Sometimes people say that water is removed from clothes in a spin dry/mqj0ru os5 g+:,lzg :b6mukler by centrifugal force throwing the water outward. Wukm b lm,gg+s/ z:l :o50r6juqhat is wrong with this statement?

Will the acceleration of a 4a7z(zx;xciuk it4 /w car be the same when the car travels around a sharp curve at a ck7z 4cx zw4;it iu/ax(onstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a h.xz430zqh :jp4m j2dg0zkz(.vg ghyp illy road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hil z z4dg.:.kmzyh2p4j vh(j03 x0zqggpl, (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 ap2dh83y9 ta.mp9n fmq merry-go-round. Which of these forces provides themt hn9y.28m3pa pdqf9 centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water rf 5le i(48zjhtln4,bspilling out, even at the top of the circle when thzjr4 8i4 nlbfh5t(e,le bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are atvpldo :9 ty+:e least three controls in the car which can be l9 :oyev:+tdpused to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comeb/dc. pham5f kbi-07f s flying over the crest of a small hill, as shown in Fig. 5–31. His sled 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. Expla/f b50p7 b-cf.mkihdain this decrease using Newton’s second law.

Why do bicycle riders ldno 0zv3 ccwnx93qd, 1ean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you co*+hcv(r gg tlx 3dhe9+mpute the banking angle given its speexgd* +h(g h+r93 clvted and radius of the turn?

A girl is whirling a :q jw7 t c40lk:vv9pujball on a string around her head in a horizontal plane. She wants to let go at precisely the right twv qvj90ut p c4l:7jk:ime so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how lacvlwenav 69 4fe 9q.e,s 66l8ug ,rheorge a force? Consider an applgq668fl,uvhre4 oa 96 enwe,lce v9. se
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doub 5xae)w+ds om9le what it is, in what ways would the Moon’s orbit be diffed+9w5s m oe)axrent?

Which pulls harder gravitationally, the Earth on4jjvfmvjf htb; u3n* vi*p0+ ( the Moon, or the Moon on the Earbfv3jv(h*p fj+ v4;umt* 0injth? Which accelerates more?

The Sun's gravitational pull on the Earth is much la;g0 p85fp ;o h2mhvy.5wmqkou rger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explyq;p5h pv.8 fom5om g;kuh20wain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What twoooxn(h*z1:64 vkja oh/v od)f effects are at1a:4 hv)o djn6 oohfz v/*k(ox work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the forc,h6 :xj3od(f ksg0cgde on the Moon due to the Sun. Why isn’(k,shj36c d:0ggxfo dt the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit a5yyw2 qh r,3m z.k+tziround the Sun larger or smaller than the centripetal acceleration of th.z r2k,mwq+h5 3yztyie Earth?

Would it require less speed to launch a satellite (a) toward the e rekoh1do* ;rr m6kwe5ja(6/y ast or (b) toward the west? Consider the Earth’s rotation direction.rrjr ah5w(dy;kk e/ m*o6o16e

When will your apparent weight be the greatest, as measured by a*fzm(zaggj*2b sw,e eg *;vi6 scale in a moving elfzb*6iseg2 je m,ga(;** zgv wevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your 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 could be adversetu*w b;: hq18kg smr1tr+ p8yply 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 objecb+ y:psrp1 m 8u;rtg1t*wkq8hts fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessn vc7b 0e+h:leprapo).guw+7eo6d oc4ess” between stevcr+ eu7woe olobad )hc 0p+ :67eg4.pps.

