In what ways is the word;tnaslwymm,w3d v:j7tf, )6 w “work” as used in everyday language the same as that defined in physics? In what ways is it wlsj7 mvta6ww3 ,n, ;:y)mdtfdifferent? Give examples of both.

Can a centripetal force ever do work on an o0f8 .bkg,abv r1k/yqwbject? Explain.

Can the normal force on an object ever do- x ajt0kgd9y stc 6iaj+9m*e+ work? Explain.

A woman swimming upstream is not moving 11ap4pxk7n rcm-a 4w pwith respect to the shore. Is she doing any work? If she stops swimming and merely flor-m anp4xp 1 w1c47kpaats, is work done on her?

Is the work done by kinetic friction fod2dp)r pb1z u5rces always negative? [Hint: Consider what happens to thrd1 pp2)zb d5ue dishes when you pull a tablecloth out from under them.]

Why is it tiring to push hard against a solid wall even thoul5ykg*-k8m umdm -)gagh you are doing no work5gmmgkd8-ya)k*m lu- ?

You have two springs that are identical except that sp fe9eqt4n w txu od3tcjv1ap6e*j-/)(ring l is stiffer than spring -eu)3 /*af1e (n4jttx owt9qdpj cve6 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 block thatogk3j e./wdwb( ),zgm-w7:o a)vjeea is free to slide on a frictionless surface (Fig.6-30). The block starts from rest at þoint A, and-j)e7 (3w agaeo/b: gk wj).vwem,dzo 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 gravim9/t,xx7nmcpon* n, 6u vv0ybtational potential energy change when you jump as high asx 6nvm7/tu,*v nymo n9 ,xbp0c you can?

In Fig. 6–31, water balloonsj)1hs 3 frl33jqroiur+xv2x ) are tossed from the roof of a building, all with the same speed but with different launch angles. Which one has the highest spv2fo)j ux3x3rirsq)h j31 + rleed on impact? Ignore air resistance.

A pendulum is launched from a point that is a heixmz , /9+u6eqmfw6b1d ya,vzbght h above its lowest point in two different ways (Fig. 6–32). During both launches, the pendulum is given an initial speed of 6,emfzw+ /b dqv z9,xam6bu 1y3.0m/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 tabls4m +e90fsw1r;t u4/ bifoe ofe. If you compress the spring by pressing down with your hand and then4fftsoeme /iofw+rs1u b0; 4 9 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 steel ** cgd 3p6u pgcg8fsqlm90h4cwire (Fig. 6–33). The instructor pulls the ball back and stands against the wall with the ball against his nose. To avoid injury t f6cpdg* *cpg4g 8c 09qhulsm3he instructor is supposed to release the ball without pushing it. Why?

What happens to the gravitational potential en7-m6sty k,zma ergy when water at the top of a waterfall falls to the poolmy,-6z7satk m below?

Describe the energy transformations when a child hops around on a poeunm(zfwgidkpiz5*f5)73 93zqru i; go stick.

Describe the energy tra t zramo/z,j((fzx;c m6k9d p2pfr4 i+nsformations that take place when a skier starts skiing down a hill, but after a tc9rrap xi +pkz/mjm,o ;4z2(d(f t6zfime is brought to rest by striking a snowdrift.

A child on a sled (total mi/hmtn ,/ roa9ass 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 otnir a,h/9/m(a) it is icy and there is no friction, and (b) there is friction (deep snow)?

Seasoned hikers prefer to step over a fallen log in their path rather than h02qb y8h 9nh3+j- qeryyrdi9 stepping on top and jumping down on the oy0qie9d3+9h 2 h8yyhj brqn-rther side. Explain.

Two identical arrows,666,q jt7z).c9 tos dqumyo wixqu ;3b one with twice the speed of the other, are fired into a bale of hay. Assuming the hay exerts a constant jtbiys3oc6 q7)o 6wdm.9qu tuz;qx6, frictional force on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain.

