Sometimes people say nu/d4p+g6rv ithat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this vdu+4ngpi 6r /statement?

Will the acceleration of a car be the same when the car travhi.fk rkx8r7vs u .:z+els around a sharp curve at a constant 60 km/h as when it travels around a gentle k7is.rrhxk:.fvz 8u +curve at the same speed? Explain.

Suppose a car moves 1 s-rz,ljb( owat constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch n sz(1- jorlw,bear the bottom of a hill?

Describe all the forces acting on a child riding a horse on a meri:kk gz, c6xc7ry-go-round. Which of these forces provides the centripetal acceleration of the child?c zi7g k:kxc6,

A bucket of water can be whirxwfuop0m)yrs5 *c5 6xpj(tpc*y:4 cs led in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upsidepp)cx*0o( cyjufxswry5s:t46mc 5p* down. Explain.

How many “accelerators” do you have in your car? There are at l/b tu,z/ocg6d east three controls in the car which can be used to cause the car to accelerate. What are they? What accelzgu o/c/t d,6berations do they produce?

A child on a sled comes flyingpavejd zpe2kv34l /2q h(w6)f over the crest of a small hill, as shown in Fig. 5–31. His pa4vf36 ke) 2vzwj2/h elq(pdsled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inwaq-y+83jf f jo kp5q*nc;wiqt4rd when rounding a curve at high speed?

Why do airplanes bank when they mj)1f vs :xfc-dey- q)turn? How would you compute the banking angle given its speed and radis ) mx):f--fdy1ecq vjus of the turn?

A girl is whirling a ball on a string -nh5z,x w*a-*wbuxq xaround her head in a horizontal plane. She wants to let go at precisely the right time so that the ball wilwn*-z*x a,-xx5hq wbul hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how larc mww- x(iit z8c4z24wge a force? Consider an ap4i-t iww xcz(w82mc 4zple
(a) attached to a tree, and (b) falling.

If the Earth’s mass wh v7bjr4s1w 4vere double what it is, in what ways would the Moon’s orbit be d471wvh4 brjsv ifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moonja61j -hm,w58zd h7o0rz d lt bmtsy3: on the Earth? Which accelerateso:w5jms,mrhtlt z 8b1h-y0dj a673dz more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet thjs hev+zro /+*e Moon's is mainly responsible for thz esr++*/jvoh e tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator o y1xba8xds: xo* wn9l/r at the poles? What two effects are at work? Do they 91d8ysbxlw /n*: aoxxoppose each other?

The gravitational force on the Moon due to the Earth i7nm-ap qn )+*za ctcy-s only about half the force on the Moon due to the Sun. Why isn’+qt7 -nznm *c-yc)ap at the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its o2sggx6znm/ /s(,4) foscjygp rbit around the Sun larger or smaller than the ym snxzgg/24 /sjog cs6)fp(, centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) ty8,dyj1ex ()o+klpdwrh)o+/ m 1 w.tx+ s yesxoward the east or (b) toward the west? Cxyw+ds,l(oy 1mpx d tjsoyw8k e.+/e)+ )x1hronsider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a smg)8k 0 mtdir0i8 rr6kcale in a moving elevator: when the elevatk6ii8 m0r0kg m) rrtd8or (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend longg7 cnt obs6,-r 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 gra, o -b6rcg7tnsvity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “freefslksz:6 4jt*utc1q5 fall” or “apparent weightlessness” between steps. :6zqlcsf*js4u51k t t

The Earth moves faster v6qhw)8xe pfhjd;w ,t8)ztg,in its orbit 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 producing the seasons — the main factor is the tilt of the Earth’s axis relathhejx8;,dg),qpw8 zw) ftvt6 ive to the plane of its orbit.]

