In what ways is the word “work” as used in everyday language the satu6b56b; ;w dyy7uyv mme as that defined in physics? In what ways is it diuud b6 ;yt5y6m;7vwy bfferent? Give examples of both.

Can a centripetal force ever do work on an objec8sf ;cx/w1: gut*wwwp4;uh mxt? Explain.

Can the normal force on mdepvh7p k6+* zw9yf:an object ever do work? Explain.

A woman swimming upstream is not moving with respect to the shore. Is she do8;y su*)trldszj nj .)ing any work? If she stops swimming and merely float.sdtj;znls 8r )*y)ujs, is work done on her?

Is the work done by kinetic friction forces always negatly iz 0fq0z3z-ive? [Hint: Consider what happens to the dishes z f-zi0zy30qlwhen you pull a tablecloth out from under them.]

Why is it tiring to push hard against a solid wall even though you are do5tztm 8q:bvs ggbn8(3ing no 8s(8bbgnq5 mz3vtt :g work?

You have two springs that ar:y5-ibys jy.zxsg a :9qff,bmaiw1;: e identical except that spring l is stiffer than sprin: js x5yabiymwq,ag:z9s 1y-f;b:.ifg 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 blocx-l6;itszd / yk that is free to slide on a frictionless surface (Fig.6-30yts/-dxli ; z6). The block starts 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 your gravitational potennt3: jdyj:xs3 qv4y+ntial energy change when yyntd + j: ysnxv3j:3q4ou jump as high as you can?

In Fig. 6–31, water balloons are tossed from i4ka)m e+nw m0+-zladthe roof of a building, all with the same speed but with different launch angles. Which one has the highest speed on4m e)+a +in0-wkzla md impact? Ignore air resistance.

A pendulum is launched from a poin i.y98h0 znmrebe2x26l8ikg83 w1 ak wj3df dot that 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 de8fieb6zh l3.1d2a ox3i w8rymj8nk gw0 92kdirected 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 aewk;40w jy :m5/fgwmc table. If you compress the spring by pressing down with jm kf/w:y0we gmw4;5cyour hand and then release it, can the spring leave the table? Explain, using the law of conservation of energy.

A bowling ball is hung from the ceiling by a steel w ;xbskd)lbk,a dx0 5s,ire (Fig. 6–33). The instructor pulls the ball back and stands against the wall with the ball against his nose. To avoid injury the inba k ;sb,d5,xs)0dkx lstructor is supposed to release the ball without pushing it. Why?

What happens to the gravitational ppms+ ge-2tzu fp8vnm u 4b/j,0otential energy when water at the top of a waterfall -gupf nu jp4e2bvt sm0 8+/zm,falls to the pool below?

Describe the energy transformations when a child hops aroun 4- 0j/scocf 1pyqmqw7mt.5dhd on a pogo stick.

Describe the energy transf k/f89 d1wsao86uq ezkormations that take place when a skier starts skiing down a hill, but after a time is brought to rest by stridak f1wze6 /q 9sk8o8uking a snowdrift.

A child on a sled (total mass m) starts from rest at the top of a hill of e5 .pk gso/cc+height+/ gp5cskce .o 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)?

Seasoned hikers prefer to step over a fallen log in their path ratn) 3wh :6a nu86iyvat:y+arpxher than stepping on top and jumping d6ati vny8yw pxh: n36u+)a: raown on the other side. Explain.

Two identical arrows, one with twice the0ua d21gjqm x5 speed of 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 how1dujgq 05m2ax much farther than the slower arrow? Explain.

Analyze the motion of a simple swinging pendulum in terms of energy, (a) igne u0l9x; 8li;4tf381xemxpqhy pp(e d oring friction, and (b) taking fri8e q(;ie13 xxyl;e fdp9ppmu4 htx8l0 ction into account. Explain why a grandfather clock has to be wound up.

When a “superball” is dropped, can it rebound to a height o. 6xp . ks+;b3tqp-at*w;gdc arlae5 greater than its original hei6*a -we .opsgtxaa+ ;3dtcpq.;bkr5 l ght? Explain.

