In what ways is the word “work” as used ino1 t:a 34fydcx b,sn 8no.t/en everyday language the same as that defined in physics? In what ways is it different? Give examples ocey,41/:8 nt3n.ota obfnds xf both.

Can a centripetal force tq 8upxrwj9e 5e- o.nn/ vs8ym r6+:ypever do work on an object? Explain.

Can the normal force on an object ever do work? Exptjb rc5g-n l5-lain.

A woman swimming upstream is not moving with respect to the sho:4/qba,vi .mo8( qqgp(q, slp rfb*jrre. Is she doing any work? If she stops swimming and merely floats, is work done onr.,qaf gpi*b4, s8b qqjqr/:v(p l(mo her?

Is the work done by kinetic friction forces always negative? [Hing- 4e0sb pgr1yt: Consider what happens to the dishes when you pull a tablecloth out fsbep14 r-0 yggrom under them.]

Why is it tiring to push hard a7v.xe8a9)n 5q ryrxr kgainst a solid wall even though you are doing no xrnx.vqr5y k8e 9r7)awork?

You have two springs tha6nt02qjv7fk s. 56c zyxh- mact are identical except that spring l is stiffer than spring 2 5ny6 xfmj -.q76zhcsctak20v $(k_1>k_2).$ 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 sl .+wbz xo9yez ca;w3x.yt3rsg-e ;0l hide on a frictionless surface (Fig.6-30). The block starts from rest at þoint A, and by the time it has traveled a distance bwc3ezsx-y;e o yz; .39 wh0+alx trg.$d$ 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 gravitationa *dkchr6n*r:/b md )fil potential energy change when ykc rdf **d n/)ih:6mrbou jump as high as you can?

In Fig. 6–31, water balloons are tossed from the roof of a building, all w jyn;u0ikyt: sn3)kbjco0.nb m/l k1(ith the same speed but with different launch angles. Which one has the highest speed3k(lnc)/kmoy; t0j1:n.niub0s kybj on impact? Ignore air resistance.

A pendulum is launched from a point that is a height h above its lowest point higz -lfh8z83q.lc.t 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 cl 8fq. -i8hzzgl3th., 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. l07tiv-ctjm +,fpb o on a table. If you compress the spring by pressing down with your hand and then release it, can the spring leave ti t0+p.7t-b ,o cjlfvmhe table? Explain, using the law of conservation of energy.

A bowling ball is hung from th-g3d ;dktejy 9ii9rh; e ceiling by a steel wire (Fig. 6–33). The instructor pulls the ball back and stands against the wall with the ball against his nose. To avoid injury the instructor is shd;te;gir3 ijy9d-k 9 upposed to release the ball without pushing it. Why?

What happens to the gravitational potential energy when hbscyk d ;65;n v8ucoz/a;ex-water at the top of a waterfx;5n/;ou szbc ea vck-d;y6h 8all falls to the pool below?

Describe the energy transformations when a child hops ak 709pf 9wxjuvround on a pogo stick.

Describe the energy transformations that tai(w4.w (g3op:j9u.j eprqirwu0n s6 fke place when a skier starts skiing dowi (rnwpfswgi j 0qou3u9j(.:.4r6p wen a hill, but after a time is brought to rest by striking a snowdrift.

A child on a sled (to/my-tc y,r )kptal 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 fy-y/rc m k),tpriction, and (b) there is friction (deep snow)?

Seasoned hikers prefer to step over a fallen log in their path rather than steppfmec6e;1zqiq6f nb93ctd sk* a)bt:5ing on top and jumping down onca e bznfqm5tiq6 et6;13k*bs9dcf: ) the other side. Explain.

Two identical arrows, one with twicy(ngy.dq u (64ecz udteu pz d-r* 6,riu6s*o+e the 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 how much farther than the sl oe. *, udipn*uzt+uugz46s (dr6cd -yq er6y(ower arrow? Explain.

Analyze the motion of a simple swinging pend/ih ou)o*nic :dw9; ddulum in terms of energy, (a) ignoring friction, and (b) w) udcd nooi:h/ 9i*d;taking friction into account. Explain why a grandfather clock has to be wound up.

