Sometimes people say that water is removed from clothes in a spin dryer l 4q6( pshrra,by centrifugal force throwing the water outplrh ( 6sr,aq4ward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels aroh4pnyr fsuw32po57 96k .w qbxund a sharp curve at a constant 60 km/h au 3yhsw9pf2rwpbk5q on7 x64.s when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along ak hzjd1* 3izo ed( r.djcck/,2 hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two .2ihj,o3c/rze* ddjk1zk dc( hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting o: :feq5l(wah in a child riding a horse on a merry-go-round. Which of (a:: whlq 5feithese forces provides the centripetal acceleration of the child?

A bucket of water can be whb/d(2 uya br xmy8ncn5-cv2v*irled in a vertical circle without the water spilling out, even at the top of the circle when tc (mv8/bn2xvd*yrbn ay -2u5che bucket is upside down. Explain.

How many “accelerators” do ttlxcig rp--o9.f0ul1vc2x * you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. Wxgxto -v*-0l ucc 2pilf91 r.that are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as sho:wv;)5: 3 j5zu8gjhkhcl 5pj / nlsyxxwn in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over ; 3jnx p5wgy hjs8x :chv: /)luk55zjlthe hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean ouv:(bv-xfu, inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute ths1 hngkh5:sfg)3 5 spzw(z1dk e banking angle given its speed and r3gnzdhs1 (:k)1 5 fpwz 5hgsksadius of the turn?

A girl is whirling a ball 4wm/z pwek)5e on a string around her head in a horizontal plane. She wants to let go )/wp kmze4 5weat precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on theqw 0x 933rf2+fj kruuj Earth? If so, how large a force? Consider an3k9ufu f+xwrqj r2 30j apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wouldmhj s3zekt( f(/2n; k1ou,sx f the Moon’s orbit bezh2mxnos3ke sk(tjf(1/; u, f different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the d h66 k dsf+a7f6ueq;gc6d +nl b6zj*xEarth? ja6kl qfbhd 6+ 6 +667zd;ux*sefgdcn Which accelerates more?

The Sun's gravitational pull on the Earth.;mwu qa8of-h is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pullfw.m; a qu-oh8 from one side of the Earth to the other.]

Will an object weigh more at (zga*y mrvi e63i8bhj3:b/ asthe equator or at the poles? What two effects are at wo* j8vbzba:y 6irieh (g 33s/amrk? Do they oppose each other?

The gravitational force on qlzw51*vxt vbffv28*dr*;h rthe Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pufd t8h; v2rz**w* xvbf r5v1qllled away from the Earth?

Is the centripetal accelerar mpp7j+;folpk690 lr dox)4ism5 gc8q m:m2wtion of Mars in its orbit around the Sun larger or smaller than the centripetal acceleratiow8r7)+ oqrcm:op26 f40li mpl5 ;9gmjxkd mpsn of the Earth?

Would it require less speed to lau+e bwpfs1ytw +t2ay pq .3-1rrnch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation directiray12w tf e +b3s1-+qwp rt.ypon.

When will your apparent weight be the greatest, as measured by a scale ikao /rf:0n3s ef2q8hyn a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) 2eha s0k 8fqony:3f/ris in free fall, (d) moves upward at constant speed? In which case would your 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 outev0nz*,c op3;9hro: afqh y8*hjrs 7lkr space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside su8j hsro9h:3f0p;, lvcnr*kzh 7oq *y arface (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 experiences t 5f8f1d,8g 9b;pm8p wl;tq ka;o u 9jirns2lg“free fall” or “apparent weightlessness” betweenq9 l;1furptgsi ;8d;ow2ak,jb nm85gp9t8lf steps.

The Earth moves faster in its orbit around the Sun in Jll kznp(v ay ,*3;h6chanuary 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 producing the seasons — the main l3hh;k vcyzl 6a (p*n,factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not knx9 rp3nx 1/kvkown until it was discovered to have a moon. Explain hvp/9k xx 3nrk1ow this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on th bxvar,68g od+sy;k1we Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one sixgak1ov+b8sr y6;w d ,de 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 1m5:0fuix fjp-980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceloqu gu( 3x*oh-(l7agq eration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Aso 3gho7u-la*(qx(guq sume 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 2.0 q cag8m/t;pq3m-h c;x-kg discus as it rotates uniformly in a horizontal circle (at ar ;;mgxqch/p -qt3 8macm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle 5dvo5kbd 2ee( is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbi5e d2koe db5v(t. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitudeu a;ub/3e7hx-k qv4 ql of the acceleration of a speck of clay on the edge of a potter’s wxu ;7b3 hekq a/ql4vu-heel turning at 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 ratec 6:ej2s 6grihi-nf2h in a vertical circle of radius 72.0 chin-h r2g j6eis:6f2c m , as shown in Fig. 5-33. If its speed 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 speed with w+ mtly(4 cfk1og/whcgwi 4p* ,hich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the hg+*cy/,4(f lgi14mp towk wcmass of the car?   

