In what ways is the word “work” as usedfit:p;e m l2h/e0y.h q in everyday language the same as that defined in physics? In wha;pmif02q :./et hhylet ways is it different? Give examples of both.

Can a centripetal force ever do work on a7ie a4dlf rkn/5eq0t/mge02n n object? Explain.

Can the normal force on an object ek-a j l2:9* m9qa bes.yw5alucver do work? Explain.

A woman swimming upstream is not moving with w/c/ 5 vjxyup aov;4h2hxij(7)ure i 9respect to the shore. Is she doing any work? If she stops swimming and merelyvra2( 5jxh) c u ue97oyh/w;xjiiv4p/ floats, is work done on her?

Is the work done by ki.*p-z idxwi28my/mw x1ox u v*netic friction forces always negative? [Hint: Consider what happens to the dishes when you pull a tablecloth out from ** iyx.xziumwvop d-2 1/8 mxwunder them.]

Why is it tiring to push hard against a solid wall even thc(6 *d/ d8* calh6ztjs8houla ough you are doing no work? 6dczc/ ja6 8 *8*lsoduhhtl(a

You have two springs tihu7v;;7*j bsgm/koz hat are identical except that spring l is stiffer than spring mhj7k u;vsozbi g7*; /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 that is free to slide 4c* nh)koomn 6on a frictionless surface (Fig.6-30). The block starts from rest at þoint oc)hmkn*n4o 6 A, and by the time it has traveled a distance $d$ to point B it is traveling withe bint $o$ point B it is traveling with speed $\nu_\mathrm{B}$.When the block has traveled another distance $d$ to point C, will its speed be greater than, less than, or equal to 2$\nu_\mathrm{B}$? Explain your reasoning

By approximately how mc9b1 ne wwj*8kt sr:lf-f2n z+uch does your gravitational potential energy change when you jump as high w c* fnn98estkb +rz1-j2fw:l as you can?

In Fig. 6–31, water balloons are tossed from the roof of a buildifo i2 :jg8)genng, all with the same speed but with different launch ang2j :nefgg)io 8les. Which one has the highest speed on impact? Ignore air resistance.

A pendulum is launched (.grxcc:dm-9cf7p0s0r em x nfrom a point that is a height h above its lowest point in two different ways (Fig. 6–32). During both launches, the pendcr -0x9c( nmdm7r:xes.fp 0gc ulum 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 springb2. uti0k5.) upl tfby by pressing down with your hand and then releatul0 .pfity)buk. b52se it, can the spring leave the table? Explain, using the law of conservation of energy.

A bowling ball is hung from flsq 5p-2 sy;zo0zvq0the ceiling by a steel wire (Fig. 6–33). The instructor pulls the ball back and stands against the walll05f - zs0qv2;osyz qp 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 poten ex3iar63 udck4j9a+t tial energy when water at the top of a waterfall ae3d 3r9aij +tc6uk4xfalls to the pool below?

Describe the energy transformations when a child 5vg/n r;n7ss f /-j:oqnuu*v yhops around on a pogo stick.

Describe the energy transformations that take p ssh x9e/2 u.me9dq0tvlace when a skier starts skiing down a hill, but after a time is brought to rest by steushv9 .0ex d/sq29 mtriking a snowdrift.

A child on a sled (total mass m) st kbl1yug2j5h r;2bl 4earts 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 (b) there is friction (deep snow)?r1jyuhbb 4;g 2lek2l 5

Seasoned hikers prefer to step over a fallen log in their 5a 3k djp1d7cgi,5zr1 z epza5path rather than stepping on top and jumping downzgpz aa17, k51jdper5c5z3id on the other side. Explain.

Two identical arrows, one with twice the szgic e3j s cynz58/3t/peed of the other, are fired into a bale of hay. Assuming the hay exerts a constant frictional force on the arrows, 8g ci3 z3c /5t/snzjeythe faster arrow will penetrate how much farther than the slower arrow? Explain.

Analyze the motion of a simple swinging pendulum in to)d3+4k 2gk97z vct-s53 oaszot aagy erms of energy, (a) ignoring friction, and (b) taking friction into account. Explain why a svzoz3)k9o 4c taadsg 2t3oa-7kyg5+ grandfather clock has to be wound up.

