In what ways is the word “work” as used in everyday language thehucm3ykgj7) 6- w vs5e same as that defined in physics? In what ways is it differe)m e csuvy h-wk65j7g3nt? Give examples of both.

Can a centripetal force ever do work on an x(h:htmam 0xx:s- lravk) +g. object? Explain.

Can the normal force on an object ever do work? Exp0tte x vj)b) ;k3fwzq0lain.

A woman swimming upstream is not moving with res;2o iv3kq7aa epect to the shore. Is she doing any work? If she stops swimma ;e qv3kai27oing and merely floats, is work done on her?

Is the work done by kinetic friction forces always negative? [Hint: C:g dbwu8h8mc 0 z;xn/gonsider what happens to the dishes when yo0 c;gxm/gh8 8:w udzbnu pull a tablecloth out from under them.]

Why is it tiring to push hard against a ftru7eia3t l6ww efi2 8u1w21 solid wall even though you are doing no w3fa l1tutw2 w72riiue6w f18e ork?

You have two springs that are identical except that s;2exxos(hkkes6p +) vpring l is stiffer than spring (o)6s; hksxkpve2 +e x2 $(k_1>k_2).$ 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 onn/v aovn r.x2+ bbl y88zxl;y,5b x+wd a frictionless surface (Fig.6-30). The block yd;.+x, 2rnn xv/ aozlb85b xv lw+by8starts from rest 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 your7ho4l. ic2rashso 4/g gravitational potential energy change when you jumplo4hgos sicr2/74.ah as high as you can?

In Fig. 6–31, water balloons are tossed from the roof ofq ju e80m0k6:+r h0 /bjlgdfuh a building, all with the same speed but with different launch angles. Which one has the highest speed on impact? Ignore air re0fq brmul hjj:d0g8e0u+6/k hsistance.

A pendulum is launched from a point thaea*m yo (9sdb n0i0tw07 q,nhit is a height h above its lowest point in two different ways (Fig. 6–32). During both launches, the pendulum is given an initial speed of 3.0m/s On the first launch, the initial velocity of the pendulum is directed upward along the trajectory, and on the second launch it is directed downward along the trajectory. Which launch will cause it to swing the largest angle from the equilibrium ponw m09edytbi0s0 h7 *na,iq(osition? Explain.

A coil spring of mass m rests upright on a table. If you compress the sprinx)pl +h. irh;ag by pressing down with your hand and then release it, can the spring leave the table? Explain, using the law of conservation of energy.+phhlxrai . );

A bowling ball is hung from the ceiling by a steel wire (Fig. 6–33)oxc,*w(w3yh7v:q9i 6twz-y(ho ha of. The instructor pulls the ball back and stands against the wall with the ball against his nose. To avoid injury the instructor is supposed to releasf :q3 how9hac,ioy-ho(yvzw(67xtw* e the ball without pushing it. Why?

What happens to the gravxv dp,ef;izl v 9m*ck 3246eksitational potential energy when water at the top of a waterfall falls to the pk*vkvsi2e x m;,dp3 ce9fl4 z6ool below?

Describe the energy transformations w05sf w 0 d6qmprn1w,vfhen a child hops around on a pogo stick.

Describe the energy transformations that take ,v e:bnovr 10v+o5t9b oy+dei place when a skier starts skiing down a hill, but after a time is brought to rest by striking a snowdrift.:roeo0y,+ 9 5dov 1tv+ivebbn

A child on a sled (total mass m) starts from rest at the top of a hzy n8.wqc6 7-ci dwww.ill of height h and slides down. Does the velocity a.i 76cwwzw-cn.qd8y w t 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)?

Seasoned hikers prefer to step over a fallen log in their path rather than iyn3-*fpg s;ustepping on top and jumping down on the other sid pgfn;u *i-s3ye. Explain.

Two identical arrows, one with twice the speed of the othe/yv )axz*dz(kka1 p03/uo.xjid hu 7uosq i34 r, are fired into a bale of hay. Assuming thhua7i/3xp1vku.uaq o/* k3jsdz4x y() o 0zide hay exerts a constant frictional force on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain.

Analyze the motion of a simple swinging pendulum in ttimv 7 ,h*oov8erms of energy, (a) ignoring fricm7h iovvo,t* 8tion, and (b) taking friction into account. Explain why a grandfather clock has to be wound up.

