In what ways is the word “pxixy*sha( 5 1work” as used in everyday language the same as that defined in physics? In what ways is isx5 xhy(p a*i1t different? Give examples of both.

Can a centripetal force ever do work(mkbubp)hjvidoo 1 521k hd -1 on an object? Explain.

Can the normal force on an object ever d y 0/txyto13h*1 vgmqho work? Explain.

A woman swimming upstream is not moving with respect to the shore. Is sh 5nwy+4h9rv ujqpt1)v e doing any work? If she stops swimmin9y+vh)w5qjv urt p41n g and merely floats, is work done on her?

Is the work done by kinetyn8t )q -/1 oyeclp8q6z puq 4ynq):jwic friction forces always negative? [Hint: Consider what happens to the dishes when you pull a tablecloth out from under them.]oq:qnu n/lwz)8 yey 1q4c 8y6)tpqj-p

Why is it tiring to push hard against a solid wall e b jo 9;yb8uxot.y7ve(ven though you are doing no work7ev(jo; .yxt8o9 bbyu?

You have two springs that are identical except that spring l is stiffer than spcur:o (3eum 54dpbol6ring 2 m3lp c6(droebu5:uo4 $(k_1>k_2).$ 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 isog48bpo+ l fyiw 5yi2lxz(oe/*5z2zw free to slide on a frictionless surface (Fig.6-30). The block starts from reiy*2l+z z x5o2( lo8 4wizgb5feo ypw/st at þoint A, and by the time it has traveled a distance $d$ to point B it is traveling withe bint $o$ point B it is traveling with speed $\nu_\mathrm{B}$.When the block has traveled another distance $d$ to point C, will its speed be greater than, less than, or equal to 2$\nu_\mathrm{B}$? Explain your reasoning

By approximately how much does your gravij()ftr ;eyx 1vd3s9bdtational potential energy change when you jump a3 ;j)t bsr9y xd1(vfeds high as you can?

In Fig. 6–31, water balloons are tossed f)hr / 1yt:3u8zrhu7 i 4nmsrjmrom the roof of a building, all with the same speed but with different launch angles. Which one has th/3h tu: 7sr rz8r4nju1)ihmyme highest speed on impact? Ignore air resistance.

A pendulum is launched from a point that is a height h above 1 od ocg; hv)d*nbu1;xits lowest point in two different ways (Fig. 6–32). During both launches, the pendulum is given an initial speed of 3.0m/ n* x1ch)1u; ;vobgdods 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 spriov(. dtw hk,3yo )k4/*hs qfck1i7:rzs ixb*w ng by pressing down with your hand and then release it, can the spring leave t ,x ts okwikc.)rdbk3hv 4z*y7w /oq1*h(i: sfhe table? Explain, using the law of conservation of energy.

A bowling ball is hung from the ceiling by a steel wire (Fig. 6–soad ,parj-f t(xe7/* 33). The instructor pulls the ball back and stands against the wall with the ball against his nose. To avoid injury the instruca-s jfra x,e/* p7o(dttor is supposed to release the ball without pushing it. Why?

What happens to the gravitational p/8w 76/w f .mqzhhf3kbzw mx3ootential energy when water at the top of a waterfalwz3 wb3 6m m87f.hozq// whxfkl falls to the pool below?

Describe the energy transformations when a child hops around onc/8.e cz 1gzc tv80hnbxy1pb 4 a pogo stick.

Describe the energy transformations that take place when a skier a(ykzkejtj.5 78pc )h starts skiing down c8(jk.k) 7hpj zy ae5ta hill, but after a time is brought to rest by striking a snowdrift.

A child on a sled (totalsg;ki)6-po aud s6byqgf t1 *5 mass m) starts from rest at the top of a hill of height h and slides down. Does the velocity at the bottom depend on the angle of the hill if (a) it is icy and there is no friction, and (b) th*;gf5-s atsb1qdp6y iko )u g6ere is friction (deep snow)?

Seasoned hikers prefer to step over a fallen log in their rbx) vh9py (-mpath rather than stepping on top and jumping down on the other six b9vp)(r-m hyde. Explain.

