In what ways is the word “work” as used in everyday language the same as that ded5ishq w2 r7e,572hewq ris, dfined in physics? In what ways is it different? Give examples of both.

Can a centripetal forcjs 8lxnl**qm) d o jvng(x+,9fe ever do work on an object? Explain.

Can the normal force on an object ever do work? Explain d/bv;6lehdmn)o8f5 e.

A woman swimming upstream is not moving with res-ee:0 *d jihxlpect to the shore. Is she doing any work? If she stops swimming and merely f*e d eh-:xilj0loats, is work done on her?

Is the work done by kinetic friction forces always nega t403gk8d y6cgaup(v8sciiu. tive? [Hint: Consider what happensu g 6cyg(8i vk3 tuas.c8dip40 to the dishes when you pull a tablecloth out from under them.]

Why is it tiring to push hard against a solid wall ckq5ozmcs b;*m02iq) cch*o: even though you are doing no w: *i2kmoc;moq* s5z )cccbh q0ork?

You have two springs that are identical except that spring mmnih)b/y pi,1nx gy0g* 0 zb*l is stiffer than spri/ n*b,0y0h ix y)m*m pgzbin1gng 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 block that is free to lgn)nh5j7 *tc+ d/k2dp;aln x slide on a frictionless surface (Fig.6-30). The block sta+ ) hjc7xnd gp k/2n*tnll;5adrts 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 change whenemwtyf eq3,/ns 7z73d 9 d,syq y fems,3wq7zde y dsnty3/7,q9ou jump as high as you can?

In Fig. 6–31, water balloons are tossed fr (g6p-sf eaf)lom the roof of a building, all with the same speed but with different launch angles. Which one has the highest speed on impact? Ignore air resisg fep a-s(l)6ftance.

A pendulum is launched from a point that is a height h above its lowest point inpgb) /ni09asaxq ,xa* two different ways (Fig. 6–32). During both launches, the pendulum is given an initial speed of 3.0m/s On the first launch, the initial velocity of the pendulum is directed upward along the trajectory, and on the second launch it is directed downward along the trajeb0aq) p x n9*sg/,ixaactory. Which launch will cause it to swing the largest angle from the equilibrium position? Explain.

A coil spring of mass m rests upright on a table. If you compress ta(jn3( +b i73rgz.to(xoc ay uhe spring by pressing down with yo (ax 37 tajzobo y+nrui.c3(g(ur hand and then release it, can the spring leave the table? Explain, using the law of conservation of energy.

A bowling ball is hung frm; f;(o3 u5 x0zqkkarxp/4zry om the ceiling by a steel wire (Fig. 6–33). The instructor pulls the ball back and stands against thrm 4qz5x r f;0k3uoypz/a;(xke 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 enmenndj 1)1h.g r5ktc4ergy when water at the top of a waterfall falls to.h1g )m4 nkrn5ctdj1e the pool below?

Describe the energy transformations when a child hops around on a pogo stick. zx) 4cvw6c.yz

Describe the energy transformations that take place when a skier starts skiing ;lo5f(ie:1uky3mqo l downyk l:ml iuqo1e3;o (5f a hill, but after a time is brought to rest by striking a snowdrift.

A child on a sled (total man8j q7zjpd v6x/;mi,mss 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 xdj,/m v 68p7;nijzqmfriction, and (b) there is friction (deep snow)?

Seasoned hikers prefer to step over a fallen ;p hgl 3 ce+nhchljul(4179y flog in their path rather than stepping on top and jumping down on the 9ph3hfy7(;cll+4j u c1gl hen other side. Explain.

Two identical arrows, one with twice /s (:btsa2xyt (wadrg0g3 legnyo k:7 x4td( 1the speed of the other, are fired into a bale of hay. Assuming the hay exerts a constant frictional fsywg g dtd or(a: k3slbxe0 2agn(1t: 4x(t7y/orce on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain.