When a “superball” is dr0rb7 (eg:zh4wdjc9 vfopped, can it rebound to a height greater than its original heig4fc h(g:de79 brjzvw0ht? Explain.

Suppose you lift a suitcase from the floor to a txw pw*+mgy npucf8l8h;o99qt y9 q +(cable. The work you do on the suitcase depends on which of the following: (a) whether you lift it straight up or along a mln+m f9w;u p8tqcw 8yp9h o+( xcyg*q9ore complicated path, (b) the time it takes, (c) the height of the table, and (d) the weight of the suitcase?

Repeat Question 22 for thegd7cpai 2t.7 x power needed rather than the work.

Why is it easier to clifvd78wzkj8weii15p9 b ,l mb t8o+jp8lx(kn*mb a mountain via a zigzag trail than to climb straight up?b5x i8kpv8pdkl bj*f+1( ez w8 9 ,7tjoinw8ml

Recall from Chapter 4, Example 4–14, that you can use a pulley and ropes ej2/1t +hggwajoi:9nto decrease the force needed to raise a heavy load (see Fig. 6–34). But for every meter the load is raised, how much rope must be pulled up? Account for this, us /hjngw:2eij+1ga o9t ing energy concepts.

  How much work is done by the gravitational force when a 265-kg pileg1 g*gsl14-3rgdcwpn driver falls 2.80 m? cl-gng1g4*1p 3rwgs d   J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m highak9; fflxxt2bv,wo +9. How much work is requir,awvf 29xlx; +o btfk9ed?    J

  A 1300-N crate rests on the e;oi9nuglbr5-(emqk6ft- q3 floor. How much work is required to move it at constant speed (a) 4.0 m along the floor against -r-nltke q(m5e3o6u i ;f q9bga friction force of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did the movers do (e)9g9eg d8+uti kq it:horizontally) pushing a 160-kg crate 10.3 m across a rough floor without acc t de9)ig+ 8ekqgti9:ueleration, if the effective coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is accel; ka0fyaxsee /d4m1q8 o 6:qjzerated by a force across a floor at a rate of for 7.0 s. Find the nfaj01x;sqz8eoya e: /kqd m46et work done on the box.   J

  Eight books, each 4.3 cm thick with mass 1.w5f3h9y0aa( qi1ulnt 7 kg, lie flat on a table. How much work is required to stack them one on top of anoth90 l(h nawt1yuiq3 5faer?    J

A lever such as that shown in Fig. 6-35 can be used to liff objects eoo4 o07rap b tk01ed .yhixj0003y xbwe might not otherwise be able to liff. Show that the ratio of oyi4day0ob0.730 xte rbo x 010o khjpeutput 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 slidesle4p6rev(8p4 ay :t(hh(zgoq 3.6 m down a 28° incline and is kept from accelerating by a man who is pushing back on it parallel 4yt(elq6r g8e vpoa: ph 4(hz(to the incline (Fig. 6-36). The effective coefficient of kinetic friction is 0.40. Calculate:
(a) the force exerted by the man,    N
$(b)$ the work done by the man on the piano,    J
$(c)$ the work done by the friction force,   J
$(d)$ the work done by the force of gravity,   J
$(e)$ the net work done on the piano   J

  (a) Find the force required to give a helicopter of massl;l6jsg; l/uu fujp53 M an acceleration of 0.10 g/ sjll; 36guf;juu5 pl 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 lineumpr/mnp x;2o*s .b7tc u7 c*iar and that $d_{\mathrm{A}}=10.0$ m and $d_{\mathrm{B}}=35.0$m. Estimate the work
done by force $F$ in moving a 2.80-kg object from $d_\mathrm{A}$ to $d_\mathrm{B}$   J