Two identical arrows, one with twice the speed oh5k z,scd-(i1 *f vbvdf the other, are fired into a bale of hay. Assuming the hay exerts a constant frictional force on the arrows, the faster arrow will penetrate hokschidbz5 f(d-v*1v,w much farther than the slower arrow? Explain.

Analyze the motion of a simple swingis4 x2mm d 1kpzhn8nl2 04bq,ming pendulum in terms of energy, (a) ignoring friction, and (b) taking friction into account. Explain why a grandfather clock 1xmdi, 40 2mslkhnz4np2bq8mhas to be wound up.

When a “superball” i7j9kkvld28iva5m0e rs dropped, can it rebound to a height greater than its original h9iv k d 02ka5vm78ejlreight? Explain.

Suppose you lift a suitcase from the floor )t)1ohurz7uw)ge pa 3to a table. The work you do on the suitcase depends on which of the following: (a) whether you lift it straighph)oaer)gu31wt )zu 7t 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 needed rather than thez.ixrsim ja-z7t r. ;* work.

Why is it easier to climb a moun0 vbvnpg((m2 (e/ 9zw6dcxtceci,mf1tain via a zigzag trail than to climb straight ut1g 0mep n9 ze6 di(2xc vmvbwc(f,/c(p?

Recall from Chapter 4, Example 4–14, that you can use a pulley and ropes t;mi-,9o9zpie w lbz+oo 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, using energy con9 bilo-o;z 9pie ,zwm+cepts.

  How much work is done by the gravitational force when a 265-kg pile driverpn0 d:w 7d+vdh falls 2.80 + 0 vdhpdnd7w:m?    J

  A 65.0-kg firefighter climbs .qrhlrx *9 fz)k08pkj a flight of stairs 20.0 m high. How much work is requilkz.0pf r )8khx *9rqjred?    J

  A 1300-N crate rests on the floor. How m/73vb xjo*l3yvorbd 7 uch work is required to move it at constant speed (a) 4.0 m along the floor against a friction force xdbjy3ro 37 lv ov/7b*of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work dibhl km:*v 3y(b(g mq,td the movers do (horizontally) pushing a 160-kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0vy(glqh,(3b m:k mb*t .50?    J

  A box of mass 5.0 kg is accelerated by a force across a floor at a rate6 bcycct5/ft7 of for 7.0 s. Find the net work done on th5ct7tfc 6bcy /e box.   J

  Eight books, each 4.3 cm thick with mass 1.7 kg, lie 3da3*9/x8crpd w2hmpchqb 8 q r lg0+yflat on a table. How much wo* acry+hx09cp lb mdqpr83qw8h2 /gd3rk is required to stack them one on top of another?    J

A lever such as that shown in Fig. 6-35c0h7 zzt 1tu-h can be used to liff objects we might not otherwise be able-0 1hz 7tzuhct to liff. Show that the ratio of output force, $F_{\mathrm{O}}$, to input force, $F_{\mathrm{I}}$, is related to the lengths $\iota_\mathrm{I}$ and $\iota_\mathrm{o}$ from the pivot point by $F_{\mathrm{O}}/F_{\mathrm{I}}=l_{\mathrm{I}}/l_{\mathrm{O}}$ (ignoring friction and the mass of the lever), given that the work output equals work input.

  A 330-kg piano slides l ;oxj35wcivz6l 7fq *3.6 m down a 28° incline and is kept from accelerating by a man 3*6xo fj7zcwql;i lv5 who is pushing back on it parallel to the incline (Fig. 6-36). The effective coefficient of kinetic friction is 0.40. Calculate:
(a) the force exerted by the man,    N
$(b)$ the work done by the man on the piano,    J
$(c)$ the work done by the friction force,   J
$(d)$ the work done by the force of gravity,   J
$(e)$ the net work done on the piano   J

