In what ways is the word “work” as used in everyday languaw2fn4:bkw:uk t4 jt3dge the same as that defined in physics? In what way:u b4k3 4ttwjk 2:nwdfs is it different? Give examples of both.

Can a centripetal force ever do work on an object hh46eac tz5 dv80lfbg( u,,xy? Explain.

Can the normal force on an object ever do worc. ;c w vo+-ha8.nw-m x:ty rsmdb idp:q(im;9k? Explain.

A woman swimming upstream is ;e+0dnc52d4pjwaz vvnot moving with respect to the shore. Is she doing any work? If she stops swimming and merely floats, is work done on ha p4+z0jwn d;v2ec5vd er?

Is the work done by ki9)wu+j/ir-ly/qb n8vio 0m sp netic friction forces always negative? [Hint: Consider what happens to the ) omw80njv/ q/p isilyb+r-9udishes when you pull a tablecloth out from under them.]

Why is it tiring to push hard against a solid wall even though you are doingfuc0 h:t5rzd5 no wohz:u 5f5c0rtdrk?

You have two springs that are identical except that spring l is stiffe)aoylzt n) a62r than springzta62a o) yn)l 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 horizonta qp m9z4ek b;62dc8clpl force on a block that is free to slide on a frictionless surface (Fig.6-30). The block starts from rest acb8 z l9ckdp4 mqp;e62t 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 wh 8 k-/zr:(umog5i4bpwx8gut len you jump as high as you can? 5 t-4 ogrwbgxkui8/8l:mpu( z

In Fig. 6–31, water balloons are to*jlz ; ms7-.xlvwfp c0 9 tlj,z;qbc2s..mhzkssed from the roof of a building, all with the same speed but with different launch angles. Which one has the highest speed on impact? Ignore air resistan0 jmzv 9.h. lws*zx.7p;;b2ztl-cfj, lsqm ckce.

A pendulum is launched from a point that is a height h above its /m8gd06rzb oa lowest point in two different ways (Fig. 6–32). During both launches, the pendulum is given an initial speed of 3.0m/s On the first launch, the initial velocity of the pendulua 6od8 g/zrm0bm 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 upright on a table. If you compress theiqss/v-xp-j v8: myc.urdu.0 spring by pressing down with your.vqj p d8ui/svc.0x- usym:-r hand and then release it, can the spring leave the table? Explain, using the law of conservation of energy.

A bowling ball is hung from the ceiling by a ed yszcshhtu ;i7gm/za7): f99k /6ua steel wire (Fig. 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 puu7ta6s u); izmh/c: 7azf9y d/kh9egsshing it. Why?

What happens to the gravitat1xyx9(n mw :3xehsj ;6kq7i 92driyhu ional potential energy when water at the top of a waterfalreqyh u (xi13yj6n2x9xi9s7dwk h:;ml falls to the pool below?

Describe the energy transformations when a child ho6tpr*4fsfc 0cdo 4* bqps around on a pogo stick.

Describe the energy transformations that take place when a skier starts skiie)r(xq; tv cnkh6iblz (7,-q8jqg jn4ng down a hill, but after a time is brought to rest by strinxn(k-tbjc 6(q rizv,el7; h)q 8qg4jking a snowdrift.

A child on a sled (total mass m) starts from rest at the top of a hill of he5ngzqvsvfn arh/pu :d603j:( ight h and slids/ q5 zr6::p gv3h0j(uanvn fdes down. Does the velocity at the bottom depend on the angle of the hill if (a) it is icy and there is no friction, and (b) there is friction (deep snow)?

Seasoned hikers prefer to st fz0+na.p hnc1s.m9afw s-(wqep over a fallen log in their path rather than stepping on top and jumping down on the other side. Explai n0pza wmss(..h+a -w qf9fn1cn.

Two identical arrows, one with twice the speed of the other, are fired i om):-e/s *yb pdxyruhacyu * :75r2hunto a bale of hay. Assuming the hay exerts rysr**cub :5)xe/mp 7 :u o2uy -dyahha 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 pen5 f2lqvkae7(l .dxi-idulum in terms of energy, (a) ignoring friction, and (b) taking friction into account. Explain why a grandfather clock has to i.i5adf2el-v7 x qlk( be wound up.