  The force on an object, acting along the x axis, varies as shown in Fig. 6–37. f58s.z7(1svkyhj e 3zncbmh: Determine the work done by this force to move the object (a) from x=0 m to j.z(y hh: z85e7bvcsfs1 km3n 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 a0u,*6ipy3geix0 w teld.rkd, cts 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) ;9dtt mbmk)ckt3o4 * ahjk9)0glmm v 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 what f*n-1dl4.,bc sdq j z/beeejz:actor 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 sivm l0)kbmtt6wpuz9 (g13rle(w; 8m ltop 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 donpx d5pr :hn*:te to stop a 1250-kgcar traveling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired fr1/7/xirml3 srsbc(* i-ow tfmb,vzpzdg; .(jom a bow whose string exerts an average force of 110 N on the arrow over a distance of 78 cm. What is the speed of the arrow as it leaves the i r ; w1vgsb 7clf3o sj*//r-iz(.mbm,x zdp(tbow?    m/s

  A baseball (m=140kg) traveling 32m/s moves a fielder’s glove backward 25 cm wha5 9r)j3sqimhe.b 9it en the ball is caught. What was the average force exerted5 ) tre9ib qh.mi39asj by the ball on the glove?    N

If the speed of a car is increased by 50%, by what factord1wokafh xkc8) 9g9*s will its minimum braking distance be increased, assuming all else is the same? kgw9sx 9f 1ka)cho8d*Ignore the driver’s reaction time.

  At an accident scene on a level road, investigatorsu6 (7e osaxz:x esixk63l/qk6ct9 fk8 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 0.42. Use these data to determine the speed of the car when the driver slammed on (and locke8xz:c/6 6osik3ex(qt7k 6 alex9skfud) the brakes. (Why does the car’s mass not matter?)    m/s

  A softball having a mass of 0.25 kg is pitched at By the time it reachesihi44jq u6/rj*n i1b e the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of a6ji4n iqrj* iu eh14b/ir resistance during a pitch, if the distance between the plate and the pitcher is about 15 m.    N

  How high will a 1.85-kg rock pjmyhg0q4 ,. 2 -kaamigo if thrown straight up by someone who does 80.0 J of wy.am2m gih4a ,q-0pjkork on it? Neglect air resistance.    m

  A 285-kg load is lifted 22.0 m vertically with an acceleration by a single c6 .karg prn4f6able. Deterrfra6 .pkgn64 mine
(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 dsys+ws2r *(8y xw;t(pa 8prt 440N/m How much must this spring be stretched to store 25yrstd wp8+(sya p r*ws tx82(; J of potential energy?    m

  A 7.0-kg monkey swings from one bran,u (eoq4lyuu w qr4o--ch to another 1.2 m higher. What is the change in potuqq-44eoro l uw-(,y uential energy?    J

  By how much does the gravitational potential energy of a 64-kga d 9c6fj7kr*b pole vaulter change if his center of697 cfdr a*bkj mass rises about 4.0 m during the jump?    J

  A 1200-kg car rolling on a horizontal surface has speedy62z3;rmnii/ mfd e m9 v = 65 km/h when it strikes a horizontal coiled spring and i/i3ednym 6mrf2;9 iz ms 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 personhwz28*yy3ufj*ycgs 85 wr r) w lifts a 2.10-kg book from the ground so it is 2.20 m above the ground. What is the potentr)*2yryu 8yj* cs 8w ww5ghfz3ial 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 yt8gf d 3k4gm+at an elevation of 1600 m and climbs to the top of a 3300-m pe gygm +34kdf8tak.
(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 hangsqk a4nec q0nc:; ipr f7g6*p5q vertically next to a ruler. The end of the spring is next to the 15-cm mark on the ruler. If a 2.5-kg mass is now attached p n6 r*7i:p4; 0c nqcaqekqf5gto the end of the spring, where will the end of the spring line up with the ruler marks?    cm

  Jane, looking for Tarzan, is running at top speed (5.3m/s) and grabs a vinhkb( bl atd5v0 om:+e,u*n3 xge hanging vertn :bdg,3*exumb kh tlv(o5+a0ically from a tall tree in the jungle. How high can she swing upward?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from rest, slides down a frymg)* a 1yn 1csu( lxub/8l9pomza ;r-ictionless 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 fricti b 9l-ld4o- zy62zpnoronless 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 gravitationautoq89(*x qs nqtp 93pl 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 barqq tp 9*xnso93 8uqpt( with a speed of 0.7m/s.    m/s