  (a) Find the force requirez1hqr 1n5 y vpt,rxb32jk(wqyq: .n2vd to give a helicopter of mass M an acceleration of 0.10 g upward n25x(3wqyqq:1rpbvjt h,vky.r1n2z .    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 dikslt9 9vb 53mostance axis is linear and that $d_{\mathrm{A}}=10.0$ m and $d_{\mathrm{B}}=35.0$m. Estimate the work
done by force $F$ in moving a 2.80-kg object from $d_\mathrm{A}$ to $d_\mathrm{B}$   J

  The force on an object, g5jmz+b v9ryjh/- 4:0 hxstyh acting along the x axis, varies as shown in Fig. 6–37. Determine the work done byx+ 0hbjtvj-rzh : hsm954 yg/y 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 exerted on a particl*x ii,n+lk3 q,g7fsole 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 moa4k j+5ho op(jo52pf tlecule, 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 factor has its speedkh a+yevv 659i increased? $ \sqrt{a}$ a =    (b) If its speed is doubled, by what factor does its KE increase?   

  How much work is required to stop a5 w5g(5s twnvfn 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 1+f2he-dlnd- l ig hn1wq( 13kd05km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whose strinsr7ta9qw7(rp ,sb:bs g exerts an average force of 110 N on the arrow over a distance of 78 cb p7: sqws(9r trb,7sam. 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 glove backward 25 cm wheq e8c( t/6ljcen the ball is caught. What was the average force exerted by the ball on the/ e(cct6ljq8e glove?    N

If the speed of a car is increased by 50%, zl 63u*jep2 6:moucw1 ej/cgw by what factor will its minimum braking distance be increased, assuming all else is theoez3*6/:p m jje1 2cgcwwu6u l same? Ignore the driver’s reaction time.

  At an accident scene on a level road, investigators mp;t9o 2y*kqx jqs f4)lql;ln8easure a car’s skid mark to be 88 m long. The accident occurred on a ra 9ol8s jf;q tqlp2qk;*l)yx4niny 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 mass oqaen -:u 1pw/ve :.xgdf 0.25 kg is pitched at By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average g 1xq.:nup:/v-wea edforce of air resistance during a pitch, if the distance between the plate and the pitcher is about 15 m.    N

  How high will a 1.85-kgg5fr2 vup+ e 6n x,w6etmr9q5g rock go if thrown straight up by someone who does 80.0 J of work on xr5w6 p+gnemgque t,59vr6 f 2it? Neglect air resistance.    m

  A 285-kg load is lifted 22.0 m vertically with an accesiwyl+9/wdgf8vb r ex)665a zleration by a single cable. Determine xyas5 +v8wbgw/6fd 69 i) rezl
(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 constjao+5x :ct/*sh1owj ly70wmu+- ra v0 +tobg cant, k, of 440N/m How much must this spring be stretched to store 25 J of potential enerxm+joh/7 bvog 0y - sjto5+arwaccu l10*tw+:gy?    m

  A 7.0-kg monkey swings from oneci,)2uyqi q wj u-4l(x branch to another 1.2 m higher. What is the change in potenti4,ijqwq )( y- xuuc2lial energy?    J

  By how much does the gravi/qj0sndo o( uo: sa1t/4ihq 8xtational potential energy of a 64-kg pole vaulter change if his center of mass rises about 4.0 m during the jd1os (sqnoo 8xqi4h:a /0t/ juump?    J

  A 1200-kg car rolling on a horizontal5 - rcg7wj6xud .kf)zm surface has speed v = 65 km/h when it strikes a horizomrzgxdwjf.7k5c )- u6 ntal 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 lifts a 2.10-kg br r( ceii f-pkxc0h;3/ook from the ground so it is 2.20 m above the ground. What is the potential energy of tc(-;r3/pi kif0 r chexhe 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 1606)ryqfhzjkj ejev4q :)f)4- pok5j( q0 m and climbs to the top of a 3300-m pe) r5qhekz4ojq)j )k:j- 6 vf4jf( epqyak.
(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 l9 (l27ptgls mthe spring is next9(sl 7lm2glp t 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 with the ruler marks?    cm