When a “superball” is dropped, can it rebound to a height greater than its orpow.bo35k4ro iginal height? Explk.rwp4o obo 35ain.

Suppose you lift a suitcase from nmld8mst /faom/ y9a;, 1 vob-the floor to a table. 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 d8tm1-ayo,fm9 /;s lnbm oav/ suitcase?

Repeat Question 22 for the power needed rat8 +1ymt jlvd(gfc* ox/her than the work.

Why is it easier to climb a mountain via a zigzag trail than t 5+xgtb t*gk)aatq 2,po climb straight up? 5t2,qxb+agt*gka tp)

Recall from Chapter 4, Example 4–14, that you can use a pulley and rnv 9j/om1 *l25 tcmpejw-d5w hopes to decrease the force needed to raise a heavy load (see Fig. 6–3hw/*m ev15od95jjc2nmtw- p l4). 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 fm0 kv3a;6.i osgh7sehalls 2.8vsg. oak e;i70h 6h3sm0 m?    J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m high;q0ega w svac wr)+.y-. How much work is requireac 0v +wys q)ar.eg;-wd?    J

  A 1300-N crate rests on the floor. How much work is required to move it at6-mlncx)qfc 8h1 7sxl constal nl-chx8)f sq7cxm 16nt speed (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 didnegk)2 ,)l syz the movers do (horizontally) pushing a 160-kg crate 10.3 m across a rough floor without accelerat e,k2gyns zl))ion, if the effective coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is acczyi/hp2 miu7k 7lbp/7elerated by a force across a floor at a rate of for 7.0 s. Find the net 2z hi p/77ubyl/pikm7work done on the box.   J

  Eight books, each 4.3 cm thick with/pvmlel3kk0j++c ru; mass 1.7 kg, lie flat on a table. How much work is requirk/c0uvp 3rkej+ l;lm+ ed to stack them one on top of another?    J

A lever such as that shown in Fig. 6-35 can be used to liff obp t*o /lad78m 7e74jj.f gqd3gu/pq yjkmt+f (jects we might not otherwise be able to liff. Show that the ratio of outl ttfug.oj7+da(/p74 y q/g7j q8em*djfm3 kpput force, $F_{\mathrm{O}}$, to input force, $F_{\mathrm{I}}$, is related to the lengths $\iota_\mathrm{I}$ and $\iota_\mathrm{o}$ from the pivot point by $F_{\mathrm{O}}/F_{\mathrm{I}}=l_{\mathrm{I}}/l_{\mathrm{O}}$ (ignoring friction and the mass of the lever), given that the work output equals work input.

  A 330-kg piano slides 3.6 m down a 28° incline and is kept from accf7+iq c1pi2l 1fty md yk;:ub5elerating by aciyubp tydf17l :2m5 f+ki;q1 man who is pushing 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 helicopter of mass M an acceleration of 0.v b0xiogkp 221xs2dl510 g xbvk2xgsp25io12 0d lupward.    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 an c-7 e20h l lx-g(7d,uz 05mzjvvqemucd that $d_{\mathrm{A}}=10.0$ m and $d_{\mathrm{B}}=35.0$m. Estimate the work
done by force $F$ in moving a 2.80-kg object from $d_\mathrm{A}$ to $d_\mathrm{B}$   J

  The force on an object, acting along the x axis, varies as shown in-7yb w; wrnbt,8mpxv-5xu*dep 8ltqt k5h h): Fig. 6–37. Determine the work done by this force to move8,-wxh;bte*lv n ydk5p - hw8)q57r: mbptu xt 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 in the2 6x. 9f*ibyze9 jm6xwz cklm5 $+x$ 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, wit lh-2 l038woh)+evdtj x tnxy3h 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 84i3xw o6khliyenbf/416bi v what factor has its speed increased? $ \sqrt{a}$ a =    (b) If its speed is doubled, by what factor does its KE increase?   