When a “superball” is dropped, can it rebound to a height greater tha*j9ig hvc6jy xe-0 kzmzm-3:w.zn r3bn its origigyj0:c 3x9.n*riz-e k-mwbvzz 6 3hjmnal height? Explain.

Suppose you lift a suitcase from thpp8x6myq( 6 izqpm9o:e floor to a table. The work you do on the suitc698q6:mqyip x o zp(pmase depends on which of the following: (a) whether you lift it straight 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::qr/ht ; a,*xdxssed rather than the work.

Why is it easier to climb a mhd6q;)uo,q0 mht6oo o2 cgc( wountain via a zigzag trail than to climb straight uc;ow2 od6moq(huch )0oq, gt6 p?

Recall from Chapter 4, Example 4–14, thaazpg , s( na +bbtx+y.1/q4rdrt 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, hows4 rg1pzx ,a+ntd+b( yb.q r/a much rope must be pulled up? Account for this, using energy concepts.

  How much work is done by the gravitational for 3y lazxa 7 u6t+tv.xklcygj c/+kn.)7ce when a 265-kg pile driver falls 2k txcvyu/ll6y+. gj7 7kt.a)+c z3an x.80 m?    J

  A 65.0-kg firefighter climbs a flight of stairs 20.0 m high. How murggd 90 n+: ztyv z3sh.yt*i,ijwj+4u ch work is reqd twzh 4v+isg,n :*i y+j9yrtu.03gjzuired?    J

  A 1300-N crate rests dkw/ ug2mcy*(yd ,nw8u3e3w aon the floor. How much work is required to move it at constant speed (a) 4.0 m alowgw*m8yaeck(n ,u y32d/3d uwng the floor against a friction force of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did the movers do (horizontally) pushing a 160og(yoj+2:d kag t)r +l-kg crate 10.3 m across a rough floor without accelerd ggoy +:ar+2)lktjo(ation, if the effective coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is acn+8m;adok4c lr 8 *blccelerated by a force across a floor at a rate of for 7.0 s. +*; cdl4rck nba8l8omFind the net work done on the box.   J

  Eight books, each 4.3 cm thj weg 9yrs6r6 h(9ggn4ick with mass 1.7 kg, lie flat on a table. How much work is required to stack them one on top 4shy9gwr6jre6 g9ng(of another?    J

A lever such as that shown in Figa(6; mdoivg wa3fe2/a. 6-35 can be used to liff objects we might not othera;2 af e(gv6oda m/w3iwise be able 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 3.6 s 5q li3k-zoa7uizh).6, zdajm down a 28° incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig.-.a 3ik6oqdl)ji z,za7ush 5z 6-36). The effective coefficient of kinetic friction is 0.40. Calculate:
(a) the force exerted by the man,    N
$(b)$ the work done by the man on the piano,    J
$(c)$ the work done by the friction force,   J
$(d)$ the work done by the force of gravity,   J
$(e)$ the net work done on the piano   J

  (a) Find the force required to give a helicopter of mass M an a0:l iyxo/ 3;tomjxo c*cceleration of 0.10 g0t ioy3xol/c;: *moxj upward.    Mg
(b) Find the work done by this force as the helicopter moves a distance h upward.    Mgh

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

  In Fig. 6-6a, assume the distance axis is linear and tqzr14)grx0yv vd9 (y lhat $d_{\mathrm{A}}=10.0$ 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 a2by1km6d 1rcp t- q6evxis, varies as shown in Fig. 6–37. Determine the work done by this 6e-v6ydkr m1ptbc 1 q2force 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 bw4 )zc*3 iodwparticle 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 oxynvm8kv 8w v /k.ptv0/2vcvs0 xgen molecule, with mass of $5.31\times10^{-26}$typically has a KE of about$6.12\times10^{-21}$ J .How fast is the molecule moving?    m/s

  (a) If the KE of an arrow is doubled, by what fa3r3hdt 0. x.b f*rgshfw0grdc-0mb l/ctor 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 sto;;0bf 6rpl nktp 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 af- ep-4yomff ,1sau1qt 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whose stkhl; lgs4- )eoring exerts an average force of 110 N on the arrow over a distance of 78 cm. What lkoges-lh 4);is the speed of the arrow as it leaves the bow?    m/s