  A 65-kg trampoline artist jumps vertically upward from the top of a platfor;ic+aw.z6hneooly6a3 j. b l.m with+hz3.y c6lia o..njloab ;6we a speed of 5.0 m/s. ($\alpha)$ How fast is he going as he lands on the trampoline, 3.0 m below (Fig. 6-38)?$v_2$ $\approx$    m/s
(b) If the trampoline behaves like a spring with spring stiffness constant 6.2×10$^{4}$ N/m , how far does he depress it? $y_3$ =    m

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

  A vertical spring (ignore its mass), whose spring stiffness constex .d77r rtq 0d,2kzxwo5pn9cant is 950N/m is attached to a table and is compressed down 0.150 m. (a) What upward speed can it give to a 0.30-kg ball when rel9tonxrew7,.5 zdd r ckq2x p07eased?    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 lr2nw j(n. s i6gljcy3m ebd*0* im/y(0;mydyyooped track shown in Fig. 6–39. If the block is to remain on the track, even at the top of the(*y0gs6nd.y ybw;y/jemcy dl*ni rim 2(30jm 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 spring (sprhrfy (3auhc wkuo6fbomkf 8b;l*( 906ing stiffness constant k), Fig. 6–40. The block *hbyuf ma(6h8rbkfl o;fc09 w6(3 kuois 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 is corvh40tyc+ah n5c:r :1 cly 4tied to a bungee cord whose unstretched length is 12 m, and falls a total of 31 m. (a) Calc5hn:y cvr+c1yh:o4 c0car tl4ulate the spring stiffness constant k of the bungee cord, assuming Hooke’s law applies. $\approx$    N/m
(b) Calculate the maximum acceleration she experiences. $\approx$   m/$s^2$

  The roller-coaster car shown in Fig. 6–41 is dragged up to p0i x /l17mphjkeh9bz2oint 1 where it is released from rest. h/jibkm7 x9ezhl1p 20 Assuming no friction, calculate the speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown with a speed of 12 m/s at an ang:t r3v,sbmo/y8bg8u e+ l .wvrle of 33 $^{\circ} $. (a) What is its speed at its highest point    m/s
(b) how high does it go? (Use conservation of energy, and ignore air resistance.)   m

An engineer is designing a spring to be placed at the bottom of :. ;gfq d loa4ref-s5aan 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 hsl4rqg a f5-f: ;eao.dave so that passengers undergo an acceleration of no more than 5.0 g when brought to rest. Let M be the total mass of the elevator and passengers.

  A cyclist intends to cycle up a 7.8 zn43d n ato,:b$^{\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 travelingy4oe1y n+f .n4pr:8p7j cdtrg 95km/h in opposite directions, collide head-on and come to rest. How much p 4y7r+8o fp:tn.y regd j1nc4thermal 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 reacptpp *;ig ydckm; 9-z6hes the bottom with a speed of 2.2m/s How much thermal energy g;c ;9y6 izp ppkt*-dmdue to friction was generated in this process?    J

  A ski starts from rest /ffsd l/,my+a-l ge 5jand 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 l43w5rbdv /r im above the ground.
(a) With what speed would it hit the ground if air resistance could be ignored?    m/s
(b) If it actually hits the ground with a speed of 8m/s what is the average force of air resistance exerted on it?    N

  You drop a ball from a height of 2.0 m, and it bounces back to a height o06rz+v5za k1timhb g.o:tdw - f 1.5 m.k- 1hart+.dmz: z5 owtib 6v0g
(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 fl:qod q .p)3pvg)2 7tistwa+lrom rest, is pulled across a floor with a constant horizontal force of 350 N. For the first 15 m the floor is frictionless, and for the na )l tqv+7s .w:t32q)o ilpgpdext 15 m the coefficient of friction is 0.30. What is the final speed of the crate?    m/s

  Suppose the roller coaster ijdau vho uj(n;o5dk : .3zcn30n Fig. 6–41 passes point 1 with a speed of If the average force of frictidkdouv;n3:5z an 0hojcj(u 3. on is equal to one-fifth of its weight, with what speed will it reach point 2? The distance traveled is 45.0 m. $\approx$    m/s

  A skier traveling 12m/s reaches the foot of a steady up. alw y8rpjs13g,uu*b/)))qi wvaqpq z 6ys8oward 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 fi t oar+c:)h1yzy4yh;e rmly attached to a very light horizontal spring (k=180N/m) as shown in Fig. 6–40. It is noted that the block–spring system, when compressed 5.0 cm and released, stretches out 2.3 cm beyond the equilibrium position before stopping and turning bey1)yr;4ay :h t+zohcack. What is the coefficient of kinetic friction between the block and the table?   