  How much work is required to stop aq0 (n5qyxq ++w/mpl tp07gus qn 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 stobqmnb7/y98h jn,7kl dp a 1250-kgcar traveling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whose string exerts an a2z yz2 l3hgrsb9 0dy6-j rkxu6verage force of 110 N on the arrow over a distance of 78 cm. What is the sz6dsg 2y k6x39r lzhrj2 u0-bypeed of the arrow as it leaves the bow?    m/s

  A baseball (m=140kg) traveling 32m/s moves a fielder’s glo8xeoznr 4 53lwve backward 25 cm when the ball is caught. What was the average force exerted by the ball on the gloex n5lwr4 oz38ve?    N

If the speed of a car is i ib9j+yrc;bu6*grpe1c ier0 t2xdd(6ncreased by 50%, by what factor will its minimum braking distance be increased, assuming all else is the same? Ignore the drjee ur6p(2c diri;x yrg0b69 c1b d+*tiver’s reaction time.

  At an accident scene0nab7y0 -0 -kadahc mc 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 coefficient of kinetic friction was estimated to be0a-hyc bkm7aa0n0dc - 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 pitm neexrkies ylm2nw-3a2xg2 j.9tfnax2*) 9/ched at By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance durixi2*2xsrn3 -l 2 e9xa9nja). fe2m mkt/ewngy ng a pitch, if the distance between the plate and the pitcher is about 15 m.    N

  How high will a 1.85-kg rock )-s xtlux ) haa()6sb3hfbsw/go if thrown straight up by someone who does 80.0 J s t6lh)xu-)a xab/ s)h (3bswfof work on it? Neglect air resistance.    m

  A 285-kg load is lifted 22.0 m vertically with an;alu, 7 ja t5xaadu99 osf(-ge acceleration by a single cable. Dete5,- fg;799aat(dslj o uuaxearmine
(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, n yha:d td660 sssiz*1k, of 440N/m How much must this spring be stretched to store 25 J of potential end:s zst 1yh*si6n6d0aergy?    m

  A 7.0-kg monkey swings fro) ixz2i+ m.sjo+nhq4ae1 m8 xgm one branch to another 1.2 m higher. What is the change in potenti qs+g ie8.o) 4nmxji+ amxz2h1al energy?    J

  By how much does the gravitational potential energy of a 64-kg pole vau3z8o i7 3m juh;x;,z2r ywpgk9zfe-eplter changeyig2,woe;ph3erf z ;u-39 pzxj8mz k7 if his center of mass rises about 4.0 m during the jump?    J

  A 1200-kg car rolling on a horizontal surface has speed v = 65.ulef05 ua70 u8va 2esu1dnieo u kx71 km/h when it strikes a horizontal coiled spring and is brou7uaenxevdsuklu0 i f1a1e05 u.7u2 8oght 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 /w, cdlb(q)y ckjymk97,j br*lifts a 2.10-kg book from the ground so it is 2.20 m above the ground. What is the potential energy of thc mb*w9j)kb,/ rljc(k yqy7,de 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 jri38t( xmrr-a*xk+)gz/ydz of 1600 m and climbs to the top of a 3300-m peak. +*-rxz( a jk /83mrgztidx)yr
(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 spring 2-qf znu cf6f(is next to the 15-cm mark on the ruler. If a 2.5-kg mass is now attached to the end of the spring, where will the end of the spring line upfzf2-cnf u(6q with the ruler marks?    cm

  Jane, looking for Tarzan, is running at t7ls6 ,oiklc,p op speed (5.3m/s) and grabs a vine hanging vertic, cosl6p7,ikl ally 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 froigjx , f 8g0(1-xeebyzm rest, slides down a frictionless 35.0$^{\circ}$ incline whose vertical height is 185 m. How fast is she going when she reaches the bottom?    m/s

  A sled is initially given asc -a1l2 ,razx shove up a frictionless 28.0$^{\circ}$ incline. It reaches a maximum vertical height 1.35 m higher than where it started. What was its initial speed?    m/s

