In what ways is the word “work” as used in everydayp4dr y x .:hf p)qxz9d2*k*5-thgmhze language the same as that defined in physics? In what ways is it9*h ph *rgzfth2kxze)dqxy 4m-5.:p d different? Give examples of both.

Can a centripetal force ever 3 7qwgn6rd9 25m feqehdo work on an object? Explain.

Can the normal force on a6gtdu 7 hbv+iu5lc69 ysl u83wn object ever do work? Explain.

A woman swimming upstream is not moving with respect to the shore. Is shc 2i9si)lui.i* jt -l0iq 4akre doing i2-i*jli .9isu ct0arkiql4) any work? If she stops swimming and merely floats, is work done on her?

Is the work done by kinetic friction forces always nwju p.p 0p7iik+xw 90gkg(kc/ly3a 0yegative? [Hint: Consider what happens to the dishes when you pull a tableclotki.0w7u9c iglap gjkk (x +0p/y0w3yph out from under them.]

Why is it tiring to push hard againc9)lomh /g4 u(v5fr fast a solid wall even though you are doing no work?)9/ca f m5gfv4olur (h

You have two springs that are identical except that sp.v;ki8fu 9k6j (cv f3;l tyt;svq/)ywbt*e tzring l is stiffer than spring 2 /tzltvsv .k(6 ib;kv )q83t9f; e ;c*tywfjyu $(k_1>k_2).$ 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 hk-scy(-o8 0aaxq1m drv:7hewfdvs44 orizontal 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 distanc1 fshe-o8mk v0a(4-rqc4d advx :w y7se $d$ 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 pohae6 yp4f)+0k(vmi ectential energy change when you jump as hig 6he+ieyk0amc pv 4)(fh as you can?

In Fig. 6–31, water balloons are tossed from the 0jxk/)*oh9+/3h(b fw2pnimmufnc fp roof of a building, all with the same speed but with different laun ncfj(ohf/pm3i/b*f x2hn) wu0pm9 +kch angles. Which one has the highest speed on impact? Ignore air resistance.

A pendulum is launched from a point that is a height h above its lilc /816ihcj9-lx mmxpc*7jv owest point in two different ways (Fig. 6–32). During both launches, the pendulum is given an initial speed of 3.0m/s ml -l7mx68 jj1 hv/*pxii9cc cOn 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 upright on a table. If you compress thsbfz i 8n, eo7.wj6ettyqy+64e spring by pressing down with your hand and then release it, can the spring leave the table? Explain, usingtne yey bq t 68.jf64,si7o+zw the law of conservation of energy.

A bowling ball is hung from the ceiling by a steel wire (Fig. 6–33). The instrci h54sm 0arr el7y7h0uctor pulls the s0 0mrc 5aer7hh4iyl 7ball 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?

What happens to the gravitational potential energy when water p, 3c/ e.u0 zmrg+l1lc4jikbxat the top of a waterfall falls to tmkiz,xucgclb 4+ /e.1j rpl03he pool below?

Describe the energy transforma-nlnuuh 1 u*-qtions when a child hops around on a pogo stick.

Describe the energy transformations that take place wh lfdehe w6iv5*ac0z,ewzq6x 0x1(w.ven a skier starts skiing down a hill, but after a time is e vzw w vh6dq1l(zx.e05w0i6e,fx a c*brought to rest by striking a snowdrift.

A child on a sled (total mass :lz5 6h(d/qo a8ijp; .yunnew m) starts from rest at the top of a hill of height h and slides down. Does the velocity at the bottom depend on the angle of the hill if (a) it is icy and there is no fri dw;oez8 l:an j5qiyun(./6phction, and (b) there is friction (deep snow)?

Seasoned hikers prefe5rjme i t4( irui:ii4h,a6m kj)(v;sz r to step over a fallen log in their path rather than stepping on top and jumping down on the other side.i4( k56 ujj)itmasm(;4ihe,: zrr vii Explain.

Two identical arrows, one with twice the speed of the other *bwc-3* dj9od,a 1lkfz :vjdw, are fired into a bale of hay. Assuming the hay exerts a constant frictional force on the arrows, the faster arrow wi f*1k:blj dvzdowjc-d*,a3w9ll penetrate how much farther than the slower arrow? Explain.