  How large must the coefficient of static friction be between the ti*6:q-zyb u yqmres and the road if a car is to round a level curve of radius 85 m at a speed ozmb6 :yy*qq-u f 95km/h ?   

  A device for training uj4o) pyuo;alx27 bb)astronauts and jet fighter pilots is 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 7.85 times her own weight, how fast is she rotating?ao)uu2yp;4 oxlb j7)b    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 from the axis of a rotati5 33.c.;caeiy qtlfgt0 k1p cpng turntable of variable speed. When the speed of 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 coefficiel0p cy 5c3.ik.ft3a;pe gtcq1 nt of static friction between the coin and the turntable?   

  At what minimum speed must a roller coastey p5s jg9r9w0yr be traveling when upside down at the top0syw y99j5 rgp of a circle
(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+pmv/ b1 m5nya:x1 uwc rounded top of a hill cv1xpmm/u b+5aw:yn 1(radius =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 per minute won:9+ ij;k39nn2cqxmbc d +opv 1(hd iruld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost point?vn ;r c(qinp++3odn2d:h9cmbk9 i1xj    rpm

  A bucket of mass 2.00 kg is whirled in)a sqvhsoh13 1t3c .ws a vertical circle of radius 1.10 m. At the lowest point of itshsv3 st.wh1cs q1a)3o motion the tension in the rope supporting the 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 ifw)k + e;;fqqcr a particle 9.00 cm from the axis of rotation is to experience an accelerr ;kf)e;qc+ wqation of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a ctn4 wnndh8g- 4ylindrically walled "room." wn d-h844tgnn (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 on a frictibn(h z,5 /(b h vtn,zdzdt(h3q ,gatg/onless air-hockey tabletop, and is held in this orbit by a light cord connected to a td,(a bqz5,((/zvn,gh/ h z 3h ttgdbndangling 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 thiz6g (tej 8v,epsoq )w-s time, by not ignoring the weight of the ball which revolvese wv8js, (- zg6top)eq on a string 0.600 m long. In particular, find the magnitude 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 ( 1n24t7)hvzuz/gvoo;ufgy+y vn+hz banked for a car traveling 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 masses jublr89cs(; c h 7jm0h$ 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 evasi, w wrlw,6(bsp x1fp4wve maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . 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 comq7tr5 ir )wu;fponents of the net force exerted on the car (by the ground) in Example 5-8 when its qr; 5)urti7fwspeed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerateh/.+2oyguu+w 3pc r sp3 :qmkzs uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential 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 agz/hps m+crq .+3puk 3y wou:2nd the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radiue(1ju/emi9 lx s 2.90 m . At a particular instant, its acceleral em1iujx /(e9tion 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 ovw 41iwx20o dpn a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfi2pwo 4w v1x0dace if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g ha k3r.b0mi;*m/gb j9qe.nc0 fm bq0zgis a magnitude qfibg3 0mgm* /r09.bk;i .0 cnqjbezm 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 t(v 13gcdnn a23:d dvzdo gravity on the Moon. The Moon's radius is 1.74 vzdacd1g ndvdn:3( 23$\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 has the same m w s0ldk5up5a)b 8flc9ass. What is the acceleration due to gravity near its )pc0d s85bua9w5kl flsurface?   

  A hypothetical planet has a mass 1.66 times q.p2y+ :7c f l,yig0p6 kzjveathat of Earth, but the same radius. What is g near its surface+afk g6l y.p7:j2zyeip0cq, v?   