Suppose you lift a suitcase from the floor t( n0xs3(c gwomo a table. The work you do on the suitcase depends on which of the following: (a) whether you lift it straight up or along a more complicated path, (b) the time it takes( (0s xo3cnwmg, (c) the height of the table, and (d) the weight of the suitcase?

Repeat Question 22 for the y.derkxt3le 5.*6d prpower needed rather than the work.

Why is it easier to climb a mountaipe;2d+i4yiv xq:d mo 0n via a zigzag trail than to climb straight u;eoddvqymi0p4i 2:x+p?

Recall from Chapter 4,a (l 9uot;/xsr1m rpu2 Example 4–14, that you can 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 u;r/stx (o1 apm r9l2ube pulled up? Account for this, using energy concepts.

  How much work is done by the gravitational force when a 265-kg pile driver ;i8u)1r;q ohxu k*bkmfalls 2.80 m? qhou;); k8ur b*1ikxm    J

  A 65.0-kg firefighter climbs7+sv+w ,m yao;gbzz/g c)gsy8 a flight of stairs 20.0 m high. How much work is required? + s),cybs z7gzo+ v8awggm;/y    J

  A 1300-N crate rests on the floor. How much work is required to move i7b2:3 5zl/ /kcwpbkt1eb2e sjlieej9t at constant speed (a) 4.0 m along the floor against a friction force i2l1ee/jkbbe97: 53 tpl/ bwj2cskezof 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did ,kgnd h.h5t-hc5lys6 the movers do (horizontally) pushing a 160-kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of fric d5 ,-sc.nthk5ghl6h ytion was 0.50?    J

  A box of mass 5.0 kgfdg813 .javns is accelerated by a force across a floor at a rate of for 7.0 s. Fnaj8 .gsfdv 31ind the net work done on the box.   J

  Eight books, each 4.3 cm thick with mass 1.7 kg, lie mk8v. x51o* (g ubzj6k1xebdwjo-e g 7g 4h9uxflat on a table. How much work is required to stack them one on top ogo j1wj68k.uxohm* b59bkuxx74dg e( - e1 gzvf another?    J

A lever such as that shown in Fig. 6-35 can be used to liff objects we might5g c 5 g8i/jj3k6kc/ hpiph*oeurg0c, not otherwise be able to liff.3*uh/g5k io 8 r06cc,/kpgjg jehpic5 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 3.6 m down a 28° incline and is kept from ad 6gfxp)w4 -nd v.z;oow3 qdn6-d +segccelerating by a man who is pushing back on it parallel to the incline (Fiqzd-64oxg gvf+n opnwsd63).dd w;e-g. 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 helicoxjhdn38 +,gc* v/.eoksgt 96nzlp jt0pter of mass M an acceleration of 0.10 g upwt.0 3jj ,z8t spxed*g 9+6c knglovn/hard.    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 sn+ dump9w1.ris 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, acting along the x axis, varies as shownjd g+.wqln: 2 t)cg(qh in Fig. 6–37. Determine the workj(td .+ hq glwn)qgc:2 done by this force to move the object (a) from x=0 m to x = 10 m    J
(b) from x = 0 m to x = 15 m    J

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

  The net force exerted.ty;b6ay 5rj a on a particle acts in the $+x$ direction. Its magnitude increases linearly from zero at
$x=0$, to 24.0 N at $x=3.0$ m. It remains constant at 24.0 N from $x=3.0$ m and then decreases
linearly to zero at $x=13.0$m. Determine the work done to move the particle from $x=0$ to $x=13.0$ m
graphically by determining the area under the $F_x$ vs. $x$ graph    J

  At room temperature, an oxygen molecule, with mass of i8ge2 p9pov/n i-:*)zomzbjg$5.31\times10^{-26}$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 ir ,p8e j),tde y3-xmuvs doubled, by what factor has its speed increased? $ \sqrt{a}$ a =    (b) If its speed is doubled, by what factor does its KE increase?   

