Sometimes people say that water is removed from clothes ik tq w25bmdlj(3kc5*2a 5vs ton a spin dryer by centrifugal 3 wj m(k5 tb5adc5k stqov22l*force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp 8r j1ave87gwv6pqw2k curve at a constant 60 km/h as when it travels around a gentle curvgjva qk62vw 8p8er1w7e at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where doe.kzm( s v-m;iz0imp3 fs the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the km(imv m-3s;zz f0.pibottom of a hill?

Describe all the forces acting on a child riding a +m xrht 3f(mn0horse on a merry-go-round. Which +(nrmh t3xm0 fof these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water gx(vpq/7*my 1wt9 gi1q (m gdnt07o/0zqubd aspilling out, even at the top of the circle when the bucket i ybt v(igdq xz/w1m/o ud07(*nqt09q1 mgp7ag s upside down. Explain.

How many “accelerators” do yob+p*k;5m exy3aykq+h3h xug* mp zv26u have in your car? There are at least three controls in the car which can be ukyx* p z3p26uh+mem;vk5 x*3qb yg+ha sed to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smal2su41f o9kxu p1ud.qwl hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the no4 .ku qxdu2f p9ou11wsrmal 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 when rounding a curve at high spee -gbl-:q)yp7m7,11mw vwmv fsw:i orz d?

Why do airplanes bank when they 7/cyevsixkz if71;k2turn? How would you compute the banking angle given its speed ank7;xks 27zii /vfe1c yd radius of the turn?

A girl is whirling a balh b hj1 *w(eh+va/z(txegq-5 el on a string around her head in a horizontal plane. She wavx*b(jqghehetw5( e+-a z/h1 nts to let go at 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 the Earth? If so, how large a forx ic bm:v+t(hb7a(fu7ce? Co+:xcf7(mbv(b 7 ihaut nsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what b3m ua)-o;tfnit is, in what ways would the Moon’s orbit betaon;u)m fb-3 different?

Which pulls harder gravido7.2vcp scpvpm a pi09jy951 tationally, the Earth on the Moon, or the Moon on the Earth? Which acceleratevmp p21dppjvs a59 iyo .97cc0s more?

The Sun's gravitational pull on the Earth is much larger v )n/sst,qvbndx3+0 sthan the Moon's. Yet the Mood,x t3s0svn+n vq sb/)n's is mainly responsible for the tides. Explain. [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 poles? What two effects are w0, +jxtozz;n at work? Do they oppose each other?jw ;,oxtz n+z0

The gravitational forc8c tp-x4 d1st,u2qgbbe on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pull b1qts2b,x4ptg8 -dcu ed away from the Earth?

Is the centripetal acceleration of Mars in its orbit aroundtwuh;g .-9h jlpy 1fh4 the Sun larger or smaller than the centripetal acceleration of the ;f. g1h9lh4jtwphu-y Earth?

Would it require less speed to launch a satelll - eei62*h5s5 ytnewve9m pf3i:6vnkite (a) toward the east or (b) toward the west? Consider the Earth’s rotation dirp 263l eef96win vm:tv5ehek-y*ni s5ection.

When will your apparent weight be the greatest, as measured by a scalr g,/b bn ddzdv4)miwe:z,f)3e in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) mo wgdb,:/b )d,)fen3zvdi4 mrzves 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 ihxp,bl:v / z fof2gj,8n outer 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 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 zf vhbog2jl px ,,/f:8gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weights5 ,ox *+ift ;d/jms dbg5xjgija-4+slessness” betwee +5diijjsa*oxs xjmsg, 4d-ft 5bg+/;n steps.

The Earth moves faster in its orbit arougy s40 ;7oe85k xzqxiind 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 producing t5i;ixo 8 zkxs e4q07yghe 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 j6b - o1pr3iyp q1rjc5known until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s ma1copj 5y rqj3-16bpi rss.

  The Sun's gravitational pull on the Earth is much lwqo7 f +cwzrgem*s kk.0)3c2u arger than the Moon's. Yet the Moon's is mainly re ecfsq0r+3go k*m)kcw 7zw.2usponsible 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 3ym8mrzb4xlvo 1oi 42 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceler ,ki pej9*n9 ufit0 y-sa n97ab+/pw hy33qlhration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radit ap*wyki rs /09be-yhiq399anuhn p+l7j, f3us 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 on1b5 r5) 4ohrbvf mt0bs a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed o4v5) t01s rm 5brbhofbf the discus.   

