In what ways is the word “work” as used in everyday language tqqf6 we7em45xduz 1: ahe same as that defined in physics? In whaaemdz: fq64q5e uwx71t ways is it different? Give examples of both.

Can a centripetal force ever do work on an object? Explak h6bt/3 5ugo a1ea4vgin.

Can the normal force on an object ever do workm/kxz05 qd/elg)bd g7:a m v)h? Explain.

A woman swimming upstream is not moving with respect to the shore. Is she doingv; t)ts5y0f( 0 gkar5ok fjqr5 any work? If she stops swimmiorr js gyf05ftt0 v;q5(k )5kang and merely floats, is work done on her?

Is the work done by kinetic friction forces always negative? [Hint: Cons+usswa keq mm/q4; k v:vq)6.bider what happens to the dishes when you pull a tablecloth ou4 bw /.avm+k qmkes:)6;su qvqt from under them.]

Why is it tiring to push hard against a solid wall even ha ;cju.t ,2 h30e/u(crpjp pu,djxx;though you are doing no wor /thh.0xjpu u( e,xrp3pd,c;;j ua2j ck?

You have two springs t su3.ofs+o k 4+rfmjm2stf u:.hat are identical except that spring l is stiffer than sprins:fo uufs3+ 4mfr.+ ko.2mjt sg 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 bloh hp u.mjn6f 66yglm/:5m4feb: 7prgkck that is free to slide on a :6/6ml4:gfgmy u6erfkmp n.5 h hj7pbfrictionless surface (Fig.6-30). 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 potential energy change3cdvge*e9x dae-w7 v1p0v j(s when you jump as high as you cae *1x(3 dvevdvejg p-w9c07san?

In Fig. 6–31, water balloons are tossed from the roof of a building,d 0io;sr;c3mr9 r *i;kgw:hgh all with the same speed but with different launch angles. ;;r m3 ;riosg9:ghr0cwd*ikh Which one has the highest speed on impact? Ignore air resistance.

A pendulum is launched from a point that is a height h above its 7meb*;uk ;wl ilowest 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 i ;mw7kl;eu* bpendulum is directed upward along the trajectory, and on the second launch it is directed downward along the trajectory. Which launch will cause it to swing the largest angle from the equilibrium position? Explain.

A coil spring of mass m rests upright on a tabv 3llj ,,82e-dtbuc gt +3bjllle. If you compress the spring by pressing down with your hand and then release it, can the spring leave b8jv,3u ldlt ,3j g2ltbec-+l the table? Explain, using the law of conservation of energy.

A bowling ball is hung from the ceilin,c:k 2jiin opiue)5e08fu0qeg by a steel wire (Fig. 6–33). The instructor pulls the ball back and stands against tu , 8:ueic2ojf5iqp00eki )enhe wall with the ball against his nose. To avoid injury the instructor is supposed to release the ball without pushing it. Why?

What happens to the gravitational potential energy when w3d4iohfp6 x fx1cc76dater at the top of a wapc36 6xfi ddc7 fh1o4xterfall falls to the pool below?

Describe the energy transformat)8d;qs*orrt0 r (xxe zions when a child hops around on a pogo stick.

Describe the energy transformations that take place when a ski f,.z*h)+yvmk hkue: yer starts skiing down a hill, but after a tim:e.v hf hyk, um)*+kzye is brought to rest by striking a snowdrift.

A child on a sled (total mass m) st+otdbmt.pns/i7 x3i kk)o))n0 m-trv arts from rest at the top of a hill of height h and slidonbv kx7)3 tk mstnm i-0) +por.ti)/des 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 ove) gmb5;pj 6qy2w tb 4lzh6vn:hr a fallen log in their path rather than stepping on top and jump:hyv;w tj)426q p lgb6bnh zm5ing down on the other side. Explain.

Two identical arrows, one with twice the speed of the other, are c0ngo g-mgz1. 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 slower arrow? g zg go1.-c0nmExplain.

Analyze the motion of zbr *om0numed)8pjs1 h-,mn 3 a simple swinging pendulum in terms of energy, (a) ignoring friction, and (b) taking friction into account. Explain why a grandfatherjue3omn1mbdn,m z8r- h*0p )s clock has to be wound up.

