In what ways is the word “w0d,d0.l 1pbqwbc rix mef( ./xork” as used in everyday language the same as that defined in physics? In what ways is it different?m lr p/.d00exfb. cbiqw1 (,dx Give examples of both.

Can a centripetal force ever do work on a-c;*esm m7; ujv;+2o b/u evlp vmh3yqn object? Explain.

Can the normal force on an objig -9+eq8g4u s3m fq,grtpgv vrx+g4l;fo7 ;ject ever do work? Explain.

A woman swimming upstream is not movingok+-ip w6ylm 4k89t my with respect to the shore. Is she doing any work? If she stops swimming and merely floats, is work done op 9y8t y+m4-ilmk6kwon her?

Is the work done by kinetic friction forces always negative? [Hint: Ccp2;qy lw:j j pgno 5:hy54(zoonsider what happens to the dis ;c y5: oj zqoynpw5lj4(hg:p2hes when you pull a tablecloth out from under them.]

Why is it tiring to push hard against amvplpqh) b: 1:ez 15yi solid wall even though you are doing no woqzh1y:5 l )mpi evp1:brk?

You have two springs thx41qp arag+,b;5 flfd at are identical except that spring l is stiffer than springdg1f;fal,xp4 + qab 5r 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 z.t- q 4 ,t5hdsqnu00szzrb,2/w xqo kforce on a block that is free to slide on a frictionless surfacetr0o/ z4h s-qdw02xt k,z,zbq us 5n.q (Fig.6-30). 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 potential energy change when vobsu( 5ghyxw:07mr (you jump as high as you :( x oyb(uwgvm57 sh0rcan?

In Fig. 6–31, water balloons are tossed fromr kon,;tsx+ o7 the roof of a building, all with the same speed but with different launch angles. Which one has the highest s, 7sxo rn;ot+kpeed on impact? Ignore air resistance.

A pendulum is launched from a point that is a height h above its lowest zs am.lkm ua.(i:i0,7 7j85ijp etuz lpoint in two die . iims u7li8jz,.5a m:zau(jt kp70lfferent ways (Fig. 6–32). During both launches, the pendulum is given an initial speed of 3.0m/s On the first launch, the initial velocity of the pendulum is directed upward along the trajectory, and on the second launch it is directed downward along the trajectory. Which launch will cause it to swing the largest angle from the equilibrium position? Explain.

A coil spring of mass m rests uf ut du7up3db8i 10ewe6y5u(cw i4zw7pright 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 consert(7dpw 5byu6 i ueeuww0dcf143i8z u7vation of energy.

A bowling ball is hung from the ceiling by a steel wire x8ywk+ bkp8 r..* y1uupv.fp)pdkss9(Fig. 6–33). The instructor pulls the ball back and stands against the wall with the ball against his nose. T+x8 9fy1k.uk p*d8ys.wvb u pp.s)pkro avoid injury the instructor is supposed to release the ball without pushing it. Why?

What happens to the gravitational potential energy when water at the top of a pdera.rt s0f jy(/f*72 /c8voouwt-z waterfa2re*c-u tdaz p8so of wrj/v7.(0fty/ll falls to the pool below?

Describe the energy transformations when a child hops around on a pogo -hhu u;tor;y 0stick.

Describe the energy transformations that take place w93 6jd*dpq9uur dwgz1 hen a skier starts skiing down a hill, but after a time is brouzu 3 pjg9dr1 6duw*dq9ght to rest by striking a snowdrift.

A child on a sled (total mass m) starts from rest at the top of a hill of heighuo:e s3a4i6u zt h and slides down. Does the velocity at the bottom depend on the angle of the h ez u3ous64:iaill if (a) it is icy and there is no friction, and (b) there is friction (deep snow)?

Seasoned hikers prefer to step over a fallen log in their path rwhy;h qmx9 g,-ather than stepping mg;h 9yh- ,xwqon top and jumping down on the other side. Explain.

Two identical arrows, one with twice the speed ofn xl.zw; wwm8; the other, are fired into a bale of hay. Assuming the hay exerts a constant frictional force on the arrows, the faster arrow will penetrate how much farther thanl ;x8n;w.w wzm the slower arrow? Explain.