The Earth moves faster in its orbit around tw::aa s23n ljzt yiw9)q(k/sc he 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 tyz a:39 i( lc)/:s2qjatwws knhe Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discok3 ccg9:mm z8f9itl d,vered to have a moon. Explain how this discovery enabled an estima,cgmctz:mfd 9 il8k 39te of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than thekm(oqqhkjxmc 7 u8u*4 4lylkwp/.y ;, Moon'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 ;,x p ku wkjumqkhmo/8l*4y. 7c4l(yq 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 198x3 wd9tzbgi: 40 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripet5vm9 yk0 jkyq7al acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Ea5kkqy70m9y vj rth. 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 exe ucm;(t7gc:f irted on a 2.0-kg discus as it rotates uniformly in ic;fg 7umc:t (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 surfacea)s rrjp *o5-y, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its pra 5j-)yrso*orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleratn942 ctzuvfkale :,( rz96v.mrspvc3 ion of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 3s9k9ccu(f: ,rvm36t4.elvz2 zarvnp 2 cm?   

  A ball on the end of a string is revolved at a uniform ratdujf a++d.q;t/r *c yr. .y;qus/rlvme in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If iu/rtufd+m sydy +.j;v rqcl/*ar;. .qts 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 a 1050-kg car can round a turn of radiu.y* t/wmrt5wtey 7x,f s 77 m on a flat road if t *yrtetfy /,.wxm 7w5the coefficient 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 t: vuyy,3 3iu)w.dvsz;g bc xb8he tires and the road c8vv sy,wug.u): ibb3;3 yxzdif a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astib4kqecyhabjk9m7zc93 uy ( 2 mox. :(ronauts and jet fighter pilots is designed to rotate a trainee in a horizontk :jc(byhczb qe3 4(m.9k79y 2u amxoial 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 ih gay38 o0s(9cl qt94o vt g)hhso:6lfrom the 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 is reached and the coin slides off. What is the coefficient of static fris 9oc l93vhs4 ytqgoti6 ) (hg:hl0oa8ction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when utip(x+1gt )3u5 t;jgwq moi lm9x*sm1pside down at the top of1q3i t gw+p9mxot)m*s5i; gtu 1(jmlx 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 to29 fsk nd-kptblqe5*sgc )yqd*z7b/ 2 p of a hill l p7gbzkq ed-y2q* ts9d5n* /sk)bf2c (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 p8yijw -sf cks3hsv:. +er minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightlesshkc s+s:w.-sy8 fvj3i” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. ,athdw;ufqkw 98oo54kbfu / )-4unddAt the lowest point of its motion the tension in the rou 4bo ntd hw,9dw)aku/8fo-kdf;q4 5upe 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) mustw 50w2qj* xhm 2b3hbua a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115hb2 h 05aum*b x2j3wwq,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" atwzb2ogr5d; qn:n+9:qm ysxy0 kl;q ;l4mey: v a carnival, people are rotated in a cylindrically walled "room." (Snm + vky;g;n l9;o qm2wy 5ez qxqs:y:bdlr:04ee 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 circle on a frictionless air-hockdjog,0c s36 kghj l0a0w4kwl2ey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 54jw0l,a0ohcj wkgk 0 sd62 l3g-
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 weid06c ctbyli7. ght of the ball which revolves on a string 0.600 m long. In particular, find the magnitudcy tild0c 7b6.e 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 ra8 waoed0sk9/pfxkbk b/g*0 o8dius of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masseh 0 1ho6jte2eqs $ 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 evas-)+c6 hgroucsi*; qo zive maneuver by 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 tangen:b+jipit5 uv/ tial and centripetal components of the net force exerted on t:itjipv + b5/uhe car (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolthzstomf.t8 (ax 7-s5is 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m5f. tt8 xazs-(msh o7t. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves inklx 9 nv;2 dnh+k,iw;yn7l +lqq bj0zdsn,r,. a horizontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.05lvnwn 7 , 9r0lqb j 2+znlx;y;ks,,h.k+iqd nd $\mathrm{~m} / \mathrm{s}^{2}$ , 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 o,+uyfg*4d d,;)dcf r0zw6iltcbb*c12,800 km (2 Earth radii) abfyo,)i c*cc +gddb* bw4z,r0dt; 6ulfove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain ,yi uqmc8e:/j planet, the gravitational acceleration g has a magnitudu/e jci: q,8yme 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 accelera7vr2 d:d(*z i-jqas 6cdryt0otion due to gravity on the Moon. The Moon's radius is 1.74 qr6d *ds7 i(jzoyr0 -t:av2dc $\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 thatiq7) ka1 j)lxw of Earth, but has the same mass. What is the acceleration du q1kx7)l ja)iwe to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times rr 5kt zp/57vethat of Earth, but the same radius. What irk/v7pr 5z5ets g near its surface?   

