Sometimes people say that water is removed from clothes in a spin dryer by cenak-j4o-u.vc ptrifugal force throwing the water out.ckoj 4-pau -vward. What is wrong with this statement?

Will the acceleration of a car *kkpk5 7d.vigbe the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a ik 7dgv.5kk*p gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alz0w. a*sw y4 zyw3; c8cszt1qhong a hilly road. Where does the car exert the greatest and least forces on the road: (a.awzhyw4 y 1 z3z8cq;cw0sts*) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the for/d3ldk 1b,zu 5s4o nph ,l2osgces acting on a child riding a horse on a merry-go-round. Which of3zkp 2 h1o,sdls5n,4dugb/ ol these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle wit; 6ha1jj bnkaovyz4/2, udk8whout the water spilling out, even at the top of the circle when dhuj 2oz8k 1aaj;/ykwb,n 6v4 the bucket is upside down. Explain.

How many “accelerators” do you have i)xz jr g*k )d-d;le2ttn your car? There are at least three controls in the car which can be used to cause the car to accele*2k edjztl);g-rt )dx rate. What are they? What accelerations do they produce?

A child on a sled comes flying over the c3 1 4ksvwvb r4;gnixh:rest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he dxn3vw1 ;vbgs4: rhi k4oes not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward whe/g gi 5jf9m-yfn rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking- o1qbz n6eqp9 angle given its speed andzqepb-9q1 o6 n radius of the turn?

A girl is whirling a ball on a string around her head in a horizyed6x 2: zi15iy6qkylxvu84 hb e b(0vontal plane. She wants to let go at precisely the right time so that the ball will hit a target on thehbke6xi e qud68z l2i:5y(4vv0 byx1y other side of the yard. When should she let go of the string?

Does an apple exert a gravit*zqx bi.wv).un .pi)e ational force on the Earth? If so, how large a force? Consider ai.z. )xq unwe*)i. vbpn apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wouldi xja.7iw4 h-c the Moon’s orbit ba- x7w 4.ijchie different?

Which pulls harder gravitatbhhjey0(si+68j 8 v zpionally, the Earth on the Moon, or the Moon on the Earth? Which ay 8h8j+ei(z0h jv6pbs ccelerates more?

The Sun's gravitatio+lox r(c5 hej;ivj+ * wi,3prjvg44sr :xvb, inal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Exprvvr;*3,4i4ig:jjch5x xbr +, ij +ow (elvs plain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the polesqt0;d.0vicj v ? What two effects are at work? Do they oppose eaiv dq.jv0t c;0ch other?

The gravitational force on the Moon due to the Earth is only abods321yqk g+bkq 5q xa0z5( ba uz/ni0put half the force on the Moon due to the Sun. 5x +kszb103a(/izbq 5ugpa nq02qdy k Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sn bh:r/b0rgtr4) hzv-fhsg.d qt9k..un larger or small9dqtr )kb. s0gh.- hr.4vzhgb:tfn/rer than the centripetal acceleration of the Earth?

Would it require less speeda( f)fv r;ht,o to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation direct), hfavr f;(toion.

When will your apparent weight be the greatest, as measured qw m4vjazfli sz-5pwg12j173v and: ,by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would you si2wvn wz-31 p,4a 5q:dvj1lzgjma7 fr weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space co.rd1i g 7vze5uuld be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a ci7gdurez.5 1v ylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner ex,dfzi ibso+pf u3p.-,periences “free fall” or “apparent weightlessness” between step +oiu,s3p z- fdib.,fps.