Analyze the motion of a simple swinging pendulum in terms of energy, (a) ign wmv m1gg6k x6he;wi40pg7mryj c:.v7oring friction, and (b) taking friction into account. Explain why a grandf7v. jmme;67w ihg:pky 0x 6 1gmcrw4vgather clock has to be wound up.

When a “superball” is dropped, can it rebouc03,vyzg a;d3k 6zdk,sq,;tey snm9 mnd to a height greater than its original height? e dz; scd ,q;,90s mk6gmv tany33y,zkExplain.

Suppose you lift a suitcase from the floor to a tablnpqwp1y4 c .x hub.q;(e. The work you do on the suitcase depends on which of the following: (a) whether you lift it straight up or along a more complicated path, (b) the time it takes, (c) the height of the table, and (d) the weight of the suitcaqun.hwy 1;p pb c(x4.qse?

Repeat Question 22 for the power needed rather thpyiws bwq9kz5pa (bj*tt3 233an the work.

Why is it easier to climb a mountain via a zigzag trail than x l hamj7e:j;f9q;m 7lto climb straight upjla9 h e7m;m:lxqf; 7j?

Recall from Chapter 4, zl, qhf44 ,vgr+ n)0p9fanzel Example 4–14, that you can use a pulley and ropes to decr 9z0rvhpz,, aelng4) lf qf4n+ease 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 gravitational force when a 265-kg pile dr+*yg) /xm98z h dfngzeiver falls 2.80 myx* dnhemz8+g/ z9fg)?    J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How much wora v/ e8:zyv z8klw9w4.uvv0cfk is reqk/8z.e9w : wzl8y0u v4vvfvac uired?    J

  A 1300-N crate rests ok (01xeusjh,i n the floor. How much work is required to move it at constant speed (a) 4.0 m ,i(j0xksh1 e ualong 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) pus u(2gd *.dbdikhing a 160-kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of fricig2ud. kbd(d* tion was 0.50?    J

  A box of mass 5.0 kg is accelerated by a forc1p nlr0nk 5t:etz ,i6ne across a floor at a rate of for 7.0 s. Find the net work done on the boz5t te6lnpkn, : n1ri0x.   J

  Eight books, each 4.3 cm thick with mass 1.7 kg, lie flat ov4l4 5cm t;rk98lz og4yzm-iuv;gdw 6n a table. How much work is required to stack them onm5ir4lkvdt - wmz49ug ;6v;cgoy l8 z4e on top of another?    J

A lever such as that shown in Fig. 6-35 can be used to liff ob w)o09jprdyd8px : kaxn 14yd8jects we might not otherwise be able to liff. Show that the ratio of output fw4dx)8 :1 rxy80dn 9aopjpkdyorce, $F_{\mathrm{O}}$, 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 3.6rxo vl *cz1-6n m down a 28° incline and is kept from accelerating by a man who is pushing back on it parallel to 1n*-olr cv6zxthe 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 he6o q )ozo8td0plicopter of mass M an acceleration of 0.10 g upward. 8)t d6 ozpoqo0   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 is3yh6 n ojuo:hboq*)7a 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, actixpzz 5 b f.3/hg+d)ddzng along the x axis, varies as shown in Fig. 6–37. Determine thddz+5 h/pgxfz.z3 d)b e work done by 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 actszgi.4dcugb7 m*u:1 r9x 6vouu in the $+x$ direction. Its magnitude increases linearly from zero at
$x=0$, to 24.0 N at $x=3.0$ m. It remains constant at 24.0 N from $x=3.0$ m and then decreases
linearly to zero at $x=13.0$m. Determine the work done to move the particle from $x=0$ to $x=13.0$ m
graphically by determining the area under the $F_x$ vs. $x$ graph    J

  At room temperature, an oxygen molecule, with mass o inixm+v 7ec, (:lntbt188bh8ri bu) ef $5.31\times10^{-26}$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 factory2,rv6t kv 9vh has its speed increased? $ \sqrt{a}$ a =    (b) If its speed is doubled, by what factor does its KE increase?   