  A 280-g wood block is firmly attached to a very light horizontal spcy71 fn/0fduya 6w7 zsring, 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 itsu1znw/a y7d 0fcf67y s equilibrium position will it stretch on its first swing?    m

  Early test flights for the space shuttle used a “glider” (mass of 980 kg7z amegzr4x4) including pilot) that was launched horizontally at 500km/h from a height of 3500 m. The glidez mg4)e a4rzx7r 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 l0,imm 9kx/ni h v*3xtmotor to lift a 315-kg piano to a sixth-story window 16.0 m aboxnm* , xt39 ki0ivm/hlve?    s

  If a car generates 18 hp when traveling at a steady 88km/h what must be the aveaqe72z v*9 tv/g9 ylmgrage force exerted on the car due to friction and air resistance? / egvl q*ta 29ym9v7gz   N

  A 1400-kg sports car accelerates from rest tocl rc .+n.uo:spmql 42 95km/h in 7.4 s. What is the average power.r:u cnmop. l2s+lcq4 delivered by the engine?$\approx$    hp

  (a) Show that one British horsc(;0 2i7 q3z.kl0 gb v*hqastt smdpn+epower$ \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 arep;j3y zlinqm; (to/s 5 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 1150-kg car slows down from to 65km/h in about 6.42qqm: )-t3z 7u wxybboxrfp ,0 s on the level when it is in neutral. Approximately what power (watts and hp) is needed to keep thezx:uoqr) 7pqbw 2,-m3tyfx 4b car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hp motor p6 v wigi-8l uvr1u4k(gb(:dxdo in 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg sh,v1ehf1.cpuyi+3 *no-udgo 9h m.zrkot from rest to 14m/s If this motion takes 1.5 s, what average power gr*v.um n+zyhe ih ,k931fu.c-o p1od was developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute through a heigrflfw g+qtz5*r 1c fv4t,) +fbht of 3.60 m. What output r*fz )54qcbrrf+w t,vg lf+t1fating (watts) should the pump motor have?    W

  During a workout, the football players at State U. ran up the stadium stairs iwycf-vuv dh 0v0hv sk7k 6,z 51a+wox,n yf h v 0uso5v1k,v,7akh v-xwc0d+w6 z66 s. The stairs are 140 m 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 climb jr-xuil)yvzx; ps64; t)a+ g ma 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+6oliw 3klg+;w4ib o m 120 hp. How steep a hill can it climb at a constant speed of 75km/h if the f wi +wk6;i lb34oolgm+rictional forces add up to 650 N?    $^{\circ} $

  What minimum horsepower must a motor have to be able to drag a 310-kg box al7 4cpkjclhg- +ong a level floor at a speed of 1.2m/s if the coefficientg7 jk hlc-4c+p of friction is 0.45?    hp

  A bicyclist coasts downcabjqw: x5 o9/ 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 areub3;ingaw*gy 67rs ) n designed to compress and rebound elastically without any physical damage at speeds below 8km/h If the material of the bumpers permanently deforms after a compression of 1.5 cm, but remains like an elastic spring up to that point, what must the effective spring stiffness constant of the bumper be, assuming the car has a mass of 1300 kg and is tested by ramming into a solid wallan;b7 ungg 6r) ys3*iw? $a\times10^b$ N/m a =    b =   

  In a certain library the first shelf pws -5m2,/s yc9hv4 ;u nfpnxxis 10.0 cm off the ground, and the remaining four sh-npcw9 4v hx52sp sy/ ;xfnm,uelves 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 lvg,z4fsdgqcz0ro 7,)tix 4 r- ong jump (Fig. 6–42) in the 1936 Olympics shows thats,40vt igogf )4 rcx 7d-,zrzq his center of mass rose 1.1 m from launch point to the top of the arc. What minimum speed did he need at launch if he was traveling at 6.5m/s at the top of the arc?   m/s