When a “superball” isgf9 g/y.uibpxm f j*5ru( : 98i7itwsl dropped, can it rebound to a height greater than its original height? Exp i9s9: f bi uix5/gm*gru8( tyfj.7wlplain.

Suppose you lift a suitcase from the floor to a table. The work you do pho k0*devsar(j7 x /-lvn;2uon the suitcase depends on which of the following: (a) whethr;ek7d j*(a 0hvxv/osl-2nu per 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 rather than the wor1su (lbisn urz5ic;.; n(eu7 ok.

Why is it easier to climb a mountain via a zigzag trail -yjf; bbfw(ag7ws5 f 5than to climb straight up?5jfgw; 7y( f bs-afb5w

Recall from Chapter 4, Example 4–14, that you can use a pulley and rop*2r3/da dg* 3gg xzplues to decrease the force needed to raise a h*gzd d3xp g/l 2ugr3*aeavy load (see Fig. 6–34). But for every meter the load is raised, how much rope must be pulled up? Account for this, using energy concepts.

  How much work is done by the gravitational force when a 265-kg py 0cen d9okb:js+e ; 3z6ttmu2ile driver falls 2.8 t2tcok: ze3dse+bj mn9u60 ;y0 m?    J

  A 65.0-kg firefighter climbs a flight ofvno tq v8abbep:7*;c 6 stairs 20.0 m high. How much work is requiredbt p nq8 boe*;6v7c:va?    J

  A 1300-N crate rests on the floor. How much work is required to move it at cons5z;nwn yq1 91h53eef/xmsr dytant speed (a) 4.0 m /n5yd1mqwhz ee fry19;nx s53along 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) pu9-d3leu )k -ka*rf** mmhzmc lshing a 160-kg crate 10.3 m across a rough floor without acceleration, iflm cl *9*-k-hz f u3r)a*ekdmm the effective coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is accelerated by a force acro 1b.vyja5w1kpq x e3vq/c2w e0ss a floor at a rate of for 7.0 s. Find the net work dov w13/eqjby 2051 xe.ca pqkwvne on the box.   J

  Eight books, each 4.3 cm thick with mass 10(c7g1 0:n sttrszw wcg:q cf).7 kg, lie flat on a table. How much work is required to stack them one on top of anotherczw0:g tc0ct)sr1:gn sq( w7f?    J

A lever such as that shown in Fig. 6-35 can be used to liff objects we mb-cwf9(. phy sight not otherwise be able to liff. Show that the r wsfphc yb-9.(atio 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 accelerating bc4 g;k+p xxy9iy a man who is pushing back on it parallel to the incline (Fig. 6-36). The effective c+x;ix g 9pk4ycoefficient 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-ttqk5/ sk d :7r k9tifv82jsv an acceleration of 0.10 g upward. rtjt:s5k8/s- v2k9d k7fvtiq   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 1kyv hsn, f2 gk.o *y/ir9xky5and that $d_{\mathrm{A}}=10.0$ m and $d_{\mathrm{B}}=35.0$m. Estimate the work
done by force $F$ in moving a 2.80-kg object from $d_\mathrm{A}$ to $d_\mathrm{B}$   J

  The force on an object, acting along the x axis, varies as shown in Faqz-, qb .a.ktig. 6–37. Determine the work done by this force to move the object (a) from x=0 m to x = 1q-,. bqkzaa t.0 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 aclzz*vkrt3fj u6kq/4(z4cj22 qv7p gz ts 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 )vo f.-i. kjmt :pbo,n$5.31\times10^{-26}$typically has a KE of about$6.12\times10^{-21}$ J .How fast is the molecule moving?    m/s

  (a) If the KE of an arrow is doubled, by what factor has its speed bgob1:a4 -h kvincreased? $ \sqrt{a}$ a =    (b) If its speed is doubled, by what factor does its KE increase?   

