Sometimes people say that water is removed from clothes in a 8(f*c opd yko;z()sa l -kjeq9spin dryer by centrifugal forceql yod(fe9;o (pc-akj *ks)8z throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car tc1v0kjyauy3 a y(3k(kravels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same 0jkk 33(ua(kc y1av yyspeed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does t -9o jkgp(j:*dmetmw, he car exert the greatest and least forces on the road: (a) at the top of a d gkj ep,(tj9-*om:mwhill, (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 riding a horse on a merryb3d( f;94fv )aejbluot5 qi7 z-go-round. Which of these forces provides7job;d qif (4vte5lfb )ua 93z the centripetal acceleration of the child?

A bucket of water can be whirled in a verticix(xfymt.s0wf8 v;u . al circle without the water spilling out, even at the top of the circle when the bucket is upsi f0fmy.vx u ;8tswix(.de down. Explain.

How many “accelerators” do you have in yo;+w)cm t7v jreur car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? m+7;rte)vc jwWhat accelerations do they produce?

A child on a sled com : w m wavkrbeqz,/l.80bp/dxf)tg;8yes flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not lewdmp.,a;fr8l/ebg8x z q bytk) v:w 0/ave the ground (he does 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 leahxv. q/(7;e.hzf-af xyogq/jn inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you comp4 j4g;i+frjm *:xozso ute the banking angle given its speed and radiu; 4zji+mgfojxo 4 :*rss of the turn?

A girl is whirling a ball on a string aroung,t,hygs4-pe u if/28j0aojqd her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a targeti20gsa,g f oh je4/ ypj8-utq, on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force ozwmu h8-wnz/c/om1 /n n the Earth? If so, how large a force? Conside1/ww/-cz8onnzu/m mh r an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass u*-2v n xil72lx )jylpwere double what it is, in what ways would the Moon’s orbit be d-2nljl7u l)pyx2vi x*ifferent?

Which pulls harder gravitationally, the Earth on the 9vp 45czm.ioq,d zp7n Moon, or the Moon on the Earth? Which an5vm pcipq4zo7zd.,9ccelerates more?

The Sun's gravitational pull on the Earth is much largm u ;/abv6:w*m+ubh dher than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: u/um:dv+6h* ;a hw bmbConsider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at f 3/59as fdkmcthe equator or at the poles? What two effects are at work? Do they oppose eacafsd kfm93 c5/h other?

The gravitational force on the Moon due to the Eart2ox 3tx w90b8rb+shahh is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled hwtobh x9sx+83a2 b0r away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Suuu v *en+f ey+k1zv5hub,j2:k )kntf5n larger or smaller than the cen1yv u u)uvnkb, et+*+h:k25kj5nffzetripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) too r9pmu6 mv6ha rv+tx9 rw+*j/ward thpxrr6* twum /+vv 96 rj9oa+mhe west? Consider the Earth’s rotation direction.

When will your apparent weighv6n3kr6/oqct(h wy* m t 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 fall, (d) moves 6yn v*3m/ ct 6kr(ohwqupward 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 cpsp(b9k(km d 4ould be adversely affected by weightlessness. One way to simulate gravi 4s((9pdpbmkkty 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 gravity you can think of.

Explain how a runner exper(x:-)*kpci2mxaj8jyvd o4j) 7 lw wkwiences “free fall” or “apparent weightlessness” between (m2 vyckp 8o)*ajxw) kwxl 4d-:ij7wjsteps.

