In what ways is the wor6kwf s;klg6hr/x0qhsxieb- u5z ):f)d “work” as used in everyday language the same as that de6ixk;rulf 6-s geh kzb5xwq0 fs:h)/ )fined in physics? In what ways is it different? Give examples of both.

Can a centripetal force ever do work on an objd5w 8 .c pylg6e)dqfs7f5 w3piect? Explain.

Can the normal force on an object ever do work? Explain. xby8y:+u:wadu8 q +lf

A woman swimming upstream is not moving with respect to the.67 yxjxalud: shore. Is she doing any work? If she stops swimming and merely floats, is work done on herj:axd 6u7yl.x?

Is the work done by kinetic friction forces always negative? [Hint 7xpkt8c lam l(z8h:( 0jllu2x: Consider what happens to the dishes when you pull a tabl z(l:l0u2ll a7( xc8tkp8hxmjecloth out from under them.]

Why is it tiring to puaj2.gf q,zf +wsh hard against a solid wall even though you are doing no wo2 gf qz,w.fj+ark?

You have two springs that are iden8ub +ymluy h) -fg2,il dtka cx6g:2f6tical except that spring l is stiffer than spring 2 -d6m )f6+bxyct :yl a ku2fuigl2h8g,$(k_1>k_2).$ 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 horizon31b mg2wskf8bj 7o)j.ltaa e:tal force on a block that is free to slide on a frictionless surface (Fig.6-30). The block starts from rest at þoint A, and by the time it has traveled a dist )j8 o al7:bm.gwf ak3es2jtb1ance $d$ 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 potentialhl nldq47w+9/ 5eev6 3kzioy w energy change when you jump as high aqwh nle6vl 4 zy5ie9+wokd/3 7s you can?

In Fig. 6–31, water balloons are tossed froiemw;h3bj9 h 5m 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 r9mj5we 3;hib hesistance.

A pendulum is launched from a point that is a height h above its lowest p/ :)pmbmmk nnqjrnleh 92)*w*oint in two different ways (Fig. 6–32). During :*) n/92pbkejnlq) *w nmrhm mboth 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? Explain.

A coil spring of mass m restc (7ko7mb*vtk 32 3scde -yf/lavo o-is upright on a table. If you compress the spring by pressing down with your hand and then release it, can the spring leaveoy/7i72svmocbd kofk- e 3v 3catl(*- the table? Explain, using the law of conservation of energy.

A bowling ball is hung from the ceiling by a steel wire (Fig;xkos9whl i:84bt3m x. 6–33). 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?49 ;iht :s8mx wbox3kl

What happens to the gravitational potential energy when water at the top of 7bn 09q qqngy b580oroa waterfall n b gr 5987bqn0o0qoqyfalls to the pool below?

Describe the energy transformations when a child i0uaa8 cdky; ;hops around on a pogo stick.

Describe the energy transformations that take place when a do :rv(xd+(zlxloe+to p+5z1 skier starts skiing dooxdz5+pl o+( dl+ ov:x(1rz tewn a hill, but after 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 heignjzrkz sue7+j.-tn)w.r 27dfht h and slides down. Does t nserun+)kfr7.zdtz 7j 2 .wj-he 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 thei+dbg9bwh9 vc89bk0o e r path rather than stepping on top and jumping down on the other ho 8b0k+ed9wb cb99vgside. Explain.

Two identical arrows, o- qe(2c3hweev-na 7gwne with twice the speed of the other, are fired into a bale of hay. Assuming the hay exertgw nwe3qva-c eh72e-( s a constant frictional force on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain.

Analyze the motion of a simple swinging pendulum in terms of energy, ( x8esiy0s lxy-:7(e+ f-bab njv(6e loa) ignoring friction, and (b) taking friction into account. Explain why a grand+l 67y (xexal-:s e(s o8v-nbjfi0 beyfather clock has to be wound up.

When a “superball” is dropped, can it rebound to a height greatby)fz/ bol9uo3ya y/ 8er than its original hyf zol8 oau) b//93ybyeight? Explain.

