os4+woua on the floor. How much work is required to move it at constant speed (a) 4.0 m along the floor agai+ma /wuoe4,so nst a friction force of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did the movers do (hs. ab 0de auox;p w+d/e+bpb8dm;(iw.orizontally) pushing a 160-kg crate 10.3 m across a rough floor without acceleration, if the ewm/uabwdxp+sbd.8+ i(;de .;oeapb 0 ffective coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is accelerated by a force5oo y q*z9uj.yfw4 u+1my;meq across a floor at a rate of for 7.0 s. ; qoymuyf4 .wqo1 +*em9 u5zyjFind the net work done on the box.   J

  Eight books, each 4.3 cm thick with mass 1.7 mc2tqs+7 xd:q x- a fmj(6wn6dv-y(mjkg, lie flat on a table. How much work m67mv:(q xj+txn(jd f-qad syw6cm 2- is required to stack them one on top of another?    J

A lever such as that shown in Fig. 6-35 can b zb npwpud+tx0ops5 0k;; 80 .tjsxks,e used to liff objects we might not otherwise be able to liff. Show that t5 xjkud0 +;xsp;.pst zo,t8k0 wnpb0she 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 :pz lanf-mp5m9u. qbcd/+k+i4 qkm g8a 28° incline and is kept from accelerating by a man who is pushmk. i4a ++p d9kb8z/nmqfp:mcu-gl5q ing back on it parallel to the incline (Fig. 6-36). The effective coefficient of kinetic friction is 0.40. Calculate:
(a) the force exerted by the man,    N
$(b)$ the work done by the man on the piano,    J
$(c)$ the work done by the friction force,   J
$(d)$ the work done by the force of gravity,   J
$(e)$ the net work done on the piano   J

  (a) Find the force required to give a vbis b9i,p+0d helicopter of mass M an acceleration of 0.10 g upwab+9id i ,bvs0prd.    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 thsiw0 ghn:as5*xasgy+//s y6 q e distance axis is linear and that $d_{\mathrm{A}}=10.0$ m and $d_{\mathrm{B}}=35.0$m. Estimate the work
done by force $F$ in moving a 2.80-kg object from $d_\mathrm{A}$ to $d_\mathrm{B}$   J

  The force on an object, acting along bw5u --bybt:x the x axis, varies as shown in Fig. 6–37. Determine the work done by this force to move thwybt ux:-5-bbe 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 a particbc6b o3c3b9x (vq8 cswle 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 rpo o3.ndx07j oxygen 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 what fa qs6eqps- dai0wdg0 n.b 1u)q8ctor has its speed increased? $ \sqrt{a}$ a =    (b) If its speed is doubled, by what factor does its KE increase?   

  How much work is require9wn*7t y 5kwujf:ljl 3d to 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 125 zheggt)yod: 5tv 4hq*s, msdf;80d k60-kgcar traveling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired /q2 +wfrpq,:zm+cln b from a bow whose 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 lrql,+z q m/ 2bfc:wnp+eaves the bow?    m/s

  A baseball (m=140kg) traveling 32m/s moves a fielk-et9-x ;q rfcder’s glove backward 25 cm when the ball is caught. What was the average force exerk;-xrc q- fe9tted by the ball on the glove?    N

If the speed of a car is increased by 50%, by what factj3hma.;mpi 53gro 7zqm u8gm()uqo+g or will its minimum braking distance be increased, assuming all else is the same? I u 5i7uz+; . jgq3gp8h (moogram)mqm3gnore the driver’s reaction time.

  At an accident scene on a level road, investigatorl1 h3qzezx)/hs measure a car’s skid mark to be 88 m long. The accz zx3hq1h/ )leident occurred on a rainy day, and the coefficient of kinetic friction was estimated to be 0.42. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. (Why does the car’s mass not matter?)    m/s

  A softball having a mass of 0.25 kg is pitched at By the time it reaclh5 djl q:ytmpii )q)i7iqj:w 8*l-1nhes the plate, it may have slowed by 10%. Neglect i*d5 tlq8 iwlpl)j yi)ih-m:n:q1q7jing gravity, estimate the average 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 J gq2-(0nmznpb tj)ywp yq -20n of work on it? Neglect air resistanc( m0 z-0bqn22n t-pnj)gwqyyp e.    m

  A 285-kg load is lifted 22.0 mrmykd)z hzp+ixy;rs6i3el6r.bg 27 k4 n:)si vertically with an acceleration by a single cable. Determine +l634hr);zr . pisbyign rme z6 d2sky7)x:ik
(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 gigusjspb2lzuw;4;p6 w b5/5 How much must this spring be stretched to store 25 ;b lgwj 5swus; g 5pbp4i2u6/zJ of potential energy?    m