  A baseball (m=140kg) traveling 32m/s moyp/biza .va 3 0.v0x4wgfckm+ves a fielder’s glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glovva i v4+.0.w b 3ak/mpyxzg0fce?    N

If the speed of a car is increased by 50%, by what factor will its minimum brak8w -y,pcnrg c,ing distance be increased, assuming all else is th8g-,pccn,w y re same? Ignore the driver’s reaction time.

  At an accident scene on a level road, investigators measure a car’s sm 7a4sf3gjuu0 kid mark to be 88 m long. The accident occurred on a rainy day, and the coefficient of kinetic friction was estimated to be 0.42. Use these data to determine the speeda sujm4u3g0f7 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 ,( 1 1ubsdfrlj(wd7kz.25 kg is pitched at By the time it reaches the plate, kdr(j 1 d1,z s(fuw7blit 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 about 15 m.    N

  How high will a 1.85-kg rock go if thrn;9;/6)b.:tjlphkh my l7.gz 6eoni yu trew7own straight up by someone who does 80.0 J of work on it? Negletz6bw/eplh7 gm9 r ji ye:.t;ok;l.) unn 7hy6ct air resistance.    m

  A 285-kg load is lifted 22.0 m vertically with an acceleratil 4jxv5u58 vzvvwke/1b5+oqlpi.n 4m on by a single cable. Determine/1n v5ivw+5 kql mz4v8 xe5p4bvoj. ul
(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, kh/re6 ,kj1xfjd70 nsn , of 440N/m How much must this spring be stretched to store 25 J of po,n dkhxjfns/76 j01re tential energy?    m

  A 7.0-kg monkey swings from one bra dz ,uf*tff3h5g29dmg8g sba/nch to another 1.2 m higher. What is the change idg,s9*/ 3a5tghgz fdmb 2 f8ufn potential energy?    J

  By how much does the gravitational potential energy of a 64-kg pole vau ym,w3:rj 4vzvb ; /4zsbnmhe)lter change if his center of mass rises about 4.0 m dur/m ,yb34 wvh m4v;ej)nr:zsz bing the jump?    J

  A 1200-kg car rolling on a horizontal surface has speed vol*u bm /ay95t( sib8a = 65 km/h when it strikes a horizontal coiled spring and is b9 usa* / b5ilmy(toba8rought 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-koa xoryjf8*gfpb 9i-23v )mn4b ;cfh+ /sy/npg book from the ground so it is 2.20 m above the ground. What is the potential energy of the book r f coj4ifnpysopa+; 98gh br/2-y/n)3m*bfvxelative 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 eleb vdy*-auo vn5 r5-tv1vation of 1600 m and climbs to the top of a 3300-m peak. 1vbu-*t-rv5 o5y nad v
(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 r i.j+lhx,3yz5uwi t ry c4;x6luler. The 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, w+ylz5,jirw4 i.;u lc6h tx3yxhere will the end of the spring line up with the ruler marks?    cm

  Jane, looking for Tarzan, im32c6 fwc 9.wkkc d06:wjj ktxs running at top speed (5.3m/s) and grabs a vine hanging vertically frm 3c: 60w2ck 9f tcjxjdw6k.kwom a tall tree in the jungle. How high can she swing upward?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from rest, slides down a friknyzcs3 p;l2 si ;x leh;j4.f2ctionless 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 qjbmi+ 0k;ll4 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, Frals)7 bqn( rm+0qd m;awyck.)kn’s kinetic energy is transformed into gravitational potenti()bqwmsqk ; k7rla d 0y+m)n.cal 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/s.    m/s

  A 65-kg trampoline artist jumps vertically upward fnh1dvs 9 8 y(eeqeter8) s21berom the top of a platform with a speed of 5.0 m/s. (9et1s 8d8ybe q 2sheen1(ev)r$\alpha)$ How fast is he going as he lands on the trampoline, 3.0 m below (Fig. 6-38)?$v_2$ $\approx$    m/s
(b) If the trampoline behaves like a spring with spring stiffness constant 6.2×10$^{4}$ N/m , how far does he depress it? $y_3$ =    m