When a “superball” i+z.eeiufz/ahc j 0*r 5s dropped, can it rebound to a height greater than its original heightiecj f*r 05uza hez./+? Explain.

Suppose you lift a suitcase from the floor to a table. The wo* ks7nel 3dk*zrk you do on the suitcase depends on which of the following: (a) whether you lift it straight up or along7kkld esz*n *3 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 6 +m7 q et1xrai(g1q ,ldysnk;needed rather than the work.

Why is it easier to climb a mountain via a zigzag trail th3d) ahk zugfuzrio *11h rj(3;an to climb straight u 3 uhzrf)* h(dug11a;riz3jokp?

Recall from Chapter 4, Example 4–14, that you ct xovvv/ + hy4qp7mb-.a4vd9m an use a pulley and ropes to decrease the force needed to raise a heavy load (see Fig. 6–34). But for every meter the load is raised, how much rope must be pulled up? Account for this, usa v/ 7dt-obv4ypmqvvh9 .m x+4ing energy concepts.

  How much work is done by the gravitational force when a 265-)36 9o ez u6kd-lpw xqzg1v:dgkg pile driver falls 2.d:w19k3go l6e z p6q-v)xuz dg80 m?    J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How much wormeg r-s3v tlvb,8n.z9 k is required? vvmg.n3bzt98r-sl, e    J

  A 1300-N crate rests on the floor. How much work is required tkyje h mio360 rj-s9r*o move it at constant speed (a) 4.0 m along theorj9he rk3 *yi- s0mj6 floor against a friction force of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did the movers do (hore:acq6 t s(b5px08ymzizontally) pushing a 160-kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0.tq5: p (yzmc0s8xea6 b50?    J

  A box of mass 5.0 kg is acceletplml09qs yy8r0n 1 ic +bbk(1rated by a force across a floor at a rate of for 7.0 s. Find the net work done on the 0rts890(il1 nq1myyl bb+p kc box.   J

  Eight books, each 4.3 cm thick with mass 1.7 kgj+efvc7 *c1nu, lie flat on a table. How much work is required to stack them one on top ofnc e7+1 ufj*cv another?    J

A lever such as that shown in Fig. 6-35 can be used to liff oe7-xwe4-a yt zqt wu20iju n,a yin89)bjects we might not otherwise be able to liff. Show that the ratio of outpuyz,w)2 naetq7e- iy894u0- ij xunawtt force, $F_{\mathrm{O}}$, to input force, $F_{\mathrm{I}}$, is related to the lengths $\iota_\mathrm{I}$ and $\iota_\mathrm{o}$ from the pivot point by $F_{\mathrm{O}}/F_{\mathrm{I}}=l_{\mathrm{I}}/l_{\mathrm{O}}$ (ignoring friction and the mass of the lever), given that the work output equals work input.

  A 330-kg piano slides 3.6 m down a 28° incline and iky-wor ofrh +idn 5 lcu*b70+96wki8ps kept from accelerating by a man who is pushing6lkf7b-i puw ni9dky0+wh*5 o+r roc 8 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 required to give a hd;f f/v(d7i.hlc+g 37nodxyr elicopter of mass M an acceleration of 0.10 g upward. d/cxy7dh3drf+ (gn7;.f vl oi   Mg
(b) Find the work done by this force as the helicopter moves a distance h upward.    Mgh

  $\text{What is the minimum work needed to push a 950-kg car 810 m up along a 9.0$^{\circ} $ incline? }$$(a)\text{ Ignore friction. }$    J
$(b)\\\text{Assume the effective coefficient of friction retarding the car is }0.25.$    J

  In Fig. 6-6a, assume the distance axis is linear and thatmy , rtqifz8gtp8 81q7 $d_{\mathrm{A}}=10.0$ 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.z63 nxq.+k ne ycptw7. Determine the work done by this force to move the object7tqyk . ew6p.cnx+ z3n (a) from x=0 m to x = 10 m    J
(b) from x = 0 m to x = 15 m    J

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

  The net force exerted on a particle actsco/o ke0w4hb, 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/6dk y.+ y fwwlwx-kd7 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 ;h(xx71ev kvd2hdu i0 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 ak6oq lqa3p*) 8e o1qoto stop an electron $\left(m=9.11\times10^{-31}\mathrm{~kg}\right)$ which is moving with a speed of$1. 90\times 10^{6}\mathbf{m/ s}$ ? $\boxed{a\times10^{b} \mathrm{J}}$ a =    b =   

