Sometimes people say t3 q:i; rkdvebjs+2c:f hat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is;sr:fdec:qbj 3v ki +2 wrong with this statement?

Will the acceleration of a car be the same when the car trav reprxnyp* w3a /lk582els around a sharp curve at a constant 60 km/h asrxn*y pe/apl38 52wk r when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where do e -/+c5hekfwmes the car exert the greac5m-ee/+ fh wktest 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 bottom of a hill?

Describe all the forces acting on a child mn5:7d5 vbv w;1h kly0svcn) 1enhi9i riding a horse on a merry-go-round. Which of these for ys5vih1 1):knm97 l 05ninvcwv;d ebhces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical ci3 9psaw h3 9sgc0 kj*hmlo7j,+vpa c9zrcle without the water spilling out, even at the top of the circle when the bucket is upside down.+c sma0jk 9w 9g*vaz37cjho 9hs3lpp, Explain.

How many “accelerators” do you have in your car? There are at least three conf5t15ehz n*htlnb7 o0 8h/dix cl;934psf s bbtrols in the car which can be used to cause the car to accelerate. What are they? cb t szn3b7dli5fnfpe/ o4bhl*5hx 098h1ts; What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as s6z-kk )g pu* x ipgg5.vtq1fzh:ev4o 9hown in Fig. 5–31. His sled does not leave the ground (he doe6 5vvg4x)*1qhg:koze fz gtukp.i- p9s not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward whe3vfgdm) md9*bws 9r39skiq m *n rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle7u* 9fal0qh*4u+sa*t8gt t uopjc lx4 given its speed a4lp7qau*xc h9 tsfju ttu+o gal4*80 *nd radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal pv.gaurc u),u34 3ib z y7jycn5lane. She wants to let go at prer ,cinyvuuu7cj3ya.)5 b z3 4gcisely 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 f;52wl ctvpq) oc d6:l1kuot.f orce on the Earth? If so, how large a force? Consider anoc;uqt)1ov5 c:f 2 l.dtl 6kwp apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it/yo-8xfdg 64w 64owy2wc3t kv jfns4n is, in what ways would the Moon’s orbit be different4knf2d6 go4-6js yvw fc3ww8o y4 x/nt?

Which pulls harder gravitationally, the Earth on the Moon, or the Moo5y mn9 dfr.f7tn on the Earth? Wh9fydtm.r 5f7nich accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet:uv12j4lth cs lxhhi j/2;+ uk+0odrm the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the othej+h+4clhtluk;2 dj m0o: x iu2/sv1h rr.]

Will an object weigh ia(: z gcwj, h2ucas-:3w r0ftmore at the equator or at the poles? What two effects are at work? Do they oppose each ww:zgsca a 2,u(-03irt hj:fcother?

The gravitational forciz0r69 fymlxz x ), z;lm.g*zje 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 pulled awayz;gl,jlf)z0 x mymr z.*6z 9xi from the Earth?

Is the centripetal actq0xn7m2twlrqk .8 8 hceleration of Mars in its orbit around the Sun larger or smaller than the centripetal a t . q88hn7mrkw2l0tqxcceleration of the Earth?

Would it require less speed to launch a satellite (a) towam-y/ u+wr .qm yrbxd-(rd the east or (b) toward the wesqr+dwm (y/r yxm b-u.-t? Consider the Earth’s rotation direction.

When will your appare bkzgbx :x.902, ndvehq xi3)ant weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free f9bqx3hed.2a:0 ,kxbix) v gnzall, (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 outer space rmw q+d5jcbdm3vd*p je ;8ic/u.ax +(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 op q5 rmdi+(dj/.bc 83c+a jexd *vwm;uur feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “appare; w2).euxned envi65bo-g*k ent weightlessness” between 5)vg -;ewo62i xnneebu ek d.*steps.

The Earth moves faster in its orbit g(sbj1l 6amc3d p 56iraround 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 producinga6(r pd1 bl5j m36isgc the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known 2c7 obv8ge;n zg8,m ihf.uawr1zs e* 9until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s ma meh v8;i*2z8auc9fge,wnb 7 1srg.z oss.