Suppose you lift a suitcase from the floor to a table. The work you do on the y+03g nyx zz1,rr,yjcsuitcase depends on which of the following: (a) whether you lift z1yg,rn c,rzyyxj +03it straight up or along a more complicated path, (b) the time it takes, (c) the height of the table, and (d) the weight of the suitcase?

Repeat Question 22 for the power needed rather than t,x1qyc )ft( kjhe work.

Why is it easier to climb a mountain via a zigzag trail than to climb straight ;sbe .f:m)1tcsxru w8upsxs m;c wue8t.1b: f)r?

Recall from Chapter 43kjy+e7mj zc x3*na5 cga :a/r:ab)i r, Example 4–14, that you can use a pulley and ropes to decreasa jr)nzexa3 *7i a:5c jb3kgary+ :/cme the force needed to 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 gravitawl922d0 f ex7 n)gpdzykz1s;btional force when a 265-kg pile driver falls 2.80 m? n)y0ze;7 lk9pd1zdbxfg 2 2sw    J

  A 65.0-kg firefighter climbs a flight of, u. -scfmru0i stairs 20.0 m high. How much work is required?rif- .c us,0um    J

  A 1300-N crate rests on the fh2fa:6dxdy j b qj ih/vf)s9,:loor. How much work is required to move it at constant speed d)j,x:jb 26i dh 9f/v af:hqys(a) 4.0 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 d01kx*pbna .xjz/ by/ oo (horizontally) pushing a 160-kg crate 10.3 m across a rough floor without acceleration, if the effexpyk/n*oj x b/b01.azctive coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is accelerated by a force across a floor at a rate of forgpj06( d8 luvryl6iv hty*yir/ s:8t/ 7.0 s. Find the net work done on the v*dhuyrlitpl8 0 s 6 tgv6yjry8(/i:/box.   J

  Eight books, each 4.3 cm thickaa)3 ioey/ ehznp137m with mass 1.7 kg, lie flat on a table. How much work is required to s3e/ny1aiz3p)h7 a eomtack them one on top of another?    J

A lever such as that shown in Fig. 61v;8a :ksf(p zvqi- ma-35 can be used to liff objects we might not ;sf1v kvp -z8ima(:aqotherwise be able to liff. Show that the ratio of output force, $F_{\mathrm{O}}$, to input force, $F_{\mathrm{I}}$, is related to the lengths $\iota_\mathrm{I}$ and $\iota_\mathrm{o}$ from the pivot point by $F_{\mathrm{O}}/F_{\mathrm{I}}=l_{\mathrm{I}}/l_{\mathrm{O}}$ (ignoring friction and the mass of the lever), given that the work output equals work input.

  A 330-kg piano slides 3.6 m dowfr6 dm,w m i+p+ gt8r9vh 3trw(d7kal+n 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 coefficient of kinetic friction ismw9mra+i+v7hrpl 6kt frd, ( t+8 3wgd 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 requireua ad6qm33a/pd to give a helicopter of mass M an acceleration of 0.10 g upward.36aapu qad3/ m    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 and thauwkj8 t8 kum-0d)s3ppk6k lq*t $d_{\mathrm{A}}=10.0$ 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 9c/yurah-i uvs, 8l/ faxis, varies as shown in Fig. 6–37. Determine the work done by /au9h vsi/y,ur8clf -this force 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 a particle acts inzlb:0n2:f qom q0bb4u 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 gum,m2ma *tbt z p +17m omjqb+mqikel9i5;). 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 factor has itsr 4ijhb cwso2(nt*46i speed increased? $ \sqrt{a}$ a =    (b) If its speed is doubled, by what factor does its KE increase?   

  How much work is requb : pzve5ed),vired 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 1250-kgqq:ff.7v 3ov+; m ez, 9cdnuuicar traveling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow y9*nu /.rfk 4uiai(apwhose string exerts an average force of 110 N on the arrow over a distance of 78 cm. What is the speed of t/a ur*uafi9ink y(p.4he arrow as it leaves the bow?    m/s

  A baseball (m=140kg) traveling 32m/s moves a fielder’s glovd ./hk8he;a i5t*oo - k)lpckne backward 25 cm when the ball is caught. What was the average force exerted byk).ao p e*/;nikocd-5hkh lt8 the ball on the glove?    N

If the speed of a car 6x m91gucmcl1,p/ qod8m*k wfis increased by 50%, by what factor will its minimum braking distance bumdkc mw, 8o*9pc q m/gfx611le increased, assuming all else is the same? Ignore the driver’s reaction time.