  A 7.0-kg monkey swings t; 6p x-8k5gc jlmg7frfrom one branch to another 1.2 m higher. What is the change in potential fx6r g- p 5;cmltgkj87energy?    J

  By how much does the gravit q 1t8 cmp;vh4yb-kj+wational potential energy of a 64-kg pole vaulter change if his center of mhw4vj1ck- pb t+yq8 ;mass rises about 4.0 m during the jump?    J

  A 1200-kg car rolling on a horiw md)ggl973cg v )5why3z6*jvsakg, d31cg zi zontal surface has speed v = 65 km/h when it strikes a horizonghdgm ygja d3ckw3v13 )5) zsc,*967liggvzwtal coiled spring and is brought to rest in 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/;l(n a2r7tm2-xex; frvl bizfee(u- so it is 2.20 m above the ground. What ise e i t xxvae;bff z/rl-r;(7n2mu(-l2 the potential energy of the book relative to
(a) the ground,    J
(b) the top of the person’s head?    J
(c) How is the work done by the person related to the answers in parts (a) and (b)?    J

  A 55-kg hiker starts at an elevation of 1600 m and cl x a0cxa/ak+i0imbs to the top of a 3300-m aaxkxa0ci0/ +peak.
(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 the s 3xj0* 0:bmpqu t5dqwcpring is ne*mtc5: dqq 0b3ujwp0 xxt 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 ru.qrxn4ms8,; g 7z)r2onvoqlik dkv n ,-zo9.ynning at top speed (5.3m/s) and grabs a vine hanging vertically from a tall tree in the jungle zqn9k.ironl- ,dvo ym 4ogz,2n)kx.vqs 7 ;8r. 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, sli9nhhj5e(6 quatl3g3x(0 1acb c73,aal lt drxdes down a frictionless 35.0$^{\circ}$ incline whose vertical height is 185 m. How fast is she going when she reaches the bottom?    m/s

  A sled is initially given a shove up a frictionless 2c7h eko7cu67x 8.0$^{\circ}$ 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 energymm9t ;zd/ kb+r is transformed into gravitational potential energy without the aid of a pole. With what minimum sm+ z9k;rd/m btpeed 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 kzfo 5:ds6qa+4t 0iob upward from the top of a platform with a speed of 5.0 o s4bt6do:afkz0q+5im/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 stscw .u9zcd 4 *0*vldrtiffness constant is 950N/m is attached to a table and is compressed down 0.150 m. (a) Wrv*clc *9 z4s.0wdudt hat 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 sliguyuc32bl:yjf2 fw;0h8s (q bdes without friction along the looped 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 height h must f 2b:quub2sc hyl g(fyw83;j0it be released?    r

A block of mass m is attached to the end of a spring (spring stiffness zxl 5bee/-qd0vm2-*hglbwo 8 constant k), Fig. 6–40. The block is given aq8e0- l-2l/x*5 dvw geobmzhbn 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 bpfv 774awi+qo2deb5xridge. She is tied to a bungee cord whose unstretched length is 12 m, and falls a total of 31 m. (a) Calculate the spring stiffness constant k of the bungee cord, assuming Hookb 7fe 4ia+p x7v25doqwe’s law applies. $\approx$    N/m
(b) Calculate the maximum acceleration she experiences. $\approx$   m/$s^2$

  The roller-coaster car shown ie:dhq b5 uvty9 odcmgit.z.e(,ne+5 2n Fig. 6–41 is dragged up to point 1 where it is released from rest. Assuming no friction, calculate td5tzq.5c eeu9o. + tyg(mhnv:ebd, i2 he speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown with a speed of 12 m/saa,2ojn52jx. jtbl 0x 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 b21xmoch -h 38km5vnpsottom of an elevator shaft. If the elevator cable should break when the elevator 5-hko mhxnc 28s1vpm3 is at a height h above the top of the spring, calculate the value that the spring stiffness constant k should have so that passengers undergo an acceleration of no more than 5.0 g when brought to rest. Let M be the total mass of the elevator and passengers.