Analyze the motion of a simple swinging pendulum w1fz wxpzoz4v gup+ 0npx7 2ia+.df/1in terms of energy, (a) ignoring friction, and (b) t1aw./xwzfxu+4n12 od gif70zp z vp p+aking friction into account. Explain why a grandfather clock has to be wound up.

When a “superball” is dropped, can juh qn0(v(xq- /fmr ij6rcx7* it rebound to a height greater than its original height? Explahi-j rv(f7 6x n 0j*qx/qcr(umin.

Suppose you lift a suitcase from the floor to a table. The s:9u7etyx, g i3zs )bmwork 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 y7ezui,msxg9bs:) t3 it takes, (c) the height of the table, and (d) the weight of the suitcase?

Repeat Question 22 for4j6z.u5u kjla the power needed rather than the work.

Why is it easier to climb a mountain via a dcolzzcb1j5f+c/;+v/e rib 7zigzag trail than to climb straight uc+z1icbrfjcb5 + ezo;7/ldv/ p?

Recall from Chapter 4, Example 4–qt*w.u+5lc i s14, 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 +5i sl wtq.uc*much rope must be pulled up? Account for this, using energy concepts.

  How much work is done by the gravitatiodhs8 4;3whj;s j)r9 tlj.mfkznal force when a 265-kg pile driver falls 2.hw9 ; jk8.;jrfmldsz hs3)4tj80 m?    J

  A 65.0-kg firefighter climbs as*yp;i;l v: pv flight of stairs 20.0 m high. How much work is required? :; ppivvyls*;   J

  A 1300-N crate rests kmqs:uw5 qa d ,n+bq12on the floor. How much work is required to move it at constant speed (a) 4.0 m along the floor against a friction fs mbkdwqq:1,q 5u+a 2norce of 230 N,    J
(b) 4.0 m vertically?    J

  (I) How much work did the movers do (horizontally) eh z2vf+nrpi+g o*4 zgp ed684pushing a 160-kg crate 10.3 m acrosifrn 6vo8z e*g+z+d2ep4 4 gphs a rough floor without acceleration, if the effective coefficient of friction was 0.50?    J

  A box of mass 5.0 kg is accelerated by a force across a flood0iuuu 0)qtp7ms a h(;r at a rate of for 7.0 s. Find the net work donem7 spdu0u 0tq()hai;u on the box.   J

  Eight books, each 4.3 cm thick with mass 1.7 5w(ritmm*f x- s,n9.us v-b uk touvrd)5 b(1ekg, lie flat on a table. How much work is required to stack them one on 9 v x o*-uf.dutk1rb(iwn5 urvt5)( es-,bm mstop of another?    J

A lever such as that shown in Fig. 62mzy613t0kg4q pa,dmn: d1vf, pkonp-35 can be used to liff objects we might not otherwise be able to liff. Show that the ratio of output f6m1 nkfa t4n2d1qdk,03:,vmy pgzppo orce, $F_{\mathrm{O}}$, 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 3- m9xvnf ic1qgd g8boe 17;zom down a 28° incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 6-36). The efz ggm7q1 evd;91fbooi 83cx-nfective 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 acceleratiobqv,ejftx1;w1c+0 3w sa g aa)h+a)do n of 0.10 g upwar +g+3aa q 0;h)jswt,c vo11aefdabx w)d.    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 axiprid:9 yaq6 u8s is linear and that $d_{\mathrm{A}}=10.0$ m and $d_{\mathrm{B}}=35.0$m. Estimate the work
done by force $F$ in moving a 2.80-kg object from $d_\mathrm{A}$ to $d_\mathrm{B}$   J

  The force on an object, acting along the x axis, varies as a mktr9g 9(ut8i0ee8rn/ p 6l pl)cft4shown in Fig. 6–37. Determine the work done by this force c8r6k 0 f4u)n tp8m(rat 9pil9geet/ lto 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 on9/f/eqz 1ad3soc pnk/ 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, .ehjhf+:e33j *asadw an oxygen 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 factor has its speed inc1t 7e0h8 wkigqreased? $ \sqrt{a}$ a =    (b) If its speed is doubled, by what factor does its KE increase?   