  In the high jump, Fran’s6xr qt*9*wg (nmt*0abb he6o q kinetic energy is transformed 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 ofqtm6rh( b*6g etowx*b0*qn 9a mass 2.10 m and cross the bar with a speed of 0.7m/s.    m/s

  A 65-kg trampoline artist jumps vertically upward fromjg pd210np0gnhqx zs40t1 2zdf6l.jt the top of a platform with a speed of 5.zg0fh2x2 6tn0jpj.tq lpzd0g1n d4s10 m/s. ($\alpha)$ How fast is he going as he lands on the trampoline, 3.0 m below (Fig. 6-38)?$v_2$ $\approx$    m/s
(b) If the trampoline behaves like a spring with spring stiffness constant 6.2×10$^{4}$ N/m , how far does he depress it? $y_3$ =    m

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

  A vertical spring (ignore its mass), whose spring stiffness constant is 950N/m i-1 3c sbp,sjows attached to a table and is compressed dojwps b 3,1-scown 0.150 m. (a) What upward speed can it give to a 0.30-kg ball when released?    m/s
(b) How high above its original position (spring compressed) will the ball fly?    m

  A block of mass m slides without friction along the looped track shown in Fa5n8 ugvewhfva11g / )ig. 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 heightugg18 ahv/n )a51fvw e h must it be released?    r

A block of mass m is attached/m lsrbus7 u*8 to the end of a spring (spring stiffness constant k), Fig. 6–40. The block is given anm8sus lu*7rb/ 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 hru 1o*lsje8 )tied to a bungee cord whose unstretched les8 jeo r)*uhl1ngth 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. $\approx$    N/m
(b) Calculate the maximum acceleration she experiences. $\approx$   m/$s^2$

  The roller-coaster car shown in Fig. ze .8j. :aynsi)b;ckw 6–41 is dragged up to point 1 where it is releaskzc in w ya)s..b8j:e;ed from rest. 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 m/s at an angledv eisw+ ,utmtmmvn:w 4(uasv :4h:72 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 ao- d:yjza, 3mq3cj n4 a4a.zflt the bottom 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 acceleration of no more than 5.0 g when brought to rest. Let M be the total mass ofqjm :jzazo.ca3 d44 ,-a fnyl3 the elevator and passengers.

  A cyclist intends to cli +/h,gu(7r sncal/ wycle up a 7.8 $^{\circ} $ hill whose vertical height is 150 m. Assuming the mass of bicycle plus cyclist is 75 kg,
(a) calculate how much work must be done against gravity.    J
(b) If each complete revolution of the pedals moves the bike 5.1 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses. The pedals turn in a circle of diameter 36 cm.    N

  Two railroad cars, each of mass 7650 kg and traveling 95km/h in opclppob0 vg *:4ps)mb ng0- 0zvposite directions, collide head-on and come to *n0ol 0vsc p04mg)z g-vbb:pprest. 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 bottom with a spe0*wcg7z vh 3umed of 2.2m/s How much thermal energy due to frictiu07gvzhc *mw3on was generated in this process?    J

  A ski starts from rest and slides +jrwd-vk g-rw gw:,9q down a 22 $^{\circ} $ incline 75 m long.
(a) If the coefficient of friction is 0.090, what is the ski’s speed at the base of the incline? $\approx$    m/s
(b) If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level? Use energy methods.$\approx$    m

  A 145-g baseball is dropped from a v vgbw5ak+3z12 ml ,qutree 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 hb g.yy)*0 lui8 : wv4qmemnj:jeight of 2.0 m, and it bounces back to a height of 1.5 m4wmvbiu:gj0nmq8)j . :le *yy.
(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 wit7;max a o9ngq1h a constant horizontal force of 350 N. For the first 15 m the floor ;mg7ax1 9oanq 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 bvki1; g0xq6f of If the average force of friction is equal tog f60k;bi 1qxv 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 upwap*mb;.- q mfw4r 4ablxrd 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 blockaj:7a ok*( s; f6ufzk) (yapux is firmly attached to a very light horizontal spring (k=180N/m) as shown in Fig. 6–40. It is noted that the block–spring system, when compressed 5.0 cm and released, stretches out 2.3 cm beyond the equilibrium position before stopping and turning back. What is the coefficient of kinetic friction;au ) aoz :ku(x*j(fa6pfs7yk between the block and the table?   