  How much work is required-;o-7tmvhnhaj8- hyh to 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 tra ;wp hsdc8a5y4)l.7rr (bthdsveling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whose string exerts an average force of 110 e5vvnh -q. q656jxs 3sdmzlqxhws7*2i )qv:fN on the arrow over a distance of 78 cm. What is the speed of the arrow as it leaves the h q*3mv v6 qqv6zn e:s5wh-fj5qd2i7s. xxs)lbow?    m/s

  A baseball (m=140kg) /dji ay/ p3h+itraveling 32m/s moves a fielder’s glove backward 25 cm when the ba/3p/i d jyi+hall is caught. What was the average force exerted by the ball on the glove?    N

If the speed of a car is increasotb;w/ibej l 7y (n+9aed by 50%, by what factor will its minimum braking distance be increased, assuming all else is the same? Ignore t9+ il(t 7be;b n/wyjaohe driver’s reaction time.

  At an accident scene on a lepo2)ju wo)3 pb-vgvp /vel road, investigators measure a car’s skid mark to be 88 m long. The accident occurred on a rainy day, and the coefficient of kinetic friction was estimated to be 0.42.voub3pv2p)wj gp/ )o- 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 pitched at By the time it reaches the viyyz5v. l j3 b:.7rjd1zml4o plate,by diy4z 5jl jrm.17zv.ov:3l 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 about 15 m.    N

  How high will a 1.85-kg rock go if th/:xmg0p8gi) a:vk ikz rown straight up by someone who does 80.0 J :8)p /xig: kimzg0k vaof work on it? Neglect air resistance.    m

  A 285-kg load is lifted 22.0 m vertically with an acceleration br m r3 3 bk1zm7e9-cqogv9owz5y a single cable. Determine vc-9 m rkqzz5eb37 3mog9orw1
(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, f1ovgp*vh5 1p,ggz rvme s9(9 4lb* jxk, of 440N/m How much must this spring be stret1g gvx1brhj4o5*,l9p*sf v9vge pz m(ched to store 25 J of potential energy?    m

  A 7.0-kg monkey swings from one branch ton/, k* r26i tlycq3be+3pekwoq),lmg another 1.2 m higher. What is the change in poten,tiq, 2ge3bo) lk pny*qk mcr+w/l63etial energy?    J

  By how much does the gravitational potential energy of a 64-kg pole vaub;:9/w kycnxqza)i-b lter change if wxybq-a/zck: )ni9 ;b his center of mass rises about 4.0 m during the jump?    J

  A 1200-kg car rolling on a horizontal surface has sbwkzb 3obdj;q 5q3 :7cpeed v = 65 km/h when it strikes a horizontal coiled spring7;z:3 b3wjb 5 bcqdqok and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?    N/m

  A 1.60-m tall person lifts a 2.10-kg book from the ground so ixg hnti+.eipwa-g5s+bd - ( 7jt is 2.20 m above the ground. What is the potential energy of the book relative to ga+t-h7 wijxe s+dnpg5i.b(-
(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 pjitb* 5.twd8n mjx 6-1600 m and climbs to the top of a 3300-m peak. m8-6bnj i5 xd.pj*wtt
(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. Tht1 oilw2s1l gyl 6*w*ke 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 up with ltylw*2kl1w1*6io g s the ruler marks?    cm

  Jane, looking for Tarzan, is runn(f;x - e ugd+non8ge/cqf;g ,jing at top speed (5.3m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How hig/8 fg gno ;egn q;-u,f+dcjx(eh 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 do) c3./8o 1i jsxng3acaznx1azwn 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 g gz04scu 0t2xshove up a frictionless 28.0$^{\circ}$ incline. It reaches a maximum vertical height 1.35 m higher than where it started. What was its initial speed?    m/s

  In the high jump, Fran’s kinetic energy is transformed into gravitational pot*b c(3j*/ tj(bf/jcuctx acj7ential energy without the aid of a pole. With whb(xjc7 (uc/jcbj 3ftc**aj/ tat 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 upwefbu;eqw28k4i 7 1pmward from the top of a platform with a skmqf; u4w 2bwpeei718peed 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 (ig(hmf8 nkvg8*+coka 2. njqj z*nore 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 0.30-kg ball when relnnhmj(qcv z+ak8.*k g 82ojf* eased?    m/s
(b) How high above its original position (spring compressed) will the ball fly?    m

  A block of mass m slides withb ..q0* 4 pgystqm+ajkobw 9u2out 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 cirq2s qw.+pky*o4 . j0ab9b tumgcle (whose radius is r), from what minimum height h must it be released?    r