  How much work must be done to stop a 1250-kgcar traveling ar )0d1pdfgi+yk w,bfg-f kp(*t 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whose string exerts an average j0,tx / l2j ipb+bhb-g 3rxtc5f9hm- vforce of 110 N on the arrow over a distance of 78 cm. What is the speed of the apgitt hrbmc -v3 lf/jbxjh29,+x-5b0rrow as it leaves the bow?    m/s

  A baseball (m=140kg) ti h adwv-y48do zfja*h5 )vv./raveling 32m/s moves a fielder’s glove backward 25 cm when the ball is caught. What was the average force exerted by the do8vhv/5 y awa*dh) .j fi-z4vball on the glove?    N

If the speed of a car is increased by 50%, by what mk:vkb)7xpb fgcy* fq5, .h d8factor will its minimum braking distance be increased, assuming all else is the same? Ignfbh,v:g7.5cf8*x my ) bqpkdkore the driver’s reaction time.

  At an accident scene on a level fwo9u,v.s 8i.af :e3bc1yb v sroad, investigators measure a car’s skid mark to be 898 bcu1vy,f of:iweb .a.ss v38 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 locked) the brakes. (Why does the car’s mass not matter?)    m/s

  A softball having a mass of 0.25 kg is pitchedx56rq akm h.noac6.z2 at By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of mac .6.zro2qa nx6h k5air 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 go if thrown straight up by someone wqxq vn:wwryk;w; k)68 ho does 80.0 J oqw yq)8nwkw;x6 kvr:;f work on it? Neglect air resistance.    m

  A 285-kg load is lifted 22.0 m vertically with an acceleration by a o nz(t/dc,f8fsingle cable. Ddo(8cn, zff/tetermine
(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 440N/m How much must thin7 usla ux08plkc)xmfuvf9o 4v3w( 90s spring be stretched to s(00f) nlpkax8f 9u4vu wo9mcu37lx vs tore 25 J of potential energy?    m

  A 7.0-kg monkey swings from one branch to another 1.2 m hsudq j5*y9)ytkx)lqxvl23 :oigher. What is the change vx5sqlt9qk:yxly*3 od)u2 j) in potential energy?    J

  By how much does the gravitational potential energy of a 64-kg 2yavlvi, 4jv:.om07 w4rk iujpole vaulter change if hirv.v,mj4 oki v a:y27lijwu4 0s center of mass rises about 4.0 m during the jump?    J

  A 1200-kg car rolling on a horizontal surface hasr855lsea+lm6 s9 sa c0la 17k-ihikv p speed v = 65 km/h when it stria-v5pea85hsa s r1m 67k+lclksl0 9iikes a horizontal 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 lisk(o8p5 j6b ovfts a 2.10-kg book from the ground so it is 2.20 m above th 5kbo8v (ojs6pe ground. What is the potential 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 and climbs to the top of a hnd)e1-(q l u*mci7ez 3300-m pehi)c z 71-lmde qnue*(ak.
(a) What is the hiker’s change in potential energy?    J
(b) What is the minimum work required of the hiker?    J
(c) Can the actual work done be more than this? Explain why. ----待选择----yesno 

  A spring with k = 53N/m hangs vertically next to a ruler. The wrrw568pkm6cg d/i 0d end of the spring is next to the 15-cm r5p6dk cm60w8irg wd/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 Tar1-m) nv6rc-ek+c 8vkn zyvjy2 an9q4lzan, is running at top speed (5.3m/s) and grabs a vine hanging vertn a k vvv8cn2 erk--yclj9+q1y)mn 6z4ically 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 aibnabf h/;/+m4 eyvh4 frictionless 35.0$^{\circ}$ incline whose vertical height is 185 m. How fast is she going when she reaches the bottom?    m/s

  A sled is initially given a shove up a frictionless1kv4adj vbe9w i)f,s; 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 transformkd efaht ;q +1dh mn4-g61b2 nzkpz2l)ed into gravitational potential energy without the aid of a pole. Withkah )-mkn2gnz bz d1t qeh1+264fldp; 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/s.    m/s

