In what ways is the word “work” as used in everycp2s2 nlwc.z) day language the same as that defined in phlz.2p c )2scwnysics? In what ways is it different? Give examples of both.

Can a centripetal force ever do work on an object h4bjbbu4a2f61c /n d8ykj(vl? Explain.

Can the normal force on an object ever do work? Expum*uz e.4l:7 l rug v116bnqphlain.

A woman swimming upsd:o auia-.gq 3tream is not moving with respect to the shore. Is she doing any work? If she stops swimming and mao:3qdug -. iaerely floats, is work done on her?

Is the work done by kinetic friction forces always negative? [Hint: Con(ckvc;29o:p-v - rvdk9k- wzboipe 6i sider what happe6-o -;cbw ip- 9pv9ik2dv: c o(zekkvrns to the dishes when you pull a tablecloth out from under them.]

Why is it tiring to push hard against a solid w g17e wl-w3i nyuty5r,83mdnslb :5aiall even though you are doing no work? w3ei8,7m53dusy5gn rnliltbaw y:1 -

You have two springs that are identical except that os01x 1c);nooth2cd6esp 5g qspring l is stiffer than springc2dns; qot11eg cx5os6) hop0 2 $(k_1>k_2).$ On which spring
is more work done $(a)$ if they are stretched using the same force, $(b)$ if they are stretched the same distance?

A hand exerts a constant horizontal force on a blo)gfx /:shxr*d* oue2f ck 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 distancxhs2dr* ff /:gux*o)ee $d$ 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 grl: /puov.p0u*sfh:i hq 3/ etu:j+kxravitational potential energy change when you jump as high as you caousxt:v/*ep/hufqpjrk0: 3ih u l+.:n?

In Fig. 6–31, water ballo9 z/hm- ilpr77j skeub0dq; l6ons are tossed from the roof of a building, all with the same speed zl-bhq6s7e lmi;j/90p 7udrkbut with different launch 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 lo + gxr5 qq xj.+p7x 5v 7qlm06yz(xxoae0:xlvqwest point in two different ways (Fig. 6–32). During both launches, 7ae6m5xqlzy7q:qxv(v . + rxx0gxljo0x+ 5pq 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 upright on a table. If you compress the spring70k-ndp l 6xbe by pressing down with your hand and then release ik60 lb7ed nx-pt, can the spring leave the table? Explain, using the law of conservation of energy.

A bowling ball is hung from the ceiling by a steel wire (Fig. ))*: sbson3 ;rhqp-x(cj jd6p5bdow p6–33). The instructor pulls the ball back and stands against the wall with the ball against his nose. To avoid injury the instructor is supposed w-h*cb ; pjq56pjn (do)b xr:d)o sp3sto release the ball without pushing it. Why?

What happens to the gravitational potential t5or 6eao4w l )lzrg852yp1sgenergy when water at the top of a waterfall falls to the powaygroz 61ls oe8 rl2tp545)gol below?

Describe the energy trans(wxl ;ei;1 csnsy( gk;formations when a child hops around on a pogo stick.

Describe the energy transformations8bebidojih)g 67-ruj.y) .dw that take place when a skier starts skiing down a hill, but after a time is bro bdw6iyi 7jj )rhdeg)8u -b..ought to rest by striking a snowdrift.

A child on a sled (total mass m) starts.ut :q/a3/mhc z:tz3 oes-xc h 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 friction, and (:ch3tx z:/ et.cz q-3auos/hmb) there is friction (deep snow)?

Seasoned hikers prefer to step over a fallen loies(pg s,s4be+fy:opa 7g9b- g in their path rather than stepping on top and bgp+,(i-9pegba7:fseoy s 4 sjumping down on the other side. Explain.

Two identical arrows, one with twice the speed of lr-.iz xab n,2m)ewj7 dsl(:athe other, are fired into a baleamlz wi)-7x(,d.nls 2b :ar je of hay. Assuming the hay exerts a constant frictional force on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain.