  How much work is required to(ncu7jiqpk g( euj 6x5e uv0)/ 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 t 15rcyhclei+ y8 4(xfdraveling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whose string exerts an avbu*hlxj : (x s/yic02lerage force of 110 N on the arrow bhu i0 j l/:*xyc2(lsxover a distance of 78 cm. What is the speed of the arrow as it leaves the bow?    m/s

  A baseball (m=140kg) traveling 32m/s moves a fielder’s glove backward 25 w(tv2+: :5nbq29g rtwsjdtqo cm when the ball is caught. What was the average force exerted by the balq s2tgvt 25n:wrbd (j9 tw:oq+l on the glove?    N

If the speed of a car is increased by 50%, by what factor will its o6 a: 6y p9d)rp-5p9e;ugsisiowa pn*minimum braking dpsrp oe;9u* yn9podi 5-w:6)iaa gs6pistance be increased, assuming all else is the same? Ignore the driver’s reaction time.

  At an accident scene on a level road, investigators measure a.8k25z7ka itdszg mmnfy 5n04zp -zj: 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 deter7ti55 j azzz kyn2kg8m0:fms4dpz.n-mine 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 pitched at ;35xrzjd 5dsds x9y6x By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch, if the distance between the plate and the pitcher is ad 93ds 55dyj;xx6rzsxbout 15 m.    N

  How high will a 1.85-kg rock go if thrown straight up by someone who doeutq d xa3pv:7v7nd p3. uc2tx.s 80.0 J of work on it?v dnvtatuxc3p u. 27:x.qpd73 Neglect air resistance.    m

  A 285-kg load is lifted 22.0 m vertii0g uyl1 p6*xpcally with an acceleration by a single cable. u 0x1*pg6 lypiDetermine
(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 6ghqo,:kg qlw(p/n5rstiffness constant, k, of 440N/m How much must this spring be stretched to store pqwrg,q:(o n5 g lk6/h25 J of potential energy?    m

  A 7.0-kg monkey swings from one branch to another y+i (h(6z zss5bsuqwk;(8 a ne1.2 m higher. What is the change in potential ener ei(uaw6s ky 8bqn(hz5+(ss;zgy?    J

  By how much does the gravitational potential en z6,yyd3w zx .*lsse a1aoh2liq(7 s7tergy of a 64-kg pole vaulter change if his center of ma2lzaq ,*yh .lids6z( xy1 sse77ota3wss rises about 4.0 m during the jump?    J

  A 1200-kg car rolling on a horizontal surface has sp7nh/2/, tfrn y n/ o/sbtz2ezfeed v = 65 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the sb/n/7oznt nt,2/he 2 zsf /frypring?    N/m

  A 1.60-m tall person lifts a 2.10-kg./ko)lf. t0uemr y9rv book from the ground so it is 2.20 m above the ground. What is the potential energy of the book relaelf) .rym09v/kort.u tive 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 andx0x2;qb uht zy- k,q 21gsjrybs1ni; * climbs to the top of a 3300-m peak. k sq;z tbxjq,20 - 2ghnbixury*sy;11
(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. Tgxmk) +jprm7 int) :*xhe end of the spring is next to the 15-cm mark on the ruler. If a 2.5-kg mass is now attached to the end of the spring, where will the end of the spring line u:x pnrkt7)+*ximjmg) p with the ruler marks?    cm

  Jane, looking for Tarzan, is running at top speed (5.3m/s) and grabs a vine ha9b) wgm ulda:s9qh,,v:x 9xd *t im(ownging vertically from a tall tree in the jungle. How high can she swiq(d h:ui:,9mgod s x )wat* 9,wblm9xvng upward?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from rest, sy/6rb7 lch-he-ckw+ 1o.of s 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 given a shove up a frica6q3g-xqpr:lq:x :hgtionless 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 transformez ,0-xzb4by n1opngxq+(uy5 md into gravitational potential energy without the aid of a pole. With what minimum speed must Fran leave the ground in order to lift her center of mass 2.10 m and cross , o(bxn q4yxbzz0m 15- yug+npthe bar with a speed of 0.7m/s.    m/s