  A 65-kg trampoline artist jumps vertically upwar8 l(zl:ml nk,ud from the top of a platform with a speed of 5.0 z ( :nlku8ml,lm/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,5s*;4zal.iuq nte2e . z idah its mass), whose spring stiffness constant is 950N/m is attached to a table and is compressenu 4ta. a,2ls5ih*.i; zeqzded 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 slid zoa3;mnj -dzg3f /ln3es without friction along the looped track shown in Fig. 6–39. If the block is to remain on the track, even at the top of the circle (whose ajf/n;dz lg3-zo3n m3 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 (spring stiffnessxzrf2n7dag ck 9 kqimi*7)7,zn3 j lb0 constant k), Fig. 6–40n3z )q 7k9mfj0ildic krg 7zba,n2* 7x. 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 is tied to a bungee tsm)6li epcc0kjl*: )b:d ,krcord whose unstretched length is 12 m, and falls a total of 31 m. (a) Calculate the spring stiffness constant k of the bungee cord, assuming Hooke’s law appliek:i: dt)lmpsc, rlje)k6 0c b*s. $\approx$    N/m
(b) Calculate the maximum acceleration she experiences. $\approx$   m/$s^2$

  The roller-coaster cax87+4nz rotf9m*i c70iyb bum *e+emyr shown in Fig. 6–41 is dragged up to point 1 where it is released froe b4 yf08ti 7ui* m++r 7ymxce9z*monbm rest. Assuming no friction, calculate the speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown with a speed of 12 m/s a,k q czw ./b; d7)lyyljsetm10l0m- 4x4fg atat 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 to2d h5/a(bvev x+ /znxa be placed at the bottom of an elevator shaft. If the elevator cable should break when the elevator is at a height h above the top of the spring, calculate the value that the spring stiffness constant k should have so that passengers und/ b(v5+anaxd/ xzv2heergo 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 cq hhc1 i;j.r ,beydwqjl3c6ktr7,2h 0ycle 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 traveling 95km/h in opposite dir ae;e,xa 0oc6raixk0rzy7 t/;ections, collide head-on and come to rest. How much thermal energy is produced in this collision?,c0 iyar 6exze ok;0/;arx7a t $a\times10^b$ J a =    b =   

  A 21.7-kg child descends a slide 3.5 m high and reaches the bsa0ws9/osmi-s: hlmxdc/ 7; xottom with a speed of 2.2m/s How much thermal energy due to friction was genesshwdmxios 9 -c/7;ma0: l/ sxrated in this process?    J

  A ski starts from rest and slides down a 2ozp( 6zbz:*or2 $^{\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 8 6 *jywlmluct r w3kd7m;l56mdropped from a tree 13.0 m above the ground.
(a) With what speed would it hit the ground if air resistance could be ignored?    m/s
(b) If it actually hits the ground with a speed of 8m/s what is the average force of air resistance exerted on it?    N

  You drop a ball from a height of 2.0 m, and it bounces back tz-qh2 )nfzo)uo a height of 1.5 mo)2 z)h- qznuf.
(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 17sg8bvz(ufr d 64fwy o.4jlwa 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 6wszj(fy8 v dlw4fo.b7 4u1rgcrate?    m/s

  Suppose the roller coaster in i x+pcd5o a-uf 18od7nFig. 6–41 passes point 1 with a speed of If the average force of friction is equal xi 7 -ao85ud+fnd1cpoto 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 lnsa+ hi n 8soxrs3 s*+rbnz e2+;i73yupward 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 attac hr*bf4 bqzj,-f3 xl)2f-e7 x9elfntm hed 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 coefficient of )2x f7e, zxlbmje3tff4h9f -q l*-rnbkinetic friction between the block and the table?   