The Earth moves faster gka, 9vw ;jqc2qf3f7+ f(ovkl in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in produci wg9f3oql kcv + 7ff2k,;qva(jng the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known ungtfcit n50c5uur /h4.til it was discovered to have a moon. Explain hotu0 tgu4r. 5ifhncc/ 5w this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on tfcfu+w cj13w2 he Earth is much larger than the Moon's. Yet the Moon'sf c3cu2w+jwf 1 is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19j g;4+p:2*;kym qibtfi qg.yg 80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Eart gz6+bgr:5x ibh in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force ongb 6+gb:ix5z r the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0t0q asor3 +s4y-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of t a0 y+srq4ot3she discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface,sf)jg//c o g p-ze9,m0yqzm0w and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space pmmsec/w00 ojqy gf) -zg z/,9shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a pdt) ug)5hri( potter’s wheel turning ap)t)5 (gui drht 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circl 0xy:kt9uqc.n e of radius 72.0 cm , as shown in Fig. 5-33. If its speyk09qcnxut. : ed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum spyt-lt 0,idty 1eed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires t0 -lyiytt,d 1and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffihvz g+j (i u*dml/ 7sj:bfrqsy:7*e4 dcient of static friction be between the tires and the road if a car is to r74d+/jm* hru*i:l zjgb7(ysqd es:vfound a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots iakg)q ta5az1 qhxv*nqk qon,n()*;j-s designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85qtag x )v)-q;*q* qa5nh n,1jko(zkan times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm f7*5 (eywzty t tt2:0 xjtz9mt-v q9sarrom the axis of a rotating turntable of variable speed. When the speed y (v 5*ewqza92t0st7z 9ty-jx r:tmt tof the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when; u wy;ds fhyag1d9u4) upside down at the top of a circle dwu 9yfua4) h;y ;d1gs
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded top x b;- :d)q8*n,*ah pffigaetpof a hill (radius : -x*n8 haifp dtqb; fp)e*ag,=95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions ped)k-0espl:vg ldst2ah2 m,j ) r minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the t2,jh:m0tl))vsgls p2 de- a dkopmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radjm, t1r1sd tog gzl2r6db453 3vvmj,hius 1.10 m. At the lowest point of its motion the tension in the rope supporting v12g,3z, o 3t 6jl1s5rvrhgdjmb4tm dthe bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.a ukh4 61lfvt.00 cm from the axis of rotationt kvh6 .f4aul1 is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cj /ix5+tc0 blbfcx:j/ylindrically walled "room5xjl/c0i+jt/:f cx b b." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle o 4bcc9+2kk.n e *syy bb91qwql-rq my7n a frictionless air-hockey tabletop, and is held in this orbit by a l yw-y27kq9 sl.1q94enm+yq*bc rbk c bight cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring pv+k(42 neobkthe weight of the ball which revolves on a string 0.600 m long. In particular, find the ma (k4ne+k vbop2gnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travelin2 1fz4 nlm4sjqg 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massen45pjpkr pb0j xta j-s.y12e4 /yms/ys $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at fw()7k. xxm (sobu-ia310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components jh f xc43oob31 6.smmaof the net force exerted on the car (by 63xs o4cj.mmao1f 3hbthe ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 acla,xonh-b 9,mcelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangelhxnobm-9 ,,antial and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal ciry.gmu vj*f 19icle of radius 2.90 m . At a particular instant, its ay 1*vgujfm9i. cceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 kma i5o;)prpgr / (2 Earth radii) above the Earth’s surface i grar/5; pi)opf its mass is 1350 kg.   

  At the surface of a certain planet, theikiysb54gl3gybs hh-qss;7au (jd 06x /p,g: gravitational acceleration g has a magnitudys0-kg u /id 6xh5s3spg;: ,jqyah 7sbl( igb4e of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravit(+/tms ,el ukdr e+rr-y on the Moon. The Moon's radius is 1.74s-le em(ku+r t/r +rd, $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but hayg0k7wf.u qai-f 4- qds the same mass. What is the acceleration due to graviikf q4w.f-yaq-7 ud0gty near its surface?   

  A hypothetical planet has a mass mcfhr:ra2kvp2+zin z* g1evl 02do.h +fi(o; 1.66 times that of Earth, but the same radius. What is g nea2 pkdoifm. of +h0n evah+lg2iz 2(*z:;vr1rcr its surface?   