  Jane, looking for Tarzan, is running at top speed (5.3m/s) and h ,dx7 (ccu: j*7ynpcwgrabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upwarx7yj cn c(dw: c*7h,upd?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from rest, s9g nyd7)2orbh)b n v+xlides 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 givq;nod ulf q)nepurgoqmk4; )f+50r05en 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 gravitational potentdqdsai0i ,7j ,ial 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 0.7m/, a, 7jsq0iddis.    m/s

  A 65-kg trampoline artist jumps vertically upward from the top of a platform wih;shk3ngb5n c 38zpk6- kz ljo+g)w8zth a speed of k jwn b+sz;zoz3hhn6c5-38 lgkg8)kp5.0 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 mass78 fq(o 2j7xdkv i m8 3hzv9qvo-ti-zi), whose spring stiffness constant 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 bal z2z h8mt3jiv87 -idqix7o(kvoqv9f- l 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 looped0g d(h0 1rue yrwo(mq; track shown in Fig. 6–39. If the block is to remain on the track, even at the top of the circle (we(q rwum0 1;o0(dh rgyhose radius is r), from what minimum height h must it be released?    r

A block of mass m is attachsqzdr3tj 6 .z6luvt4( ed to the end of a spring (spring stiffness constant k), Fig. 6–40. The block st3rtlqzv(6d6 u4zj .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 is tied to a bungee coq8jzzb9nk0 8ehq 66l.st)c/ hghcqa b95fd e2rd whose unstretched lengfjk82zeh6059)9 hbbzn6s8qdt agqhqe l .c/cth is 12 m, and falls a total of 31 m. (a) Calculate the spring stiffness constant k of the bungee cord, assuming Hooke’s law applies. $\approx$    N/m
(b) Calculate the maximum acceleration she experiences. $\approx$   m/$s^2$

  The roller-coaster car shown in Fig. 6–41 is drag me :ipyz5 cfe; :3;xrkx4fzd/ged up to point 1 where it is released from rest. Assuming no friction,y /;m:f ;p3z5kcxf4eexi rdz: 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 e ysp4x*;/jb7 dvjmt29oio x-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 spring to be placed at the bottom of an elevator shaf lmpd29sm w4n 2 5qpz9,ze0ptut. If the elevator cable should break when the elevator is at a height h above the top of the spring, calculate the value that the spring stiffness constant k should have so that passengers undergo an acceleration of no more than 5.0 g when brought to rest. Let M be the total mass of the elevator andd mn402p 2step9,zwz 5mplu9q passengers.

  A cyclist intends to cy.cr-k03- 3x sjx w fausmtb49ncle up a 7.8 $^{\circ} $ hill whose vertical height is 150 m. Assuming the mass of bicycle plus cyclist is 75 kg,
(a) calculate how much work must be done against gravity.    J
(b) If each complete revolution of the pedals moves the bike 5.1 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses. The pedals turn in a circle of diameter 36 cm.    N

  Two railroad cars, each of mass 7650 kg and tdivlz77 d ((t -x9umfgraveling 95km/h in opposite directions, collide head-on and come to rest. How much thermaludm 7v 9(dxlizfg- t(7 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 speedn zk1l) zjx:jbc .(a)a of 2.2m/s How much thermal energy due to friction was generated i n:aj)) xjc bz1(kaz.ln this process?    J

  A ski starts from rest and slides0hi:ii 9dncc; 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 aboveb u 9gpwud6(u ew0b8m* 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 oh)nshrd l6e t1 x+d((lf 1.5 m. r1tsnhd(xl6(+d el h)
(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 ,g 5nruvalc a42(y cq)inwj+6:;iy vba 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 0.30. What is the final speed of the crate? a bg2iy4n r5q,nucilacy):6wjvv;+(    m/s

  Suppose the roller coaster in Fig. 6–41 passes point 1 with a speedsdwp +ug/:c- ,xexq;o of If the average force of friction is equal to one-fifth of its weight, with what speed will it reach point 2? pxo+uxgd/c;-s, ew :q The distance traveled is 45.0 m. $\approx$    m/s

  A skier traveling 12m/s reaches tf*;ca0nw.5kv qd oa9 fhe 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 augbjksk)8q-a sb + 26attached 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 coefficien-8kkjbsga )ba+2q 6su t of kinetic friction between the block and the table?   