  A 280-g wood block is firmly attached to a very light hori e),z r2ffqq:wzontal spring, Fig. 6–40. The block can slide along a table where thff zq2)eqw: ,re 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 stretch on its first swing?    m

  Early test flights for the space shuttle used a “glider” (mass of w * iz-ybcjkrn)2 o 0cqi:v*nl)fg5l0 980 kg including pilot) that was l-bzf:wyqorvgin2i)j* ) 5 l0ck0c *lnaunched horizontally at 500km/h from a height of 3500 m. The glider eventually landed at a speed of 200km/h (a) What would its landing speed have been in the absence of air resistance?$\approx$    km/h
(b) What was the average force of air resistance exerted on it if it came in at a constant glide of 10 $^{\circ} $ to the Earth?$\approx$    N

  How long will it take a 1750-W motor to lift a 315-kg piano to a sixth-st v v37q;e:wn*d ieni0nory window 16.0 m aboiwn3 0vq d*;ve7n i:enve?    s

  If a car generates 18 hp when traveling glm 0cwf851jqr rlsg3k 2j)i* at a steady 88km/h what must be the averaggr sc*lwj1 jm3)5ilkfq r2 g80e force 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 sld4nk0s0 8l fm. What is the average power delivered by t4 8 0lsnd0kflmhe engine?$\approx$    hp

  (a) Show that one British hogle/g/o 0 y5grrsepower$ \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 “kilowat e0wopl 3ai.rq3f fa(4t-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 slo,fjw+/zvyb;ytp*j* (+v( l 8jo mwlcs ws down from to 65km/h in about 6.0 s on the level when it is in neutral. Approximately what power (watts and hp) is needed to keep the car traveling at a con *yw ,ov m;sb++ jjtv(l/fyz c8pj*l(wstant 75km/h.    hp

  How much work can a 3.0-hp motor do in 1.0 h? 3g736cpij zm r$a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg shot p;twsa:t.3ji from rest to 14m/s If this motion takes 1.5 s, what average power was dei sj3. t;twpa:veloped?$\approx$    W

  A pump is to lift 18.0 kg of watt( 71fh /3cui einha+ter per minute through a height of 3.60 m. What output ratingu+cn(e7 it1a tf/h3i h (watts) should the pump motor have?    W

  During a workout, the fo9*,fngt v:6*r.5ji.ejdrbyuvv y o z.otball players at State U. ran up the stadium stairs in 66 s. The stairs are 140 m long and inclined at angrv5. o, d*.y6bji.une r:yvvz9t fj* 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 cyclvz ,msd4gi; swu8m iq:or2 .8rist 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 outputzg7qz5rq,i7 vx ) 3hkt of 120 hp. How steep a hill can it climb at a constant speed of 75km/h if the frictional forces add up to 650 N? kxgz)5v,z7q q htr 73i   $^{\circ} $

  What minimum horsepower must a motor )3-)xj f/y 6egxnfh- sue.q5jjz;qh yhave to be able to drag a 310-kg box along a level floor at a speed of 1.2m/s if the coefficient of friction is -jy )jejhfes 6zuf3 5x)y -qx;h.qg/ n0.45?    hp

  A bicyclist coasts down a ah.q; mt 30zkd+pn flja5gpdita/41a3 h z;-f7.0 $^{\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 h,1je/: - icl zeqr,m-6 mpiqegave built “5mi/h(8km/h) bumpers” 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 mass of 1300 kg and is tested by ramming into a so /rzq-e6-: pqij1l,c,mmgeei lid wall? $a\times10^b$ N/m a =    b =   

  In a certain library the first shelf is 10.0 cm off the tmw ghh+ cqmnaa:(-8x,:0 u dgground, and the remaining four shelves are each chu0 m:-(wm:gt8 dgqah+,xn aspaced 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 jwdw81r4a-/ouee, p pfamous long jump (Fig. 6–42) in the 1936 Olympics shows that his center of mass rose 1.1 m from launch point to the top of the arc. What minimum speed did he noedw8/w-,1j4 arppe ueed 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 yhn 5/vr,rfc4ej( 2g .bgz0l sfriction along the looped track shown in Fig. 6–39 is to remain on the track at all times, even at the very top of the4yg2, vfl.cejr(g/ nh 5r0sbz 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 afterqe(c2n) te(+6ivtr hn jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but s) +(r2inqn t(cvth6eeurvived 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 m1zr kn.fvv1i h;8 qm6(Fig. mm1zhf;vq6 rn. 1k8iv6–43).
(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 topn4e yv+di +9wk8;wy kg of a 3700-m-high mountain. The climb is made in 5.0 h starting at a+nw4y8 wg9yikdv+k; en elevation of 2300 m. Calculate
(a) the work done by the hiker against gravity,   
(b) the average power output in watts and in horsepower,   W    hp
(c) assuming the body is 15% efficient, what rate of energy input was required.    hp