  The Sun's gravitational pull on the Earth is much larger than the M+c z3411m0gq q5eaz f ,jecrjpoon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round mgfejr 54 emz1q0ac3q1c+ ,zjp oves 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 travelingoy8b4k) pb u2,n *vzkq: om wf;c5)xeb zmj6w3 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 acceleration of the Earth in its orbit around the s);(pyxy.hv . hdo,gn Sun, and the net force exerted on the Earth. What exerts this for d.xshyg.y(vn;o)ph ,ce on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discusj*ep bla1 b1t)(wmka5 as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. jb aw51 )*ep(kmb tal1Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circcl n; h0a)s)xr(,d sqlles 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 g l;hc qn, s0(dxaslr))ravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleracp*ld*ilc jl4gy 9-h6tion of a speck of clay on the edge of a potte4l-d* ilc hy gl9p*c6jr’s wheel 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 u 7ue84u/r 9g;ruafuw22 eojre 1x4qeuniform rate in a vertical circle of radius 72.0 cm , as shown in Fig.q2uug4r49e2e/ur o 1efj8 awu; 7uxre 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 which ajqryk,g85g(f3yfgp,9 z s7u58qfpdj 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 re39p 7yz8jf sgg5fyupfj qd,8rg5q, (ksult independent of the mass of the car?   

  How large must the coefficient of static friction bhwu(cd:*n d, 0yhmof /e between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95k*f/nchw my d:h(uo ,d0m/h ?   

  A device for training astronauts and jet fighter pilots is desi -tk6f j(z (k1xhx whkbeg( zqff88i):gned to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by tjz 8t-z(( kh8f)xqxhb1if:ke 6f (gwk he 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 the axis of a rotating turntabsllvza6n m3nr/-0 umuq9)j:r; p sdy1le of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turpnu; 3 m9lq0)l zud sr6 :snr-/1jvmayntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when-orf, k +olg5m upside down at the o+rfkol-5, gm top 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 th fdwciw/., c1he rounded top of a hill (,/ c1fw. cdhwiradius =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 would a 15-m-diameter Ferris wdztlq 02sf:lotos52q7jd5t , heel need to make for the passengers to feel “weightless” at the topmost poinstdlt5 dj5 lq072fos t,2o:qzt?    rpm

  A bucket of mass 2.00 kg is whir 7e .af)j,rw7g;d5 joi2zdn mxled in a vertical circle of radius 1.10 m. At the lowest point of its motion thdfrxje.nim 75g ja 7zw; 2o)d,e 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 if a particle 9.00 cm from thei qou8on+r)rnv0j ::w axis of rotation is to experience an accel n+v)r0qr 8n::uijwoo eration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated ie2 : z/jhpn 3pzo c5hqcm;p8ib s,9ok-n a cylindrically walled "room.co9, nb kp /3;je-q h:h2pco8zmzpsi5" (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 ci5wjn*cn h 80ycrcle on a frictionless air-hockey tabletop, and is held in this orbit by a light coc 8 wcnjyh*5n0rd 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 ignoriuxlw59/f *wsa3c wr p/ng the weight of the ball which u/wwx5fa93r l*wpcs/revolves 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 banked fo6/o*r ,ww 9er+rhbnx dr 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-5w4t aaxgp/ h $ 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 bi ma ngq16kqp , 8n:- :mt64t/aijkvdhy 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 centripe;n-6o z) kq7)7wv hy 9xf op9)dtqsjiital components of the net force exerted on the car (by the ground) in Exax)iwjq6osi k-h;zfq) v7o 9n9)dt py7mple 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 acceleratesk s8bdlcvlnx- jl/0-: 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 and the road to provide/: 8lbllnxvs-j0kc d- this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular i q-d2c addn -ou/00ektnstant, i-qe2 ddauodc0/kt0- nts acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earo6 ox7q:qpe b3th radii) above the Ep36x ob:eoq7q arth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g ha.h a6)pf /pmtks a magnitude of 12 mpp 6.ftkha/)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 h k0(n/ja;qk sew 7ou,the Moon. The Moon's radius is 1.74 ; ,/snqko e0wjka 7u(h$\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 odvv*sm, m6t 7pf Earth, but has the same mass. What is the acceleration due to gravity nearv vtmms*6dp,7 its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sam 3 hf4np*7ahso;o5rp de radius. What is g near i 4 5dsaon 73*fhrpph;ots surface?   