  A 280-g wood block is firmly attached to a very light horizokww7z k(ohhk*poo9d 7tx6t. 0a 4,wqqntal 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 will it s wwkkt7w0tqha9z.4d* xqo,7k 6hp(o otretch on its first swing?    m

  Early test flights for the space shuttle us6ez8n2m7 *l 1ha jhfp xsb5)hqed a “glider” (mass of 980 kg including pilot) that was launched horizontally at 500km/h from a height of 3500 m. The glider eventually landed at a speed of 200km/h (a) What would its landing speed have been in the absence of air x j2 zbmh8seh6)75fq*p n lh1aresistance?$\approx$    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 mtnblg / 2ve0a1zt4u5o otor to lift a 315-kg piano to a sixth-story window 16.0b 5tu4/atlvgz 1no2 0e m above?    s

  If a car generates 18 hp when traveling ati 8w98danu z/;2-89 mgtjbl fjbdgy ;q a steady 88km/h what must be the average force exerted o9q ybm8;dg -2lj8wn jz9i a/8 u;gdtbfn the car due to friction and air resistance?    N

  A 1400-kg sports car accelerates from rest to 95km/h in 7.4 s.0 )m9szr jsqqskk7x0, What is the average power deliveredqsk0xsz7jk0 rs9,m) q by the engine?$\approx$    hp

  (a) Show that one British horsepowero4qhe y)q+ze4 $ \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 often30 f:3(x xmi viw)dgzb 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 6.0 +: wz or3i3 agbl3zos/s on the level when it is in neutral. Approximately what pasolg /bi3z:+wro3 z3ower (watts and hp) is needed to keep the car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hr9b xl.oo2+czwqs1nyj0c :(qp motor do in 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3- oqf*6zksv .3,le5us/cb ksa+kg shot from rest to 14m/s If this motion takes 1.3,5cs* ko zsfb/a ueq 6+lv.sk5 s, what average power was developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute through a hedpsgn* 8-p;y2j95iorb6 vdzz ight of 3.60 m. What output rating (watts) should the pump motor h pd98p- od;6znj5gyrvs2 b *izave?    W

  During a workout, the football players at Statllb / vj:1k+maebwu zq;au90k-ck/p kgd u(39e U. ran up the stadium stairs in 66 s. The st01uqumk ;( lkd j+9/ka cw 9l:g3-/pbv zkaebuairs 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 cycliswgorr0-* b:bxa9a p )kt 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 stpoo6o.bm iig7u -*;g reep a hill can it climb at a constant speed of 75km/h if the frictiop*b76o -gg iu .or;mional forces add up to 650 N?    $^{\circ} $

  What minimum horsepower must a moto3 a4kzha(wa9je*q f*br have to be able to drag a 310-kg box along a q3(kze9aa4bhwja f **level floor at a speed of 1.2m/s if the coefficient of friction is 0.45?    hp