Analyze the motion of a simple swin uv .j19knokr1.6gnfihao -c 0ging pendulum in terms of energy, (a) ignoring friction, and (b) taking friction into account. Explain w6a-f.1o.org 0knhuv i 1c j9nkhy a grandfather clock has to be wound up.

When a “superball” is dropped:x.qbn)pf iqtw nhx9( 2 dnc: v5a8nt6, can it rebound to a height greater than its original height? Exnq f8)v .6xn9 :bndp: nwih2ctxta(5 qplain.

Suppose you lift a suitcase from the floor x;eqos/hb-t7l.g b2f to a table. The work you do on the suitcase depends on which of the following: (a) whether you lift it straight up o -g fq2e;/ bh.botlxs7r 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 rrmnf2. 082ys- 5aco juieh . al3jxt8pather than the work.

Why is it easier to climb a mountain via a zigzag trail than to climb st:6v-m:/* g,ncv lneofmlmwr p15b( wvraight upb6, fn-w1mn5vvmler m(g/w*po vlc ::?

Recall from Chapter 4, Example 4–14, that yo/ldabupvg 7,5xc+ m+l;7 irv wu can use a pulley and ropes to decrease the force needed to raise a heavy load (see Fig. 6–34). But for every meter the load is raii/5lv7 gl p;mwv,xd+car+ bu7 sed, how much rope must be pulled up? Account for this, using energy concepts.

  How much work is done by the lzhme xk:c- lx)r/( r)gravitational force when a 265-kg pile driver falls 2.8- rxl xmlh()e:c)/k zr0 m?    J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How much wd.ly3;o h/5 4 ei5h gf0rredkdork is required?5035fehddr;4o rd.hl eyk /i g    J

  A 1300-N crate rests on the floor. How much work is requiredk5 qif v+/-51hvhva cvx1oo/n to move it at constantvcav5x+/v iovn- /oh5 fkhq11 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 did the movers do (*7it0tso:g*kt z lse +horizontally) pushing a 160-kg crate 10.3 m across a roi*s o:0ge* z7t +tsktlugh floor without acceleration, if the effective 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 n+16vn c -lvnz for 7.0 s. Find the net work done on the box. z +vl-nv cn16n  J

  Eight books, each 4.3 cm thick with mass 1.ccdb/ mwsf-56 7 kg, lie flat on a table. How much work is required to stack them one on top fw6 s5-bcdm/cof another?    J

A lever such as that shown in Fig+uh55p j6 gk*eav.gjz95idlk . 6-35 can be used to liff objects we might not otherwise+a*g9ze ihp du6l. j5jkg55kv 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 down a 28° inclig8c2gy nc -y .tn) 7a26yew6sm8ojjjl)d+ dldne and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 6-36). Tj +dy8 6 -nalecson wj )t m2d7).26cg8gdyyjlhe 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 accelerati pv*xolcg2 *0ion of 0.10 *vip*c lxo2 0gg upward.    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 the0)j:x zgex 9am distance axis is linear and that $d_{\mathrm{A}}=10.0$ m and $d_{\mathrm{B}}=35.0$m. Estimate the work
done by force $F$ in moving a 2.80-kg object from $d_\mathrm{A}$ to $d_\mathrm{B}$   J

  The force on an objectkue ehh7l:k4h3 c* :jx, acting along the x axis, varies as shown in Fig. 6–37. Determine the work done by this force to move the o*leh:4j:e kcxk7hhu3 bject (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 tcs,k. mf1;z-k (v.owoqy sds (he $+x$ 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 u*2 i4rkb v s4-rrmo0aoxygen molecule, with mass of $5.31\times10^{-26}$typically has a KE of about$6.12\times10^{-21}$ J .How fast is the molecule moving?    m/s

  (a) If the KE of an arrow is doubled, by w ,jv11vmqa/x8yat-uzl q j4x: tw., cwhat 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 requiredz+9 f(cpie4+q vqp 1ii 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 12508hvd7mh3 ksqd(p 3m.g-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 average5kzsm+pkn9 z b3, 8jrae+o.sx force of 110 N on the arrow over a distance of 78 cm. What is the speed of the arrow ao kzmx +.bj8ak3s p zs5,ne+r9s it leaves the bow?    m/s