  A 280-g wood block is firmly attached to a very light horizontal spring, -bih d5 j p)jhv3bh6.pFig. 6–40. The block can slide along a table where the coefficient of friction is 0.30. A force ofd- bh3 pvjp).5ibh6jh 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 s jn6;ij k0(tlopace shuttle used a “glider” (mass of 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 wo(6;jt o 0jlinkuld its landing speed have been in the absence of air resistance?$\approx$    km/h
(b) What was the average force of air resistance exerted on it if it came in at a constant glide of 10 $^{\circ} $ to the Earth?$\approx$    N

  How long will it take a 1750-W motor to lift a 315-kg p+8*. d7ai2bvc.lsvxtaa f r)qiano to a sixth-story window 16.0 m above? ca t.* + idx)vsl.q7brf8 vaa2   s

  If a car generates 18 hp when traveling +k;s abai0yt.ou:hx zqa;5(rat a steady 88km/h what must be the average forceh. ryq5 +xz (s:;u0 oa;bakait exerted on the car due to friction and air resistance?    N

  A 1400-kg sports car accvepn*c e 4ww0;elerates from rest to 95km/h in 7.4 s. What is the average power delivw4*p ew;v0ecnered by the engine?$\approx$    hp

  (a) Show that one Britisfmh 15dpye,jf;86h4mdy zxf h):vfub4dt 9:x h 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 “kilowatt-h93cd 6 60pq+xij73 eceoffgm sours.”
(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 slw6 gzbd;2 pxwr*:6bcprs x 3m,ows 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 need2x*6 rdmwbg3x;s ,rw b6z:pcped to keep the car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hp motor do ineut .rw4ox8 h5 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg y ,jf0;aoyckx+ cij(1 shot from rest to 14m/s If this motion takes 1.5 s, what average power wa+1(jkyj; ,y c xiaf0cos developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute throug:vz+iks 20cv ny nm2x/h a height of 3.60 m. What output rating (watts) should thnkvy: m+ziv/ x2c0n2se pump motor have?    W

  During a workout, the football players at State U. ranzq7be;rih7gi.10e r r up the stadium stairs in 66 s. The stairs are 140 m long and inclined b;hegrqii 1ezr 77.0rat 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 y- l)vg4omtj 4climb 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 stee:bkid j9 kyh :lj.ub51p a hill can it climb at a constant speed of 75km/h if the frictional forces add up to 650 N? 5jj ikh1bby9.d:u:kl    $^{\circ} $

  What minimum horsepower must a motor have to be able to drag a 31wojez5j qh1jet692(wdg:dlz8awc3 1 0-kg box along a levec6dwww9jezj(g512 dl e3ja zho:1q8tl floor at a speed of 1.2m/s if the coefficient of friction is 0.45?    hp

  A bicyclist coasts down abtz9-mr z)r dg194viv 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 :1xnusskn1y g rc-k v. + 5p;eb:+zsftcars have built “5mi/h(8km/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 permanently deforms after a compression of 1.5 cm, but remains like an elastic spring up to that point, what must the effective spring s .zv; 1xf1sks:-nyb e+kp5:uct+s g nrtiffness 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 remainin2*zz5y -4rb s vtiwmo1g four shelves are each spaced 30.0 cm above the previous one. If the average book has a mass of 1.5 zvr y*1zwb mo4i-5ts2kg 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 Owens’s famous long jump (Fig. 6–424i vdk -7a-c(6jgwnfw ow5( hv) 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 wad(v wwv4- fk 6w i5-hac7nogj(s traveling at 6.5m/s at the top of the arc?   m/s

