Sometimes people say that water is removed0myasz3 yv5tb39 t dpw)mkg +5 from clothes in a spin dryer by centri33t z0k+gvs5mp) ab yymtd59w fugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels/slxc://jx(5l c ie so around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the s/secxo /xi(/5lj: l csame speed? Explain.

Suppose a car moves at constant speed along a hilly road. W7g5cw ffs23ftk l6cy v q:*ij;here 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 hills, (c) on a level s 5cw;6c3 :fkifft27jqlsyv*g tretch near the bottom of a hill?

Describe all the forces acting on a child ri9*42;n xa;n dikozoupktc2a1ding a horse on a merry-go-round. Which of these forces provides the centripetal acceleran4o2ano;zk9cxk udi a2p ;* 1ttion of the child?

A bucket of water can be whirled in i9yq 4+.:d2+,rwxaw3l zwu61qap4af lrj huza vertical circle without the water spilling out, even at the top of the circle when t: ywqr+1w 3,6lzuad9 4p aa+wr.qxihz24flj uhe bucket is upside down. Explain.

How many “accelerators” do you have in qq,.anlyb(oh /m f)8lyour car? There are at least three controls in the car qlabh(f / .ql,8nmyo)which can be used 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 small hibm.pk 7b hm,o2mnx) z:ll, as shown in Fig. 5–31. His sled does not leave the ground (he does not achix, k )pobbh2mzm: .m7neve “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 when rounding a curvelu.p)hzf ke +h2nh s:5 at high speed?

Why do airplanes bank when they turn? How woulw7+wlw, ;rqln0 wst4a d you compute the banking angle given its speed at+w waw4w r ;7,qsn0llnd radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal g9e g;j f7p c4eb9ium1ky3-olplane. She wants 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 offckly -1 ge9u3big7oe9;j mp4 the string?

Does an apple exert )+kh( mtnac nb,5:ipba gravitational force on the Earth? If so, how large a force? Consht)bai k:m+ nn,( pb5cider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whasmlh3 c 68 )vd/tv(-mlc-vyewt ways would the Moon’s orbit be dimst-vd (m/ )vcy8c-3 lhwv6 elfferent?

Which pulls harder grad3ttbu, .dey *c1dmys+ 9w;hd vitationally, the Earth on the Moon, or the Moon on the Earth? Whtes* ,mb1 dy9 hwyd+t;ud3d .cich accelerates more?

The Sun's gravitational pull on the Earth is much lwdx rokdb)s;y::nk+ag +7q1 earger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitakdxeywob7sg) +1 +qd :akr ;:ntional pull from one side of the Earth to the other.]

Will an object weigh more at the equator or an5c1(l 6fdaozt the poles? What two effects are at work? Do they oppose each otherl 15ad6zo cn(f?

The gravitational for76ixcb* 1tl* pcqy1znce on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why ix6* cb1 i17*tcqpznylsn’t the Moon pulled away from the Earth?

Is the centripetal acceleration6-ry 9pnk:,reuzys. c of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of theze n.prkuy,r 6c -ys:9 Earth?

Would it require les4 kiun,a -q4tjs speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation diretu,nj4qk -a i4ction.

When will your apparent weight be the greatest, as measured bf8 ety; )rviv1y 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 your wefvrivyt; e) 18ight 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 63rg(2h zg 4mbcd*d2mde*r cmlong periods in 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 c6 gmg2 dr3cdrem* bz2mh*4( d(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 “free fall” or “apparent weightlessness” betg6 xf0lcgihd*v-pwgy.9a l ;c(s6ib3ween s-s;a .dhl6cgg 6cp xgfiy9li *3(b w0vteps.

The Earth moves faster in its e n(;hoga fr2)sd:rp8orbit 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 produgh8 fa d o;nes2pr)r(:cing 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 oocsko*f:1 mz1alpnt;.u(- vknown until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s vzsc1:o t;-k( .plufm *noa1o mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's.. )a++eqqp f xco,*x3zvn d;qd Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference x ;o d)e qvq. c+x3ndp,*fqza+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 1-klm2f3btky vj605 s3 8 szc jan5mex2980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Earth in iblu67z s 9(m7t 7vujeets 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 l7u7 e6bumv ezt 7js(9a 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+: iwug/4wbmi g ho0)dul3 x.p on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at wgu+ hldbp0i4 omwux/).:g3i arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circlctkb j57 ae*ps;z6 ;zies the Ea;e5kp; 7cjt azzb6si*rth about once every 90 minutes. Find the centripetal acceleration of the space shuttle 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 clag7mamf7gk:af t ;7(coyol1bfl : wc :5y on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is to;mylab ( 7wc7gfo1 lf: :kg7m5:acf32 cm?   