  How much work is required to sd2u,v 8j +hr+: p-dcpx6y eu -zdqukf*top 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 a.y+fu*l(/ wh/ ewvs: w5mbot to stop a 1250-kgcar traveling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired; p ,mb:1bak s(uyn/.tajp7pi from a bow whose string exerts an average force of 110 N on pakpp jnb(1:mat, isyu / .b7;the arrow over a distance of 78 cm. What is the speed of the arrow as it leaves the bow?    m/s

  A baseball (m=140kg) trav*dmdu g.7j /f wi zjvx(+8s5jn.foh7qeling 32m/s moves a fielder’s glove backward 25 cm when the ball is caught. What was the 8uijhf5+n v *o.d fdqxj7m/(7 g.wszjaverage force exerted by the ball on the glove?    N

If the speed of a car is increased by 50%, 5) p;,xa0me b3w df*vlc8tv fn (nhg8sby what factor will its minimum braking distance be increased, assuming am d 58c pgfnvxwhb (3f0*len8, s;v)tall else is the same? Ignore the driver’s reaction time.

  At an accident scene (bx3 yyg;6gmoz:;e uz on a level road, investigators measure a car’s skid mark to be 88 m long. The accident occurred on a rainy day, and the zmu o( y;;3zebx6g:gycoefficient 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 massduslkob3 .708 ow y:xd of 0.25 kg is pitched at By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch, if the distanc obyu8 d 073.o:sxwkdle between the plate and the pitcher is about 15 m.    N

  How high will a 1.85-kg rock go if cg .8zp/- ftq5(u 4saa;xdcncthrown straight up by someone who does 80.0 J of dp nfscagq;/z58t.u4cc- a(x work on it? Neglect air resistance.    m

  A 285-kg load is lifted 22.0 m vertically with an acceleration by a singu)5 mfqj3w wt;le cable. Determine 53m ;twjq)wuf
(a) the tension in the cable,    N
(b) the net work done on the load,    J
(c) the work done by the cable on the load,    J
(d) the work done by gravity on the load,    J
(e) the final speed of the load assuming it started from rest.    m/s

  A spring has a spring stiffness constant, k, of 440N/m How much mb l8m3lc-azk.0hl 0y lust this spring be stretched to store 25 J of potential e8a l0 ylm-c30l.hlzbk nergy?    m

  A 7.0-kg monkey swings from one branch to anorxhpfti rej,c)ag ( x;-c2+4b az3dz4 ther 1.2 m higher. What is the change in potential energy?hji b42xz(e4 a pc;f,cd)axzg r+-rt3    J

  By how much does the gravitational poxnh nmm5:x.l(tential energy of a 64-kg pole vaulter change if his center of mass rises about 4.0 m d.xx m(lh5n: mnuring the jump?    J

  A 1200-kg car rolling on a horizontal surface has speed vv. c-p iqxg)g) = 65 km/h when it strikes a horizontal coiled spring c-v) x.pqgg)i 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 2.10uw .h6t /m5 ;lp1slfzk-kg book from the ground so it is 2.20 m above the ground. f. /ks;5 lz pm1lwhu6tWhat is the potential energy of the book relative to
(a) the ground,    J
(b) the top of the person’s head?    J
(c) How is the work done by the person related to the answers in parts (a) and (b)?    J

  A 55-kg hiker starts at an +y1hf us 8wal/qbs0m (elevation of 1600 m and climbs to the top of a 3300-m peak. afms ul+(1hqy8 b0w/ s
(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 nrlakzm60 q:d4r0 ,mjhext to a ruler. The end of the spring is next to the 15-cm mark on the ruler. If a 2.5-kg mas,:kd0qm m4hrj 6lrza0 s is now attached to the end of the spring, where will the end of the spring line up with the ruler marks?    cm

  Jane, looking for Tarzan, is running at top speed (5.3m/s) and grabs a vin sf 9ntlqy3vqc:4(ug +e hanging vertically from a tall tree in the jungle. How highqugc4q:yn +(fl s93t v can she swing upward?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from re l4qxtsk;f,6s (dw)oust, slides down a frictionless 35.0$^{\circ}$ incline whose vertical height is 185 m. How fast is she going when she reaches the bottom?    m/s

  A sled is initially given a shove up a frictionless 2..+sqd fjg6 aswhl33axao- k68.0$^{\circ}$ 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 8bf,)ukw-l75i1f ta yvrv+iqenergy is transformed into gravitational potential energy without the aid of a pole. With whvru8qvib 17 aw it+5f)-,fylkat minimum speed must Fran leave the ground in order to lift her center of mass 2.10 m and cross the bar with a speed of 0.7m/s.    m/s