  At an accident scene on a level road, in) esa 14lop*ltvestigators 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 0.42. Use these data to determine thaell4)* o s1pte 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.wcb86 *vlzz ai i/ 1mrcu;vq1425 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, w ;1rci lc v/1qbvm*48auz zi6if 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 80.8ybfxrb6uz3 qjni)*)) -orw yq(g3kk 0 J oro)byk3-br 6j qq x u(*y8nw)fk3gi)zf work on it? Neglect air resistance.    m

  A 285-kg load is lifted 22.0 m verst7n3v*tk a;ztically with an acceleration by a single cable. Determ;tnsvz a3 *t7kine
(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 Hi+roty; ncy):fdhg q 3157ymdow much must this spring be stretched to store 25 J of potentn:;t3iy)g q75fhmyy1 rcddo+ ial energy?    m

  A 7.0-kg monkey swings from one branch to another 1.2 m higher. Whatmqqhn:r*x/m 40h rq(x is the change in pmq:h0*n /rhx 4 (mqxrqotential energy?    J

  By how much does the gravitatioeg.2 vf3(baf :bu+ hjr2bsk3i/w6o bdnal potential energy of a 64-kg pole vaulter change if his centerv2e.br gb of+uf(d/: b6bawjk2i3s 3h of mass rises about 4.0 m during the jump?    J

  A 1200-kg car rolling on a horizontal surface has speed v = 65 km/h when it st-ycvw 78viv3d rikes a horizontal coiled sv y-iv7wdv8c 3pring 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 so it is 2.20 m abovehi 8u 6gxzs:a*/cd/v50u 1 mavxhysh0 the ground. What is the potential enemah:ui8gvxv1uy s a/*hx6zh 0 d05c/srgy of the book relative to
(a) the ground,    J
(b) the top of the person’s head?    J
(c) How is the work done by the person related to the answers in parts (a) and (b)?    J

  A 55-kg hiker starts at an elevation of 1600 m and climbs to the top of a 3300r5fh;9:9 d yimnai7wj-m peakih97:j fyd9ari n ;mw5.
(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/3 vpphbkj*+ -jm hangs 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 nojp+ *hpb j-3kvw 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 runnin4rqp/: kprb 6q) :fob ,ax/nglg at top speed (5.3m/s) and grabs a vine hanging verticallb:rgoa):nbp /qrlkq fx, /p64 y from a tall tree in the jungle. How high can she swing upward?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from rest, slidesy:2oriln v +-xlv p)o- diq31p 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 anpw5vo2y- qv j5i-7zup 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 transfoe, tcf-g xos-*rmed into gravitational potential energy without the aid of a pole. With what minimum speed must Fran leave the ground in order to lift her center of mass 2.10 m and tgeox *c f-,s-cross the bar with a speed of 0.7m/s.    m/s

  A 65-kg trampoline artist jumps vertically upward froj-.fl1 ib sf+ym the top of a platform with a f1ilj+-.bf ysspeed of 5.0 m/s. ($\alpha)$ How fast is he going as he lands on the trampoline, 3.0 m below (Fig. 6-38)?$v_2$ $\approx$    m/s
(b) If the trampoline behaves like a spring with spring stiffness constant 6.2×10$^{4}$ N/m , how far does he depress it? $y_3$ =    m

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

  A vertical spring (ignore its mas.t)p.xl4:uhe cwjskc9 3be,f s), whose spring stiffness constant is 950N/m is attached to a table and is compressed down 0.150 m. (a) What upward speed can it give to a 0.30-kg ball when rc .fe l3 xws,.bk:u)ptej h94celeased?    m/s
(b) How high above its original position (spring compressed) will the ball fly?    m