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

  A vertical spring (ignore its mass), whioa9cf , -xa9l9z0,.caeldalose spring stiffness constant is 950N/m is attached to a table and is compressed down 0.150 m. (a) What upwac .c 9l,a,ll 9z0fxi eodaa9-ard speed can it give to a 0.30-kg ball when released?    m/s
(b) How high above its original position (spring compressed) will the ball fly?    m

  A block of mass m slides withouxpfm b u5g2 sdk9tpslv)-a 7 *8xu/)aat friction along the looped track shown in Fig. 6–39. If the 9 )x ftu2k/)lv-bugpps8 xmsaa5d*a7block is to remain on the track, even at the top of the circle (whose radius is r), from what minimum height h must it be released?    r

A block of mass m is attached toa 1:nbut7zeu j,:ff;y the end of a spring (spring stiffness constant k), Fig. 6–40. The block is given an if7b;e:1u: nazjt,f yunitial 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 fu 8*y2ud.vs 1k:mcoqt rom a bridge. She is tied to a bungee cord whose unstretched length is 12 m, and falls a total of 31 m. (a) Calculate the spring stiffness constant k of.vu stqouyc8: 2dm1k* 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 upmjsore(y5 ( u, to point 1 where it is released from rest. Assuming no friction, ceysm(( , u5ojralculate the speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown w2t. be8(e6,p(r0jw( wug+h f3wfmkn7lsgt lrith 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 plah g9ot t.n,4amced 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 undergo an acceleration of no more than9mt4g ,hnato. 5.0 g when brought to rest. Let M be the total mass of the elevator and passengers.

  A cyclist intends to cycle up a 7.8z8/mph+:h8fwl lqd 6 a $^{\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 md/4)tbcz)b nft)uif v ,(vu;c*;ll v of mass 7650 kg and traveling 95km/h in opposite directions, collide head-on and come to rest. How much thermal energy is (bdtbf*lfn) z4c;tci) v/;m)u,v luv produced in this collision? $a\times10^b$ J a =    b =   

  A 21.7-kg child descends a sx f2 pwgq*))t .d nhi,lynic(4;(iekq lide 3.5 m high and reaches the bottom with a speed of 2.2m/s How much thermal energy due to frictnx)tei i h).w,pi y(qflnck (;g* qd42ion was generated in this process?    J

  A ski starts from restb ,s6 ir ex*,ouwxhg8)jau4 msk,z2;r(lw u:y and slides down a 22 $^{\circ} $ incline 75 m long.
(a) If the coefficient of friction is 0.090, what is the ski’s speed at the base of the incline? $\approx$    m/s
(b) If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level? Use energy methods.$\approx$    m

  A 145-g baseball is dropped from a jyexf-6bh,0vhqmg;/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 o(gdwh p+ g33mc1hr7x ef 2.0 m, and it bounces back to a height of 1.5 m.(x+1cg r d7hhg3 pwe3m
(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 a constantd9 - e j2nzyk/(hcc:cu horizontal force of 350 N. For the first c2cjz/ - 9 k(udyh:ecn15 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?    m/s

  Suppose the roller coaster in Fig. 6–41 passes puv476bpkiovt 7 h:+ma oint 1 with a speed of If the average force of friction is equal to one-fifth of its weight, with what speed wilvkb 4:ov7u 6mih7p +tal it reach point 2? The distance traveled is 45.0 m. $\approx$    m/s

  A skier traveling 12m/s reachesp u9,rz jbtwymaz9xblq3oo 3i44l 993 the foot of a steady upward 18.0 $^{\circ} $ incline and glides 12.2 m up along this slope before coming to rest. What was the average coefficient of friction?   