The Earth moves faster in its orbit around thea 7hp 2(nuomho050s cwki*)je Sun in January than in July. Is the oha*(w pkj7mn)5uh c 0es2o0i Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to hav uk,jfc;pvq 48e a moon. Explain how this discover 8pk4c ;vqf,ujy enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much lk :*x9rmynqv .jqk* *a6rg6lk arger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in graqn*mxkjkgr.qk 9 *lav 6r*y6:vitational 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 19b af/)ss o6e;g80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 x9 mqart;dvn-2x 8s) uorbit around the Sun, and the net force exerted on the 8vsn ;-xur2t)qda9 xm Earth. What exerts this force 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 discus as it rotates t./d j v0h9t1frhsqx: uniformly in a horizontal circle (at arm’s length) of radius 0.qvhrtxhtj1d/f0s 9 . :90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and cir0hyfelc* j b)jf3 n3f/cles 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 gravitational ac3fef fn3/hcj*yj0lb )celeration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a spe9 b(t kepe6;acck of clay on the edge of a potter’s wheel turning at 45 rpm (r9 ce6ekp;ab (tevolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a qu/ oyl *hh*fc+tt8)kvertical circle of radius 72.0 cm , as shown in Fig. 5-3 ttyhkl*8uq c+*f)o/h 3. 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 whv4pfyxb+)pu w d9x e lvwlcq8/8:) rac*v7f7aich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static frict xv ev*adw8: cq7 y8r4apcxl) bl+up9/fv7) fwion between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the ww:h og1v+kk, wk5 9ldtires and the road if a car is to round a level curve of radius 85 m at a speed of l5k1kgvw9h+ :,kdw ow95km/h ?   

  A device for training astronauts and jet fighter pilots i 66:nqa;lw ites designed to rotate a trainee in a horizontalqw n:6i6at le; circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    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 thhylshs73re;v /:w+lue 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 a rate of 36 rpm islv :r73; /s uyhe+whls 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 coasdsz ) esc3ibni+6tj6 -y8kf8 cter be traveling when upside down at the top of a circlycfe88s3ti+ s6d) iz6- bcjkne
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded 4y,egc1ggdv 6top of a hill (radius 6g, cgv4e1gdy =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 wheel need toif gue90r3gl) make for the passengers to feel “weightless” at the te9gl)u0gf 3riopmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a 96)7kx wxslc pvertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0xwps)cl9k6 7 x 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 centrifu jiv8 jk+9v0jlge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleratio0i9vlvjkj+ j 8n of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnizshxd a 6q-0i.val, people are rotated in a cylindrically walled "room." (See Fig. 5dq6h. z-ais x0-35.)
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 rwyr 6cav8lv7o l5-be3 otated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) throuy8l6cve v5l3ba7 r-wo gh 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 vb1ngw t6yr2 18f c1pbball which revolves on a string 0.600 m long. In particulabt1wf rbpv ng1y8c2 61r, 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 car th;ixv (pph;yh7h k(9q raveling 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 nht6 0)6l:fo+g mzkzm $ 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 vertdv50xamj-x:4 h4:0 rc ulekpyically 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 force exerted wu e-zb0 /mh2fon the car (by the grou0fh wb e/zu2m-nd) 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 acceleratesm.l hnbvg:)g; uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. :gv;hg )lm.nbDetermine 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 slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a par uvkm,bbu )(,lticular instbk (,vm ul,b)uant, its 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 12,8 ,f12i qpk3bpx00 km (2 Earth radii) above the Earth’s surface if its mass is 1353 12k q,pfxibp0 kg.   

  At the surface of a certain planet, the gravitational acceleration gm utoc61/*w(*yfi d mk has a magnitude of um fit6oy*m( w /*dck112 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 tou+n,9x48et xf9fk dzoj ih05f :bc3xg gravity on the Moon. The Moon's radius is 1.749fx,e on93:ub d4f ihckt j f05zgxx8+ $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tidtvm nl/enzv.+ f91g, mes that of Earth, but has the same mass. W 1.g,n+nmzelv/9 vt fdhat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Eaa4xf;/sdm3 w/a/c br 0*zciu qrth, but the same radius. What is g near its f axbc uwmcdzs*i3a/0r;/q/4surface?   