The mass of Pluto was not known until it was discoveredk-*lh5c:b gb2: a xldd to have a moon. Explain how this discovba x:- dl*5klgh:db c2ery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on th)zmqe4 s9k o7+g:pn uwe Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gsnp:mek4q9u 7 z gow)+ravitational 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 j8)x1q+pljc j 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 thqc7 3bzu q.rm *qmr69ge Sun, and the net force exerted on ugmcqr z6q m .r3b9*7qthe 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 isriuy. 1e3 vtunccjss ,ie(pi+v 7;5 3k exerted on a 2.0-kg discus as it rotates uniforml(c i;5suetv,ruc +p7 n3 vike3i.y1s jy in a horizontal circle (at 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 dgo; 5 l3;o( pozqga,usurface, and circles the Earth about once every 90 minutes. Find the centri; glqo(3ogoda u,zp;5petal 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 clay on the edge of +z,ihj0:7ni s6xvwp 8g 7ckdva potter’s wheel turning at wn vz+ dpi7jg07,k 8s:vhcxi645 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of -qpuj;+ ed20u4dba ema string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. I4-+be;q p0 2 amdudejuf 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 s+oz 8h1 ty9nz:kc0 q-ircf(hy;7ilr q peed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficientqt:c; r9inzrq7yy-kz(i+c h h 801ofl of static friction 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 tires and tv1ht dgq7cqy805t bnsnc2(9 yhe road if 2hc9(ntq 7q1tg8cd b0yyn vs 5a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet f ;s1.9ty:celcp:xo(7ybbi nb ighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fastpoc:cbin t 1e7.:;( lb9bsyxy 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 axic oe-u) vg*t6zs of a rotating turntable of variable speed. Whene6 cutz-og*)v the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rouf v)bi*:/1 vp redjq.ller coaster be traveling when upside down at the top obe)*dv: fji ./1vpq urf a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded to02l1geq c 39afyt6pk xp of a hil6fa91c3l kyg x qe0t2pl (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 would a 15-m-diameter Ferris wheel need to make x 6w6vos7kr,*u- 1n2i zk tqti o,m8yxfor the passengers to feel “s*wznti6kyxt2- omr6i k q,87 ,vux1oweightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At/ghe)k eks1xa,8i pd4p8p4 jd the lowest p 4k dapk/igs8p) 8 x,deh4j1epoint of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotbs(yz9 s1k2 hxr iv/r-6o lfw/fzs 14cate if a particle 9.00 cm from the axis of rotation is to experxvyzzs//k c4(oh bs-6s 2l11fr9 f rwiience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carniva jt o1t ;qi:wvaqz,w+-+ jj.nll, people are rotated in a cylindrically walled "room." (See q. -:+t a ,qj+ozwn;lwt1 jjviFig. 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 ipg go:hj/;tg( n a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling bloggt( ;p:gjo /hck (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 n6p;nw8t9rdo d d - lx o..efao)(ylb5hot ignoring the weight of the ball which revolves on a stri-.)6dtrx;8yfoph9d 5 dbnol( e loaw.ng 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 bankee 00vyr jnlgsr n2hr *y +a9+humm*v0.d for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massesvgkr/r8 gpd+ s6wd.9w $ 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 vert kh /3n5ma;ic8 mju)mzg9-fz mically 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 forb9 x1853zjz* fqphuk ece exerted on the car (by the ground) in Example 5-8 efh98u 3zj5q*k x1pz b 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 500f(2kky:c -vwli2m fg . accelerates 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 radia k y2mvlw2f.g:i(kc-fl 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 radi3 a85qptjcn4 h6 op3rdxc(rnf1q,t y-u(5y eius 2.90 m . At a particular inste hd -6 i3urcp f5x ajc4((n,1po5ntyqq3t8ryant, 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 gr2 q5tns)euo:n*v u,f w5 eji*oavity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass ):2to*eq5eovn n*ji5fwus ,u is 1350 kg.   

  At the surface of a certain plbi,m,1u 8iekx5vwv 4,xg 4 eyat 6ri;xanet, the gravitational acceleration g has a magnii8x;w4a 5v,em1yxb46x,, v ktigeriu tude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravityzjgot *3.e 5af on the Moon. The Moon's radius is 1.74 tzf3o.eag j*5$\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 thv2 gsf1e:1 i0k p c2axb*3fkzqat of Earth, but has the same mass. What is the acceleration due to gravity near its1 fbfz230*cg vkaxkepsi q21: surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but tkdjk6;aze2;q8 e. jbb he same radius. What is g near its surf;jk d b8be.;6jzaeqk2ace?   