Analyze the motion of a simplel5k6fekr0kv(: n y i;yf38hzc swinging pendulum in terms of energy, (a) ignoring friction, and (b) t 5 8yke :c3yvi 0z(;fh6nrfkklaking friction into account. Explain why a grandfather clock has to be wound up.

When a “superball” is dropped, can it rebound to a height greater than its orkyvb;v pteq 3cio5:48 z0vdu8iginal height? Expl3q88vc b45vuo ie;0 pv:ydzk tain.

Suppose you lift a suitcase from the floor to a table. The work you do on the fp1hbjf;ng; f0c is1) 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 suitcase?b)f0j ;schf i; gnf11p

Repeat Question 22 for the power needed rathe pidedoh5,om156 w 2sn r2y+vdr than the work.

Why is it easier to climb a mountain via a zigzag trail than to climb straigcy- ui0,cc3t zht u-yc3ci ut,z0cp?

Recall from Chapter 4, Example 4–14, that yorkz*jm /b e itqo*09f ;.tpg*gu can use a pulley and ropes to decrease the force needed to raise a heavy load (see Fig. 6 m b*g/;.oj0t9gktizqef *pr *–34). But for every meter the load is raised, how much rope must be pulled up? Account for this, using energy concepts.

  How much work is done by the gravitational force when a 265-kg pile driver falls3 a, -byv+sspp.kvhijx:, qg mh2-wh; 2.hj2:hpvx qg-s,- k,h +vp3yb.mw;s i a80 m?    J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How much wom04)e7zg9 qvnqjza g0 rk is requ4g qn)q0az0m e79gzvjired?    J

  A 1300-N crate rests on the floor. Howb+;iz 6ug8 3 w+umjshe much work is required to move it at constant speed (a) 4.0 m along the floor against a friction forch i g86mb3z+uuwj+;see of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work didsa vvl.xaa762 o c2a*q the movers do (horizontally) pushing a 160-kg crate 10.3 m across a rough floor without acceleration, 7x vco *2 v6sal.qa2aaif 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 ofobwwdcq sma- lt65.18 for 7.0 s. Find the net work ld-co5qa 1w6wt8mbs . done on the box.   J

  Eight books, each 4.3 cm thick with mass 1.7 kg, lie flat on a gl5ro 4uw6c+atable. How much work is required to stack the+rc wug 5ol46am one on top of another?    J

A lever such as that shown in Fig. 6-35 can be used to liff ob5 e 4lvs p5pp88 dg0ou.u5usqoiwb6-q jects we might not otherwise be able to liff. Show that the ratio of output q. e6l-i54 50guqd8usp5 pws poubvo8 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 28lgu 6 2l4d1oyz° incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 6-36).olyud264g z 1l 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 heliyeshb yj(hm9 k;4kf0n:t u,:icopter of mass M an acceleration of 0.1yu ,k9j kh4(; itm beh:sn:y0f0 g 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 the distance axis is linear and tf1zb.sry:noc+ly0ilq* z8 ; 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, acj(z oml pbc3ms, b+c3)ting along the x axis, varies as shown in Fig. 6–37. Determine the work done by this f,pb(cl+3z)c osjm 3bm orce to move the object (a) from x=0 m to x = 10 m    J
(b) from x = 0 m to x = 15 m    J

  A spring has $k=88$ N/m. Use a graph to determine the work needed to stretch it from $x=3.8$ cm to
$x=5.8$cm, where $x$ is the displacement from its unstretched length    J

  The net force exerted on a particle acts irt;e;a7 vlq0kkpyjt*y tau 9 c,)3)vnn 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 3,*bovy 5 wnh*g r7u p4zolzldd-f4bulf(7u8 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 arroww7:s es. iaw i97aa qamj9,3dx is doubled, by 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 a2 9jk59ubr4y,pj ofq. derqr1n electron $\left(m=9.11\times10^{-31}\mathrm{~kg}\right)$ which is moving with a speed of$1. 90\times 10^{6}\mathbf{m/ s}$ ? $\boxed{a\times10^{b} \mathrm{J}}$ a =    b =   