  A 65-kg trampoline artist jumps vertically upward from the topw5c yr:(7n5ne,fkaw p of a platform withe 7k, r an5(fcnyw5:wp 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 (igneo .1vuadkz l6 8q.ag0ore its mass), 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 080 lu6qoea.d.g1vkz a .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 slim hicuo/u wg;qtu 62(dpwysh7+: t5,hdes 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 radius is r), from what minimum heightc /miuh6otp: 5 7tw ;(q,su2 uwdghy+h h must it be released?    r

A block of mass m is attached to the end w0 z5plsf6 .kaof a spring (spring stiffness constant k), Fig. 6–40. The block is given .5ks l6z 0wpfaan 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 cor9i /u: lnvb9pxit tz()6,w 7gkzzy 4cnd whose unstretched length is 12 m, and fall wkn 6)lpv 9nc:b /tyg( z7xu,4itzi9zs 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 dragged up 7jyot4u lq 8wt0 .ee*3zw3ypzto point 1 where it is released frompwy .te4q jel 0*w8yozz3t73u 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 **qh- s 98neytoxl2kwwith a speed of 12 m/s at an angle of 33 $^{\circ} $. (a) What is its speed at its highest point    m/s
(b) how high does it go? (Use conservation of energy, and ignore air resistance.)   m

An engineer is designing a spring to be placed at the bo 6+0kzyqq/ crcttom of an elevator shaft. q0+ r/6ckzcyq 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 and passengers.

  A cyclist intends to cycle b ((pargg*xc1up 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 dire96gnsj1e :/x vush +3o;fqvkbctions, collide head-on and come to rest. How muchxho+/ e:j3v 6sk qfgub9; sv1n thermal energy is produced in this collision? $a\times10^b$ J a =    b =   

  A 21.7-kg child descends umge,r;5a kwj,8 l0dp/e 0dvya slide 3.5 m high and reaches the bottom with a speed of 2.2m/s How much thermal energy due to friction was generated iue0mvje k wl 0r;,aydd/g,p58n this process?    J

  A ski starts from rest and slkhpek5h;mj0zb8l) jp0 yx;i 8ides 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 bk 7smxb* i5z-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(7dlyv f sv3.jk/rj *l6v xwl)70v kax height of 2.0 m, and it bounces back to a height of 1.5 m .r 7svl 3xk j6l*xyw0dav()vjfvkl7/.
(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 fro;hoxzisj5r*;ye ,rk . m 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 next 15 m the coei z; kjy5r.e,xrohs* ;fficient of friction is 0.30. What is the final speed of the crate?    m/s

  Suppose the roller coaster in Fig. 6–41 passes point 1 with a speed of 3 np:*bgrn4m cj6-h;fqwv /lg If the average force of friction is equal to one-fifth of its weight, with what speed will it reach point 2? The distanbc-rjq; nplgm* /h nw v:g43f6ce traveled is 45.0 m. $\approx$    m/s

  A skier traveling 12m/s reaches the foot of a steady,gybs) +8l 6f3wq6 abarn dmqu j31k1y upward 18.0 $^{\circ} $ incline and glides 12.2 m up along this slope before coming to rest. What was the average coefficient of friction?   

  A 0.620-kg wood block is firmly attached t 6gti*,wu 2s0aue: rajo a very light horizontal spring (k=180N/m) as shown in Fig. 6–40. It is noted that the w*,i2gj easuu0:r6at 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 kinetic friction between the block and the table?   

  A 280-g wood block is fi*xwmsypt g0a0: qd;gnx 41r m-s,x)h4i (djswrmly attached to a very light horizontal spring, Fig. 6–40. The block can slide along a table where the coefficient of friction is 0.30. A y(nsrxqmx4*ag 1w;h4,p-s d 0diw)g jx0s:tmforce 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 shuttle1 d9 -+wgss8-uyan)g fa2hnem used a “glider” (mass of 980 kg including pilot) that was launchna+gs eas 28m nd-)uy -w91fhged 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 pmo 9f d: y1 s4fz0y(2sz5dmcw315-kg piano to a sixth-story windo5zsc:94ymf dsp2yw o (10z dmfw 16.0 m above?    s

  If a car generates 18 hp when traveling at a steady 88km/h what must be thpv095 zr1vh3as slr a;e average force exev zs5hvpa9s0ra 3lr1 ;rted on the car due to friction and air resistance?    N