A block of mass m is attached to the fa j49eak; nv:end of a spring (spring stiffness constant k), Fig. 6–40. Tnva4: jfk9a; ehe 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 tiedx0 7; -9zfch4h hzcg v0ymmcp6 to a bungee cord whose unstr hxf 9p;m70zmhhv06z ycg4c- cetched 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 applies. $\approx$    N/m
(b) Calculate the maximum acceleration she experiences. $\approx$   m/$s^2$

  The roller-coaster car shown in Fig. 6–41 is dragged up to point 1 where it is ac3 77 y.6ikdcworqvtm/70 pp( 5xowureleased from rest. Assuming no friction, calculataippo77ymxrw03 .o/ c(7 w 6quct kd5ve the speed at points
2    m/s
3    m/s
4    m/s

  A 0.40-kg ball is thrown with a speed of 12 m/s at an angle of 3fn4uzrpm*4x ; thso pyim4j +) 21pxj13 $^{\circ} $. (a) What is its speed at its highest point    m/s
(b) how high does it go? (Use conservation of energy, and ignore air resistance.)   m

An engineer is designing a spring to be placed at the bottom h qoj78mnhpra7v- e*5of 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 than 5hpo 8n7-7 *vqajherm5.0 g when brought to rest. Let M be the total mass of the elevator and passengers.

  A cyclist intends to cycle up arj2o05x4o1kt9sxu032t e df pl / jkwf 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 dirern1 ;3zi0cnrk ;.ziuq ctionsnkn.zr; r uq;1 i0ic3z, collide head-on and come to rest. How much thermal energy is produced in this collision? $a\times10^b$ J a =    b =   

  A 21.7-kg child descends a slide 3.5 m high and reaches the (9h: e4 zherklp)s/2naj,glzrs0r 4nbottom with a speed of 2.2m/s How much thermal energy due to friction was gen(9 r rs2rha4 )ll0:ezns 4ngzekh,/jperated in this process?    J

  A ski starts from rest and sls.5 w.thctxw. di20cuides 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 dropcb upbe y8 8b;b6pn0)eped 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 6of;d d s7(pfse.k x +41sjcoqback to a height of 1.5 m. j;ofpxof.qsc se4d+sk7 1(d 6
(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 cor gspm,j1m p.4os ke:)nstant horizontal force of 350 N. For the first 15 m the floor is frictionless, and prep j, 4m)osk1g: ms.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 inf 361. tf yj61xd+n:p3emsobi jeg :hw Fig. 6–41 passes point 1 with a speed of If the average force of friction is eq3 es. f+tm6:e x3bnhfijdp6 g1j1:y woual to one-fifth of its weight, with what speed will it reach point 2? The distance traveled is 45.0 m. $\approx$    m/s

  A skier traveling 12m/s reaches the foot of a steady upward 1895bqyx9f hge 4.0 $^{\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 firmly8 d3)b-ugdkd0 * jy/v8i 0skdwtphqq0 attached to a very light horizontal spring (k=180N/m) as shown in Fig. 6–40. It is noted that the block–spring system, when compressed 5.0 cm and released, stretches out 2.3 cm beyond the equilibrium poig0dh0*kq8-8vyjkbdt qdw/ )0sup 3d sition before stopping and turning back. What is the coefficient of kinetic friction between the block and the table?   

  A 280-g wood block is fiald; tic 8el0v(/apnwhlk hfx62o1 55rmly attached to a very light horizontal spring, Fig. 6–40. The bl;o1kc5ai hxv la5df0hl/28enl wp6t(ock can slide along a table where the coefficient of friction is 0.30. A force of 22 N compresses the spring 18 cm. If the spring is released from this position, how far beyond its equilibrium position will it stretch on its first swing?    m

  Early test flights for the spac.ftqo v 2y+i/fe shuttle used a “glider” (mass of 980 kg including pilot) that was launched horizontally at 500km/h from a height of 3500 m. The glider eventually landed at a speed of 200km/h (a) What would its landing speed have been i v oqi.2t+ffy/n 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 pianjtc9q l-vu f9x9jd/e:o to a sixth-story window 16.0 m abovet9 dcj 9q l9vf-/:jxue?    s