  A block of mass m slides without frictw1m4 u4o. . bvmu1e1ey )qudb7uj9j tzion 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 it be release91eqwuz74)jt udjumme1o4 yvb ub 1..d?    r

A block of mass m is attached tn kx.r ax,mmk(: j:a*6dhs: odk)rh;no the end of a spring (spring stiffness constant k), Fig.:s*jn mx r :;6m. ,khnaak od:r(xhdk) 6–40. The block is given an initial displacement $x_0$ after which it oscillates back and forth. Write a formula for the total mechanical energy (ignore friction and the mass of the spring) in terms of $x_0$ position x, and speed

  A 62-kg bungee jumper jumps from a bridge. She is tied to a bung ag/c)9qx jyyr*o-o6aee cord whose unstretched length is)9oa o j6 /xg-ryayqc* 12 m, and falls a total of 31 m. (a) Calculate the spring stiffness constant k of the bungee cord, assuming Hooke’s law applies. $\approx$    N/m
(b) Calculate the maximum acceleration she experiences. $\approx$   m/$s^2$

  The roller-coaster car shown in Fig. 6–41 is dragged up to point 0ueaz /zn4hzm+mmhvc26+qs .1 where it is released from rest. Ass zn 6a+uvm eh+/mcm42 qzz0h.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 speed of 12 m/s at an angle of 331vg mj2bjqr0- $^{\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 bottomxbx(6u b xw0cq2yd8 ,1p(v ykv of an elevator shaft. If the elevator cable should break when the elevator is at a height h above the top of the spring, calculate the value that the spring stiffness constant k should have so that passengers undergo an accelerad(yx8 ybq0upvc 2 ,v1( xx6wbktion 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 7.8oj.2h(/ kxxet $^{\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 trave m0bo)*hw(v xq 726f bslp.vryhbud .c/z: 6bfling 95km/h in opposite directions, collide head-on and come to rest. How much thermal energy is prodrcl./ (6b2vb*0 y.hw u xzd sfqmfv)pbbh6o7:uced in this collision? $a\times10^b$ J a =    b =   

  A 21.7-kg child descends a slide 3.5 m high and reaches the bottz z1(0 gois x m1o;3csarc4kq.om with a speed of 2.2m/s How much thermal energy due to friction was generated in this so4so qkcma; c. r03 xgziz(11process?    J

  A ski starts from rest and slides down a 2c9swb4z0d0 zp2 $^{\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 dropp0k e br.*fxms9i,z(4zy/sikz ed 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 ed fm74fwmmc/+ -cp f/bounces back to a height of 1.5 m. cf7efd4p//mc+- wm fm
(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 flj*d b2k8oy* bqus4kc)oor with a constant horizontal force of 350 N. For the first 15 mukd*8b2s j)qk* 4ycbo the floor is frictionless, and for the next 15 m the coefficient of friction is 0.30. What is the final speed of the crate?    m/s

  Suppose the roller coaster in Fig. 6–41 passes point 1 with a speed of If tp erhx xpv5+tg*py,+/g 27ilohe average forh 57e/lx2 ppx+*p,+yo v grigtce of friction is equal to one-fifth of its weight, with what speed will it reach point 2? The distance traveled is 45.0 m. $\approx$    m/s

  A skier traveling 12m/s reaches the foot of a steady upward 1)v inu01z9qyo :3*s m+ewm stk8.0 $^{\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 m7:,msb z nwd/ zt(gw5attached 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 positio (gdsz/7nz w:m,tbw5 mn before stopping and turning back. What is the coefficient of kinetic friction between the block and the table?   