  The block of mass m sliding without f3bgafk,5+ kfj riction along the looped track shown in Fig. 6–39 ik3ak,bffg+j 5 s 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 fel igzzo*9b2(m el 370 m after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived wi9*be2 giz(oz mth 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 horizofeb3ify:n e: .6ge+ yj)r4qay g8f v9nntal cord of length L whose other end is fixed (Fig. 6–43). 96 bffegiy) fqe 3+4n.ej :yvan8r:gy
(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 t +yh4 8lxsitz: m2zsr;he top of a 3700-m-high mountain. The climb is made in 5.0 h starting at an elevation of 2300 m. Clz:x z m2+ ssyih8t4;ralculate
(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-k q8 v7-y d7sr/p.tjkj)x s,otbg 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 Califoro4byy4nq. d /wnia claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the b/qywo4 .4dnypower needed.$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and falls verticall x0w.3xh)u+bermb;a4l, tnl my 81 m before strikinmwbte b,;xmlh 3.al)u0r +x4ng the turbine 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 circular vertical loop (Fig. 6–44),q 2u. kqf7sdu0 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 kq7fu .0 us2dqthe loop or how fast you go through it.    mg

  (a) If the human body could convert a candy bar directly into work, howcbd 9ao0d yxfk6n a9iy3+xx): high could an 82-kg +ac:6bod 9ny)yxdi 0xx3 9 kafman climb a ladder if he were fueled by one bar (=1000kJ)    m
(b) If the man then jumped off the ladder, what will be his speed when he reaches the bottom?    m/s

  A projectile is fired az+x3gt7tmd* jmb 9i ddn3gf,- t an upward angle of 45.0$^{\circ} $ from the top of a 165-m cliff with a speed of 175m/s What will be its speed when it strikes the ground below? (Use conservation of energy and neglect air resistance.)    m/s

  If you stand on a bathroom scpp7t-.oid1 bw ale, the spring inside the scale compresses 0.60 mm, and it tells you your weigh1wp dopb-7t .it is 710 N. Now if you jump on the scale from a height of 1.0 m, what does the scale read at its peak?    N

  A 65-kg student runs at 5m/s grabs a rope, and sw. f 9js,/52-;f)o5qgyjbj*lpnf n1tszwtit v ings out over a lake (Fig. 6–45). He releas)f./ *l-5gfnnsv; 5i,jfpb 9yjzqtt1wj ots2es the rope when his velocity is zero.
(a) What is the angle when he releases the rope?    $^{\circ} $
(b) What is the tension in the rope just before he releases it?    N
(c) What is the maximum tension in the rope?    N

  In the rope climb, a 7 z (f99 g,vbxn6j+kcg s/f/phv2-kg athlete climbs a vertical distance of 5.0 m in 9.0 s. W( nvgfj9/ phg+vsf69kbz c/x,hat minimum power output was used to accomplish this feat?    W

  Some electric-power companies use water to store energy. Water is pu1bbiu8mxd5e4f. scqqqg6 6 ;ymped by reversible turbine pumps from a low to a high reservoiq.qus6c x18 bq5fmg;de by64ir. 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 constant k is cut in half. What is the spring sti9nsn6+ dl um8mffness constant for each of the unlmn68d + 9smtwo resulting springs?   k

  A 6.0-kg block is pushed 8.0 u-d1ummka 2 7wm 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 frouupo-b,- 9:o0cne e ydm 35km/h to 55km/h in 3.2 s, how long will it take to accelerate from 55km/h to 75km/h Assume the power stays the same, a9-o:ue,ed n 0opy-bu cnd neglect frictional losses.    s

  In a common test for cardiac function (the “stress test”), thw 4ykkvy,) 1v mvt6tp+e patient walks on an inclined treadmill (Fig. 6–46). Estimate the power required from a 75-kg wy 1+yv,vv) 46ktkmptpatient 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 ve2t5 honsq5;p faon:k4 rtically upward a distance of 500 m, what was its velocity when it left the volcano?a5 h fokpqn;25 t4no:s $\approx$    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 ofdeq0 b in34l)z 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 p lnd43i)b 0qzeower output?    W
(b) What is the speed of the water as it hits the wheel?    m/s