  If a car generates 18 hp when traveling at a steady 88km/h wht),+glxq(ew8p w( d i2a0+a- mrc sdquat must be the averl-dtigq 82x)uqcwaaew(0,smp ( r+d+ age force exerted on the car due to friction and air resistance?    N

  A 1400-kg sports car accevx1 ,:(ip lfudlerates from rest to 95km/h in 7.4 s. What is the average uf (v:dl,ix1ppower delivered by the engine?$\approx$    hp

  (a) Show that one Bra/ wgpiq fec*abp:3 jp6f( h44itish 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 of hsql,b4b k:y 7d*b(vdten expressed in the form of “kilowatt-hours.”
(a) Show that one kilowatt-hour (kWh) is equal to $3.6\times10^6$J
(b) If a typical family of four uses electric energy at an average rate of 520 W, how many kWh would their electric bill be for one month $\approx$   kW*h
(c) how many joules would this be?$a\times10^b$ J a =    b =   
(d) At a cost of 0.12 dollars per kWh, what would their monthly bill be in dollars? Does the monthly bill depend on the rate at which they use the electric energy?    dollars

  A driver notices that her 1150-kg car slows down from 49m;:.l* q wtqcu ioow 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 ke q ;qwm.4:ocl* tuiwo9ep the car traveling at a constant 75km/h.    hp

  How much work can a 3.0-hp motor do in 1.0 h?3wf fcn*;n:y.e hkey/ $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg shot from rest to 14m/s If this motion takes d m gih;b )*dv/rse-u21.5 s, what ave2 bv ur);m-*ehsi/ dgdrage power was developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute through a height oexl5m+nua*aw jf 5 24jpq4a l:f 3.60 m. What output rating (watts) should the pump mw 5ae4j5qafu*xp4l:2l jn + amotor have?    W

  During a workout, the football players at State U(swugj6 w1gv1xnv6 *wf,xe +c . ran up the stadium stairs in 66 s. The (j6 nvcwuex1v6* gw, gs1wf+ xstairs are 140 m long and inclined at an angle of 32 $^{\circ} $. If a typical player has a mass of 95 kg, estimate the average power output on the way up. Ignore friction and air resistance.    W

  How fast must a cyclist climb a 6.0;e;7k4cdsvlgf9n y 5a ga5op9 $^{\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+ y*p1 ynmdvi( 120 hp. How steep a hill can it climb at a copm iy+*vn y(d1nstant speed of 75km/h if the frictional forces add up to 650 N?    $^{\circ} $

  What minimum horsepower must a motor have to be alx57(lb gg*mb ou-ey x:.lh r)ble to drag a 310-kg box along a level floor at a speed of 1.2m/s if the coefficient of frictio5hg )l:g .eo x u-bmblx(rl7*yn is 0.45?    hp

  A bicyclist coasts down yfa:rj7 )fqy k4:q1ffa 7.0 $^{\circ} $ hill at a steady speed of 5m/s Assuming a total mass of 75 kg (bicycle plus rider), what must be the cyclist’s power output to climb the same hill at the same speed?    W

  Designers of today’s cars have built “5mi/h(8km/yhiek:t43ddd6 ,k t p8h) 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 solid wky,h8 3t: tipkd4 d6deall? $a\times10^b$ N/m a =    b =   

  In a certain library the first shelf is 10.0 cm off the ground, and the remaik.g4kyrjt, p po2j; .qznm b08ning 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 holds 25 books, how much work is required to fill all the sheln j;k j..,y rgq4m80kppbtzo2ves, assuming the books are all laying flat on the floor to start? $\approx$    J

  A film of Jesse Owens’s f dg)shh;bgbez)8 2 q/ramous 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 need at lazb)rd ;ebq2hs/ ggh8)unch if he was traveling at 6.5m/s at the top of the arc?   m/s