  Suppose the space shuttle is i/1fpk1pvj a5zn 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 orbit. Express your answer in terms of g , the gf5avpp jz /11kravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay odw:3p (p naf ),dp7iidn the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm? n,df(ap i7:p)3ipwdd  

  A ball on the end of a string is revolved at a uniform rate in 4yw,*.m n.rl 2 nwuvnea vertical circle of radius 72.0 cm , as shown in Fin4ly.nn*v u2em.w,r wg. 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 wp 8qhdwp4.e,rf; on 5g gaql/1d+c:bspeed 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 and road is 0.80? Is this result independent of the ma pn51pc;drb/ .qw la 4e,hg:o8dq+gwf ss of the car?   

  How large must the coefficient of static friction be between 9lsr/x;j cdtv 567qqalqlts8:9 qdstvv +w;7the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/htvltx6csw vqslj9v/9;q8d t:s;57rql 7 q a+d ?   

  A device for training astronauts and jet fight og)gbu/rlk* 1er pilots is designed to rotate a trainee in a horizontal cbogr*k )gl/1u ircle 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?    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 q7ahk p,y+ fd3the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until 7q+af3, phkdy 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 coasteacldrt :zr.;7u cqe3 v9 fgj./tp*w;jr be traveling when upside down at the top:l;9ftqr3d;wjj.7tc c/r .zev*gpu a 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 (invhs9 u; :nada5rx gkb9s.cy;3cluding the driver) crosses the rounded top of aybuassgha.9n; 9cvk d 5x3r;: hill (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 mz u*ngz0w;d 4iinute would a 15-m-diameter Ferris wheel need to make fornwzzd*u 0g4 i; the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.1:e6q9ricdwv:1r; aw)jzm 1dn0 m. At the lowest point of its motion the tension inr dwjein6va z)rwm11d9 ; ::qc 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 centrifktjqyjt3z6bspir( 4)df/6 ( fuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acc3y 4s/6idtr6)ptkjf(fz( j bqeleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peopleoo734n(wmd5 glia *y,xbdk5 p are rotated in a cylindrically walled "room." (See Fig( kyobm ,id galp*n73w 55xd4o. 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 cwf(b6d;1n lk3lh :iisircle on a frictionless air-hockey tabletn6l:d(b i f;ikwsl3h1op, and is held in this orbit by a light 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 the weight of the+3v-vic t 7qrf ball which revolves on a string 0.600 m long. In particular, find the magnitude o + tfvriqv3c-7f $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 per il/oe;7pxbc*-z qm4hra+ 0xr86zrnb fectly 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 massea s/y e-k95zk5o w0(xngznz 8hs $ 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 310gkbns.kn ;u*7 4(h ;5jshnen d $\mathrm{~m} / \mathrm{s}$ . 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 com+akx, avs4 h41p khvl 1na7r nxty:e/:ponents of the net force exerted on thenp44/ ::a tel1,akvkhs+ rv xxyh17n a car (by the 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 accelerates uniformly from the pit h6zkig l+h b;n4ym 36qarea, 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 and the road to provide this acceleration with no slipp;bqy3+h g 4hkliz6nm6ing or skidding? $\approx$   

  A particle revolves in a horizontal clj09,)sbg*r)-gffj6 rd)fq 4by mn t circle of radius 2.90 m . At a particular instant, its accelgs brf) 40l)rmytg6qn)fj,* jd 9f -cberation 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 spacecraft5ej m 4i8w+ubeeh-l tnyc,cwl7ep1.*c0 w7 lg 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1icwyc87l4w l e et1 *n+pl-cb .ge5ej,h0m7 wu350 kg.   

  At the surface of a certain pla5hh pl7qj6+cvnet, the gravitational acceleration g has a magnitude of67hlh jpv qc5+ 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 gravity on the Moon. The Moon's radius as- dia+:/s h/wpif* gis 1.7:/+w fp i-g idasa*s/h4 $\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 z7e)6z ybq4 0-4y9w+8t iyodaxycv xvthe same mass. What is the acceleration due to gravity near ye -b04yv cy d7t)+ 49w6xzxqyvz io8aits surface?   

  A hypothetical planet has a mass 1.66 times that of Eaw5tj;fu)w;l p rth, but the same radius. What is g near its surfacw;lutjfp );w 5e?   