  A 65-kg trampoline artist j+e btz /fzj3(yumps vertically upward from the top of a platform witzbj(tf 3eyz/ +h a speed 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 mass), whose spring stiffnw(4 ly6.8rmkk +bz. vt0jm sqmess constant is 950N/m is attached to a table and is compressed down 0.150 m. (a) What upward speed can it g6kljm(vms + 8 qtbzkr.4.ywm0ive 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 without71ow2vh az y 1ac7l7ml friction along the looped track shown in Fig. 6–39. If the block is to remain ov ylm 7w71z1aolc2 ha7n the track, even at the top 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 thehg.prsx yw(jit989 ,u b ms8)fesc5)n end of a spring (spring stiffness constant k), Fig. 6–40. The block is given an initial displ5mhnic u9)8s,)rbesjt. f98y sp x(wgacement $x_0$ 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 *sqxqi* 1ir*2*x rbo //,mmjpcx,iyxkg /cb* a bridge. 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 Hooke’s law applies.i/r/*jpcr*xb, /,q oxbmx cs1i*qimgx *y k 2* $\approx$    N/m
(b) Calculate the maximum acceleration she experiences. $\approx$   m/$s^2$

  The roller-coaster car shown in Fig. 6–41 is dragged up to point 1 c c qbvfuz s5k0ji q1/o+ky;9g ws8y70where it is released from q;0oj +cszbfq yik 59kw vus1/c 0g87yrest. Assuming no friction, calculate the speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown with a speed of 12 d8f.9rju yqh udrvr;jde,q:i, .* qp8m/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 ofz6;fjg 9e+g )/aip/rxj aa+n hjydz0) an elevator shaft. If the elevator cable should break when the elevator is at a height h above the top of the spring, calculate the value that the spring stiffness constant k should have so that passengers undergo an acceleration of no more than 5.0 g when brought to rest. Let M be the total mass of the elevator and passen+;r6ejgijza /azj 9ydgf )ax)+ h/n 0pgers.

  A cyclist intends to cycle up ayyaa qmbqa5h(h461g 6 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 76502 bzd v .nu7vw+49m s2duysh9p kg and traveling 95km/h in opposite directio2u+2ywzu md.pv4n 9s dv97bhsns, collide head-on and come to rest. How much thermal energy is produced in this collision? $a\times10^b$ J a =    b =   

  A 21.7-kg child descends a slidei xm*dsc 795td 3.5 m high and reaches the bottom with a speed of 2.2m/s How much thermal energy due t7md9 dxc s5*tio friction was generated in this process?    J

  A ski starts from rest and slides down a 22-d kf20di61tog ylok 8(kcck 3 $^{\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 dron c;ees2w:3 1:pygpnl, bkaj,pped from a tree 13.0 m above the ground.
(a) With what speed would it hit the ground if air resistance could be ignored?    m/s
(b) If it actually hits the ground with a speed of 8m/s what is the average force of air resistance exerted on it?    N

  You drop a ball from a height of 2.0 m, and it bounces back to a hei0.ax0nxq ojx4 os x-nq 2e7bq +l*ccb+ght of 1.5 m.ln c 0e*4+qx j -sxa+b.qqo7obxx2n c0
(a) What fraction of its initial energy is lost during the bounce?    %
(b) What is the ball’s speed just as it leaves the ground after the bounce?    m/s
(c) Where did the energy go?

  A 110-kg crate, starting from rest, is pulled across a floor wit h-2g4oan* vqoh a constant horizontal force of 350 N. Fovq ngoh-4 o*2ar 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 of the crate?    m/s

  Suppose the roller coaster in Fig. 6–41 passxj mm5 fi0qpf4 a c;8)3l6n6hj2irr utes point 1 with a speed of If the average force of friction is equal to one-fifth of its weight, with what speed wilq l34cp2rmj6fhar 5tu i; x0n8fi) 6mjl it reach point 2? The distance traveled is 45.0 m. $\approx$    m/s

  A skier traveling 12m/s reativi(9 ;y.z)ogs y.uk ches 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 to a very light h;p jfql7er )e-5 ,lfmvorizontal 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 beyonf;vm 5lfeq l)pr7 j,e-d 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 firmly attao*g7wn phh; *essbf4* ched to a very light horizontal spring, Fig. 6– s74;weo***fhsh bp gn40. The block can slide along a table where the coefficient of friction is 0.30. A force of 22 N compresses the spring 18 cm. If the spring is released from this position, how far beyond its equilibrium position will it stretch on its first swing?    m