  A baseball (m=140kg) traveling 3ca 3 bql pcvldp7/m;)02m/s moves a fielder’s glove backward 25 cm when the ball is caught. What was the c q;advm /plc07b3l)paverage force exerted by the ball on the glove?    N

If the speed of a car is increased by 50%, by what factor will its;h;c--48irsbaw euud minimum braking distance be increased, assuming all else is the same? Ignore the driver’s reacti;4rw8bsd a-;h euc-uion time.

  At an accident scene on u rvm 1g2ye3c.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 be 0.r2m3vyug 1.ce 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 m.) , 6vmhnnnlyass 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 duri6v)n.m y,hlnn 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 go if thrown szaq 8 q-o/e3oktraight up by someone who does 80.0 J of work on it? q8z3oak /q eo-Neglect air resistance.    m

  A 285-kg load is lifted 22.0 m vertically with an acceleration by a sing04mac yyj9x/c )gcc(ele cable. Detjycg mecc4y)xc 9 a(/0ermine
(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 sprinvc t8c08p6mumylp1 y 7g stiffness constant, k, of 440N/m How much must this spring be stretched to store 25 J of potential enl8pcc6t y7 0m81muvpyergy?    m

  A 7.0-kg monkey swings from one branch to another 1.2 m higherf 6+c;1qsov i q,w-.xuf in,zq. What is the change in potentialqfs;w nx6 iofq. z+1c,qiu-,v energy?    J

  By how much does the gravitational potential energy of a 64-kg pole /2..znbuw 2nk oz5q +4xav hppvaulter change if his center of mass rises about 4.0 m duriozwznn.2vxph.q+bu /5p ak24 ng the jump?    J

  A 1200-kg car rolling on a horizontal surface has speed v = 65 km/h whemh, t 7ze9dm/cgm/v(y n it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spri(v ztg,d//cemmy7mh 9ng stiffness constant of the spring?    N/m

  A 1.60-m tall person lifts a 2.10-kg book from the grounawlq khhq/q +y5*et 6*d so it is 2.20 m above the ground. What is the potential energy of the book relh*yql+q*/ah teqk6w5 ative 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 clii*t o8(tx-japi ;vk m.mbs to the top of a 3300-m pe*iaovkmjti -x;. p8 t(ak.
(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 sprz qbxw:p g 78ap2lez9;0hj: wking 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 th2pqwg ehzblz8 k ;w:9 p7a0x:je spring line up with the ruler marks?    cm

  Jane, looking for Tarzan, is running at top speed (5.3m/;s) l*q ,e.vppjb x;*kzridei: lo- 4 h+lk3vps) and grabs a vine hanging vertically from a tall tree in the jungle. How high v) k ib; *4r;hqiolzp+dpel3-ls:, kv*j.pxe can she swing upward?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from rest, slides down ahm.3x,z oa+s qs+4f.xy1clgg 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 28.0 x9k-t-lu0 p8yi+h gss$^{\circ}$ 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, Fra+ 033o2ui,buy uylg2lr f/vkdn’s kinetic energy is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must Fran leave thel23yubgyv r kf2,uil odu+/30 ground in order to lift her center of mass 2.10 m and cross the bar with a speed of 0.7m/s.    m/s

  A 65-kg trampoline artist jumps vertically upward from the top of a platfe,1xm m .pigbl7 r1s(morm with a speed of 5. gm1brpm(7m ix.e s,l10 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), wh5 *;,;fobkrip0a gwdhose spring stiffness constant is 950N/m is attached to a table and is compressed do5pb g hd;fw*i r;,oa0kwn 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 94) c 8imjrnddzl7b p0without friction along the looped track shown in Fig. 6–39. If the block is to remain on the track, even at the top of the )bd lz8jpr407idn c9m circle (whose radius is r), from what minimum height h must it be released?    r