  How much work must be done to stop a 1250-kgcar traveling at 105k 1pnp169bj 5rt:jgltfm/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whose string exertt *nda)tjz *qt*6 hpo2s an average force of 110 N on the arrow over a distance qttn*p)aj2 tz**o d6hof 78 cm. What is the speed of the arrow as it leaves the bow?    m/s

  A baseball (m=140kg) traveling 32m/s moves a fielder s.2br.jt(x fo+/m zuw’s glove backward 25 cm when the ball is caught. What was the avera s(m.rj2t+uow zfb/x.ge force exerted by the ball on the glove?    N

If the speed of a car is increased by 50%, by what fact6l ) yym4)ydqq *xsp-aor will its minimum braking distance be increased, assuminyyad )s*4 6 ly-xqm)qpg all else is the same? Ignore the driver’s reaction time.

  At an accident scene on a level road, investigators measure a caj;sgk 2 qax1j*r’s skid mark to be 88 m long. The accident occurred on a1ajkx;j *2 qsg rainy day, and the coefficient of kinetic friction was estimated to be 0.42. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. (Why does the car’s mass not matter?)    m/s

  A softball having a m/9 e.frfh 5kibass 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 bf k5h9/ie.rfduring a pitch, if the distance between the plate and the pitcher is about 15 m.    N

  How high will a 1.85-1qk ;mh 5y1 h)ixkpb-1 p6b8kus4jfxwkg rock go if thrown straight up by someone who does 80.0 J of work on it? Neglect air resb6mh-yj)u xkfp;sxkpi4q18 khw 1 15bistance.    m

  A 285-kg load is lifted 22.0 m vertically with an aw v k/+s)0r1nvp x9rylcceleration by a single cable. Determi w0/nl9s+rp y1vv)xrk ne
(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, o t.,,jbgi wgz+f 440N/m How much must this spring be stretched to storgz t,w,b+i.jg e 25 J of potential energy?    m

  A 7.0-kg monkey swings frocn9 l0r(fus/ fm one branch to another 1.2 m higher. What is the change in potential eneufs0fr n (9/clrgy?    J

  By how much does the gravitational potential energy of a 64-kg po/8w +*:buh*goblpe ev 2os7 ghle vaulter change if his center of mass rises o7 s+bg l8g:*pev*woehhu2/babout 4.0 m during the jump?    J

  A 1200-kg car rolling on a horizontal surface has nvpu2yc1d)q3 /2tfrld ch l79 speed v = 65 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is thnl)f21d2/p hdrt vyc 39c lu7qe spring stiffness constant of the spring?    N/m

  A 1.60-m tall person lifts a 2.10-kg book from the ground so it is 2.20q /z,*7 qdmsl3jbi5wz *vlg0d m above the ground. What is the potential energy o,d7zb g q*5lwvsmq*dlj0z/ 3 if the book relative to
(a) the ground,    J
(b) the top of the person’s head?    J
(c) How is the work done by the person related to the answers in parts (a) and (b)?    J

  A 55-kg hiker starts at an elevation of 1600 m and climbs e49pttxh ajv3y n ,v6;to the top of a 3300-m 4te,n96t phv v3a ;yxjpeak.
(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/azsyn *1 bb(d9cr lz4*m hangs vertically next to a ruler. The end of the spring is next to the 15-cm mark on the rud 4b cby*1lz ra*(s9nzler. If a 2.5-kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler marks?    cm

  Jane, looking for Tarzan, is running at top s*h b:i3xq x ,zmgcuid4 .0nugw:l qg:3peed (5.3m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing up. m* hzx0:4u:l33:,gi gudq qcbgw xinward?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from restmk2 z-+fu b) etm6:hggyjp+x0, 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 sh;oqi:sws eez*7xi; w7ove 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’s kinetic energy is tb08y3no xi(r 3:uz / i;klyoftransformed 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 ofo riyu (y0/3 fo:;tbinkl z8x3 mass 2.10 m and cross the bar with a speed of 0.7m/s.    m/s