  A 0.620-kg wood block is firmly attach uzkd e:/wy em/ty*c6vi/w; +ued to a very light horizontal spring (k=180N/m) as shown in Fig. 6–40. It is noted that the/y;udckveu+:6e* y// t mwwzi 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 firmly attjrdoekdk3 b7zhj),u/4 /0ddg3:kx: u rudh:wached 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 force of 22 N compresses the spring 18 cm. If the sprin3,du )ugkh d dod j0r34/ k7wj hkzxr/u::dbe:g 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 ovl3m3npa m5x ,f 980 kg including pilot) that was launched horizontally at 50m 35m xln,pva30km/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 sivsb,+ 04 h(j fom4qbnsdpv5acz7-u8bxth-story window 16.0 , z7b5vbab(p4dcq ou8 js-shv 0n+mf4 m above?    s

  If a car generates 18 hp when traveling at a steady 88km/h what must be the 7qszg:3 gsi v1average force exerted on the car dz:sg3qg71 isvue to friction and air resistance?    N

  A 1400-kg sports car accelerates from rest to 95km/h in 7.4r- oncc4l,a4p i1kh *u s. What is the average power deliveu-riakh4, opc 1nl c4*red by the engine?$\approx$    hp

  (a) Show that one British 5o7)mdb xm; xhmz9kp8y:;cnn horsepower$ \mathrm{ft}\cdot\mathrm{lb/s}$ is equal to 746 W.
(b) What is the horsepower rating of a 75-W light bulb?    hp

  Electric energy units are often expressed in the f o pift92yzv s(*)gqy(-cw 9ecorm 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 slowsk8w/r5v5hd w/jl ih ;j 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 nrhwl5k8hiw;/v /j5jdeeded to keep the car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hpz n 3(p5khrb10h2pzj2cn owzkj6-g*q motor do in 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter acceler4y9d2o ova pj3ates a 7.3-kg shot from rest to 14m/s If this motion takes 1.5 s, p 4yd39jv2oaowhat average power was developed?$\approx$    W

  A pump is to lift 18.0 kg of water per xle+l3 v 9.h;kcljgh :ij i9z/minute through a height of 3.60 m. What output rating (w/9z;l ce i vjjilgh:k3+lxh9.atts) should the pump motor have?    W

  During a workout, the football players at State U. ran up the stadium stairs ir;x8awwa/gu:h 0t ji8,:z bcpn 66 s. The stairs are 140 m long zxb; ,w8c:w pg/iru0:taa j8hand inclined at an angle of 32 $^{\circ} $. If a typical player has a mass of 95 kg, estimate the average power output on the way up. Ignore friction and air resistance.    W

  How fast must a cyclist climb a 6.0k98f,ms/kb drsy+ hn 2 $^{\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 tk*db m*sy fjn0a ./h1rg:7zhoutput of 120 hp. How steep a hill can it climb at a constant speed of 75km/h if the fricjg/.ry7:t a*1mbhkns h*dz0f tional forces add up to 650 N?    $^{\circ} $

  What minimum horsepower must a motor have to be able to drag a 310-kg8xua 28i*3vmp* 7gwm drnhi8y box along a level floor at a speed of 1.2m/s if the coevi *u8rxy 2am*7w8 d3pimghn8fficient of friction is 0.45?    hp

  A bicyclist coasts down7 +n+txi:q8szw0 a cklxow q18 a 7.0 $^{\circ} $ hill at a steady speed of 5m/s Assuming a total mass of 75 kg (bicycle plus rider), what must be the cyclist’s power output to climb the same hill at the same speed?    W

  Designers of today’sjh6 x1nj71xxf cars have 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 po7jjx xnh1f x61int, 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 fig 6sju:5swa(t g;x.le rst shelf 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 hee;sx : l6.uj(wa gst5gight of 21 cm, and an average shelf holds 25 books, how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start? $\approx$    J