A block of mass m is attached to tfmnhsfl4o+1 dx),z )p he end of a spring (spring stiffness constant k), F)n h+)1,m plzsdfx 4foig. 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 jumpsrb1r 0bims+ (lgyi7,l from 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 applilsmlb1b(0 r7y,gi r+ies. $\approx$    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 wheres bo,)gv:dib: it is res dobgi,:vb: )leased 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 zk,.dkt52c ui0wf (,:zu gd tlwith a speed of 12 m/s at an angle of 33 $^{\circ} $. (a) What is its speed at its highest point    m/s
(b) how high does it go? (Use conservation of energy, and ignore air resistance.)   m

An engineer is designing a sp wdc7i9vw3l b7o,u j7tring to be placed at 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 of the e9c v77tw u3b,ilwdo7jlevator and passengers.

  A cyclist intends to cycle up 58yt: e edm2ulzqmc3(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, eachpvlu0 asyl wo; ,o:1a; of mass 7650 kg and traveling 95km/h in opposite directiow,olpao u s:l;; ayv01ns, 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 slide 3.5 mvmcj)i fmu9(s c g;5(z high and reaches the bottom with a speed of 2.2m/s How much thermal energy due to friction wvj;i mcg m)9( cfu(s5zas generated in this process?    J

  A ski starts from rest and s 36b6otvzdb: slides down a 22 $^{\circ} $ incline 75 m long.
(a) If the coefficient of friction is 0.090, what is the ski’s speed at the base of the incline? $\approx$    m/s
(b) If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level? Use energy methods.$\approx$    m

  A 145-g baseball is dropped from a tree 13.0 m*5baa3hu l xa-r vy s/;59vrrg 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 hc 8 ear-fcb((weight of 2.0 m, and it bounces back to a height of 1.5 mwc(fcb(8 -ear .
(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, startin)ju5kkl-p; ho kj6( 5ah :fwrjg from rest, is pulled across a floor with a constant horizontal force of 3:p-fawl5;k(oju 6hkkr j hj) 550 N. For the first 15 m the floor is frictionless, and for the next 15 m the coefficient of friction is 0.30. What is the final speed of the crate?    m/s

  Suppose the roller coaster in Fig. 6u+)f7lkc e-/c dgvc3k–41 passes point 1 with a speed of If the average force of friction is equal to one-fifth of its weight, with what speecfc/ku- cl+gvdk3 7 )ed 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 steady2ypl 2p6m*cbn 1gvcl, 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 lig3l*,g 5pod4qhgbb r41 lokk0pht horizontal spring (k=180N/m) as shown in Fig. 6–40. It is noted that the block–spring system, when compressed 5.0 cp4,rp1d 3qb * obk504kgllhgo m and released, stretches out 2.3 cm beyond the equilibrium position before stopping and turning back. What is the coefficient of kinetic friction between the block and the table?   

  A 280-g wood block is (8lbpv3+yv7au9a gb mfirmly attached to a very light horizontal spring, Fig. 6–40. The block can slide along a table where the coefficiebvbyv+lap9a3 u ( 87mgnt 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 “gl)ts.t*ze w 0 aze0olgtyl+ q1+r2 ur-oider” (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 would g * te-2yoz s+uz)1wq0rela.lrt+t0 oits landing speed have been in the absence of air resistance?$\approx$    km/h
(b) What was the average force of air resistance exerted on it if it came in at a constant glide of 10 $^{\circ} $ to the Earth?$\approx$    N

  How long will it take a 1750-W motor to lift a 315-kg piano to a.bm ;zt9om9 .vpi5gc y sixth-story window 1g; z.mp 99c o.itb5vmy6.0 m above?    s

  If a car generates 18 hp when traveling at a steady 88km/h what must b46xld7u cnu 52n 5lruke the average force exerted onu n4255 d c7lurxk6uln the car due to friction and air resistance?    N

  A 1400-kg sports car accelerates from rest to 95km/h in 7.4 s. What i og;hlzn*r+uykzqud:3 -g*3 os the average power delivered3 l:+odug3krzz *;ohy -qn*ug by the engine?$\approx$    hp