  Two objects attract each other gravitationally with a forcldc)t.w1a4v 7g c)p obe 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 accelerk6o(j9c qjt: txaed 73ation of gravity, at (a) 3200 me:(a79 3 ok xjqdj6tct    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth*xkde73n d fci vc3ef2. 4wmks2j;s.t’s center to a point outside the Earth where thegravitational acc;w k.c4mxf2cki 3j v3e. nssf *d7ted2eleration 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 * iwxn 0cq/r/xof our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on thi/n qr0*wcxix /s monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun ok3:2y 3d ualsbut is now in the last stage of its e dsk3oa3 y2lu:volution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining whyr1+7zp nd8kd b(a wn+y astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was jus8w+az1y7d (bkd n pn+rt a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60,9 akyc3v :mym m. Calculate the magnitude and direction of the totcvmay: y 3k9m,al gravitational 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 up on the same side of thf,jf, uken.j9 e Sun. Calculate t n,fuj9.kf, ejhe total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of whxb40:pda fp3w9j9c bl/hu 2qfs4 yn*yat it isf4pa9x*cfp dsb04ny3/9 bql2 w :jyuh on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun u:h44yczl i1hysing the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obli:hy 144h yzctained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed ow3z3i 6lib a(jf a satellite moving in a stable circular orbit about the Earth at a i6ai (bzlwj33 height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 65xumm 9x j9 *n1c0j.kut0 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurmj ctx*u1u9x 9jk0.mns?    $\times 10^3$

  At what rate must a cylindrical spaceship p0e5 kww 7eu4protate if occupants are 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 one revolution. (See Question 21, Fig 4w 7we5u0p kpe5–32.)   

  Determine the time it takes3 lzj:wjri0 +r for a satellite to orbit the Earth in a circular “near-Earth” w:0lzri3jj+ rorbit. 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 of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launcheqs2; w:/b,vr/gazb rcd from the top of Mt. Everest to be placed cv bb2/;qzrwr ,a:gs/ in a circular orbit around the Earth?   

  During an Apollo lunar landing miss(.7pt-n; pz 5u:zw udh+, qv5h eouoakion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once-.5wto:hpn( + a;,dz7eu khqvpo5uuz?    s

  The rings of Saturn are composed of chu: fog8 q6mktr-nks of ice that orbit the planet. The inner radius of the rings is 8-k6mqrot f:g73,000 $\mathrm{~km}$ , 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 (see Fig. 0egf09dwmfch3 fs/t 65–9). What is the ratio of a person’s apparet3esh60g0f /9 ffwm dcnt weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent wei-wp5uwdd jxa3 4e0r5gj q(m d(ght of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a sppd 53gm-d5uwe0j w(adq jr(4xace 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 consists of two starnlai oi5jyhz/ 2;5zi 1fvmt+ y.xe()as of equal mass. They are obsi.lny/o21y a(v mh)za z5+;xe5 tjfiierved to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read le9ylg:7r 8h qfor the weight of a 55-kg woman in an elevator that 9eq8ygh 7 l:rlmoves
(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)8cdgm 1804mop mukaz from a cord suspended from the ceiling of an elevator. The cord can withs8 d0p8kg4 mmcaum1z)o 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 of a planet with mam c*6b; rh8sz2xs 3kkox ,l,period T , the density (mass/volume) of hklkx8a sbm r*z , ,x3m;s6co2the 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 (27.4 d) to determine thec.gb)4dp, -ai*e mpsc period of an artpdc m*si4g-p bc.a,)e ificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters hhze2, pg h.2gacross, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun,p2 hggz he2h.?    $\times 10^{11}$

  Neptune is an average distance ocl*hcl;s aan 5d25n j 5v1vq;df 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 roughmzjx3f8blvfr1rx/ .z + yjo6r d7)/obly once 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 corm 1z+37 8vb6xrlod./fo)/ yzrfjx jb met 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 center+mgz-mw hr9t6 d15jl i 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 distamj1n** z ,+mzknd+l fance for the four largest moons of Jupiter (those discovered by Galilmn, *lfnd 1*+kzm+a zjeo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the )ourff w2uo- j/o6 -jfb*pmr*Moon. ofupr*-o)2 rbf* j-/ou6 j fwm   $\times 10^{24}$