  Early test flights for the space shuttle used a “glider” (mass of 980 kg inc- 82kr jzoqoa.luding pilot) a o-kjo8.q2zr that was launched horizontally at 500km/h from a height of 3500 m. The glider eventually landed at a speed of 200km/h (a) What would its landing speed have been in the absence of air resistance?$\approx$    km/h
(b) What was the average force of air resistance exerted on it if it came in at a constant glide of 10 $^{\circ} $ to the Earth?$\approx$    N

  How long will it take a 1750-W m9wuz8if2mh) pc r1b 4yotor to lift a 315-kg piano to a sixth-story winmw r hz)pu c12f984ibydow 16.0 m above?    s

  If a car generates 18 hp when traveling at a sta k tcy07co:;meady 88km/h what must be the average force exerted on the car due to friction and air resistanctcmya;7:k o0 ce?    N

  A 1400-kg sports car accelerates from rest to 95km/h in 7.4 s.t811 *lku 9 lxizp/nhod)fr0 l What is the average power delivxhp)zln9d8 1f0kui t*or 1l l/ered by the engine?$\approx$    hp

  (a) Show that one Britir2:pjmt +q / /g8o9v2 aeudiqzsh horsepower$ \mathrm{ft}\cdot\mathrm{lb/s}$ is equal to 746 W.
(b) What is the horsepower rating of a 75-W light bulb?    hp

  Electric energy units are often expressed in the form of b62o))h. kx* wkmlnhp “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-t n0vt z-p)o;ya/:jpakg car slows down from to 65km/h in about 6.0 s on the level when it is in neutral. Approximately what power (watts and hp) is needed t0yotn/:;tppza)a - j vo keep the car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hp motor dylq-) xp 33r4+uypr4uy8fjo/o( lsywp 4:yg zo in 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-+ rqjdk2b11nfkf) v*zkg shot from rest to 14m/s If this motion takes 1.5 s, what average power was deve 1 ff2jk)*d z+rvqbn1kloped?$\approx$    W

  A pump is to lift 18.0 rv1ondq.b;-rme +i7 p:bme0ukg of water per minute through a height of 3.60 m. What output rmm+r.neb 0er p:; o 7vqu-db1iating (watts) should the pump motor have?    W

  During a workout, the football players at Sta t-ochn1v) i s4g;x2note U. ran up the stadium stairs in 66 s. The stairs are 140 m 2 ic;gnn 4)vx-s o1othlong 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 climb a a+ b8zd0dzq o0tw-)ay p.4q, m3zglyr6.0 $^{\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 (rqz,if f395 zd9w9ajdchku. power output of 120 hp. How steep a hill can it climb at a constant speed of 75km/h if the frictional forceszwicqdu9df5 3zjf, 99ar(. kh add up to 650 N?    $^{\circ} $

  What minimum horsepower must a motor kau9cx 5fzhk 2xtb,84have to be able to drag a 310-kg box along a level floor at a speed of 1.2m/s if the k2h,x b495u t 8zfaxckcoefficient of friction is 0.45?    hp

  A bicyclist coasts downpmq 9f8b j).wl 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” tkix ny;sgwp 2)f/p5 2ghat 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 i x ppws5gg/22ynk;)f 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 remattyp :92gjh:vgj+cx 7f. g/pvm ye;0zining four shelves are each spah 9g7+eyjft/:gj gcxv m:yzpp2.t 0;vced 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 laying flat on the floor to start? $\approx$    J

  A film of Jesse Owenu +pjwm/6s+sxib, m :ze1p/lk6 *cqn ws’s famous long jump (Fig. 6–42) in the 1936 Olympics shows that his center of mass rose 1.1 m from launch point to the top of the arc. What minimum speed did he need at launch if he was traveling at 6.5m/s at thew1*k : q z6n,plimju6+pcmsexb+ //ws top of the arc?   m/s