  (a) Show that one Britis5wp26 -xvm6uzyj c)42ibcumz 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 unitytj; :tp4 rb(ts are often expressed in the form of “kilowatt-hours.”
(a) Show that one kilowatt-hour (kWh) is equal to $3.6\times10^6$J
(b) If a typical family of four uses electric energy at an average rate of 520 W, how many kWh would their electric bill be for one month $\approx$   kW*h
(c) how many joules would this be?$a\times10^b$ J a =    b =   
(d) At a cost of 0.12 dollars per kWh, what would their monthly bill be in dollars? Does the monthly bill depend on the rate at which they use the electric energy?    dollars

  A driver notices that her tecj0pdjc i*n1 2yh,qmz /(1 j1150-kg 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 to keep the car travel*cj1citj 1 mhdqy e n2,(zp/j0ing at a constant 75km/h.    hp

  How much work can a 3.0-hp motor do zu8*xlx f5u*( e(q dg i2ldq;xin 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerate 9f l5futl30 jhn:,f wwlv8zi1s a 7.3-kg shot from rest to 14m/s If this motion takes 1.5 s, what average po,ul lzjw 8095:ff13vflhwint wer was developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute through a height of 3.60 m. Wha.; g j1vn:o5 -rjfnwizt output rating (watts) should the pumwvorj5.z;jf1n:-g in p motor have?    W

  During a workout, the football players at State U. ran up the stadium stairs inb(dc-pi/ix 7n .9 hnee 66 s. The stairs are 140 m long and inclined at an anglei(dbh-n x7cpe 9e. /ni 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 cyclkc4aqvv4 b+ )bist 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 hildhrp quifo 0(n(3 11ayl can it climb at a constant speed ofyr 0iqnaufh (o1(1p 3d 75km/h if the frictional forces add up to 650 N?    $^{\circ} $

  What minimum horsepower must a mo)ty7 zrpooo (*5q pq0jtor have to be able to drag a 310-kg box along a level floor at a speed of 1.2m/s if thyqp j *z0or(qt5 7p)ooe coefficient of friction is 0.45?    hp

  A bicyclist coasts do / 7dpk1i5fzrfwn a 7.0 $^{\circ} $ hill at a steady speed of 5m/s Assuming a total mass of 75 kg (bicycle plus rider), what must be the cyclist’s power output to climb the same hill at the same speed?    W

  Designers of today’s cars have built “5mi/h(8km/h) bumpers” that are design57mpv pfh7tz)sn ch1uqrs.i ) z1y7 +sed 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 liphpi1m+ c5us sqt1zv7) nzr7.h )y7sfke an elastic spring up to that point, what must the effective spring stiffness constant of the bumper be, assuming the car has a mass of 1300 kg and is tested by ramming into a solid wall? $a\times10^b$ N/m a =    b =   

  In a certain library the first shelf is 10.0 cm off the ground,kef7b6*38tb 0 0e7zui xwu xzi and the remaining four shelves are each spaced 30.0 cm above the previous one. If the averagex3*bwtxkeu z77e i0zu6fbi 80 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 Owens’s famoulv ehut sb)z/,4op0ie q07u d2s 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 pu/s qd uzb)itl47eeh2v0o,0 of the arc. What minimum speed did he need at launch if he was traveling at 6.5m/s at the top of the arc?   m/s

  The block of mass m sliding withoubp91lxbb6.j ws +7dmnt friction along the looped track shown in Fig. 6–39 is to remain on the track at all times, even at thjdn67msbb.b9+wp1l x e 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 jncp;oyk v- r5bz ,;wdud:)s m8umping from an aircraft without his parachute opend ;5cyrm;)dku,p : ozsnv8-bwing. 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 uqhh r:l85jf5t*jmrq,t n ;q-whose other end is fixed (Fig. 8qn-qr q;f ,mjr:ujhh tt55l* 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 8aculqbuom3q3k/dhw 5: g/.c 3700-m-high mountain. The climb is made in 5.0 h starting at an elevation of 2300 8guq5qm:o c3/ckhudw3a lb /.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 5jv ) xzteee2g5mr)tt,c ;k7w 920-kg elevator is 28 m above a huge spring ($k=2.2\times10^{5} \mathrm{N/m}$) at the bottom of the shaft. Calculate
(a) the work done by gravity on the elevator before it hits the spring,$\approx$    j
(b) the speed of the elevator just before striking the spring,$\approx$    m/s
(c) the amount the spring compresses (note that work is done by both the spring and gravity in this part).    m