  A ball on the end of a string is revc 5a;usyqlqn141j 9sm olved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its sp915cluj4yqs;m a1qsneed 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 which a 1050-kg car can round a tua*e3 ya1*fqcl rn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0c*l*a y3 qe1af.80? Is this result independent of the mass of the car?   

  How large must the coefficient of sti,4f- 7hlr83(uihklnl0w rny: :kjuwatic friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/h ?i0 -lkwlfrn wiu, luh(7kr:h3:4 j yn8   

  A device for training astro21yjhu m6 ux(ikrvt(:nauts 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 wetv uh62( k(1mxy urj:iight, 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 the axis of a rotating turntable of va1n9qec5h/g biriable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm icg1q eh b95i/ns 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 upside down at thd(7n5o vbbm w+e t +(onm7dvbw5bop 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 dxz6j y4rgnfh4 6vsev s*o3 :h9river) crosses the rounded top f g4h : e*j9x vv6z6hn4syrso3of a 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 minute woui/l*7p rhcj5s brbbw:e0wyf;7 ;:db gld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at thecwli7db5 ehb gbbfr jrs*w/ 0;:7 y;:p topmost point?    rpm

  A bucket of mass 2.00 kg is fe3 g14tz;fvplmw .u2 whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucp 1ew;ufzvl.mf3t42g ket 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 9.00 cm from t si x 9o,7dymaek.:i1she axis of rotation is to experience an as di7kos ema9xi :y.,1cceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotatr exnmrw 6 y/k c2ungz5*.e:.ped in a cylindrically walled "rooyu egn.x6zmpw :ce 25kr/.r* nm." (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 inzna ;kxyya5prz) :i4ug3 z:e 0 a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cory:z4 : ieupzrz0 a3);na5xk ygd 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 ofls,,o.t* wnv c the ball which revolves on a string*, w .cvn,otls 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 banked for a cjqf: *+b6bj ejar 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 massesja 80 x-)mtbjf4lo8r e $ 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 verticallykjq2icv,a-to 7)2 z qy 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 components of the net fo;)k ts*xlk3(ryc g (bwrce exerted on the car (by rwk(g3*k;(txcy ls )b 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 areacfe/8 1sxk3mt , going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial13kte mf8/xcs 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 circle of radius 2.90 m . At a parti:gr/yyl o6tm y..l ,1uvwm7pbcular instant, its acceleration is1og:m.7b wlmyuylv p./ 6t,yr 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 gravity4ar)f7eh t nt8 on a spacecraft 12,800 km (2 Earth radii) above t)ha7 rft8n4e the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, tjd+ gkc+ 9s1s.2pgbtwo 3wo r6he gravitational acceleration g has a magnitude of 12 c62 9gs 31kpj or.gbd+ ow+wstm/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 thv*v8oc8 0 8e-goi eubre Moon. The Moon's radius is 1.74 ebr cve8v og*88- 0uio$\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 mae p5u rr8g zi:n;vb69yss. What is the 9y:8rve z5pr6bi u;ngacceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sy2up20 jj ra+/cr j,8w-pwym-y g7hw pame radius. Wajywj0,2 p2cp7mjp h-+uw8/gy y rwr- hat is g near its surface?   