  A cyclist intends to cycle up au6ybu1 p;o d)vn27lv s 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 u xj29gnbqx5 fy/6 )d:n8ze hw95km/h in opposite directions, collide head-on and come to resyn5xj6nd e9b)uz/2fx gqw:h8t. How much thermal energy is produced in this collision? $a\times10^b$ J a =    b =   

  A 21.7-kg child descends a slide 3.5 m high and reaches the bottomre5)fsa*yf urj1 w./sk((u tq with a speed of 2.2m/s How much thermal eneef/)5qswka y1u sfj(u r.(*t rrgy due to friction was generated in this process?    J

  A ski starts from rest and slides down a 22bkkxxg 3d5zy0zu,w4h c e157k $^{\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 l4awz kv5 m+(aa 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, anp793*- hep1d r cpkspid it bounces back to a height of 1.5 m. h9k*ps7-dp i1cppr3 e
(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 re c(zyar,95v b; rbrwyad( r+/dst, is pulled across a floor with a constant horizontal force of 350 N. For the first 15 m the floor is frictionless, and for the next 15 m the coefficient of friction is 0.30. What is the final speed 5rzvd(,br y+9rc d;(w/y r aabof the crate?    m/s

  Suppose the roller coaster in Fig. 6–41 passes point 1 with f8 i6c*r8rpcq a speed of If the average force of friction is equal to one-fifth of its weightir6*fcr88cqp , with what speed will it reach point 2? The distance traveled is 45.0 m. $\approx$    m/s

  A skier traveling 12m/s rc k.pi5e*hta 4eaches the foot of a steady upward 18.0 $^{\circ} $ incline and glides 12.2 m up along this slope before coming to rest. What was the average coefficient of friction?   

  A 0.620-kg wood block is firmly attached t +,wp5teo dqv -wz,s8ro a very light horizontal spring (k=180N/m) as shown in Fig. 6–40. It is noted that the block–spring sysw8ro, wsz-d5,qv ept +tem, when compressed 5.0 cm and released, stretches out 2.3 cm beyond the equilibrium position before stopping and turning back. What is the coefficient of kinetic friction between the block and the table?   

  A 280-g wood block is f6bvi 9e.( 1) pg/i1 yeh8 xdzkfd;txydirmly attached to a very light horizontal spring, Fig. 6–40. The block can slide along a table where the coefficient of friction is 0.30. A force of 22 N compresses the spring 18 cm. If the spring is released from this position, how far beyond its equilibriu1zky;p81dx ig6fitvyh9 x ddb()e/e .m position will it stretch on its first swing?    m

  Early test flights for the space shuttle used a; *3qweeb byl3 “glider” (mass of 980 kg including pilot) that was launched horizontally at 500km/h from a height of 3500 m. The glider eventuallye*y3q3bel ;bw 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 aixjyx f2al3kv bx6+;2 315-kg piano to a sixth-story window 16.22j k6xay x3i lxfb+;v0 m above?    s

  If a car generates 18 hp when traveling as2 ms2(bl.ninakq 9 0ut a steady 88km/h what must be the average force exerted on the car du.ms9 0 ns(bk 2q2ulinae to friction and air resistance?    N

  A 1400-kg sports car accelerates from rest to 95km/h in 7 61c2vg)kprk4h 94yek1 ixvk z.4 s. What is the avera 4 g92k1kcphxv1 r4y zv)kk6eige power delivered by the engine?$\approx$    hp

  (a) Show that one Britiskdqjqs i xx0u9kc:- 79b )x0nfh 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 expr g5e6yc)/ngfn fd*hz 6essed 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 her 1150-kg car slows down from .(bemau )j6 ;wsr vpq4to 65km/h in about 6.0 s on the level when it is in neutral. Approximately what power (watts and hp) is needed to 6 )4.bwr (psm vj;queakeep the car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hp motor do in 1.0s43/ ieqzq3 y aav fbzvmq+86/ h? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg shot from rest to 14m/s Iag xxb;p9o(7 4pakn6 if this motion takes 1.5 s, what average power was develbxn o ;k pxg64ap(i7a9oped?$\approx$    W

  A pump is to lift 18.0 kg )5l1.g zbo o ocbkb,3ww6lku4of water per minute through a height of 3.60 m. What output rating (watts) should the pump motor havlw.uco 31)ogbk o, z6lb5kbw4e?    W

  During a workout, the football players at State ni mqd0bzjkk6u*.t 9v7b lc33U. ran up the stadium stairs in 66 s. Theu.l6* ktvb3cj3z 9 7 miqndb0k stairs 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 cliejn-q3ey2 dwp7+gg3ci y (fbz /*hcn ;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 power output of 120 hp. How steep a hill can it clil cv-r+ b+fm5t5ynoh-mb at a constant speed of 75km/h if the frictbt mhcnf+ r5lo -+5vy-ional forces add up to 650 N?    $^{\circ} $

  What minimum horsepower must a motorn3 1l/yndb 8at1y.+szgff4h o have to be able to drag a 310-kg box along a level floor at a speed of 1.2m/s if the coeffahn1g8sz+3d f lybon t4/f1y.icient of friction is 0.45?    hp