Analyze the motion of a simple swinging pendulum in terms of bp+wsvmcpiiuv;+5m e 4dc,e 3s14yk 4energy, (a) ignoring friction, and (b) taking friction into account. Explain why a grandfather clock has to be woun3vc4b4d4u +mw,skpes c; pym+i iv5e1d up.

When a “superball” is dropped, can it rebound to a height greater than itsn j 9w3vf, r+) dipwpc**wbjb0 original height?p0rcij)*w,w3db*jfn p9v wb + Explain.

Suppose you lift a suitcase from ther zzkw*i8r sf5w2r .4a floor to a table. The work you do on the suitcase depends on which of the following: (a) whether you lift it straizwsr2f. 8w*z5rari k4ght up or along a more complicated path, (b) the time it takes, (c) the height of the table, and (d) the weight of the suitcase?

Repeat Question 22 for the power needeg) p;kc 4mjl;bd rather than the work.

Why is it easier to climb a mountain via a zigzag trail than to climb st7skj*r . ws)cbraight up 7wc)b s.jks*r?

Recall from Chapter 4, Exorb x+6iby a;jg+xp-1b7cb: h ample 4–14, that you can use a pulley and ropes to decrease theao1 6j+; :bb7 piyrcgx+ b-xbh force needed to raise a heavy load (see Fig. 6–34). But for every meter the load is raised, how much rope must be pulled up? Account for this, using energy concepts.

  How much work is done by the gravitational force when a 265-k3n/3xj g2of)k mrjt9 pg pile driver falls 2roxfg9j 23pk/ )j3mnt.80 m?    J

  A 65.0-kg firefighter climbs a fliypk .g wjeoq ;*6.oy5eght of stairs 20.0 m high. How much work is requigye 5jwoqe py;. 6.*kored?    J

  A 1300-N crate rests on the floor. How much work is r24.xa1bq v p0tj02 sgq:it ajvequired to move it at constant speed (a) 4.0 m along the floor against a friction force o0p jas0tb qj 21ia xq.24vvtg:f 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did the movers do (horizontally) pushing a 160-kg crate 10.3 mv//7qmoktkljeo-w h 6-6 rwu, across a rough floor without acceleration, if the effect6q6ljk kwtw/ -er-v7,mohou/ ive coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is accelerated by /xf0 kmnnmcfti l4 0i4o-0:cta force across a floor at a rate of for 7.0 s. Fi4n40i0ok n 0ic:c/ mxff-ttlmnd the net work done on the box.   J

  Eight books, each 4.3 cm thiy8 g .ka ,hux0b5.q7j4fvf*dx vxji5sck with mass 1.7 kg, lie flat on a table. How much work i55xj*.vf.bag xvu04 qxhfi jds,7k8 y s required to stack them one on top of another?    J

A lever such as that shown in F(2e 8xn(h,fsmfi74uab, qgi) + bulwoig. 6-35 can be used to liff objects we might not otherwise be able to liff. Show that the ratio of output hxe, fw() (+mfongiausb 8i q 4b7lu,2force, $F_{\mathrm{O}}$, 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° incl8 udv1dw(33aqy,um zoine and is kept from accelerating by a man who is pushing bamwavu 3o83y1d, d q(zuck 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 toe bhe sle*8j;: give a helicopter of mass M an acceleration of 0.10 g upw 8es:*h;blee jard.    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 and5ha* .by:vsya+wbvh , 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 xf,;xxm79 mqy x axis, varies as shown in Fig. 6–37. Determine the work donex x7mf9qx,;ym by this force to move the object (a) from x=0 m to x = 10 m    J
(b) from x = 0 m to x = 15 m    J

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

  The net force exertes16*zkahxe;.-u w ioi d on a particle acts in the $+x$ direction. Its magnitude increases linearly from zero at
$x=0$, to 24.0 N at $x=3.0$ m. It remains constant at 24.0 N from $x=3.0$ m and then decreases
linearly to zero at $x=13.0$m. Determine the work done to move the particle from $x=0$ to $x=13.0$ m
graphically by determining the area under the $F_x$ vs. $x$ graph    J