  Two objects attract each othd/by ewqwcqg/ 22 qu/, (s;ofher gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of f0e5.fbo dfb tr,8. +wuhhiy3gravity, at (a) 3200 m fr 8o. 3f.y0 bw 5i+e,duhbfth   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to g 2 d0j /,m(lh)p6q ik+dsmuteiqn)7ea point outside the Earth where thegravitational aq7+ipg(/ qiek ) htlm,sd6nj0mu)d2ecceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five timess9y-ig,s aqxg :i-5bnru/t ziat559 j the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster 5b-u/ai:9it,9sj-argg q5i s5n tzxy .    $\times10^12$

  A typical white-dwarf star, which once was an average hxk+ jbg:;4khr+r uu+star like our Sun but is now in theg jhu+kub xh:r4+k r+; last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the sj9; 2l rhnlw g;uo z8drhw/(i8pace shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravitynzjgwrw9 ;8 il(hdhl /8;u2 or 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corner/xf b 8g-vq.379d jpshk *psxcs of a square of side 0.60 m. Calculate the magnitude and direction of the total gj9h pqbcx8x./ fvdk3* sg7p-sravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line :i9 hpcc8s* )d;abpwzup on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The c*a b:pd i9);szhw8pcmasses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravi)khm2fgw 7b z lacfw(lo;:ig48hs 6-aty at the surface of Mars is 0.38 of what it is on Earth, and hw w6lml h kas g7b)8-4cz;i:2g(affothat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the b ir8wmnx4- 9xe:ia /yperiod of the Earth and its distan- m8 9exawn/xb4iir:y ce from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a 7ye;:d o*qd ukstable circular orbit about the Earth at a height of 3600 km; y7 *oekdqdu:.    $\times 10^3$

  The space shuttle releases a satellite into a 9596v6ks nu 2y uvmuupcircular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the r n5k6vus6yuv m 92u9upelease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experienc00e5i09n iz, xja.zliye7 al wu( *zxbe simulated izb(iie .0ja ay0l9n *zz7luw 50,xex gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to or smi--;q hc.arbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your resul-sq-i; macr.h t depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to bd,lxa l+ln6 wjxub; rn*m8g45t)2tffe launched from the top of Mt. Everest to be placed,w8nul a)glnf+fd*l 52x bmx 6rjt;t 4 in a circular orbit around the Earth?   

  During an Apollo lunar .v7y,xd pe+tavz bxyx4h*o (. landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go aroundx .x+dh4ye*z v,o.yb7(v tpx a the Moon once?    s

  The rings of Saturn are composed of chunks of ice that o/c/ dxnsyzg 963j mmi6rbit the planet. The inner radius of6ym/g/ns9i6m3cjdz x the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s/n, hio cm2h7t (see Fig. 5–9). What is the ratio of a person’s apparent weight to her rmnho/hc, i t27eal weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center oa/t)bdvw 7ext7 ,cs;hf the Earth's Moon in a space vehicle (a) moewbch7)xsa7ttv /d, ; ving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system vv3gohh/ :0 ,k 2pvmcsconsists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of eac v3h2p mk ,sho/gvv:c0h?    $\times 10^{29}$

  What will a spring scale read for the wei1v, jvh-d m.htght of a 55-kg woman in an elevator that m,t.dhv j1v m-hoves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended fr-b o.3offb7pi7ol3ij om the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What wasii -off7b. j ol37o3bp the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period Tvfu 4.rzaj 40c g*b:in , the density (mass/volume) of the pla44:ugjirvnf z cb0*.anet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period o emf q1l2gh f:s:z()dof the Moon (27.4 d) to determine the period of an artific2feds f l(m)hq ozg::1ial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the 1avit8 o3p ;peSun like the planets. Its period is 410 d. What is t;i1pe p8v ao3its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.ky9d wq in-hxyl1/.( s5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly on-pnc5u+ukt utwgl/ ulh772a8 ce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet fuupl5w8kgl+c 7 htun u-/a2t7 rom the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about geq 1b90 vu94 0jckoifthe center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean disil.mnd-1-7pmne di7z tance for the four largest moons of Jupiter (thospdz.m1i e m7n7id l--ne discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Mo3 fv m(uq2uqx8*ti:dmhc: me 1on. eqm*2u3q1 i8mt:cm vx(d :uhf   $\times 10^{24}$