  How much work is required to stop6cs t7p,gxucv39bik- 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 travecjlvl ;fl/kh ( ,nbh+;ling at 105km/h?$\boxed{a\times10^b\text{J}}$ a =    b =   

  An 88-g arrow is fired from a bow whose string exerts an averaga/ j0: m.pkmyaz6 e 9/:cr oumba67qkze force of 110 N on the arrow over a dp6. 07a 6q ::krkuo/cy/ mam9zbeajzmistance 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 glovi t+++t ((pwdpkqtm: oe backward 25 cm when the ball is caught. What was the average force exerte m(o++ dkq+p:pttwi( td by the ball on the glove?    N

If the speed of a car is increased by 50%, b;lw6,-h6g wmeui w -qz :ehz2ry what factor will its minimum braking distance be increased, assuming all else is theuiw;r-m: hlwq6w 2-, 6eehgzz same? Ignore the driver’s reaction time.

  At an accident scene on a level road, investg*r 1: 9qk+ocab noa5tigators 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. 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 nog:q +5o ob*a 9rkcn1att matter?)    m/s

  A softball having a mass of 0.25 kg is fabe, g0cv9h7c 87i flr4mi;i pitched at By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of af me9i8 0 rhcgac;if,4b 7v7liir 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 ifq 87w+hm(n ehr thrown straight up by someone who does 80.0 J of work on it? Neglect air r 8hrne(+7mq hwesistance.    m

  A 285-kg load is lifted 22.0 m vertically with an acceleration by dtcl5n2sjvt8s(v0 q4t6+ l vba single cable.bttlv+0 8 v s (q24nctdv56jsl Determine
(a) the tension in the cable,    N
(b) the net work done on the load,    J
(c) the work done by the cable on the load,    J
(d) the work done by gravity on the load,    J
(e) the final speed of the load assuming it started from rest.    m/s

  A spring has a spring stiffness constant, k,unevl 8(ak2n) of 440N/m How much must this spring b l2k8ane) (uvne stretched to store 25 J of potential energy?    m

  A 7.0-kg monkey swings from one branch to another 1.2 m higher. What is :gd2)d: n4 bettdgq +qy)uk4 g1cx oj/the changgd:2d /yg)t4gjqe4cotud) bq: xkn+1e in potential energy?    J

  By how much does the gravitational potential energy of a 64-kg poleptmah 4p,xo8ik; 40l(5gfcsn vaulter change if his center of mass rises about 4.0 m during the4;0k8cga(5oisl,n ptp 4f mhx jump?    J

  A 1200-kg car rolling on a hor( *iakgi 4/3,znfan atizontal surface has speed v = 65 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What,tk/a (4nzi *ing3aa f is the spring stiffness constant of the spring?    N/m

  A 1.60-m tall person lift +x s6gj:g( al+bqf5qus a 2.10-kg book from the ground so it is 2.20 m above the ground. What is the poten6a:qubfs gx5j +(qgl+tial energy of the book relative to
(a) the ground,    J
(b) the top of the person’s head?    J
(c) How is the work done by the person related to the answers in parts (a) and (b)?    J

  A 55-kg hiker starts at an elevation of mo5b4( wal v+j9*tinm 1600 m and climbs to the top of a 3300-m peaal(m4+bitv o5wnj *m9k.
(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. k9; mc f1ekap-The end of the spring is next to the 15-cm mark me1cfa;9-k pk on the ruler. If a 2.5-kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler marks?    cm

  Jane, looking for Tax 19lh 2;-h kytpvmp-yrzan, is running at top speed (5.3m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing2 ;pl-tm x-k1v9phy yh upward?    m
Does the length of the vine affect your answer? ----待选择----yesno 