  At room temperature, an oxygen molecule, with mass ofi8i ,um i 1d)l6ag+sl4iub jm3 $5.31\times10^{-26}$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 doyvbb/ k7 nc/*mubled, 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 a0yedh bmn2*c18a p3ssn 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 tw o0v 5xp s,xv:wshl:mwuv47 79l,f9a be lcn;o stop a 1250-kgcar traveling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whos xv*hspwtlvpe8e. 455x cuo4*e string exerts an average force of 110 N on the arrow over a v5* .oh et5*x84usp xwcpv4le distance of 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 glove4v w1sw+ke4k.y7s(zfw:p5q7 z ganyg backward 25 cm when the ball is caught. What was the averagvpgnw:z5wws.y4k+ egk7f4 zsq(7 y 1 ae force exerted by the ball on the glove?    N

If the speed of a car is increased by 50%, by what factor will its ls bxmd);/ ke44;blr tminimum braking d)l x4ek bts l;d4/mr;bistance be increased, assuming all else is the same? Ignore the driver’s reaction time.

  At an accident scene on a level road, investigators measure a car;ic*aa3: hjqm ’s skid mark to be 88 m long. The accident occurred on a rainy day, and the coefficient of kinetic friction was estimated to be 0.42. Use these data to determine the speed of the car when the driver slaahc*m :3;jqa immed 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 pi+8p jloj+vz*j tched at By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch, if the distance between the plate and the pl8 j+o*p j+zjvitcher is about 15 m.    N

  How high will a 1.85-kg rock go if thrown straight up by 6g-htu t1nri*mbiyx 6c.d39u someone who does 80.0 J o9 ituxh.c6i-b6g1utrd3 nm*yf work on it? Neglect air resistance.    m

  A 285-kg load is lifted 22.0 m vertically with an acce43l( 4hgt5c swj hgiov,um+q- leration by a single cable. Determine is4gc 3h-+wvql ,g5m(oh jtu4
(a) the tension in the cable,    N
(b) the net work done on the load,    J
(c) the work done by the cable on the load,    J
(d) the work done by gravity on the load,    J
(e) the final speed of the load assuming it started from rest.    m/s

  A spring has a spring stiffness constant, k, of 440Nr* +y6i/1,q itdq rneif: t)no/m How much must this spring be stretched to sto n tfri yitq1/*+dio:6q),ernre 25 J of potential energy?    m

  A 7.0-kg monkey swings from one branch to another 1.2 m higher. Wharf3 s: 4hews2u0a :ecwt is the change in potential sr h0ws:43we2feu a:cenergy?    J

  By how much does the gravitational potential energy oc tom1x km4+,mf a 64-kg pole vaulter change if his center of mass rises about 4.0 m during the14m+om m xkt,c jump?    J

  A 1200-kg car rolling on a horizontl5 rv2+m8 e ,ba) cblou)zrnv)al surface has speed v = 65 km/h when it strikes a hori)lvz+) rb8) eorncm, 25luavbzontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?    N/m

  A 1.60-m tall person f8kos7dq9bm 8d-l ,vulifts a 2.10-kg book from the ground so it is 2.20 m above the ground. What is the potenti-87dd q9olsubk 8mf,val energy of the book relative to
(a) the ground,    J
(b) the top of the person’s head?    J
(c) How is the work done by the person related to the answers in parts (a) and (b)?    J

  A 55-kg hiker starts at an elevation of 1600 m) m 3rlut9x474hwalop 8kstk/ and climbs to the top of a 3300-m peak. /lrk4 t p38)mu4 xl9s wktah7o
(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 spr ce 56pdgf9rh8ing 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 up wi re8gd h6cf5p9th the ruler marks?    cm