  A 65-kg trampoline artist jumps verticar tgwem4xh qix* fdt6042*jl4lly upward from the top of a platform with a speedr6* igqt44tehw 0lxj *dm4x2f 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 (inqv,8fe-wz4t f/7 y fkgnore its mass), whose spring stiffness constant is 950N/m is attace4f fynf/8- qtv,kw z7hed to a table and is compressed down 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 Fig. 6gla*iq/p l :krr7-bw,–39. If the block is to remain on the track, even at the tob/alql r-,ki*gp : r7wp 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 the end of a sprinvsp yto v+m6),g (spring stiffness constant k), Fig. 6–40. The block is givep+vys tv6), omn an initial displacement $x_0$ after which it oscillates back and forth. Write a formula for the total mechanical energy (ignore friction and the mass of the spring) in terms of $x_0$ position x, and speed

  A 62-kg bungee jumper jumps from a bridge. She is tie dbtkyx w9*4qb9e,;k (hbf;mwd 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 theebk9w ;*;fhxdk(mbyb4, w9 qt 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. ,f7vz(ai hf;g 6–41 is dragged up to point 1 where it is released,g;i fza7hfv( 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 m3y;q8,. ztsx qf.4mj xyfwku,/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 spt 8.t xgir ,d./* o8wyth9wixcring 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 d9, /ry i.x.wwt gto8tcxh8i *brought to rest. Let M be the total mass of the elevator and passengers.

  A cyclist intends to cycle up a 7.8 gr6n: :m( n, +dppbp4edt4pqn $^{\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/ jswow/51mg.r2 bdgoc7(;m fo ue 7:wih in opposite directions, collide head-on and come mgwbo wj/ud.s( o 7c 5i:w2 f7e;gmro1to 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 m high and reaches the bottom with a -p4nn-k es/q.ozk7j, 6ye fx fspeed o./ek7- ok z nsq,pfn4ye-fxj6f 2.2m/s How much thermal energy due to friction was generated in this process?    J

  A ski starts from rest r qn7 ne*do*e7and 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 frood cb us2l:).vm 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 1+fq 26wc zuniof 2.0 m, and it bounces back to a height of 1.5 m6iuf+nzc 2wq 1.
(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 with a cornd8 -;c/xp/h 4tinh dvf-df ur-6-bwnstant horizontal force of 350 N. For the first 158h-vr-x dwfpfi n4 / dd; 6ntr-hubc-/ 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 passes point 1 with a speed of If thes fda/83xtt3rxquw54g6vqh. t9 gnl 2 average force of friction is equal to one-fifth of its weight, 8 3 dlgx2qq vts4 tgxauh 6rw/9tnf3.5with 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 ouh1bv38s ff. 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 verl:e;sg)myu1 l . i)e6ltxdcg *y light horizontal spring (k=180N/m) as shown in Fig. 6–40. It is noted that the block–spring system, when gc esx.em t i6;l l1*ygld:))ucompressed 5.0 cm and released, stretches out 2.3 cm beyond the equilibrium position before stopping and turning back. What is the coefficient of kinetic friction between the block and the table?   

  A 280-g wood block is firmly attached to a very + ;3gqn;o dzie 1)nucrlight horizontal spring, Fig. 6–40. The block can slide along a table where the coefficient of friction is 0.30. A force of 22 N compresses the spring 18 cm. If the spring is released from this position, how far beyond its equilibrium position wr +g q;1c3dnn;u)zeioill it stretch on its first swing?    m

  Early test flights for the space shuttle used a “glider” (mass of fe0qc 9t5i; he980 kg including p5 fec; 9t0qheiilot) 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 motoir a5a*0-3le m;-u mko,a iopxr to lift a 315-kg piano to a sixth-story window 16.5aa me;-i ,pml a3-o ikx*0rou0 m above?    s

  If a car generates 18 hp when traveling at a steady 88km/h -c -kxj)o+dk 9tmb7ylwhat must be the average for ky7k +tlo-bj)xd9-c mce exerted on the car due to friction and air resistance?    N