  A film of Jesse Owens’s famous longzz6 c*(j ogu.8iq yl**oda p9f jump (Fig. 6–42) in the 1936 Olympics shows that his center of mass rose 1.1 m 8o yg9jz*flp ui6.ao(q *z*cdfrom 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 witbj ak 3r;fxz7-.l 7kaahout friction along the looped track shown in Fig. 6–39 is to remain on the track at all times, even at the very top of the loop of radius r. k7 la-7baazrjf ;.3k x
(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 swn.v1-a8 dwwparachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assu.waw1-n8wd s vming 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 otherhh0rjc d5q2bq96 pf)c 2ujy3e end is fixed (Fig. 6–jhjq)qc 03hu5 rd9e22c y6bfp43).
(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/g5sw62 mb9ub5 utxe h to the top of a 3700-m-high mountain. The climb is made in 5.0 h starting bs29 ux6b5t u5 ghemw/at an elevation of 2300 m. Calculate
(a) the work done by the hiker against gravity,   
(b) the average power output in watts and in horsepower,   W    hp
(c) assuming the body is 15% efficient, what rate of energy input was required.    hp

  An elevator cable breaks when a 920-kg e+-t7rmuxy-nqvm sf, y,x5r ,iu6q g*j levator 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 Caliukuhl nlr;dhxrc0/i)q:6 i4t6/ r ha6fornia claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the powe al;rthr/i 6 60:6kc)hnr idq/hlu4ux r needed.$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and falls ver; -no4o;+socnh g :od/y zx:ictically 81 m before striking the turbine bladx:csnzo yh:;+ng- 4cooid; o/es. 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 div,3tbds e(8bpfference in your apparent weight at the top of the circular loop and the bottom of the circular loop is 6 g’s — that is, six times your weight. Ignore friction. Show also that as long as your speed is above the minimum needed, this answer doesn’t depend on the sizpsbe(8v,d 3tb e of the loop or how fast you go through it.    mg

  (a) If the human body could convert a candy bar directly into atag,y k;zjy34 -*rkxwork, how high could an 82-kg man climb r*tzy3-ky ;,4g jax aka 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 z-l3xiw v:a7.g) tngeat an upward angle of 45.0$^{\circ} $ from the top of a 165-m cliff with a speed of 175m/s What will be its speed when it strikes the ground below? (Use conservation of energy and neglect air resistance.)    m/s

  If you stand on a bathroom scale, the spring inside the scale compresses 0.60c0(o epdhay)/m/zi - r mm, and it tells you your weight i(p 0mh-i/za/e)ro d cys 710 N. Now if you jump on the scale from a height of 1.0 m, what does the scale read at its peak?    N

  A 65-kg student runs at 5m/s g/, -;t+a fq8ynecw+yvvnenlfzn(1 o+rabs a rope, and swings out over a lake (Fig. 6–45). Heo nnvnal ++yyqv n8c,+e1et(f-wz/;f 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 athlete climbs a ve3w+m0y;ti z;jp4nv-0gu sjydrtical distance of 5.0 m in 9.0 s. Whadyjpv 3 mw;sg4z+ tu- 0y;ni0jt minimum power output was used to accomplish this feat?    W

  Some electric-power companies use water to sto8b a3s yb6mn0ire energy. Water is pumped by reversible06m 3ya nbi8bs turbine pumps from a low to a high reservoir. To store the energy 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 stiffnh totegkbmk(6h -,c6l so2 xp.q. (x1bess constant k is cut in half. What is the spring stiffnes, p 6sbhhm( otq6b(c.2lk1 xk.x- geots constant for each of the two resulting springs?   k

  A 6.0-kg block is pushed 8.0 m h. tpl vcobcl 7y,+nu)7e9z*6ch4ug u 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 fij;yuu8 hwm -y05kf e7rom 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 kh07f-y w8 5uuymi;j estays the same, and neglect frictional losses.    s

  In a common test for cardiac function (the “stress test”), the patient walks on /0j a6/.kme2aip sp lq1 .m8-yctnhjhan incliaqp/h lsphjt01.jm2/ c e8yi- .ak6m nned treadmill (Fig. 6–46). Estimate the power 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 : cbg bx+ju8zwk c,x3*vertically upward a distance of 500 m, what was its velocity when it le 8zcub jwxkbgx, 3c:*+ft 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 whj8zr( oy .qijo myz-24ndjr) 3eel from a height of 2.0 m at a rate of 95kg/s (a) If th zdr(zj3y4nq 28y .jomj i)-rois water 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