  Jane, looking for Tarzan, is running0 i5al:tcdee)zs f6s.wqsy05 at top speed (5.3m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can 0)c0 lssq5 e. s:aw ey6fidzt5she swing upward?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from c mxt5 gua5/r6vi3j(crest, 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 gi48wdoyq 0q5skc m*+ykven a 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’s kinetic energy is transformed into gravitatinxdx id,m; .vgbi9,c0 jt.j7 tonal potential energy without the aid of a pole. With what minimum speed must Fran leave the ground in order to lift her center of mass 2.10 m and cross the bar with a speed of 0.0c,9gtm b iidjxn. vx;d. jt7,7m/s.    m/s

  A 65-kg trampoline artist jumps vertically upward from t/w-i * ,d3.u lfcxowz igo8:behe top of a platform with a speed of 5.0 m/s.:oz,fe. ocx b*i83w/ldu g-wi ($\alpha)$ 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 constanv z: pv)h/wa5nt is 950N/m is attached to a table and is c/ vpva h5)z:nwompressed 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 0pigi,lulyl v 1 2s7 ;qsl(z2mthe looped track shown in Fig. 6–39. If the blo sml;2 1 s(u7l2qpg0vi,yizll ck is to remain on the track, even at the top of the circle (whose radius is r), from what minimum height h must it be released?    r

A block of mass m is attached to the en6cn6),o9a*izd ewsou4g uf m)d of a spring (spring stiffness constant k), Fig. 9egu6f*o 6 iosz d 4m)n)cuaw,6–40. The block is given an initial displacement $x_0$ after which it oscillates back and forth. Write a formula for the total mechanical energy (ignore friction and the mass of the spring) in terms of $x_0$ position x, and speed

  A 62-kg bungee jumper jumps from a bridge. She 4 s 0fn9g ysvpjp( g9l)j bqxlt +d8-k;(agtu/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 Hsgtly kj(9jp-4 bpd0)tnas+9 ;/ gf ulxv(8 gqooke’s law applies. $\approx$    N/m
(b) Calculate the maximum acceleration she experiences. $\approx$   m/$s^2$

  The roller-coaster c,bmze3az9xwwquh 28 fz0 ud ;wscv8-8ar shown in Fig. 6–41 is dragged up to point 1 where it is released from rest. Assumwe0 d b2wq8m;hzx8,s c-f8u3zuzav9w ing no friction, calculate the speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown with a speed of 12 m/s at an angle of ckp 4/j/lj )tfdp1e 1i33 $^{\circ} $. (a) What is its speed at its highest point    m/s
(b) how high does it go? (Use conservation of energy, and ignore air resistance.)   m

An engineer is designing a spring to be placed at the bottom of an elevator shaiso:k*s1 1)clg rso h+ft. 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 t)1g*+ ksrh 1slscioo: he total mass of the elevator and passengers.

  A cyclist intends to cyd0qx -q a6frhotqq:k- 77 dhc1cle 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, eacmjq pz 6f:kiu 7*-/lrw;j6w l-,rgsz kh of mass 7650 kg and traveling 95km/h in opposite directions, collide head-on and come to rest. How much thermal energy is produced in this collisiwkj, ;fgwl7l6qri pz-s/6ukrz m:* -jon? $a\times10^b$ J a =    b =   

  A 21.7-kg child descends a slab9l15b* u mz8rl-v iaide 3.5 m high and reaches the bottom with a speed of 2.2m/s How much thermal energy due to friction was generated in th51vz8lla* 9aim- b rbuis process?    J

  A ski starts from rest and slizd+tmdxpt2(977yoi, )1ztw6bt orza des 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 above cmw1 n 7+sjv9-cgql4;aur 9zpg +t+t ethe 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 heigh t4yvk1li(g5 ik kft(zw 3;uu)t of 2.0 m, and it bounces back to a height of 1.5 m(uzk;ti (1 3kk yfw)i5 vgl4tu.
(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 acwb/u een4deoyuc 1 -hb 6:3n)kross a floor with a constant horizontal force of 350 N. For the first 15 m the floor is frictionless, and for the next 15 m the coefficient of friction is h dune:-3eb )ubnkcw16/o ey40.30. What is the final speed of the crate?    m/s

  Suppose the roller coaster in Fig. 6–41 //vh2 ogl,lhppasses point 1 with a speed of If the average force of friction is equal to one-fifth of its weight, with what speed will it reach point 2? The distance travh 2/ ,g/hplolveled is 45.0 m. $\approx$    m/s

  A skier traveling 12m/s reptxk fcvf9489aches the foot of a steady upward 18.0 $^{\circ} $ incline and glides 12.2 m up along this slope before coming to rest. What was the average coefficient of friction?   