  Two objects attract each otheb, /*mw/ f9:obt pbswur gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration*hyleq o+9n. d of gravity, at (a) 3200 m q.+odny* he9 l   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whgvfq7+4rmsw1u cz; 5f ere th5vr q1c;+fgfmsu 7z 4wegravitational 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 packed into a spher7b/nw 11xb/tu y9 a swdm3hg6ipv31spe about 10 km in1p s1y/31amg6b d9v h nu3wt/ ps7bxwi radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averaga-hz i +dhi -nol-fm5,0dufvp7;bdz9e 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 gravity9zu+ 5dpf - oi,z-md7l 0nfd;hh viba- on this star?    $\times 10^7$

  You are explaining why astronauts feel weightwp(d3,z1+s5md 7c oruh ndq g:less while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot w+d3 p1 qco5hnz :d(gsw7,durmeaker 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 located at the corners of a squarec:yis(5df x fj7wf0j 8 of side 0.60 m. Calculate the magnitude and direction of the total gravitats5i d(7w:8xf 0j cyjffional force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line upxe.am5ouf :fm;1j0bo on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a af u0xem:;5o1o. bjf mline (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 gravity at the surfab, mq(h4j+9jlgyz:h ace of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 kma9jq4( zj bg:,mlhyh +, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knowfcr;:4 udng8m n value for the period of the Earth and its dn d4;u:m crf8gistance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about ther2 gal5:wg9we Earth at aagw9 r 5wg:2le height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circulzt2 -h 0zr/bkdar orbit 650 km above the Earth. How fasthrb z-d2 kzt0/ must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupb-ou t: a9se.pants are to experience simulated gravity e9 otba:-psu. 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 Earwb+ngywo- p2 )th in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass p yw-wbgno)2+of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launch fqkx/*4dwd4o oj8 jaj1d74c/v9dptoed from the top of Mt. Everest tt p aj*84o9jk wvf4do4dx17d q o/dc/jo be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command modulegqa4h *p( wj,e continued to orbit the Moon at an altitude of about 100 km. How long*e4hga jq(pw , did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks olu :x5 nx2c-yrf ice that orbit the planet. The inner radius of the ringsn :xx ucl2y-r5 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 1no9m 3eeh9v3m5.5 s (see Fig. 5–9). What is the ratio of a person’s appare3 93m eoen9mvhnt weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fr gcfry5oy z)(,om the center of the Earth's Moon in a space vehicle (a) moving ,f)c5 g royzy(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 binarumo3 7 7oeg;c kdkr,o7y-star system consists of two stars of equal mass. They are observed to be separated by 360 mill;gc7,omu3rkd7k eo 7 oion km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevab n,spze5kzno)r h493tor that moves )n3eb n54 9,sphzro kz
(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 ceiling ywntg4 * 4 8ttvbr5j(jof an elevator. The cord can withstand a tension of 220 N and breaks as the elgj4trtbv*wyn5j4t( 8 evator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite o/5ki wh 1h;*vdgpf bn/rbits very near the surface of a planet with period T , the dens*;1fvknw /5hi/b pg hdity (mass/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 td g-vw92v2:-k4go eyrdq - oimhe period of the Moon (27.4 d) to determine the period of an artificial sateeiogdq 4 vrdm-w:-ov9-y k2 2gllite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though onhcuf,6s1-0 rsoj bx7 zly a few hundred meters across, orbits the Sun like the planets. Its perif7,0ho6-b xsj s1 crzuod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 7 3 uv2+ajnnpn 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 c;sva/)zj e/ixoq48,l.x m yaonce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet 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 nearestv c ;/lmxiz, 8q/xs4eaj)o a.y and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the 1jhouw+r7q; q;3 ahbncenter 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 mooyta9 kw q; w fc.2(4o mjzdoffn.69p,hns of Jupiter (those discovered by Gali; h4n2c 9, wof tp.(fdmf.akwj6 zyqo9leo 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 Earthxd (;t4ymgs*sr3t c5 j from the known period and distance of the Moon. mg cj3;(4d5y t*rxtss    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moon hr5 8 ppdbta/s-ixxcwxlr /+7;8ebv-s, using Kepler’s third law. Use the distance of Io and the perie85dbat+rcx h7swx -//lb- v;ip px8rods 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 ma8kigb :xkxxe0kg1/5u2r gm/d ny fragments (which some spaced15mgukge8x2igxb0 /k r :kx/ scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form olj3 e) .jvdax-f 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 t jd3vx-).ja lehe 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 ywbatjhcw5n.8 l8n3. a4g2ggarc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a forcacg w852gwt..jl n34 8ahn ygbe 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 Eartm91xz upec u+0 ufh7x+h’s surface will the acceleration of gravity be half what itfhu cpz79 +x+0xmu1 eu is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spw , l96mh1xs:sdvdu4min in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how ha1mld6vmw duh4,9 :sxs rd are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the bw uzvi+i9;4 j9x,u9ei/ywfxapparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fractionu;+fvwi9eu, 4wi/9zx xi 9ybj of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft tr 1dbzd: r5l, b:9wsity0q w6c e*f5ocqaveling directly from the Earth to the Moon experience zero net force becausi yft0cdo,5*w96sd5 eb qqlbz::rwc1e the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when kbk 2(c5 qycc-you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the52k cbk(- cyqc elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tub 5vxych u8ng3*e that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (u3ng 8yxv 5ch*1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop j6 ywe/)c qko2(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 itsgefqe:/ 5j sax( 6o +uhsa cjfbu4q*,( radius r, the acceleration due to gravity at its surface an:jb*u(aqc /efh ,+ fssg4 q(5jxoua 6ed the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflectep03sdugd l: 2yd from the vertical by an 3ld20gy: duspangle $\theta$ 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 d;+/p:i 2kp2*1llqqltoe gt:o tp ki ( If the coefficient of static friction is 0.30 (wet pavement)2lipt o qpklq:2i:*p/+(l gdo e1t ;tk, at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at l /d a5ng)9itithe equator were apparently weig/ )l i9natigd5htless?    $\times 10^3$s