  Squaw Valley ski area in California claims thhz5q5 gk2tppwqr8 f(,at its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the q2( tk5 q58,gpfrh zwppower needed.$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and falls vp u: /rj adb5vuxmx+kd4+y(3pertically 81 m before striking the turbine(3r uxjku+ py4: md/+p5xbvad 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 pzcbc c9+ k*0,*u-nsl7bk z:tq .erescoaster with a circular vertical loop (Fig. 6–44), the difference in your apparent weight at the top of the circular scczlbre,e+: zbk*su9 -k 7.n0 qtcp*loop and the bottom of the circular loop is 6 g’s — that is, six times your weight. Ignore friction. Show also that as long as your speed is above the minimum needed, this answer doesn’t depend on the size of the loop or how fast you go through it.    mg

  (a) If the human body could convert a candy bar directly into work, how high c w9rchi.u 2dv5ox ou04bk;.sp ould an 8r.vbuod.xh 0wc o i;95uk 42sp2-kg man 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 at an upward angle of 4d6) bpk e+zdals riw5asn+7,f z+.s; j5.0$^{\circ} $ from the top of a 165-m cliff with a speed of 175m/s What will be its speed when it strikes the ground below? (Use conservation of energy and neglect air resistance.)    m/s

  If you stand on a bathroom scale, the spring inside the scale compresses 0.60 evu :u*.-ok ekmm, and it tells you your weight is 710 N. Now if you jump ono. - ek*u:euvk 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 roq8 u0iyomt1; ,zqx 2qortw5 c8 i,(dzlpe, and swings out over a lake (Fig. 6–45).tm18oo tzxdw qr5,q c ;8,(ii2 0lyuzq He releases 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 72-kg athlete climbs a verticabbsy.3l ;j+ia *.nrue xq9eo 3l distance of 5.0 m in 9.0 s. What minimum pba b.srl9eyx+n;q.* j3oe3ui ower output was used to accomplish this feat?    W

  Some electric-power companies use water to store energy. Wa1lwt w00 ,t)luwt9,i bqv;+n dd+vd jzter is pumped by reversible turbine pumps from a low to a high reservoir. To store the energy produced in 1.0 hour by a 120-M0v,j b+dl n+dwvl w1d )itt,tz;q0 uw9W ($120\times10^{6}$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 e;xgq4 78(gwm- ewgql stiffness constant k is cut in half. What is the spring stiffness constant for each of the two resulting spri;7 8lmee-wg4(xg gqwq ngs?   k

  A 6.0-kg block is pushed 8.0 m up a rouk/ 6(i 7hvyxrngh 37 $^{\circ} $ inclined plane by a horizontal force of 75 N. If the initial speed of the block is 2.2m/s up the plane and a constant kinetic friction force of 25 N opposes the motion, calculate
(a) the initial kinetic energy of the block; $\approx$    J
(b) the work done by the 75-N force; $\approx$    J
(c) the work done by the friction force;    J
(d) the work done by gravity;$\approx$    J
(e) the work done by the normal force;    J
(f) the final kinetic energy of the block.$\approx$    J

  If a 1500-kg car can accelerate from 35km/h to 55km/h in 3.2 sne zm,ur o 8h);k;xoa;, how long will it take to accelerate from 55km/h to 75km/h Assume the power stays the same, and neglecuexn; ookz ,r;)8mah;t frictional losses.    s

  In a common test for cardiac funct9 ;)xaa d4(emkv;zse cion (the “stress test”), the patient walks on an inclined treadmill (Fig. 6–46). Estimate the p ea)xd(akmv es; z94;cower 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 50s 8q2s 9gjtor60 m, what 6sj2ts 9qgo8rwas its velocity 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 rate of 95kg/s (nkexf8t / 9k,wl2m:ne a) If this wat:lxne 89/wkfk2mne,ter wheel is set up to provide electricity output, what is its maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s