  Determine the mean distancckx+mru4nx ju2h2+ z8e from Jupiter for each of Jupiter’s moons, using Kepler’s tuh uxrzcnk48 m22 +x+jhird law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter ,-qk0mxm0(q 4ghcf:2 5ntb+evkzx g bconsists of many fragments (which some space scientv kgb q0be-hkxzf(5mc+2 , :0mgqxtn4ists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale dzgg, m9jzn o0x wu;gu -)bkg)t+/+mnxescribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet'0xmmuzg/ jw+o9n g )ggbz n;,u- t+kx)s year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig.h5*oj 21a m//z, jh vgemif3pb 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is/jo,ajmmfv 2/b3ehh *pz1g i5 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half wyg lhfu th+ a et(7*)k+8syx;phat it is on the surfaceyk tl g+pt*xy; e(a)+fhu 8h7s?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handsg1tw1aq,k pnprki/dtn; j/ 0s )w1lt3 and spin in a mutual circle once every 2.5 s. If lt 3krww /;0,q1j/ tdn 1nga pk)s1ptiwe assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotatejzn u* 9*swo . (p5r4p.mhcugfs once per day, the apparent acceleration of gravity at the equator is slightlp *4ushnmf.jzuop( c.w* rg95y less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the E zw7bkb gfgi1ni :969varth will a spacecraft traveling directly from the Earth to the Moon ex1kn 9g97 6 :bgzfwibviperience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass iqkk:r xl*w+ (h:,quwz s 65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which dikwz,+q r x:w*(uhk:lqrection?     ----待选择----upwartddown 

  A projected space station consists of a circular tube thabziv)3z3 tg hi5wv b,;t will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to b5b; 3zv,w )v iih3gtzbe felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5– a:zqcs014 tzdp95t vw43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet 3dz ytj ;6s4nt j9jgo6in terms of its radius r, the acceleration due to gravity at its surface and the gravitatio 693 ndtjt; j6zj4gosynal constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertidf* 9socqv 5hz2 5:qyrcal by an angle dc5yf9h srz5v:q *oq2 $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient8 1q(jjxf 0pnrudln(mxiw8.7 of static friction is 0j8 (nq wx0 8xjnd1fpl.ur(7m i.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotatingi/;y2bxzq4fz-bwxljf2v 5z . so fast that objects at the equator were apparently weighwfz j2/. zbv bxxq-4l2f 5y;zitless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8 9+g 6eyya cn2/1acvqa.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a oy(m kls+ 3qn)curve of radius 235 m. A lamp suspended sloym( )k3nq +from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive aj*g4uty( ,)xusk88gf ; uunj ss the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Ju8yuj*fg,ktj8 s;n4ug )sx(uupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubb zh1p:iw+f zg+le Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a blzz gih1w+f:+pack hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant sp3m8d.zu,fqq,fpf y c. eed as it traverses the hill and valley shown in Fi f p.yd8mufz,.f3 qqc,g. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellitesmz5s m6oj e85vhm gfj.rxtk6 t g3b90+ orbiting the Earths j+mmkt h 55 83rtgv6egm0j .ofxb69z. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, -z7iv 91x xfffis meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40f- x7ifxz1fv9 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of 03, tz nx3ttj 0 -)kiyiwn))d*g aaocarepair. You are inttcagt) , )3xoyi )0-*wnanzk ai3j 0d a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a pem0: uj)+ro r8oo /zav)v1qq9hi po-bh7 ;aqvkriod of 3000 years. (a) What is its mean distance from hr0iqv1am 8j-qpohov;:o7 v 9 zroaqbu) k+)/the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of a-:/:e n;ktp:r(.nl0lk r qymsr xau, G would need to be if you could actually "feel" youru :st. k0m aqyap:,xrl(er:r l-/k n;nself gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of th1ftchtx*m(b3qiyr w9n,.r*.trn 9 aee Milky Way Galaxy (Fig. 5-46) at a distance oft.i, rm twx1rqyh**re.9c9ntn(f b3 a about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50q:)a +pa4 /7pfe w1r,*htsawbxxht4o m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint ax1r o q/x,*tb4s4 ep+pah ):ahw7wt fof the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eartqp.h;y w2 vb,uz ,2mrxh $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep secone hw ddhwq+208lccy8* d ha8 yl8cd+qe2w*d c0hwhnd on your wrist watch?    $\times 10^{-4}$

  While fishing, you gbs dp.33 nei9wet bored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of nds bwp3.i3e 9fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed s 7c xe yr17vssfey;y9( zy8be(o that a car traveliyye cre7 x 1b;9f7yy (ss8ve(zng at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of/,lnr0kx * rz)1bbwdxjgj-3 f the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience lexd3,r0 )bwfj -r/b1gxk lzn*jss friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$