  A 0.620-kg wood block is firmly atta1uec/p/pncv/ ol7v .b/ tg.qoched 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 coeffi/eog oqtpu7/p1l ..cb/c/vv n cient of kinetic friction between the block and the table?   

  A 280-g wood block is firmly attached to a very light horizot;)hxbbh9 m7untal spring, Fig. 6–40. The block can slide along a table where the coefficient of friction iux b9;7hmbh)t s 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 “gw uds pzax l5()z etln53.pwa,7r(u: qlider” (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 its landing speed havez.xp w: satpawz (d5n5)q3lrlu ,(u7e 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 2*m:mn ez5ywa 315-kg piano to a sixth-story window 16.0 m abe2a*:w 5zmnmy ove?    s

  If a car generates 18 hp when travelpwupbr.1 q3d 4ing at a steady 88km/h what must be the average forceq.4d bp 3pr1uw exerted on 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 is the avpa,v ) 9cxo-pr9(eubo erage power del o eupx o-bvra),9c9(pivered by the engine?$\approx$    hp

  (a) Show that one Br aoo2k 0fulw-9,ut/.;ezyq y ditish 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 “kilowatcb fh*bwr9)v 5t-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 au qzibo(6b44gjw/6alro 9/vwe 2*h ;tmx0zf from to 65km/h in about 6.0 s on the level when it is in neutral. Approximately what powe 9wz/at 6um xzw0ib6o4/; (*a4vj2l fgboqrehr (watts and hp) is needed to keep the car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hp m yfq+tp9h5el86(ym xt otor do in 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg shot from rest to 14m/s If this motion ta 5ypjch-c *fa8auh/l. pu6d 55lstib xc o0e81kes 1.5 s, what average p uuoc8 *tc1yp6i f8h5/ 0-daasx.55elcbjl phower was developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute through a height of 3k 0u grv:-o1ra.60 m. What output rat rrvu 1og0a:-king (watts) should the pump motor have?    W

  During a workout, the football playvxm60u5w oaqn gj69x+ers at State U. ran up the stadium stairs in 66 s. The stairs are 140 m long and incl69a6owx v0nq +m5gxuj ined 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 cycldf mbvrz62l ,q p,j cl8ws0it8q; b-/tist 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 hill can it 2tiee2,y do4 s.j 2nvbclimb at a constant speed of 75km/h if the frictional forces add up to 65yb,.2t2eve24os jndi0 N?    $^{\circ} $

  What minimum horsepower must a motor have to be * mkhcw+f*epsh 0 1:zeable to drag a 310-kg box along a lesf*+1h m 0ezc*kph e:wvel floor at a speed of 1.2m/s if the coefficient of friction is 0.45?    hp

  A bicyclist coasts down aaly38v7g aqc/r/xwo7d3r zp-o 3/ohu 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” tcsnar q6p;l x8 9u0/uahat 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 compressiax ucl6q 08r upn9/as;on of 1.5 cm, but remains like an elastic spring up to that point, what must the effective spring stiffness constant of the bumper be, assuming the car has a mass of 1300 kg and is 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 t7 wd6/eq d5ncjhe remaining four shelves are each spaced 30.0 c enq6dw75cj/ dm 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 Olyq-3/ ozy8ry eimpics shows that his center of mass rose 1.1 m from launch point to the top of the arc. What minimum speed did he need at launch if he was travelin-z eoy3q 8ry/ig at 6.5m/s at the top of the arc?   m/s