  A 1400-kg sports caruxrcmp*aoo2*/) ;o+ 1 wgrupi +e7hhu ;yu9bx accelerates from rest to 95km/h in 7.4 s. What is the average power delivered by t oxu ) iwb;y2aurh7/x*ceg9; pur+mp1 h+*oouhe engine?$\approx$    hp

  (a) Show that one British horsepow4j zf5t;)jd*ql m*v)orn2qo ler$ \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 fojz:em,e*s+:nvc; jk orm of “kilowatt-hours.”
(a) Show that one kilowatt-hour (kWh) is equal to $3.6\times10^6$J
(b) If a typical family of four uses electric energy at an average rate of 520 W, how many kWh would their electric bill be for one month $\approx$   kW*h
(c) how many joules would this be?$a\times10^b$ J a =    b =   
(d) At a cost of 0.12 dollars per kWh, what would their monthly bill be in dollars? Does the monthly bill depend on the rate at which they use the electric energy?    dollars

  A driver notices that her 1150-kg car slows down from to 6a t8 y )5pci qplrkfvd15m:*9k5km/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 travelidyck i vtq9k*pr15)58a lpf:mng at a constant 75km/h.    hp

  How much work can a 3.0-hp motor do in 1.0 5 ysc8p* 9u5) k ( 7ttztudyukohl3k8mh? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg shot from rest t le0;*n *wc) bnt:zhfio 14m/s If this motion takes 1.5 s, what average powertfcl; zn*ie*nbw) 0:h was developed?$\approx$    W

  A pump is to lift 18.1/ l07 hrpdwxz0 kg of water per minute through a height of 3.60 m. What out 1/7z0xdh wrlpput rating (watts) should the pump motor have?    W

  During a workout, the football pwdrlshpy yf 5+p,p+gr8rf ) )(layers at State U. ran up the stadium stairs in 66 s. The stairs are 140 p )r+f(phwfg ,ldrs)5r+y8 pym long and inclined at an angle of 32 $^{\circ} $. If a typical player has a mass of 95 kg, estimate the average power output on the way up. Ignore friction and air resistance.    W

  How fast must a cyclist climzvc/sg +qtp +:b 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.ulm.twb3j tvr;g-y tja7 1+m of 120 hp. How steep a hill can it climb at a cons-t+l b. v.jtwyma;3tj1gu r m7tant speed of 75km/h if the frictional forces add up to 650 N?    $^{\circ} $

  What minimum horsepower must a moton4;eq9l)5d2 bifwx lrr have to be able to drag a 310-kg box along din4x5l rbl e 9fw2q;)a level floor at a speed of 1.2m/s if the coefficient of friction is 0.45?    hp

  A bicyclist coasts down a 7.kl(0va t:gc o-6:mkyg x7d.v n0 $^{\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” tx4f a)8nd1 kgvhat 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)x n 4a8vg1fkd 1.5 cm, but remains like an elastic spring up to that point, what must the effective spring stiffness constant of the bumper be, assuming the car has a mass of 1300 kg and is tested by ramming into a solid wall? $a\times10^b$ N/m a =    b =   

  In a certain library the first shelf is 10.0 cm off the ground, and z qmb95cq/h9m the remaininqm/q z h5cm99bg four shelves are each spaced 30.0 cm above the previous one. If the average book has a mass of 1.5 kg with a height of 21 cm, and an average shelf holds 25 books, how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start? $\approx$    J

  A film of Jesse Owens’s famous long jump (Fig. 6–42) in the 1936 Olympics shkmut(;(;) +pwvk xvh xows 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 tux;(vv(kh wx)k+; tmp raveling at 6.5m/s at the top of the arc?   m/s

  The block of mass m sliding without friction along the looped track) s5;gd dvxk*o6zf 3ls shown in Fig. 6–39 is t d3)kf5 d szlxv6;og*so remain on the track at all times, even at the very top of the loop of radius r.
(a) In terms of the given quantities, determine the minimum release height h (as in Problem 40). Next, if the actual release height is 2h, calculate    r
(b) the normal force exerted by the track at the bottom of the loop,    mg
(c) the normal force exerted by the track at the top of the loop,   mg
(d) the normal force exerted by the track after the block exits the loop onto the flat section.   mg