  A bicyclist coasts down a 7.0 - bci p4f0ynk5l gtl-2$^{\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) bum)czgp qq8 3abe- ibn.5pers” that are designed to compress and rebound elastically without any physical damage at speeds below 8km/h If the material of the bumpers permanently deforms after a compression of 1.5 cm, but remains like an elastic spring up to that point, what must the effective spring stiffness constant of the bumper be, assuming the car has a m-5bc na )i pg83z.bqeqass 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 grourg d1tu(06scb.x mbkdf/g ,x/nd, and the remaining four shelves are each spaced 30.0 cm above the previous one. If the averagb 6rf /d c,ux(k1g/dx0tsg.mb e 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 Owengpalk k+rlnd 73r8p*tw023 ul s’s famous long jump (Fig. 6–42) in the 1936 Olympics shows that his center of wn 2 l7r rl*du8kg03p alpk3t+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 wim4; zq:zas)y rthout friction along the looped track shown in Fig. 6–39 is to rey;) mzq:4s zarmain 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 fe,gps17wta2sff 7gtfjbyr47 m* 4y2yxll 370 m after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with o f7gxwjaf bp*7ts 4yy y7mt 2,gr42s1fnly 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 l.m+ f omq(*psq-ymxx:ength L whose other end is fixed (Figomx:sq f (x +myq-p.m*. 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. hg;:d exqqk9t msl3/7lk wn:2 The climb is made in 5.0 h starting at an elevation of 2300 m. Calculatedlkk 7htq2mlxns/q93gw:; e :
(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 28 m abov5tba ekq ripsz.rdo;2qd2spr + (p+4:b0w( bse 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 kzj/ z-.8urfwm ho( y al,kg*7move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimat -z8 al7*w ./yorm(kugzfjk,h e the power needed.$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and fallss n0 m(w)jk9+sspq9ta knv +7f vertically 81 m before striking the turbine blad ak9+n7vws p)0+m9njf (q kstses. 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 dif4 xsd m7rz)1nxlmnz/-ference in your apparent weight at the top of the circular loop and the bottom of t rn-)zxmnl 4dm1sxz/7 he circular loop is 6 g’s — that is, six times your weight. Ignore friction. Show also that as long as your speed is above the minimum needed, this answer doesn’t depend on the size of the loop or how fast you go through it.    mg

  (a) If the human body could convert a candy bar directly into wor sd:wc(v-9:buuc h,el k, how high could an 82-kg dchw, l(ec9: - uu:sbvman climb a ladder if he were fueled by one bar (=1000kJ)    m
(b) If the man then jumped off the ladder, what will be his speed when he reaches the bottom?    m/s

  A projectile is fired at an uptt8/tv2q e +4 5wc oxmsnh;sp)ward 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 compr/5uob,y o;di )h :qwhpesses 0.60 mm, and it tells you your weight is 710 N. Now if you jump on the scale from a height of 1.0 m, what does the scale r/ohbdohpy:5w ;, uiq)ead at its peak?    N

  A 65-kg student runs at 5m/s grafxn+ y/vkif zl p:l5 5ap7eq9*bs a rope, and swings out over a lake (Fig. 6–45). He releases the rope when his velocity is zero i79 vff5 5lknep:/ *lqza+ypx.
(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 vertical distance of5r *xpeev;( r0ygfxe- 5.0 m in 9.0 s. What minimum power output was used to accomplis-p05*ryv f;g xeee (rxh this feat?    W

  Some electric-power companies use wa9 kb l5t 1z bx+ee*kw*)gkhuv6ter 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 houv )e91e*kbz+htukxk l*56gwbr 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 izkk0kbi1(: lf s cut in half. What is the spring stiffness constant for each of the two(fk:l0 zb1 ikk resulting springs?   k

  A 6.0-kg block is pushed 8.0j pj923z;d cru 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 accelet*f i8:m dxy73sur6dlrate 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 the6 7fy*dx d3iu :m8ltsr same, and neglect frictional losses.    s

  In a common test for cardiac function (the “stress test”), th.w34 cq,zr;nbh(z pvqe patient walks on an inclined treadmill (Fig. 6–46). Estimate the power required from a 75-kg patient when the treadmill is sloping at a3q4 ( v,z.hqzb;pn rwcn angle of 15 $^{\circ} $ and the velocity is 3.3km/h (How does this power compare to the power rating of a light bulb?)$\approx$    W

  (a) If a volcano spews a 500-kg rock vertically upward a di9 jti6.a0o1qvm:0+tqa g s gf8yl6wlcstance of 500 m, what was its velocity when it left thetatysq9:0 gi a1 6j+ wvmqc g8f.6oll0 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 whgo c u /7-b15ed1a4nr6n gksc.z+d)rahjvww5 eel from a height of 2.0 m at a rate of 95kg/s (a) If this water zjcargv)sc 6denwdn1 u1ag rb5w/k45-+7 oh.wheel is set up to provide electricity output, what is its maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s