  A bicyclist coasts downl rs -gy,u5( hff/eqf+(qw1ws 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(8kmdq7.yzyk d a m f*sav)o, (bhnbdc795//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 perm,7.vbhnako/(5)9f y*ddmb q z csayd7 anently 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 first shelf is 10.0 cm off the ground, and the r(gm/b;gi5 :e8 bdzhwlemaining 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 ti8hgw: ;dmb(e zl/b5g he 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 showg2 (k8 hccvybm 0lvz9f.j6 g.q 4u/fncs that his center of mass rose 1.1 m from launch point to the gjnq06/2c 9hul fy4vzkcm8. b.f vcg(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 slidiu3 b3p( mor7v ged3qbk7+bc6cng without friction along the looped track shown in Fig. 6–39 is to remain on the track at all times, e b3dvkoc3m7 (rc p7bbqeg+63 uven 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 jumpin6p r*, y lpyf mds.(-oja n39jd84flvqg from an aircraft without his parachute opening. He landed in a snowborj ,.8m ld*s njp6a9f v (ydfqy-l4p3ank, 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 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 c ge5g,r; ro.cpa:bhs *ord of length L whose other end is fixed (Fig. 6–43 *oh,p grreb:gs5ca .;).
(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 tormam)4iz yf/ 8u0vxb3y zcme08w) e,hp of a 3700-m-high mountain. The climb is made in 5.0 h starting at an eleva/fw8ermi8a b) h 30x,) 4czvuemyyzm0tion 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 break yn l,x jig;)8)xha/rts when a 920-kg elevator is 28 m above a huge spring ($k=2.2\times10^{5} \mathrm{N/m}$) at the bottom of the shaft. Calculate
(a) the work done by gravity on the elevator before it hits the spring,$\approx$    j
(b) the speed of the elevator just before striking the spring,$\approx$    m/s
(c) the amount the spring compresses (note that work is done by both the spring and gravity in this part).    m

  Squaw Valley ski area in California clarj 4i3e 19(a7b- /y+q:zflkn rgvrd gwims that its lifts can move 47,000 people per hour. If the average lif9g qre(b3l1n7/ykf-:grdv4+ airwj zt carries people about 200 m (vertically) higher, estimate the power needed.$a\times10^b$ W a =    b =   

  Water flows over a dam atoxxwkd9/:e *u the rate of 650kg/s and falls vertically 81 m before striking the turbinexe9 d*w o/xu:k blades. Calculate
(a) the speed of the water just before striking the turbine blades (neglect air resistance), $\approx$    m/s
(b) the rate at which mechanical energy is transferred to the turbine blades, assuming 58% efficiency.    W

  Show that on a roller coaster with a circula a2 .h:8s6ozaqfv /nobr 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 ansfvahb8:s./o q 6a2zno wer doesn’t depend on the size of the loop or how fast you go through it.    mg

  (a) If the human body could convert lk: r-r+b l)maa candy bar directly into work, how high could an 82-kg man climb a ladder if he were)l: -krbml+ ar 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 oaihy *yp7ub4-28m9k b7zw kw uf 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 compresst fd)83zm anvk(a6: sxes 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 do3mv)aank(s d 8z:xt6fes the scale read at its peak?    N

  A 65-kg student runs at 5m/s grabs a rope, and swings out over a lake t w c6:je.zz w6cp(im,(Fig. 6–45). He releases the rope when his velocity is z6.icw mec zztp,j(w :6ero.
(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 athleocn ci )ygr)ceh0 0-a(te climbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used to accompliccgayre-0 )onci( 0h)sh this feat?    W

  Some electric-power companies use water to store energy. tbo bf(*t,o+uWater is pumped by reversible turbine pumps from a low to a high reservoioo*, u(fbbt+t r. 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 const7ha( o1f*mvh*qfko n z:7nlw4ant k is cut in half. What is the spring stiffness constant for each of the f4 aovf7oh*whn*mkz(: 1nql7two resulting springs?   k

  A 6.0-kg block is pushv88,rsv x:,jblq2r f0bx/sqfed 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 from 35km/h to 55km/h in 3.2 sto i d -2wuyp(/-c /u9-ggisdf, how long will it take to accelerate from 55km/h to 75km/h Au 9g-dtd gpwciy( /s-/u2iof-ssume the power stays the same, and neglect frictional losses.    s

  In a common test for cardiac function (the “sia i0 a8d0p4edtress test”), the patient walks on an inclined treadmill (Fig. 6–46). Estimate the pow0i0p4da edi 8aer 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 distance of 500 hqyqgz6 m)/+) q3e0 /zgq .byhlq ai:zm, what was its velociqal )+0 qzmqe)/.qyhzz6/hbqyi :gg3ty 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 wat8hezel60 u/ r:.rupewer wheel from a height of 2.0 m at a rate of 95kg/s (a) If this water wheel is set.lzh r 0rpe:w6/u8e ue up to provide electricity output, what is its maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s