  A 1400-kg sports car accelerates a +v2y+p);25 ts, vv mkju3yhrr(rhfs from rest to 95km/h in 7.4 s. What is the average power delivered by the h+22rv, (hf;5pymv v ) ratsuy+r3skjengine?$\approx$    hp

  (a) Show that one British horsepower it awtjvg8g)1 71t5ysg vu,r6$ \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 “ d5av4x5:sstt4pe 6 )x q/sinikilowatt-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).orhvp-wx.q -kg car slows down from to 65km/h in about 6.0 s on the level when it is in neutral. Approximately w)hwqrp.o .x -vhat power (watts and hp) is needed to keep the car traveling at a constant 75km/h.    hp

  How much work can a t z5 4gs9vw*4 phqxf.u3.0-hp motor do in 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg shot from rest to 14m/s If this moxg s piw 6n 12xyk4zd40vf:f2 tps:*uftion takes 1.5 s, what average power wafxi1v p0wg d psk*fst2:u y4fxn6:4z2s developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute through a height o 9mc4;:auyvwke+oa *p f 3.60 m. What output rat94puov:ac mky;w+*ea ing (watts) should the pump motor have?    W

  During a workout, thy s-o3u.ui0 jxe football players at State U. ran up the stadium stairs in 66 s. The stairs are 140 m long and inclined at an anj-i3syu.o0 x ugle 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 2y,mlcdh 0qd. climb a 6.0 $^{\circ} $ hill to maintain a power output of 0.25 hp? Neglect work done by friction, and assume the mass of cyclist plus bicycle is 68 kg.   m/s

  A 1200-kg car has a maximum power output of 120 hp. How steep :(1gig/tn(vyn vbqf 0hh:x 1q j1fx-i a hill can it climb at a constant speed of 75km/h if g1g/hx(h(j0i i 11 xfytbqv::n-n qvfthe frictional forces add up to 650 N?    $^{\circ} $

  What minimum horsepower must a motor have to be able to drag a 310-kg box alo/wc0noyxgsq k 4- j j)ah0pw+(ng a leveqng4k -psjc y+0x /(awh)0ojwl floor at a speed of 1.2m/s if the coefficient of friction is 0.45?    hp

  A bicyclist coasts down aw-k)9 1gwyqb ej ()asn 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 buixp/8qfc3h0byla) 4 owlt “5mi/h(8km/h) bumpers” that are designed to compress and rebound elastically withou w fq0y3h4x/8acbpl) ot 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 wall? $a\times10^b$ N/m a =    b =   

  In a certain library the first sheidwv 9lw-ey(:lf is 10.0 cm off the ground, and the remaining four shelves are each spaced 30.0 cm above the previous one. If the average book has a mass of 1.5 kg with a height of 21 cm, and an average shelf hew :d( wi9-vylolds 25 books, how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start? $\approx$    J

  A film of Jesse Owens’s famous long jump (Fig. 6–42) in the 1936 Olympics h p(+zpu5a0d7+szd z lshows that his center of mass rose 1.1 m from launch point to the top of the arc. What minimum speed did he need at launch if he was traveling atld+( 5zpzads +7p0zuh 6.5m/s at the top of the arc?   m/s

  The block of mass m sliding without fricti-uoac s67 of0 k.;pne oly.(myon along the looped track shown in Fig. 6–39 is to remain on the track at all ti.ayluso o0n.o7y;fm 6 c-epk(mes, even at the very top of the loop of radius r.
(a) In terms of the given quantities, determine the minimum release height h (as in Problem 40). Next, if the actual release height is 2h, calculate    r
(b) the normal force exerted by the track at the bottom of the loop,    mg
(c) the normal force exerted by the track at the top of the loop,   mg
(d) the normal force exerted by the track after the block exits the loop onto the flat section.   mg