  Two objects attract each other gravitatiob: gpg qbd*,;onally 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 gravity, at (a) 3200 jyr9ig oco ,mtoe26u(v) b(5 wm2w(roo 9go5, uit(cvmj6eyb )    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earthpsbhrf-76ol ; yotu x89.t u69lt:bnh where thegra-y7ux:bp6fotst9 8 ot. u;rh9 bllhn6vitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun pa;is/ p1o 5:gol5 srbvhc;;v-mw sz/z vcked into a sphere about 10 km in radius. Estimate 5;ph /;glvor-ois w/:zs;cz5b1v svmthe surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average st wtmy;qhgm6rm),tti/, 8p)j car like our Sun but is now ih 6)jgty rp ;)t/8mwim,tcm,q n the 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 f:rfu* a(hmo+, zyluovkg6e/ts/60 w in the space sh wzv,gok( u f*uaofs0 +t 6h/m:r6/eyluttle. 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 gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are loc4r4 1em fdq+ykfgw +/yated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the oth mgrfqfk1w /y+4d+4 yeer three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on-f23( 3u pawwx6oejemh 5mg3nahf+4 j the same side of the Sun. Calculate the total force op54 -njm+ ( 2mo3ge33hjfwx6aaeuw h fn the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses 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 grav8)k zbz;frxm2h c3 ducn84le9ity at the surface of Mars is 0.38 of what it is on Earth, and m3 )x be4z8cdhn;lk 2u c9rf8zthat 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 period 1u jbch;o/hj*h. 6w liof the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.] .ohh6 1u /lwj*b chi;j   $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the u j3ytp7 ryna 01u-6avEar031jn-y a 6p uuy7ratvth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km aboo3um bvd)i2n3 ve the Earth. How fast must the shuttle be moving (relative to Earth) when theobmd3)u2 nvi3 release occurs?    $\times 10^3$

  At what rate must a cylindrica tq-+ 7w0xfnbyl spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your+y0nftw7bq- x answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular rurb/vo v8nm6;)ju4 k“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 radiunu;4ov/k j6r m8r )buvs of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the tope)m4lq)z dsq qf;jp;(nwr/ 2m of Mt. Everest to be placed in a cirm2zpfse /qw)m)nd(l; ;q rqj4 cular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module l.s us3j)vce7o p0w:j fy +:spcontinued to orbit the Moon at an altitude of about 100 km. How long did it take 0u7 .jp:fowyv :l)sec+jss 3 pto go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that ord) j*ugfpg)ij5 f9y 4qbit the planet. The inner radius of the ri p4* g95ygj)fuiq) fdjngs 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 eva( 3 0pi 3yo udjn*2hqv-4kyalery 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bo3uy2- n0o3(p*dlyhkjv 4qai attom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of v5ldan( xq*5r;y*q duthe Earth's Moon in a space vehicle (a) moving at constant veyrxddl (5 un;5 qa**vqlocity,     ----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 consists o-s7p f.h 4zqnsf 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 hf7sn-zs.p 4qthe mass of each?    $\times 10^{29}$

  What will a spring scale read f dkmji,10jm s( ijur sfi0+*o9or the weight of a 55-kg woman in an elevator tha i ij*+f,1dss m0j0jm9ioruk(t moves
(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 from the ujl/ ofc00q6t ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accfc0t ou6jql /0eleration (magnitude and direction)? a =   

Show that if a satellite orbits very near f0s:b 6 zjgsa-the surface of a planet with period T , the density (mass/volume) of the planetz 06jba sg-f:s 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 hnj2p0y+p ) ko5df xx(i1sgf.r rmn+ :the period of the Moon (27.4 d) to determine the period of an artificial sa)(nx+:fg+xk ipfhomr502nrs d1jp.ytellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters l/zuw;y2r +v :lrf st2across, orbits the Sun like the planets. Its p t 2/zu;vlsrw:l +ryf2eriod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance 5ix d7: r3p.yvwhi,ai of 4.5 $\times 10^{9} \mathrm{~km}$ 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 once ev8uor +h+ kf/t)s4zfk rery 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 from the Sun. Is i)4 frt++ z /hk8foukrst 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 the center ofudgvrc;2;fl 3q ;f-cnc .6hwwo9n6 ua 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 distance for the fg4.ui csql3u0 our largest moons of Jupiter (those discovered by Galil s.43ugi0l quceo 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 know 2lfs5xn+ xha-n period and distance of the Moon. f +-2 hxanxs5l   $\times 10^{24}$