  Two objects attract each other gravitationally with a force of 2b 43w- /e0(n5fvmr(p,c ad. bgxypyzu.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 gravitynw6.o+w geqb;, at (a) 3200 mgw.nwoe b+q ;6    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance 6.vqr4g5iv gf4vnmo dztj +5) from the Earth’s center to a point outside the Earth where thegravitational acceleration dvvg vz6df5j4o ntg)m5i4. q +rue 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 packed into a sphere n s3ykr8 gs d5,i:8vl zf.tx+ xcqk5o8about 10 km in radius. Estimate the surface gravity on thisx8+l5oi:c3yvkd5. zqg8,rkn xf st8s monster.    $\times10^12$

  A typical white-dwarf star, which once was an average sbeaz 3q6i51.bfc, 3l2n ssgqztar like our Sun but is now in the last stage of its evolution, is the size of our Moon but hizc,gb3sn1q ez 5 .qf3lab6s2as 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 tr,f;kl, c5uain the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t soa c,k5,lu ;frt by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 jkfsdgpx.9p,l:b5g1 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere x ,l51pk gp:g.9s djfbby the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yearvd76 h)nr9wxvxs 0h h9s most of the planets line up 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 isr07h h69vwvd9h x) nxn 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 accelerationa 9khbk l 5dl:/ng:+pk of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass oh 5kk gp9ba:ll/d:n+kf Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Eq1i c:-blo w ,rwvh.s+arth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example v1:cw+si-bl , orq. wh5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in c g ;xzrbom,*4cdy5+h a stable circular orbit about the Earth at a h g4;hr o z+bc*,mxy5cdeight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the s*-cn,zp/ (oaxgq3 pe Earth. How fastxp,qz-(/3e pgs aonc * must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship r/ lu8vq1kpv.w otate if occupants are to experience simulated graw.8 p qvv1klu/vity 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 orbit the Earth in a circula0xkqi2ed8 y 7ur “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Eart0xe y u72ikdq8h which is very small compared to the radius 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 topk ot2nby,k inugyvi0*85l2 q ) of Mt. Everest to be placed in a ciyv*l8uik 2y 2oi,0)nqgt bkn5 rcular orbit around the Earth?   

  During an Apollo lunar l*v 40f1;0rbe 4f b es-fgg/rmshmzd1manding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take trv;b-1m hzgsbrf 10 em4*f0/ fegd s4mo go around the Moon once?    s

  The rings of Saturn are composed of chunks oturh(8 dn vu k;te p/9tnl:e53f ice that orbit the planet. The inner8vdu; rpn/en 3(htkte9utl:5 radius of 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 gaq5 zu.phnnd) w 9qbd)x/0o3aa4)d b rotates once every 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, a5. qa9dbuwxa)0zn )o3bd /4da)n qp hgnd (b) at the bottom?
(a)    (b)   

  What is the apparent wei5mw 7q bnftmvg+hz z8l n +1oh555h3lcght of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a5 ozh5bmv hc+ 1g85nlz7lw+qm n5 3thf space vehicle (a) moving 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 consis w.of8v-xpxquo jm:1/ts of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit ab/x fxjm.puw 1v8-q :ooout a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read fo 9bv5;m51xr+ltm ai nar the weight of a 55-kg woman in an elevator thatv ;tr+mb19ma xin5la 5 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 frt ,n4ovxx22vr om the 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 acceleration (magnitude and direction)?4o xtxn2, vr2v a =   

Show that if a satellite orbits very near the surface of a plma k4mn4ra; wh36z i4vzgw(m9 anet with period T , the density (mass/volume) ofw4mwa 39gz4 mmn6a(4 v ;zkhir the planet 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 of the Moon :)tk: prhld0 8 x8(juoyno:on0ct4w q(27.4 d) to determine the period of an artificial satellite orbiting very nexlwotn ckj oh(r0dp: 4 )n8o0::tyu8qar the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits td 6)j m,,uaqjohe Sun like the planets. Its period is qj6,udm)joa,410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagq-iw (6ss+jv(d ouoh)e distance 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 every 76 years. It comes very c bl f0xj79*17fxl5fwiow9ri1;av y pulose to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from 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 t159wrfillp x 7 fw0yo;a7b9u*1jfi v xhe sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the ce 6 m lwl7,p6,sxyeu.tpq:ui/k-x6vd4x0niwn nter 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 distance ehtnh7tff g.,;vt ;:pfor the four largest moons of Jupiter (those ;tttn ,:hefgph7.vf;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 uf02q: rmmb8s the known period and distance of the Moon. 8b0ms2 fq r:um   $\times 10^{24}$