  Two equal-mass stars mainta7w4aodpi6rp ,in 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 speed rounds a curveniam*h tc z:2)26 9o wu5yuksj of radius 235 m. A lamp suspended from the ceiling swings ouzu9o wm c ki6*s5un2:a2y)jhtt 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 Earth. Thus, it has be6.mnq x2 -u1mkc* u)rgqb.caten claimed that 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 fortubmg.x qu 1-r)* a.c2 nmkc6q 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/c5g r, 2mesile Space Telescope deduced the presence of an extremely massive core in the dist/ci ge 5srlm2,ant 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 consta 0aab,z4jgf8 c dg v,buzw,o*+nt speed as it traverses 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 idjga wzb0*bv,a+u, 8 zog,cf4 s 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 satellites o3ltwx5h 7 9 6lckpoal7rbiting the Earth. Using “trix llp7 3altwkhoc59 76angulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after.p l- 8iaek.zzq3hi(8hz1 yu0nm 7hh n traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of n87mhuyel 0.a- 38hn(hizizqkp h 1.zabout 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 neexkv g9s()6 s q9in-rh feu*p1md of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behinxrnhfqes u *9-g s(6m )v9ikp1d 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 ha/k.+ koqnh-7vrga c2rqr0 q *js a period of 3000 years. (a) What is its mean distance from the Sun7nr jkq/vark qg.- h0qc*2+r o?   
(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 actually "e sj 2,q+hx;eo e-uei2feel" yourself gravitationally attracted to someone near you 2eexio-s +eu,qh;e 2j. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a ;i1) gut/pf:vtt1h ca distance of about 30,000 light-years from the centet ;hf)u1ac gi/t p:1tvr $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m otm+ v67c:y+fli*nv khn each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at th+v kmnfl+yh i6:7*c vte midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits 6z58xlly8 b-kp6 fogmtf z3h,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 acceleration experienced x1f uyq.)e-w rp 7boecf7;d)yby the tip of the 1.5-cm-long sweep second hand on your wrist watch? )yf17bduq x ).-;oerfwepc7y   $\times 10^{-4}$

  While fishing, you get bored and stihm+f a6ot,2n3m* r 4wrqhe i;art to 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 angle that the fishing line makes with theohrqw2r,hia6 t4e+n f*im;3 m vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a ut7dyuy ;2v4i car traveling at sp2 ;7ud tyiyv4ueed $ 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 j2 +jvf( m:i6n,cby ;evyu6qfAcela, 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 comfortable. Consider an Acela train that rounds a cf y,e;f u26vjb+nv :mqcy6i( jurve 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.$\approx$    $\times 10^2$