  The block of mass m sliding without friction along the looped track showns:7rp3pcp+s d in Fig. 6–39 is to remain on the track at all times, even at the very top of the loop of radiu+p:pspc7rd s3s 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 mghd x1rx:q p:wh**z;u,kdb0 m after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a cxg*q p :;xdzbkruhhm0,*1:dwrater 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 en6l f6)s(uc2c vc;dajm2, ,c zdb7rchq jlks;/d is fixed (Fig. 6–43).m(csqc2;2djl;l s z6ucj,dc c )/ 6 vbkhf,r7a
(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 s ntv ufhq w5*p,.dq08climb is made in 5.0 h n8,q5u .wtqpf0*v dhsstarting 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 breakvj;m3 :q 8 fgi+cx,u+pb9k dcks 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 Calife.rc)ht2igi)p /v);l9 8ck2gmpuidyornia claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the powe .)/9uc2vgdgri 8ihp k)p mi)t yl;2cer needed.$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and falls vertically 81 m before b8f+fffan.u( striking taun b8(+fff. fhe turbine blades. Calculate
(a) the speed of the water just before striking the turbine blades (neglect air resistance), $\approx$    m/s
(b) the rate at which mechanical energy is transferred to the turbine blades, assuming 58% efficiency.    W

  Show that on a roller coaster with a circular vertical loop (Fig. 6–44), the difp. qo pm3a(cki;un) 3s0 jzdb3ference 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 almjipb3q 3 c()3p ;.osdzua 0nkso 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 dirm1k .9ygzk4k f t)wh*wectly into work, how high could an 82-kg man climb a ladder k.fhgzt*ww) 41ym9 kkif 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 ank z:-sm :o/k5l,+nc8m2i q ai5 vxeutr 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, the spring inside the sddx ;n:c/bpkg5t uv82cale compresses 0.60 mm, and it tells you 5:gd/ u 8tc;vkpnbxd2your weight is 710 N. Now if you jump on the scale from a height of 1.0 m, what does the scale read at its peak?    N

  A 65-kg student runs at f:,c 7ml /qzyfj/a,i d5m/s grabs a rope, and swings out over a lake (Fig. 6–45). He releases the rope whe a7il :zd,/mf/yjq,fcn 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 vkezn6eus)z2 4ertical distance of 5.0 m in 9.0 s. What minimum power output was used to accomplish thisze4s62 k znue) feat?    W

  Some electric-power compadi9( k3sqp.wjajl 7 u5nies use water to store energy. Water is pumped by reversible turbine pumps from a low to a high reservoir. To store the energy produced in 1.0 hour by a 120-79a3us5lpw(dj.ki j q 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 inad -w(ocmkq2v xme+63e0la,c half. What is the spring stiffnessm vq 3lk0mx6,+ae-e2ad c ow(c constant for each of the two resulting springs?   k

  A 6.0-kg block is pushed 8.0 m up a rough k* /6ljsehe)t pnf)2q37 $^{\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 accelera98d;ap2q a 9 z6)ojr3bjb rsbpte from 35km/h to 55km/h in 3.2 s, how long will it take to ac6p3 rjbzobr8a99ab;)pdj 2 q scelerate from 55km/h to 75km/h Assume the power stays the same, and neglect frictional losses.    s

  In a common test for cardiac function (the “stress test”), the zws3 xx8hg7b r66grvvw kv,,7 patient walks on an inclined treadmill (Fig. 6–46). Estimate the power required from a 75-kg patient when the treadmill is sloping at s6zx7,wg 6xgr 3kwvr 87,vhvban 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 r kfn e:z6ti*fvyink; a0-/cl0ock vertically upward a distance of 500 m, what was its velocity when k alk;i czvtnef :*/fny60i-0it 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 omrhb2)(3g m8j7n up lcf 2.0 m at a rate of 95kg/s (a) If this water wheel is set up to pbu) 2lc8( nr7mhgp3mj rovide electricity output, what is its maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s