  Two objects attract each other gravitationally with axec, 6egy l4v:+8j: g,lh3da.nrjuu r 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;ffso;d)+am6t* w s mi, at (a) 3200 m fo;w s;6i d)sa*mmf+t   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the E):kwro3nr6.qgyl8iub0 bmh dhd11 ) xarth’s center to a point outside the Earth where thegravitational acceleration due to the Earth is mkhn 8ro qdwd6 yl)1)bbir10hxu.3:g $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fe+/h 4 oo9adxiive times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this x/ eohi 4d+a9omonster.    $\times10^12$

  A typical white-dwarf stoe 0f;5wfn1fn, f;lyn ar, which once was an average star like our Sun but is now in 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 sf0fen1fnw5lf; n;, yotar?    $\times 10^7$

  You are explaining why abhi+ u;1d ;kxistronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince ;uki;i x b1d+hthem 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 located at the cor8okd c3/he/po,w3pxo ners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerkh8 oe33/dpxo ,/opcwted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same sih :;:bt *tnivyde 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*;htntib ::vy-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 gra p6bxkskj, ;av u(q*kh1hm5,f7vg hn+vity at the surface of Mars is 0.38 of what it is on Earth,aujk*m7;,qhb k5h vvks61n+xf h ,pg( and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usmr:eev9p5emy-t.u5 p ing the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obeeprm.:t5yep-u 9m 5vtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circm,lxos;y0i h 7e709 jjdy coc0ular orbit about the Earth at a heiyc x0,yc9;0od 7hsl 0jj7mo eight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into at+- 5hb9k0x csrqbo-r 4-fumh circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earthr+u4hsr-9qc5h b-fb -mxt ok0 ) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants a wtp lh1 +m9c*jcf4d2sre to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for cmfs+ *4wp912cd j lhtone revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite tombdqj;(0 a(mj ;dz g0h orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above th(a(m zd; bj;q0j0mh gde surface of the Earth 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. x v+t0l8qckw launched from the top of Mt. Everest to be placed in a+k8l w.xcqt 0v circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to ork.tbkrf h e1;u o.g,pd3v6gw 7bit the Moon at an altitude of about 100 km. How long did it take to go around the Mooew 6dp r.k.guv1ogfh3k; t,7 bn once?    s

  The rings of Saturn are composed of chunks of ice tq9fs7h8p x d8xcox 72dy-+puvhat orbit the planet. The inner rapcxfy q9xp- h2s8u d8x 7+dv7odius 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 rotates once every 15.5 s (se56glxmscdrpuo+8(5:zm i2;e oxs s- ue Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b x(sogu5di:8mlso5p2 ;x6- s ur+zemc) at the bottom?
(a)    (b)   

  What is the apparent weighxw lx4iy6qa 83t of a 75-kg astronaut 4200 km from the center of the Earthy6a8wil3x4 qx 's Moon in a 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 sys9 mc:ge6b)j (9cyo/jd0nw ny;6tkref tem consists 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 thjm0f ng:6(69k;bncyo ctrwyee)d/9j e mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman ij5 u 0*fnuoi(mn an elevator that moves ofn0im( *u5 ju
(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 su.,u.j:s s uvghspended from the ceiling of an elevator. The cord can withs:gu.s huvsj,. tand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface ww jsjs1amrk pc8.) 0g:ln,8p of a planet with period T , the density (: 0j cs8s.p ,wl1pjnmw a)rkg8mass/volume) of 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 +mkr+s+u vhe-9s1 awo7/ tcdc the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surmcs+9a/e st v+wkoh1+ur7d-c face.    s

  The asteroid Icarus, thoughs atkr.qg96ntztg /gl3e4h /7 7cqw*p only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its g kaqewr gtz.9 h6/lpn7/ts 37cqgt*4mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averag* v;1 ,rvvdqnie 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 rouguvuqw :0,rtym; h:q4chly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Es0tc;m :wrqu:,yuvh 4qtimate 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 the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the czi5v4aq+cu p xd45mc-v- /;h hb3ephw enter 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 for the four largest moons okrz9hyk vm *4*f Jupiter (those discovered by Galileo in 169 h **zkykmvr409).
(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 known7pk 6)st*;;bmn;kzv, f x mech period and distance of the Moon. zvcf;x kn *hme;k;,b7tms)6 p   $\times 10^{24}$