  A novice skier, starting from rest, slides down a fri- 2zzqul ffj8,j .g1luctionless 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 ujb2p)i yrtxi w4 1kdvim,i1 7,p 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 transform ;qh,3sc,echcv w*4mtqw)5qx +qp qj;ed into gravitational potential energy without thctq;;* 5qqvmq, +hsh ,e)cwxpjc43 wqe 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 from the top of -,pj do20gqgex b,z1ea platform with a speed of 5.0 m-gdeexo, 01, 2qzpb jg/s. ($\alpha)$ How fast is he going as he lands on the trampoline, 3.0 m below (Fig. 6-38)?$v_2$ $\approx$    m/s
(b) If the trampoline behaves like a spring with spring stiffness constant 6.2×10$^{4}$ N/m , how far does he depress it? $y_3$ =    m

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

  A vertical spring (ignore its mask5ks u wuv6 ao5/*z-ebs:,t gps), whose spring stiffness constant is 950N/m is attached to a suza5gt ko-ubwe /vs:p65*k, table and is compressed down 0.150 m. (a) What upward speed can it give to a 0.30-kg ball when released?    m/s
(b) How high above its original position (spring compressed) will the ball fly?    m

  A block of mass m slides without friction along the looped track shown in 7fn ez;7rgzp, z9i6 ly3wkxn3 Fig. 6–39. If the blockwy6pg 7,zne3 3nr;fzi z7l9xk 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 to the end of a spring (spring dpb nrxb36 07tlb7 ,vdstiffness constant k), Fig. 6–40. The bld7r7dl b,3 t6pbvxnb 0ock is given an initial displacement $x_0$ after which it oscillates back and forth. Write a formula for the total mechanical energy (ignore friction and the mass of the spring) in terms of $x_0$ position x, and speed

  A 62-kg bungee jumper jumps from a bridge. She is tied to v616 b;b)ggvmrjx rh;a bungee cord whose unstretched length is 12 m, and falls a total of 31 m. (agjg;h;)rb6 1vb r mx6v) 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.w94 dt8jlajuyaz ye( 7 /yc*ln 9-5msl 6–41 is dragged up to point 1 where it is released from rest. Assuming no friction, calculate the speed at points* ju/ 5ed yw4n7a la9smzjyl-9lt8( yc
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 az6u4,cb7y8ampom8o vngle 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 ts 2och/dr koy-98bz3npe9 em-he bottom of an elevator shaft. If the elevator m/3o 89 nyo-pd2hk9crse z-ebcable 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 up a 7.8 mtxw(;js)vf8zkns -3$^{\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 andr5bhxrp ejzfh25w(g0 i 0 2z/x traveling 95km/h in opposite directions, col0 z0hixx2 zjwbrer25 (pgf/5hlide 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 bottom with a spee2lq( 6ifx-r-ilqvi.k d of 2.2m/s How much thermal 6i2l ( iqrkq.vifx-l-energy due to friction was generated in this process?    J

  A ski starts from rest and slides )c a :cm 1un0edw9ilf-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 85it qwe0eps; p; v4:lw8wvyr dropped from a tree 13.0 m above the ground.
(a) With what speed would it hit the ground if air resistance could be ignored?    m/s
(b) If it actually hits the ground with a speed of 8m/s what is the average force of air resistance exerted on it?    N

  You drop a ball from a height of 2.0 m, and it bounces back to a wq2g0w5fpu/e)y(bvr84j cmxheight of 1.5 mjv pem48g5w2/qf)x0w rby(cu .
(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 -id4s( kb ra7gwith a constant horizontal force of 350 N. For the first 15 m the floor is frictionless, and for the next 15 m the coefficient of friction is 4(a-krgs 7idb 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 y tk9 z/g4wisrfd:-)qof If the average force of frkf 4):sd- tiwq/ yg9zriction is equal 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 kwg -/hi; bivk9e q0b;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 attached to a very light horizontal spring .ucajg t -rup8i i3qz,kej70 9(k=180N/m) as shown in Fig. 6–40. It is noted that the block–spring system, when compressed 5.0 cm and released, stretches out 2.3 cm beyond the equilibrium position before stopping and tju 9ctupajr3,q i 8g.k0 7ie-zurning back. What is the coefficient of kinetic friction between the block and the table?   