  The block of mass m sliding without8(7u9ci6 xamgt3 * ag0b kaot7cu7bab friction along the looped track shown in Fig. 6–39 is to remain on the track at all times, ek9m7 ocu (taag60ubcxb 7ai*b3 8t7agven 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 jumpi t ,*,nud d9wdx2fhoc:ng from an aircraft without his parachute 9 2od,*udw,cfdx:t hnopening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the pilot’s mass was 78 kg and his terminal velocity was 35m/s 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 entjgc: rvkif y9.l6ktj)sci 7t; m 9z;xc,s* v0d is fixed (Fi)ixzt7;y*j srg k , vv6i0kcclf ;t:m9ts9jc. g. 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 the top of a 3700-m3oni2g ,o5 rep;7 7s1cstx mlp-high mountain. The climb is made in 5.0 h starpt1ri ;cl27s emoxn7o 3gs,p5 ting 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 above a huge skio +y 9ayf)av.uds054.q ghwpring ($k=2.2\times10^{5} \mathrm{N/m}$) 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 Cax.i l,gy)-p1w yad 0utlifornia claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) wy0ax.)1 i gpu,ly -tdhigher, estimate the power needed.$a\times10^b$ W a =    b =   

  Water flows over a dam atuo+ mgggfs d6 68e9nk. the rate of 650kg/s and falls vertically 81 m before striking the turbine blades. Casgeg98m6gu n. +ofd6klculate
(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 ci9. 5eg + x*bx2kzugfyircular vertical loop (Fig. 6–44), the difference in your apparent weight at the top of the circular loop and the bottom of the circular loop is 6 g’s — that is, six times your weight. Ignore friction. Show also that as long as your speed is above the minimum needed, this answer doesnb29*e+f igxz. xkuy 5g’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 bsn 1ll :x;xsbo:uy5; bar directly into work, how high could an 82-kg man climb a ladder if he wer5xslul:yn;s: ob;x1 b e fueled by one bar (=1000kJ)    m
(b) If the man then jumped off the ladder, what will be his speed when he reaches the bottom?    m/s

  A projectile is fired at an upward angle of jk4 e j,ull/c745.0$^{\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 in;7nd k x-ghl(tside the scale compresses 0.60 mm, and it tells you your weight is 710 N. Now if you jump on the sc-dtxh7l g(n ;kale 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 swings ouo*x hiueww918d 9(2ov:pagjyt over a lake (Fig. 6–45). He releases the rope when hisawvgye j1*xu h(i d98o: w9o2p velocity is zero.
(a) What is the angle when he releases the rope?    $^{\circ} $
(b) What is the tension in the rope just before he releases it?    N
(c) What is the maximum tension in the rope?    N

  In the rope climb, a 72-kg athlete climbs a vertical diqm(3oo;jod-fr-ad4 ke:a f/ ,ntpp,s stance of 5.0 m in 9.0 s. What minimum power output was used to accompl-sk;n m,(f:pod4efr/dot qao,3 -ajp ish this feat?    W

  Some electric-power companies use water to vb+pn,u i8 -vwstore energy. Water is pumped by reversible turbine pumps from a low to a high reservoir. To store vp,vbui8 nw+-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 stmnoj i,0 :w.lziffness constant k is cut in half. What is the spring stiffness constant for each of lm.0wzino:j ,the two resulting springs?   k

  A 6.0-kg block is pushed 8.0qph,+d1 bto rx .1kx)e 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 aceszodkcfvs 00uerb -z:xw(k,9 e6, u*celerate from 35km/h to 55km/h in 3.2 s, how long will it us ,ke 0(*z:v xbse,r0-wo9 6kfuzdec take to accelerate from 55km/h to 75km/h Assume the power stays the same, and neglect frictional losses.    s

  In a common test for cardiac function (the “stress tevp x49vrec2r5kx qm:1st”), the patient walks on an inclined treadmill (Fig. 6–46). Estimate the power required from a 75-kg patient when tr9e 1pcqxxv 2kmvr:54 he 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 upwjho4gd8i(t204 azmj hard a distance of 500 m, what was its velgh(i hz0o4ta48j2mdjocity when it left the volcano? $\approx$    m/s
(b) If the volcano spews the equivalent of 1000 rocks of this size every minute, what is its power output? $\approx$ $a\times10^b$ W a =    b =   

  Water falls onto a water wheel from a height of 2.0 m at a ry4zd8/kkh s+1-jmojh+l klb z6f36w m ate of 95kg/s (a) If this water wheel is set up to provide electricity oulwy4mkl+zo 1kf3 jb 6kdhs-8h/6 mjz+ tput, what is its maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s