  A 280-g wood block is firmly attached to a very light horizod+adg/ij ;, uo ar5zlb9ep,6cntal 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 equilibrium posia 5 ,d;oijc/b6,+au g l9dperztion will it stretch on its first swing?    m

  Early test flights for the space shuttle used a “glider” (mass ow7 7sllj.a bto;6svw.tbx468mpvxh- f 980 kg including pilot) that was launched horizontally at 500km/h from a height of 3500 m. The glider eventually landed at a speed of 200km/h (a) What would its landing speed have been x6ws 7so;vltwv8a- b.j6pbt7 hl4m x.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-stoc mr(lp-py 6x a tx*o-zc;y.t1ry window 16.0 m ab(l -p6- xyyr1ma*ot cc px;tz.ove?    s

  If a car generates 18 hp when traveling at aprx vpm 2t.nga.ru *1z0/zq3k steady 88km/h what must be the average force exerted on the car due to friction and air ru pz0/ap 12zxrk3*.ngtmr. qv esistance?    N

  A 1400-kg sports car accelerates from rest to 95km/h in 7.4 s. Wha5cww+uzh uzy j 2yjfrk 11*;)ot is the average power delivered by thew y2cor )1f5kh+yj;uzwu*1j z engine?$\approx$    hp

  (a) Show that one British horsepow7npn6 -di;f3zdm7m0:qft neohu ,gy0 yz-wa 1er$ \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 th a oex;s(tk34ce 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 to 65km/h in*m7g9ivp gn;y about 6.0 s on the level when it is in neutral. Approxim;ng* 9 vygi7mpately what power (watts and hp) is needed to keep the car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hp movr j4g915f5 tuobwn9 ltor 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 m ymk 4cbb;*go9otion takes 1.5 s, what average powe4bk;*ygbo c m9r was developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute through a height of 3.6 drzd)wt4 9m cl/83gl,7cpxv p0 m. What output rating (watts) should tl37 g/)x 89 dpvz tp,4cmwrdlche pump motor have?    W

  During a workout, the football players at State U. ran up the stadium stair4yu 9jmujhn m cf/a;9dc .i9s*s in 66 s. The stairs are 140 m long and inclinmnc.f9u9yj* /jsc d94uamh i;ed 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+auadcl q8q ab8- ,pth9qv0+a climb 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 hilomrn 6b4z/o s,l can it climb at a constant speed of 75km/h if tm bsron ,4/o6zhe frictional forces add up to 650 N?    $^{\circ} $

  What minimum horsepowd y bwamb6g kc+x.66*vs er+0ter must a motor have to be able to drag a 310-kg box along a level floor at a 6w6e vd+atybc s+kg0.b6 *xmrspeed of 1.2m/s if the coefficient of friction is 0.45?    hp

  A bicyclist coasts down a18 ojyu- wjfxims,7 yne u*2b /ehz/9o 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) bumlvbjr. 7jc a--pers” that are designed to compress and rebound elastically without any physical damage at speeds below 8km/h If the material of the bumpers permanently deforms after a compression of 1.5 cm, but remains like an elastic spring up to that point, what must the effective spring stiffness constant of the bumper be, assuming the car has a mass of 1300 kg and is teste -a7vj.cljb -rd by ramming into a solid wall? $a\times10^b$ N/m a =    b =   

  In a certain library the first shelf is 1z-5qpyk14wz ib*7 war0.0 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 t5rkw zzwpq*7 yb1i4- ahe 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 Olympics4uq,evxq9hro.t)w u9 k/)rb r shows that his center of mass rose 1.1 m from launch point to the top of the arc. What minimu.oh wqkv, e)t/)u b9qux4r9rrm 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 slidin *jfe0t 4 c.0-mjg kc7fijz0ocg without friction along the looped track shown in Fig. 6–39 ioi40k-jc.jc 7cg0j*m ef zft0s 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 a4 ag4pyp * fdr. ep,iy+w2xa;5e-jqq jcnfo30n aircraft without his 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 wjg,ae3*ny epoj5 fi.4qwyc+;pp 2d 0 aqfx-4ras 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 horizontal6, g0nci w.seb cord of length L whose other end is fixed (Fig. 6–43)cew.6b,g 0ns i.
(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 ofpu+ x,to- 6o;hyf 0xww, am,fa a 3700-m-high mountain. The climb is made in 5.0 h starting at an elevation of 2300 m. Calculate +o6;um-yax p,wtfow xfh,, 0a
(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 ti4 )8gpc+ydy 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 Califg-k t+m*w0 vu 2v,/fp2ovwkalornia claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the power need,luvvtvak w2p w-+/*m0 2kg ofed.$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and falls ver8t: gm*sj31bjw kubf4tically 81 m before striking the turbine blades.sb4tm: *wuj j8f3bg1 k Calculate
(a) the speed of the water just before striking the turbine blades (neglect air resistance), $\approx$    m/s
(b) the rate at which mechanical energy is transferred to the turbine blades, assuming 58% efficiency.    W