  Two objects attract each other gravitationallyjz3n95r7* pe;e(z yuyf w8 +xbuq: 1nrqjne v( 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 vamew6;tafqa r1+ 5wz-bns+f(f j f)c;jlue of g , the acceleration of gravity, at (a) 3200 m6 fqwn1 mwf+ ajaft;e(f;zbj-r+5 sc)    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from qg+v14 jt6 0c9kan871mn p z*mejrgkcthe Earth’s center to a point outside the Earth where thegravitational acceler1 +a cq kgjctngr4*9pmev0m7kzn8 1j6ation 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 mat7pd klf3 i:2r5lj(h oss of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity 75rfdtklo2p ( :lij3hon this monster.    $\times10^12$

  A typical white-dwarf star, which :gvs0 ftz u-+tldl4q; once was an average star like our Sun but is now in the last stage of its evo4u:q0 ld+f;glttzvs-lution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why aqtsn5al4lxb7xvas94cc 0 k 9u 98(3gy gpzo)d stronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weac7g9ox d49asgaztu4lk(8 0) s qxb539pyclnvker 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 m. Ca/.xsuh( +nrmiu2j l2d/lzys 0 lculate the magnitude and direction of the total gravitati 2.sul0sl rzyi+hnudm /xj/(2onal 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 the - l+wb2gun w0+en ,jweSun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are inn,ljbe-2+en wg0 ww+u 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 Marodsrg45w )h+t.o;sfx x),lops is 0.38 of what it is on Earth, and that Mars’ radius is 34;,hf +).xol4rd)swox5t sg po00 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the periowl 61 3k2za rtj6z+hczd of the Earth and its distance from the Sun. [Note: Compare your jazwltrkz236 1+zh 6c answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving i7eby-p anv3cb u+,y2h n a stable circular orbit about the Earth at a height of 3600py73n+b,2 v ey acbuh- km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abov: suk9rsjt4ep9tgw vcq159 w)e the Earth. How fast must the shut grw9tk 95uev): j4twqss91cptle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical sy2 tj f;0gv g-2ikgb;wpaceship rotate 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 5–32gjgi;k22b;v f0tw - gy.)   

  Determine the time it takes for a satellite 8j4bu /w xo)vato orbit the Earth 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 Ear4 )boav 8x/juwth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the tou+bxygmx4 p*oj9v(z 2 s2 ong.p of Mt. ubx j+y2x2o4.pn(og*z mvgs 9Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module r 1u6 fl*gtlrm5k)nk /4v*2w3yi tydvcontinued to orbit the Moon at an altitude of about 100 km. How long dm36nt y tyrw5/fi*4rkgv 2lk*vu)1 ldid it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit tjzl,w:we9i5e4 o3 zryhe planet. The inner radius of the rings is 7e ojry, l:ziz5e94w3w3,000 $\mathrm{~km}$ , 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 ikdlt:i7no8y3 w+1j opn diameter rotates once every 15.5 s (see Fig. 5–9). What 7owypod 3n:ktli81j+is the ratio of a person’s apparent 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 from the center of the yf+ow ft./;u 1qhdr 9xEarth's Moof1fq u.9;yxow+h d tr/n 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 system consists of two stars of equal ma+qebq1/c --h.cbujaf l-( jtp ss. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point mccp ah-j1bqt-ul -.j(qf+/be idway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg wom/vqtw) m ah,zy5:4nd van in an elevator tha4a wzt ) :hvdmvn/5yq,t moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an ewua7l qw.9tlg1t/-kty q5f s-levator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s m--51 /qqtw7g s ktlflaw.t9uyinimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with*j 9-vr7pm*;rweo jug, om n-k period T , the density (mass/volume) of the *, ro9-jm jknrugv-e*opw; m7 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 anfd g 8xf-96.3ov cgenxd the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s su dxfvg 639x.g-of 8ecnrface.    s

  The asteroid Icarus, though only a few hundred meters across, orbi82w /d7opc ve6,lt; jx 2iokjpts the Sun like the opeto2k,l xij c 7w/d2v6 8;pjplanets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance oif/jswq; cj4-dc 4 9pjf 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 o u.igtn 7;;oc6j+ 4 ob:nhttuence 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 nearest and farthest distance from the Sun.] 4ht gooiu;tcn .tu6;je:+ b 7n    $\times 10^6$

  Our Sun rotates about the center of b6jbqiff ) /)g;oo r/eq m-r0athe 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 fu.ike (1vqiy w5b az,0our largest moons of Jupit yqwev.ika 51,(uizb 0er (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Moon.lz na57h5 c)cmq lw2/y w2q5n 5l)lyac m7c /hz   $\times 10^{24}$