  Determine the mean distance from Jupi4ai 2m *mbskz*ter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the valuezs* mbi4 m*ka2s 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 fragmeu7 3yrm hkmm+7lfo98 bnts (which some space scientists think came from a planet that once orbited the Sun bul3 y879rmu7ofmhkm b+t 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 descrztqu.s+jmy 3 3ibes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revoluti j+m.t3syq3uz on, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by:(ig14e,jqgfkupi l, swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vink(14 pi,iqgju:l fg e,e, 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 w8bnq9f3pik e6 ill the acceleration of gravity be half what it in3 8ef9bi6kpq s on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cir)**owdd o thq0cle 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 hard are they h**w0t q )ododpulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the agf83g4cg(lb oo 6ew no5r;yn)pparent 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 fraction of g68 gy4bn)wolrng f35oc(o;e g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the m o;fgzms(yf3 5ml);6jj t,ul16st guEarth to the Moon experience 16;g j)3u o6m; gsfly,m(s zu5tmtlf jzero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on az kyf8.p *op0v bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in o.0p y8zvk*pfwhich direction?     ----待选择----upwartddown 

  A projected space station consists o(/le /nc,siq, dx8r0v ohta,of a circular tube 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 o x,vis/ h0can,/t,dlrooq8e (f the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a verticamdyvp) q bk7k+qx:4j5l 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 tausk+vw6p0 4 tt 1ot0werms of its radius r, the acceleration due to gravt vok 006wt+tp 41swuaity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a s7. :kj htdks7vtring) is deflected from the vertical by an angle:kthjvk7.s 7d $\theta$ 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 I1v (f7m- ,h-3zt qzwa9vnqwjzf the coefficient of static friction is 0.30 (wet pavement), at whtz(zw j-h 9ma-q7fn3wq vzv,1 at range of speeds can a car safely handle the curve?

  How long would a day2 an/h7khb qjf06 d,we be if the Earth were rotating so fast that objects at the equator were d h6nfk h/ 70jwbae2q,apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0bds q,)a;jri i7pdfg37h0l9q $\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 r4xu7l: gv1pwfwp +eo: c2i j6aadius 235 m. A lamp suspended from the ceiling 21e4iw+vpwcu :og xla:fp76 jswings 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 Earth. Thus, it has been cla .,a39ewo axoqimed 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 soa o3,ewq ax.9uch 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 .,jku dfeu+b) ;b7 dayHubble Space Telescope deduced the presence of an extremely massive fj, yueud.7 k;bad)+ bcore in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley show 38xp+bec ,hff.. esvhn in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces actin+bvpcxhs. efhe f.83,g 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 P, iuu*pzrr53zy ..da7n peyc:*y wk(hositioning System (GPS) utilizes 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 continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical midz,7z:.3i.pr(ry *he wnca* 5kpyyuu les [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 5(lel n/m zbu +lh7fhdnt d1,6billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is /ent5lhdlfd,( 1u+7 bn z h6lmroughly 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 nb5e/ 3wd6 vxxnda9a) leed of repair. You are in a circular orbit of the same radius as the sa bd9e6a)/3nx5lavx wdtellite (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 jp45f)jc r:wadistance from the Suc:paj45j)r w fn?   
(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 va b,* 6cq4y9edtnal5 uflue of G would need to be if you could actually "feel" yourself gravitationally attracted toedcyf5ubq,*4ln96at someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arouno vau /-ent8( on:uhrn7rkh76d the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-y (urr h7v-nt6 e7 hao/n:8nukoears from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each side. F- .wjpf ,g6y,-offjifind the magnitude and direpf6fj fo.g ,wy -jif,-ction 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 kg orbitsiksov5zd; q *) /1k0*/bcw gb edncq9c 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 by the tip of the 1m. (nz 0b2faey.5-cm-long sweep second hany2 ab(n. fzem0d on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around inj) kq)dreaul8o*v3 nv-/ x+ to a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. nuv3*j)/ +8)o kav t olqex-rdWhat is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of rf .v.c i5swqq( 4w,t ewkc7sogxx5(/aadius R in a new highway is designed so that a car traveling at speed.cqc .vwekw( t5wgxo(,5s/xf7aq4 is $ 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 Acel,0ku6 dmi1eqkria0u 2 f6s6n da, 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,d6k2u1umqik rni e0a0fs66d 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.$\approx$    $\times 10^2$