  Show that on a roller coaster with a circular j6d( 4j:(wzc1c dph4s,ty kayk 5g 3tkvertical 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 on the size of the loopc6c5p( 1d(z4j ywk4k3 t:, jtadshykg or how fast you go through it.    mg

  (a) If the human body could convert a candy bar directly into work, h /5tn e+j5vmg)fz;kqx ow high could an 82-kg man climb a ladder if he were fueled by one bar (=1000kJ) ;xg jtqv)e5/+nk5zf m    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 up6y 9rbmg3r pgr)m(zum v89 w.m9r4vrd ward 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 inside7zfjm 6m ad*,t ;kbqak 0n:a:c the scale compresses 0.60 mm, and it tells you your weight is 710 N. Now if you jump on the scale from a heightk 7bm actzf0qa:kajm,nd6*: ; 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 kb 2f4el fy)s.swings out over a lake (Fig. 6–45). He releases the rope when his velocity is zero. .l)4fkfb esy 2
(a) What is the angle when he releases the rope?    $^{\circ} $
(b) What is the tension in the rope just before he releases it?    N
(c) What is the maximum tension in the rope?    N

  In the rope climb, a 72-kg athlete clim0k/y u2gtfj6x tz.en 6bs a vertical distance of 5.0 m in 9.0 s. What minimum power outputt 6nyu.62x j/getz0kf was used to accomplish this feat?    W

  Some electric-power companies use water to store energy. Water is pumped by r uaqg *k,z1jy gjza49rbm+:r3eversible turbine pumps from a low to a high reservoir. To store the energy produced iuy3qbaz9z kgm4graj1 jr,:* +n 1.0 hour by a 120-MW ($120\times10^{6}$W) electric-power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Assume the upper reservoir is 520 m above the lower and we can neglect the small change in depths within each. Water has a mass of 1000 kg for every 1$m^3$.    $m^3$

  A spring with spring stiffness constant k is cut in half. Whsc: kl cc30 zrgxyk((8at is the spring stiffness constant for each(80kc src( gy:xzkl 3c of the two resulting springs?   k

  A 6.0-kg block is pushed 8.0 m up a rough golwwl4t,kol bm*q3 genel4t7 (:9 4p37 $^{\circ} $ inclined plane by a horizontal force of 75 N. If the initial speed of the block is 2.2m/s up the plane and a constant kinetic friction force of 25 N opposes the motion, calculate
(a) the initial kinetic energy of the block; $\approx$    J
(b) the work done by the 75-N force; $\approx$    J
(c) the work done by the friction force;    J
(d) the work done by gravity;$\approx$    J
(e) the work done by the normal force;    J
(f) the final kinetic energy of the block.$\approx$    J

  If a 1500-kg car can accelerate from 35km/h to 55km/h in 3.2 s, how long u w5 jalmj 55tefwe:*+xq4q4hwill it take to accelerate from 55km/h to 75km/h Assume the power stays the sf5we:ux5 t 5jeqqhjw*l 4ma4+ame, and neglect frictional losses.    s

  In a common test for cardiac function (the “stress*g51xw y; yjn 9irqqw8 test”), the patient walks on an inclined treadm qg;ry9qwj w*8yxin1 5ill (Fig. 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 distance of 500 m,9r+em l hw5fy,g)i(rn what was its velocity when it left the volcano? )5nrg ,fe +wiryl9 m(h$\approx$    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 fromwx(l3xmbz( a +wh *2-l rrfk2x a height of 2.0 m at a rate of 95kg/s (a) If this water wheel is set up to provide electricity output, what is its maximum powe-xx w2ra b xw(r l+3*(l2mzfhkr output?    W
(b) What is the speed of the water as it hits the wheel?    m/s