  Determine the mean distance frw lb)wutjiqte +8 *.ew;;se:nom Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the pe; sqw*8);:ti .je nbtwewlue+riods 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 m t;h6 .cvadxol-w+,e qany fragments (which some space scientists think came from a planet that once orbited the Sun bc,d-h6+eatvw. xq l;out was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of hkf7*2*: t(sc3o o bs)v,t esoa2bgb 2wwu3gva band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside s*c v22 t gs:,bogesskbt3 *u7vowb2)w3ohf a(urface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swia93rh b;zzpg6.w9v km nging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of ez6z.9 3; ra9vpw hgbmkxerting 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 whabo(ne jzj q) iazixr y0.1l673t it is on the surfa7jj)n1aq(l i ozzri 6xy30b .ece?    $\times 10^6$

  On an ice rink, two skaters of cy9 y1nh28i duequal mass grab hands and spin in a mutual circle once every 2.5 scu8ndy 2y 9h1i. 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 rotates once cuubrmby ;,e :38g xhv:ld.f*per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth gu.:d u8vlfce3 h r:,ybx;*bm didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly f8d.90,k gaalo e m6jkg-n9oyprom the Earth todj pk9 o9 .meko-8gn g6ala0,y the Moon experience zero 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 st3/jfhrbl ,zetfr 88 7pand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which dfb8/p l8e,rzfr3 7tjhirection?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotatlv mn30q9st/k+ bxn8oxfz02 f0aezk 8 e 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 surf bn0ezlmkz9sn38 0txqfk fv0 /28aox+ ace of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft ijsh /76c /s(i wdv2cz02otmh en a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the acceler)c9rfp v tjcerxc3;xe) 7, 2/a2la w kg7fvgi:ation due to gravity at its s9 i/jpxcx:r7v ee)wg,c2 a73 2gftavl);fk crurface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical bl06:saq qynhk0/g9 kc y an anqclh/0qa: k skn gy069gle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient a7d4/0hmc;j+u1 dv ozu(s3 phjv8 tw fof static friction iow/ 7v a3m 48huuhjc1d +;p jt(v0dfszs 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth wer1) ,eyg j 7qunp97yrn xvy6uv-e rotating so fast that objects at the equator were apparently weightless?vg-xu jnvyrpnqe9u y 7y),671    $\times 10^3$s

  Two equal-mass stars maintain a constant distal en.b39 xv7kqnce 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 curve of radius 235 m. A lau;1a m8cvqe;h7o51ndx-dr bg mp suspended from the ceiling swings out to an1a; r8h 7eobvnc;qd1uxgd - m5 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 bee8gz(5b9mx duba3nsd:8a ,0z 0eovtufn 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.mtba:as zvn8,db 09o3 f05g8 du(zeux 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 presen-xzhy p52s m;hce 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 core to be-hx;y2mhsp5 z 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 sh yfnc5uq ecf bqs334h(b(9wu+own in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the non9q(3qbhs45fyef 3( u cwb c+urmal 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 sate93 v-5mjnr,rjo .knvcllites 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.vrk,jr n9-5j. vncmo 3 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 traveling 2.1 b8k( ew9ixu-vf (* nkz6i sisc+n-hv ,xillion km, is meant to orbit the asteroid Eros at a hei,8-i(w *k-fhzs s6xnk nv evx9(i+icught 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 gaw7kawp6*h z4pan, u*hzs39in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellnw 6 7aakh*4wg*93, sah pzzupite (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 meang -kbydarq(zx n0y0 kbez;+ +.oa;e2f distance fry by(+;q0e2r0aoa+d-fbgze z. xn; kk om 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 wo ftia6heem.6maw*p.,8 5jpyb uld need to be if you could actually "feel" yourself gravitationally .5pb a6yej h* t8ewm,m6 ipf.aattracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gal3l xc 6d.n 0:tzee.nxxaxy (Fig. 5-46) at a distance ..nzx 60t dlcn3xee:xof about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each sidtm2eu hm-5y1 q99kmk ehs;h+ w0p)hnde. Find the mag0k;my hu qhw)5+s2e hdh m199e pmtk-nnitude and direction 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 orbits(x -ddb ucr0zx(idl 45 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 1.5-cm-long swe+-: ggx;ky3wzt a+ug rep second han+grat3uz-+gwx kg:;y d on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swn 4c:lfu+om0nesd2b 8ing 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 the v:e+l2 bmc dsno84u f0nertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radiucmo) / k.vi 0j2ais-qzs R in a new highway is designed so that a car travelin mai)i jq sc2vzk0o/.-g 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, (xctiw(53 us j2+j,a+wt hsjpvtu;s 9 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 for (tws25ts(t s;+auvwjx9,jcjhpi3 + uce 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.$\approx$    $\times 10^2$