  Determine the mean distance from Jupi9zl 9d ej r(r:eio)x)fqf)h1 pter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and p r h(:9)feoedr1xfz )9jq)li 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 consists of many fragmentsct vtwy:+y* * i1,mdzq*sjur 4 (which some space scientists think came from a planet that once orbited twr 1*s4q **:tcz +tdy,viu yjmhe 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 deyxfa c8 .7d+yascribes 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 a8ad+x.yc7 fyband 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's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc.jjjg;u1cj m8jq im:- from a hanging vine (Fig. 5–41). If his arms are capable o1 jc8-jm; jm:jjq.ugif 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 gravity be half wha1ix( ckt1c d-w4v fuil. 3-txkt it is on the sur.1vd4x -3ckliixcf1wu-tk (t face?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab:ha.,yg mv esf9pp5a/ hands and spin in a mutual circle f: .h9spp,aey m/ga5vonce every 2.5 s. If we 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 rotat0.m 0b2hzujo tes once per day, the apparent acceleration of gravity at the equato .02oujhzm0btr is slightly 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 Earth will a spacecraft traveling direcds mjt :pf84m3tly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal anm3t djs:8 p4mfd opposite forces?    $\times 10^8$

  You know your mass is 65 kg,os *;g ylj xgk9rqw)p 7p8:he8 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 directsl q:7k; g j9ppgxr8 w)*8eoyhion?     ----待选择----upwartddown 

  A projected space station consax ypwrl93 n; imr:f/u *lp7;pil;6opists of a circular tube that will rotate about its center (like a pr;fwrxlli o:uim nppp7/6y; a*9l ;3tubular 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 be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vet1 buawr-*mz g+*r wi*rtical 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 thequh d1)llvo:)7 zla:p mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitatio)aoq lp:vud lzh)l:17nal constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verticalptpz7hoi7 :2us5 4axz6/ m zuo by an z7i6ua2z/ 7 zumh4 5tppo:xsoangle $\theta$ 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-pcw6 u8c:mi r a design speed of If the coefficient of static friction is 0.30 (wet pavement),mir cc8 :6u-wp at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotatincbjq9999if cjg so fast that objects at the equi9f99q c9jcj bator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apar3iowrqcsgu *+w2/f + rt 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 speed roue e4jl(; 6lklunds a curve of radius 235 m. A lamp suspended from the ceiling swings out to a4e(lej6lu ;kln angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Twf06c2x i fm5)atlmh 8hus, 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'txaf506 tw hlc2)i8mmf 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 prvsd5 .c(2iej/ ;:(epsrstvna esence of 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 the s:atcn;v sre/j2(sipv. d5(ecore 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 trp 0() 455kykvnl;izfbihbu)iaverses the hill and valley shown in Fig. 5–45. Both the hill and valley havp;h(by nifk)05b 4uiiz5l)k ve 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 f,i,9r19ytxph+g (xl hqh ic0 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 continuous navigational “fixes.” Thlhxr x+q1(t h,h,c9p fyig09ie 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 billweuy -7mtn c6svi7 q98ion km, is meant to orbit t 98qu- ewvts6c7mn 7iyhe 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 repllw ra8w6u*0 qqqh 8:vpq3lu0air. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 250qulu :avp qwlq6h0 r3wl8q8* 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 *rhnaoe,,-a6o9q5 m hun ee0ihas a period of 3000 years. (a) What is its mean distance fromiha,0,96 u hen-5*rq naeoo em 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 G would need to beb8z )ly:l vcyg5.vb3v:y jaq+ if you could actually "feel" yourself gravitationally attracted to someone near you.yc+.:85q jvvyl yb3zva)bgl : Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center os w4 6br,hx(dof the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years 4,drxb(hw6osfrom 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 corners36)qb f0 lbrnw of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass plarw )6b0fb lqn3ced at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth r i+-fax irhf,7(e hc;$ \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(: wz)- z9lbiwcu zskr7; lek a1err1) experienced by the tip of the 1.5-cm-long sweep second hand on your wrist watch? 9ri-as : k 17wc zz)k;br)rzle1uwle (   $\times 10^{-4}$

  While fishing, you get bored and start to swinghajzu 5 c2tkb 0lbv9(+ a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a completbc zabkhv(t lj59+20ue 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 fmrsin yupu5h6:)-n5car travel:h p -nr )mnyfs5i6u5uing 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 th13ak w5 m+8+iuiht hzv/kt kfg;lws7 /e cars when negotiating curves. The angle of tilt is adjusted s1wmhlfk7u ks t8whi+/i35 z; tgk+v/ao 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 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.$\approx$    $\times 10^2$