  Determine the mean disb + siw6z/:zhktance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare tozs :zwkh6/+bi 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 consists of many fcca6,f: p;outmn 5 c.vragments (which some space scientists think came from a planet that once orbited the Sun but was destroyc,5ctoaup vfc:.m n; 6ed).
(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 describes an )o7awv kw2 q9enh sh5.c9/lqp 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 ewao7ch )qkpn5vlq w 9s2/h 9.planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from azgu 1ocz v:vh+j2:0dy hanging vine (Fig. 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 thej c dvh2o:y10+ :zuvgz lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be h6l+s;b/2a tjss gy)g;bg-a s9hu c+u calf what i;j/ a)saclug+ h gs -t;gsu2+s96ybc bt is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handtkl;.-lvv- yx s and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long an lyv. ;-kv-xtld their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity y wrp b2s3-k ;+46hick:tg pkpat the equator is slightly less than it would be ifp:hwst3 -pk+2 rk6g 4 byi;pkc 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 Earth will a spacecraft traveling directly from b66aup1hcnzn: *r8 pcthe Earth to the Moon experience zero net force because the Earth and Moon pull wit : 6rncza *cnp1pu8b6hh equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand onlw*x)vo )g um* a bathroom scale in an elevator, it su **) vxlm)gwoays your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abogo4,ko,al( a yut 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 tok4lg(oo, y,aa be felt?$\approx$    $\times 10^3$

  A jet pilot takes his an42 x4pa -ici.4 1atokh +z9idbx 1bdgircraft in a vertical loop (Fig. 5–43).
(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 in terms of its radius r, the acc)1xe-pzu 0ap* xlh s(yeleration due to gravity at its surface and t*-y sxx)u 10apz leh(phe gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vc3jl-5 hyw393cyol.t-,g y r1cbvmwk ertical by akyrt,5h-93m c.1wb 33 wlocyyl -jcgvn angle $\theta$ 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 coeffi51 (ktt uoc2bibe ic/6cient of static friction is 0.30 (wet pavement) 1( becbcto6 i5ui2kt/, at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rm8a4 v/t7u id sv9xo7totating so fast that objects at the equator were apparentlytt d/8v79i74 oasmu xv weightless?    $\times 10^3$s

  Two equal-mass stars matkldz3(8 (nx u b;s5/8xh5dmx1irduhintain a constant distance apart of 8.0 $\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 smlbi0bx8 * g-m4iok d+peed rounds a curve of radius 235 m. A lamp suspended from t04d8b* m-l iimk+o bgxhe 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 massiq21l3ibazso ;1k ywx +.ezrfhq9e s..ve as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive myxiz e .o2 s+ .9bqh.z31qas1krw ;lfeore 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 Hubbl 3f9sdjv clck+s;awh8z3o;et68 c a y*e Space Telescope deduced the presence of an extremely ma;sl wo;ejfcv98a z6 * 3sk3+cda 8thcyssive core in the distant galaxy M87, so dense that it could be a black 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 speed as it travoqa+fk 5qqcg2 2 +ef:0u-rsy yerses the hill and valley shown in Fig. 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?2gfuo+2yasqq e0:k+cf rq 5 y-

  The Navstar Global Positioning System (GPS) utilizes xgp urq i.z(d7*)bxqq-ac 5( da group of 24 satellites orbiting the Earth. 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,b7u.(qz-pd(5) qarg qcd*x i x 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), aft4 y zusstfji 0 vnx: tf8mk.53+tq8gm(er traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40fvxz qnfk 53 mu(8 .g4t:s8+js 0timyt $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 bb4y/od3h-7 mitw pe)the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (40tbedh)4 pym3bo/w7- i0 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 period of 3000 yearl7gh,ap ko4 z.s. (a) What is its mean distance from the Sunlga7,.po h4 kz?   
(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 G would need to be if you could actu4c xo,ta 90ms o k7 lm8j ,tlcsava/ii:uh7-u,ally "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, lik4vja stomul:,,,cukamh70/ 9o-l7 i 8axic ste F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at alra s3pi12rg.v s *t,n distance of about 30,000 lighttispnag,* r.2 vls3 r1-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 m5gbk lds 63.q0 ini5da square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpo g6l q5.in5dids03m kbint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the w2 cl:v; ham)yqaild 6 s:yu09Earth $ \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 seconv 0ckpa ecgtmbi;ac:2:5*qt5yi/-k ld p:k5 t/y* -m2 5ali 0t c;:keqcvgabichand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start todicv41j;*pc r swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the acicv jd41;*p rngle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a ne,, tmss81/bl rllt4a*up vj6r9*tj gzw highway is designed so that a car traveligsm,tvtr,* zl1lbtr4 9lj8a6 pu /j*sng 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 tra//,tub 5kd2duymi .lqin, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to providd dmy biulk2,uq./5t /e the centripetal acceleration, is the normal force. The passengers experience less 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.$\approx$    $\times 10^2$