  The block of mass m sliding fvs1t+7nnw 3g without friction along the looped track shown in Fig. 6–39 is to remain on theg tf3+wsv17n n 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 without h ) dgpw5*+t+3wm a7hsshe/uzhis parachute opening. He l5h/peu 7+atshwzg3 +s) mwhd*anded in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the pilot’s mass was 78 kg and his terminal velocity was 35m/s estimate
(a) the work done by the snow in bringing him to rest; $\approx$    J
(b) the average force exerted on him by the snow to stop him;$\approx$    N
(c) the work done on him by air resistance as he fell.$\approx$    J

A ball is attached to a horizontal cord of length L whose other end is fixed (Fdh;s/ xje6;( kd s7fvqig.xq;7sks;d v j6e/ fhd( 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-m-high mountain. The climb is made invv+4 od*iwsm/zbz(pf78 z p z+ 5.0 h starting at an elevatio(*8v+7s/m+ pwz idz b4opzfv zn 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 brz d 2 wae d3ojbr6sf4(y/k;7kreaks when a 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 that its lifts can moveds -j+v1 c2tinnuj2g/ 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate t in1n+/cv2sd-jj2ug the power needed.$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and f/ iv1 cr;bfif.alls vertically 81 m before striking the turbine blades;1c. / rfibvfi. 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 ouagl2 o/qnhf66d5 0 6 qvbb9mwith a circular vertical loop (Fig. 6–44), the difference in your apparent weight at the top of the circular loop and the bottom of the circular loop is 6 g’s — that is, six times your weight. Ignore friction. Show also that as long as your speed is above the minimum needed, this answer doesn’t depend on the size of tu92b 6o/gdq5l0fmah6 vn6ob q he loop or how fast you go through it.    mg

  (a) If the human body could convert a candy bar dirs; ,*ssfres s,ectly into work, how high could an 82-kg man climb a ladder if he were fueled by,s*e;s f,sr ss 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 exw-yb w3*pg7/zcch1n,: o di angle of 45.0$^{\circ} $ from the top of a 165-m cliff with a speed of 175m/s What will be its speed when it strikes the ground below? (Use conservation of energy and neglect air resistance.)    m/s

  If you stand on a bathroom scale, the spring inside the scale compresses 0.60 mm o(w(fmirs+se42 (q0oh4kbfp, and it tells you your weight eri4 f4 0(o (+ kqhsw2sbpm(ofis 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 swindx ;scg 7*nb.69xe*bp bg6 rgcgs out over a lake (Fig. 6–45). He releases the rope when his velocity is zero. xb*cd9 rgbe.cbx*p gg67;6s n
(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 verti .wh ye.yqq l3wk3y0(lcal distance of 5.0 m in 9.0 s. What minimum power output was used to accolhkw wey q( q03l.3y.ymplish this feat?    W

  Some electric-power companies use water ton gp/6/eaowp4o sw8* p store energy. Water is pumped by reversible turbine pumps from a low to a high reservoir. To store the energy8a/6onpw pp*ogs e/w 4 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 spriiok15oni 5f a9ng stiffness constant 9onak1i5o5 if for each of the two resulting springs?   k

  A 6.0-kg block is pushed 8.0 m up a rough 37 9c*t n2+;kbo fax+)fq-yi z ty$^{\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 (+0iagn 7: r:) py5dtaghoytwjm/*niaccelerate from 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, and neglect frictional logyjt ah*tai wrno 0 /:5ignm(y+:p)7 dsses.    s

  In a common test for cardiac function (the “stress test”qvp y-mkfg/04), the patient walks on an inclined treadmill (Fig. 6–46). Estimate the power required from a 75-kg patieny/p4m kq-vg 0ft 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 upw 6ep xixvd s*gr.,oj-j0/zp dlr;i)9vard a distance of 500 m, what was its velocity whenxp) zgojvxpvidr9*0j d6/s ;el ,.ir- 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 hei)or n: hx+bc,sght of 2.0 m at a rate of 95kg/s (a) If this water wheel is set up to provide electricity outp :bn), o+hxcsrut, what is its maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s