  An elevator cable breaks when a 920qv0*g6jws8nrz ,c wr- *.ge go-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 chu*i0 3,0f6 ptzssngr an move 47,000 people per hour. If the ave*psfu0g0,inz3t hrs 6 rage lift carries people about 200 m (vertically) higher, estimate the power needed.$a\times10^b$ W a =    b =   

  Water flows over a dam at tt/ecnaj 4.zaf )x+lq -he rate of 650kg/s and falls vertically 81 m before strikingl/+a4zf n .)aq-txjec the 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 loo:xl9bpct9d qc( . )zzfp (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. Ignoq bp d f(zl:)zt9.cx9cre 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 zjm 4nq;prh m)-r/c*jcandy bar directly into work, how high could an 82-kg man climb a ladder if he we cq )/phj4 mnr-z;rjm*re fueled by one bar (=1000kJ)    m
(b) If the man then jumped off the ladder, what will be his speed when he reaches the bottom?    m/s

  A projectile is fired at an upward angle opdnu;;ts) m, jf 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, b5 rl dj4f-c7kthe spring inside the scale compresses 0.60 mm, and it tells you your weight is 710 N. Now if you jump on the scale from a h54lb7j -k rfcdeight 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 swings out over a lake (Fck bu aovfb .3cf e8kw;)m)r+7ig. 6–45). )m ) eokc+a bcr;u378kbf.wfvHe releases the rope when his velocity is zero.
(a) What is the angle when he releases the rope?    $^{\circ} $
(b) What is the tension in the rope just before he releases it?    N
(c) What is the maximum tension in the rope?    N

  In the rope climb, a 72-kg athlee q;vq;0g12yx;zc n pfte climbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used to accomplish thisq;0 n ;cxepzfqg1 y2v; feat?    W

  Some electric-power companies use water to s* x 7vf;mgj dzy+brx2;tore energy. Water is pumped by reversible turbine pumps from a low to a high reservoir. To store the energfg* jyzm;v rb+;dx2x 7y produced in 1.0 hour by a 120-MW ($120\times10^{6}$W) electric-power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Assume the upper reservoir is 520 m above the lower and we can neglect the small change in depths within each. Water has a mass of 1000 kg for every 1$m^3$.    $m^3$

  A spring with spring stiffness constant k is cut in half. What is the spring stia; mq3y pdvb 574hss)uffness constant for each 3hb57qpamsv 4); dsyuof the two resulting springs?   k

  A 6.0-kg block is pushed 8.0 m up fl,.5z p+ejz: xxwwj,f;5bkta rough 37 $^{\circ} $ inclined plane by a horizontal force of 75 N. If the initial speed of the block is 2.2m/s up the plane and a constant kinetic friction force of 25 N opposes the motion, calculate
(a) the initial kinetic energy of the block; $\approx$    J
(b) the work done by the 75-N force; $\approx$    J
(c) the work done by the friction force;    J
(d) the work done by gravity;$\approx$    J
(e) the work done by the normal force;    J
(f) the final kinetic energy of the block.$\approx$    J

  If a 1500-kg car can accelerate from 35km/h to 55km/h ink1iclcfj9 2ugq)bg x;+uoc5- 3.2 s, how long will it take to5-ulg c ij9xqcc;21 kuog+) fb accelerate 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 patient walks )5x.le+5gu djyke rzu2f26ax on an inclined treadmill (Fig. 6–46). Estimate the peyuud 2z rg).kfex25a 65 xjl+ower required from a 75-kg patient when the treadmill is sloping at an angle of 15 $^{\circ} $ and the velocity is 3.3km/h (How does this power compare to the power rating of a light bulb?)$\approx$    W

  (a) If a volcano spews a 500-kg rock vertically upward a distance of 500 m, whak zw4brb n-16yiq jl44t was its velocity when it left the volcano?z4b-y1b j446 qnrliwk $\approx$    m/s
(b) If the volcano spews the equivalent of 1000 rocks of this size every minute, what is its power output? $\approx$ $a\times10^b$ W a =    b =   

  Water falls onto a water wheel from a height of 2.0 m at a rate of 95kg/s yii i4nf-up 27(a) If this water wheel is set up to provide electricity outpui2iun47p y-f it, what is its maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s