  A 280-g wood block is firmly attached to a very lilh; ;g -bldm.,aw gif(ght 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 compr bglmlh (f,gi ad;.w-;esses the spring 18 cm. If the spring is released from this position, how far beyond its equilibrium position will it stretch on its first swing?    m

  Early test flights for the space shuttle used a “gl.6xfb (cq9xsdider” (mass of 980 kg including pilot) that was launched horizontally at 500km/h from a height of 3500 m. The glider eventually lande. d9b cfqs(xx6d 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 .8 yet7g e:uzzto lift a 315-kg piano to a sixth-story window 16.0 z: y.eet8gu7z m above?    s

  If a car generates 18 hp when traveling at a steady 88ru8. bvfkuvb0 688am3 p0quh kkm/h what must be the average force exerted on the car due to friction and air resist08kmva8f uvrb3p .k80 qhu 6buance?    N

  A 1400-kg sports car accelerates from rest to 95km/h in 7p;vv0/e l b;w*f 2wiom;+rnlc:x( jzy .4 s. What is the average power delivered by the engine*w +;p2fn ;0 yc bvxiwj:rzve( m/l;ol?$\approx$    hp

  (a) Show that one Britixx ,+)ohe3 nd5 n0wowofhx*3 nsh 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 -no5yu6 )ssv:hxr kn-dq5 5s4bg0u9/jvsiqein the form of “kilowatt-hours.”
(a) Show that one kilowatt-hour (kWh) is equal to $3.6\times10^6$J
(b) If a typical family of four uses electric energy at an average rate of 520 W, how many kWh would their electric bill be for one month $\approx$   kW*h
(c) how many joules would this be?$a\times10^b$ J a =    b =   
(d) At a cost of 0.12 dollars per kWh, what would their monthly bill be in dollars? Does the monthly bill depend on the rate at which they use the electric energy?    dollars

  A driver notices that her 1150-kg car slows down from to 6lk0n7c:h8 rha5km/h in about 6.0 s on the level when it is in neutral. Approximately what power (watts and hp) is needed to keep the car traveling at: n0rhc 8alhk7 a constant 75km/h.    hp

  How much work can a 3.0-hp motor g:ifo )(n8yaj*pjd 6xdo in 1.0 h? $a\times10^b$ J a =    b =   

  A shot-putter accelerates a 7.3-kg shot fromx gpk*ukl7 0m. rest to 14m/s If this motion takes 1.5 s, what a.kkgmu xp0 7l*verage power was developed?$\approx$    W

  A pump is to lift 18.0 kg of water per minute through a height of 3.hy9h vgso c z6wz9m93) edk,h.60 m. What output rating (wattsdco3g mh,ws9ve z ) y9hhzk.69) should the pump motor have?    W

  During a workout, the footbax/q(9pap sz3nh qz*h 8ll players at State U. ran up the stadium stairs in 66 s. The stn *(hzsx9 8 p/z3hqqpaairs 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 cycliss w ,dz4elpay-*: vvn2t 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 1jl f(;s:nwmv6 20 hp. How steep a hill can it climb at a constant speed of 75km/h if the frictional forces add up ;wvf nm(jsl:6 to 650 N?    $^{\circ} $

  What minimum horsepower must a motor have to be3a9es9ir)sd r+m( e9gy m1wpk able to drag a 310-kg box along a level floordrm+93i9a(wgr1 y) esp9 semk at a speed of 1.2m/s if the coefficient of friction is 0.45?    hp