  An airplane pilot fell 370 m after jumping from an aircraft without his parani+b 0n/.7wpqr ay ,teqtg n9bdiy/tn/6( ja:chute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the pilot’s mi9jq i teqnn+ 7t /ap0 :6byyn/a/gn wdr,tb.(ass 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 endy 8fk 3+te eok g/dz+o;um(wh7 is fixed (Fig. oz+/(+8y7 th;3wegu dkofkme 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-mh28mf*0autfc g43qw .jm 6g q pna(uk4-high mountain. The climb is made in 5.0 h starting at an elevation of 2300 m. Calculate (u km 4g* q.jh4fut682af 3qg0pwn cam
(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 92k(u+io o3h*af pje m420-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 t /rd5,f y6dndjhat its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (verticald5dr f ,/dj6ynly) higher, estimate the power needed.$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and fallshrxqkmtd 0wm9 )dg;m.le2opfd()37g vertically 81 m before strikimok hd20f t )m)xemgd9.3gw;d q7p( rlng 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 wq9a bu-f -v/j-24bnil3l caj sith a circular vertical loop (Fig. 6–44), the difference in your apparent weight at the top of the circular loop and the bottom of the circfl-nacq9s j -ua- 3lj24bv /ibular 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 work, how hi v9x4.c 3j0jrwg id2ysgh could an 82-kg man climb a ladder sgc2xy0rj d 3w9vi.4jif 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 upward angle ;k-xakj +h)f4b: ncotvdv72g 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 wid99s,s ds:a hg2r5escale, the 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 height of 1.0 m, what does the scale wa5,: diss9ges2drh 9read at its peak?    N

  A 65-kg student runs at 5m/s grabs a rope, and swings out over aue fj*1j)hi)2 j9+zn0acu ipv lake (Fig. 6–45). He releh2fv 0j)ujie) n *iua1z9p+cjases 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 athlete climbs a venmk t kxmq(:s18z)xn)-3r kebrtical distance of 5.0 m in 9.0 s. What minimum)n- z)k1net :mqxmbk(skr x38 power output was used to accomplish this feat?    W

  Some electric-power companies use water to store energy. Water a * 0;egos:bzfkx3ze j i,-fy0is pumped by reversible turbine pumps from a low to a high reservoir. To store the energy produced in ix0f:;kz0 oz gej* sf-a e,b3y1.0 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 con(i9c6 tdku4cqy st8d5 stant k is cut in half. What is the spring stiffkdy (stc 69 uqdci458tness constant for each of the two resulting springs?   k

  A 6.0-kg block is pushed 8.0j(ffj3k5ot7y:+ if qp m up a rough 37 $^{\circ} $ inclined plane by a horizontal force of 75 N. If the initial speed of the block is 2.2m/s up the plane and a constant kinetic friction force of 25 N opposes the motion, calculate
(a) the initial kinetic energy of the block; $\approx$    J
(b) the work done by the 75-N force; $\approx$    J
(c) the work done by the friction force;    J
(d) the work done by gravity;$\approx$    J
(e) the work done by the normal force;    J
(f) the final kinetic energy of the block.$\approx$    J

  If a 1500-kg car can accelerate from 35km/h to 55km/h in 3.2 s, howz2y8dp ei -bkl*2+ibb long will it take to accelerate from 55km/h to 75km/h Assume the power stays the same, and neglect frictional lossy8ie 2lp+i2 b -*kbbzdes.    s

  In a common test for cardialiyf w hu3i7e f1wu,z / i5jn865fe;hcc function (the “stress test”), the patient walks on an inclined treadmill (Fig. 6–46). Estimate the power required from a 75-kg pa/jh7f6 zuh51uf53wi 8 fiye niw ,cel;tient 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 500d 6q/se :sh)ut-kg rock vertically upward a distance of 500 m, what was its vt: )hu6qd /esselocity when it left the volcano? $\approx$    m/s
(b) If the volcano spews the equivalent of 1000 rocks of this size every minute, what is its power output? $\approx$ $a\times10^b$ W a =    b =   

  Water falls onto a water wheel from a height of 2.0 m at asp -) pz znr)mk,j1z/;7bz mjd rate of 95kg/s (a) If this water wheel is set up to provide electricity output, what is its maximum p7z,bpjdn /zz1 zj r)-m sp)k;mower output?    W
(b) What is the speed of the water as it hits the wheel?    m/s