  An airplane pilot fell 370 m after jumping from an aircraft wit)vagqx:o /tt-7a-) a+p ndxzp+6 gimthout his parachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the 7)v+t6tpztan : xi-)+ opgmaax/- dg qpilot’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 leng ya oekobz4)x. q4.jg8th L whose other end is fixed (Fig.4 qxz8jeb gy.4.oko)a 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-dad)3b x i)8 d1 maj3:-njjc4utnzgc,m-high mountain. The climb is made in 5.0 h)jt) di 481abd ng3m,ca3-:dzn xcjuj starting 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 /2rwsrh3 ehgz nqw*;(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 o: rec6z1lx96g,( an/xf iahg California claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) hig1 x,6:ga/nagce h rfo9zl(xi6her, estimate the power needed.$a\times10^b$ W a =    b =   

  Water flows over a daen1fu2:o/s7oe59 sewhv .rrib5iyc)lxz5w , m at the rate of 650kg/s and falls vertically 81 m before striking t1s oov7fc9:ri bn,s /ye 5u5 weeix rhzw.52l)he 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. 6–4u inb4x33jev p,c( figj))rmvr qn//. 4), 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 wcjnfn 4/xe))g/(3 bq.p3r ur,j vmiiveight. 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 dq/gv6 x-h3zda candy bar directly into work, how high could an 82-kg man climb a ladder if g -dvq hx/63dzhe 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 an2- mlrtb5q/dmi dv, v v79q1gn 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 scale,( nkknw 9b(pn8 the spring inside the scale compresses 0.60 mm, and it tells you your weight is 710 N. Now if you jump on8bk(n(k pwnn 9 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 ro3 y: mii(/ax2lubj/y 8;jaqtxhk po992bzp h3pe, and swings out over a lake (Fig. 6–45). He releamjbhi/xza apk3 y8iy ;b up:tx9hjlo 93q(2/2ses 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, atscvl uqiev.-.2y75lm:g*vk 72-kg athlete climbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used.utcvyk ie-l v5vm: s.q7 2*gl to accomplish this feat?    W

  Some electric-power companies use water to store energy. Water is pumpepxg( /at1z*uno)kua7zl;( f ld by reversible turbine pu/fp)ul n7otz1*(xalkz ;( gaumps from a low to a high reservoir. 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/ r gba81nn)s 0ue7wzr stiffb7u )rwzn18/esan gr0 ness constant for each of the two resulting springs?   k

  A 6.0-kg block is pushck6ko(v,3 4/ukwlh* y r mjw-i;kr4iced 8.0 m up a rough 37 $^{\circ} $ inclined plane by a horizontal force of 75 N. If the initial speed of the block is 2.2m/s up the plane and a constant kinetic friction force of 25 N opposes the motion, calculate
(a) the initial kinetic energy of the block; $\approx$    J
(b) the work done by the 75-N force; $\approx$    J
(c) the work done by the friction force;    J
(d) the work done by gravity;$\approx$    J
(e) the work done by the normal force;    J
(f) the final kinetic energy of the block.$\approx$    J

  If a 1500-kg car can accelerate c( -uc3 socc;gfrom 35km/h to 55km/h in 3.2 s, how long will it take to accelerate from 55km/h to 75km/h Ass-( coc gcsu3;cume the power stays the same, and neglect frictional losses.    s

  In a common test for cardiac function (the “streshuiu-snn4poz,7jxfk 2c1y 2( s test”), the patient walks on an inclined treadmill (Fig. 6–46). Estimate the power required from a 75i,1s(pcnyh u7u-z2x4no 2j kf-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 up.)to w5-xao veward a distance of 500 m, what wvo eta.w)xo 5-as 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 ratcy:;3o-y;j,j svh6da 2qca eae of 95kg/s (a) If this water wheel is set up h,a y ja3cc;v -6j2d;:sqeaoy 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