  The block of mass m sliding without friction along the looped trac0 tx;k w14umbq0 ;rbfck shown in Fig. 6–39 is to remain on the track at all times, even at the very top of th4 0bft01x;mwbc ru;kq e 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 s:-p /ys+;qphhefw y4his parachute openin/p+;ps s4qhyh y:ef w-g. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the pilot’s mass was 78 kg and his terminal velocity was 35m/s estimate
(a) the work done by the snow in bringing him to rest; $\approx$    J
(b) the average force exerted on him by the snow to stop him;$\approx$    N
(c) the work done on him by air resistance as he fell.$\approx$    J

A ball is attached to a horizontal cord of length L whose other end is f 8 z6x.tlwoix6ixed (Fig. 6–xz6wo8t 6.xl i43).
(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-mng(pw0ny8mn7a -b7 x s-high mountain. The climb is made in 5.0 h starting at an elevation of 2300 mmg 78yw(snp n-nax0 b7. 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 breaksulb bs.g+im.n(oby -9 when a 920-kg elevator is 28 m above a huge spring ($k=2.2\times10^{5} \mathrm{N/m}$) at the bottom of the shaft. Calculate
(a) the work done by gravity on the elevator before it hits the spring,$\approx$    j
(b) the speed of the elevator just before striking the spring,$\approx$    m/s
(c) the amount the spring compresses (note that work is done by both the spring and gravity in this part).    m

  Squaw Valley ski area in California claims that its lifts cua0y iu*06ppvb r1ij9a0pz6y an move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the power n0p*vjyab 6rpy9zi0ui1a0pu6 eeded.$a\times10^b$ W a =    b =   

  Water flows over a dam at the raol;b-ucw9h uav5 4w*0sm w7fi te of 650kg/s and falls vertically 81 m before striking the turbine blades. Calculate f7;cms4 ba9v o0*5u ww wulh-i
(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 c 2w:blnt a9:l84 ydwthircular vertical loop (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. Ignore friction. Show also that as long as your speed is above the minimum needed, this 2hwyl: wlnat :d8b94tanswer 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 direc aoobcj0-t cxj.y0(a* tly into work, how high could an 82-kg man climb a ladder if he were fueled by oj c.oajc-* o( 0by0txane 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 ang*o7rrk a.k 8rxle 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 springa;i(b w(w+cge inside the scale compresses 0.60 mm, and it tew;ibc g+e( wa(lls you your weight is 710 N. Now if you jump on the scale from a height of 1.0 m, what does the scale read at its peak?    N

  A 65-kg student runs at 5m/s grabs a rope, and swings out over a lake (Fig. 6–mzf3wd 0 le9 (b0pc3ui45). Hce f3(b0 im wp9ud3l0ze 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 cli5+zz b igl4y u9v/o+oryo2 k ds/-gos;mbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used to accomplish this fl4+ozyuo;sg2/5 +o/yr9kb gzds- vio eat?    W

  Some electric-power companies use water to store energy. Water ipz q*npw;bf0 -vm62pynlwt c8 v: so5,s pumped by reversible turbine nyl-mpvw0nqf* s 5c6:2 t popw,z 8vb;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 stiffness constant k is cut in half. What is the spt/mbz ,ylq13sz(9nly; ey p(uring stiffness constant fby9p mlen( y(zuy lz3,qt;/s1or each of the two resulting springs?   k

  A 6.0-kg block is pushed 8.0 m up a1s+ /ahpgs+c2oe2ff k;8j+liyrx) p v 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, how lon7 sv ih 1,7 mgd-7pvp 6wv1+vxv tbnfcrya(6)eg will it take to accelerate from 55km/h to 75km/h Assume the power stays the same, and neglect frictional losxp )gamb -hvi yv7,cv 6 f7n1vs6e(wtvp7 +dr1ses.    s

  In a common test for cardiac function (thx(6a ;ard 2gvoe “stress test”), the patient walks on an inclined treadmill (Fig. 6–46). Estimate the power required from a 75-kg patient when the treadmill is sloping at an 2d;(a ag6ovr xangle 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-kdj 5 b/eisq(bi gkp+46g rock vertically upward a distance of 500 m, what was its velocity when it l 5( e6j4b+g dik/sbqipeft 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 6ptsma(srh cg:5zqu 5n2iodu*; ui (9of 2.0 m at a rate of 95kg/s (a) If this(i t6a;(*nu cg55usu r dqs:ho2pmz 9i 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