  Determine the mean distance from Jupiter f b/xqs07 +cvuzor each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io azq/x v sb+uc07nd 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 and8i4-lggz hb;u Jupiter consists of many fragments (which some space scientists think came from a planet that once orb;bhg guz4 i-8lited 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 describes an artificial "planet" in the form of ezd q79i a3m:( vapv lbl*p,/ea 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 Earthi v a am7*3pee (:/9,dqvzpllb. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an aah. l1lm he1n1rc from a hanging vine (Fig. 5–41). If 1.1 lnlhameh1his 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 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of grao)onf-q2v b-rvity be half what it is on the surface? o-rqof n-2v)b   $\times 10^6$

  On an ice rink, two skaters of equal xx wli d-b67iqi51k9p mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 ixbid579qw-p kix1 l6m long and 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 appare 2 9p2zy5jn2dfzjt1;0bmuk cgnt acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimg9jz1p5 j 0ky2tdmu2bzn ;cf2ate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecr/(ed,k2ogzp raft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and op2 ( kgro/,edzpposite forces?    $\times 10^8$

  You know your mass is 65 kg;e*ou vtl2*wq , but when you stand on a bathroom scale in an elevator, it says yo 2v*wl; otu*qeur 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 tub 7 g,i lsjq m-./7hmf3iay3+hyvqwrp 2e that will rotate about its center (like a tubular bicycle t2h i 7 q3a,q3rfljw m+vyp-igyh7m/s .ire) (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 be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircrafqbak vr l)pq1xi;+f+; t 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 acn1m(dor g-)qfv(z 8wo y(z hl;celeration due to gravity at its surface and the gravity1 -lr;(w()dm oo vgzhnzfq(8ational constant G.

A plumb bob (a mass m hanging on a string) is deflected from d3ky4c)o4uua3d fe+;7;8 hyq dgfv epthe vertical by an angle c)8gd4 4+avhedf3 k3fpy u;u7o dey q; $\theta$ 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 coefficient ov (x /aj nqebryqdm0nh9v*)( -f static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the cur)hm a-(9 j byed*v0/rxvnqq(nve?

  How long would a day be if the Earth were rotating so fast that objxe)im.b ;lu8 zects at the equator we)il mbe8.z ;xure apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 p ll b4pc m9)vg6,etc:$\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 curve of radius 235 m. A5lij;m):q ehi lamp suspended from the ceilin i)5hjileqm: ;g 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 as the Eat;-bmd)s p 5tsh)oy b+rth. Thus, it has been claimed thasby)t;tm ohpd+s-5)b t a person would be crushed by the force of gravity on a planet the size of Jupiter 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 Hubble Space Telescope deduced the presence ofy 5ar4pnp vqnpp8 90lr6c:b(p an extremely massive 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 the4 v 6p:5cppqpayr l(nn8rp90b 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 traverse,un2igaal 9f0s the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of cuala9g i2fn ,u0rvature 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) utilive f)r, 17uilwq4 /5*cqplozazes a 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, allowing contizq)*,r ce45fwllapvu1 o/ q7inuous 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 Rendezvorz5(g io1ggx86h:xwq us (NEAR), after traveling 2.1 billion km, is meant to orbit th gz:q(hxr8ogiw1xg 56e asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 repair akh+1lv8k :3hdmd5m z. You are in3:m 81zkdmk+ da hhl5v 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 period of 3000 years. (a) What is its mean distanc104k88v y i)t7sz rdjjzkx-e xe from the Su7 81j jtdxrkksz)04 zxiey8v- n?   
(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 co sfc:kwtam34sv3- 4 qjuld actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like F sa44ms3ct:vqj -3fwk $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of tx9q9lty/vvp(iukl eag6 +s 61 he Milky Way Galaxy (Fig. 5-46) at a distance of about 30,00+i 9eya 1ku(v llv6psx 6/tqg90 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 coywnkl0x jtfs88j, -5brners of a square 0.50 m on each side. Find the magnitude and 0ftnk-ly8sw,b5 jxj8direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 k9o2 k)f. gqu5euz7 eoqg orbits the Earth $ \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 accelerati*t34ap svfk y0g*5io mon experienced by the tip of the 1.5-cm-long sweep second hand s g at0yfp*4vimo k3*5on your wrist watch?    $\times 10^{-4}$

  While fishing, you get boru-qc7/ m)8zvq shz134xzg m mqed and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complz4zmu)h-q8 73 /1 scmgmx zqqvete 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 so that a c4oug2 )9 nlzniwm w6;uar traveling at speed uzwim2gnwln; 9) u4 6o$ 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 Abx* 2;c shmj ewbga:m 7hn0;rw q64e0ocela, utilizes tilt of 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 less friction force against the seat, thus feeling more comfortj4hse;ww *cma 6r0;n07m2oeq hbb: xgable. 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.$\approx$    $\times 10^2$