  A bicyclist coasts down a 7.0tr:aq(1opwex8z+ q/ g $^{\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 “5m/lqts/8qo.iy /jl 2 rzi/h(8km/h) bumpers” that are designed to compress and rebound elastically without any physical damage at speeds below 8km/h If the material oftz / olrq28.isqljy// 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 sq0k9b jvglmu8c ;gb1 (helf 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 holds 25 books, how much work is requivbu;qgcj1 ( 9gbm80klred 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. 6–3y+ddjwu1e7t 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 hew3 d+et7 1ujyd 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 without friction along the loohwfo26 a j-sj+ki5so8 ped track shown in Fig. 6–39 is to remain on the track at all times, even6i2swo -shj jk8o5f+a 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 /fn z+rdj;c (vu84mmj,h1 ucrwithout his parachute opj /,+zhmr ;c(mr 4cnf1j vd8uuening. 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 w. otecw1i:7 vehose other end is fixed (Fig. 6–.:et v7 eo1iwc43).
(a) If the ball is released, what will be its speed at the lowest point of its path?
(b) A peg is located a distance h directly below the point of attachment of the cord. If h=0.8L what will be the speed of the ball when it reaches the top of its circular path about the peg?

  A 65-kg hiker climbs to the top of a 3700-m-high mountain. The climb ig9gz)kslm8ba:v nim m51uyz jz 04+.zm6 gei7 s made in 5.0 h starting at am m+y1be)8 . i zin4g6um 5v079zk:agz lzjmsgn 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 erdvo3a , do2umvjj7x- )g. xk5levator 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 caad+ n l-k2jr )3xdmid,n move 47,000 people per hour. If the average lift carries people about 200 m (vij2nad3dr-mxk ,+)d l ertically) higher, estimate the power needed.$a\times10^b$ W a =    b =   

  Water flows over a dam at the rate of 650kg/s and f,78o w0l i3psfsyrwn +alls vertically 81 m before striking the turbine blades. Calculate ws0i nor3+f,l s7 yw8p
(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 ., -ktggx,jjo with 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 circular loop is 6 g’s — that is, six times your weight. Ignore friction. Show also that as long as your speed is above the minimum needed, this answer doesn’t depend on the size of the loop or how fast you go throo gjjtgxk ,-.,ugh it.    mg

  (a) If the human body could convert a candy bar di:xah yih)ck(oo /vc4+rectly into work, how high could an 82-kg man climb a ladder if he were fyk:+4i hh(/oco cx)avueled 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 upwa 9p :)ynu0ghk dc+-mnprd 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, th6 ,ir1j xzo-lo+ x4rmye spring inside the scale compresses 0.60 mm, and it te6orrljz y1 x -mix,4o+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 5mv (wowf/lf43x /s grabs a rope, and swings out over a lake (Fig. 6–45). He releases the rope when his velo(fwl4f o/3wv xcity 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 ;d(qg8 u 8kfrwclimbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was usedugfq8 kd(rw;8 to accomplish this feat?    W

  Some electric-power companies use water to store energy. Water is pumpe liei25(mmrw8t 4zt -ld by reversible turbine pumr4i eml-5wmlitt z (82ps 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 cifvi*) pf020vxyi f7 cil q5:fut in half. What is the spring stiffness constant fiv*l5vqfyix p07if) 0f2c:i for each of the two resulting springs?   k

  A 6.0-kg block is pushed a2ag/pp 9j; mjy:y:brpp0 (4zcc o9vb8.0 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 i3a.. gzxzp.y/h in 3.2 s, how long will it take to accelerate from 55km/h to 75km/h Assume the powezgxa3ypzi. .. r stays the same, and neglect frictional losses.    s

  In a common test for cardiac function (the “stress testtf rn 2p*het 2*fbbkn+2 d0rg8”), the patient walks on an inclined treadmill (Fig. 6–npkr8*dt2f + b20t* hn 2egfbr46). 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 vertically upward a dyqqds,p( 2t-aistance of 500 m, what was its velocity whe-a2q qysp (dt,n 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 ofd;ld9sg2m3)r8 mqyj yzj/(h v 2.0 m at a rate of 95kg/s (a) If this water wheel is set up to provide electricity output, what is ;/j dmj2hldy )g(98 3szvryq mits maximum power output?    W
(b) What is the speed of the water as it hits the wheel?    m/s