  Two objects attract each other gravitationally with a forcws -xcklb31o405vt-rz rb6 m06thmh ue 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 accelerati a4dbk 7/vwwu;on of gravity, at (a) 3200 m v/wd;a7 buwk 4   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center bl 4xxk2l j6q3to a point outside the Earth where thegravitational acceleration due t 2q3l x4bx6jlko 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 sp35t( yc6veflasy2 vthlr+ k,)here ab + evkya2flrv)tth35 s6cyl ,(out 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our S53 :vvsnxz7xdd -glfk4n)1zdtzm 78xun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is7 7l xd)138zvkzdzxs: v4m-dtg5fxn n the surface gravity on this star?    $\times 10^7$

  You are explaining why astrom57d kv:r mc1fg (kj;bnauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that m: mvf51djck7(br; gkit 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 sqg5zg,ko p -8souare of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exertk-gogso8z5 ,ped 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 fubjq(9 9pv6pthe same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuu qfvbp969pj( ming 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 accelu coa5,u:lhll 1xkh:kgo7 z--eration of gravity at the surface of Mars is 0.38 of what it is on Earth, 1-a7okzou: u5:h,h -lkl xlcgand that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the periw9if6l;4t qe2 5 -gijv pos9aood of the Earth and its dist 4sqii t59oov 2fp 9jewg-al6;ance 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 satell ss+ 4nh 92pggt1ly4oi js.b1yite moving in a stable circular orbit about the Earth at a heig4yh o1 jg ns+ygb2.pi9s4lst 1ht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 0rzx gi.x97nn 650 km above the Earth. Hownzgr0 .xxin 79 fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical st5 hwnt+4 z uskm7o+r8paceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceshsu87z5 k4t rnoh+m+twip’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 tojetg9f7,4qni 0z) o vq 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 Earth. Does your result depend on the mav4n g0zo9)iqeqtj ,7f ss of the satellite?    s ~    min

  At what horizontal velocinyg 3hsdnk7t) i;ay/q; t:-lf ty would a satellite have to be launched from the top of Mt. Everest to be placed kn 3h7stnt/ );i y; :ag-dyfqlin a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the commzf:.k7b-zs4bnga275 frm a9zd s:b wr and module continued to orbit the Moon at ansr bd7m-:z4b 5sr.g: k fz72n9a wfzab altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pj zc/wc(b-mk5 lanet. The inner radius of the rings is ccwk z (-mj5b/73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fic6kf)qjv o9a ,asw(f+g. 5–9). What is the ratio of a person’s apparent weight to her rev swjkf+)f9coq( 6aa ,al weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km f gqsdt9z/wavi2;*o4i rom the center of the Earth's Moon in a spav2/ w 9qa4tzsi i*o;dgce 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 syste tkl4xp +o0oy+m consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Ept4y lxok++0 oarth 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 5ilm bj(bmy1u:ky8v +bi +/e l:5-kg woman in an elevator that :v +y1 u8ykjlbemi:mbi + bl/(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 f6xvc57p kc9d ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s mic 9dvf5cxp67k nimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very u+ailv*yg* wd13km(wd + p d/xpsb9g )near the surface of a planet with period T , the density (mass/volum++wbx1y iw(lv msk* u/dd g9pd g)3p*ae) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period w4luqdb g0xr89 pn -k*of the Moon (27.4 d) to determine the period of an artificgdnrklb8x-4* 9u0w p qial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, thoughw7ct5i+j/lcue h,1u k only a few hundred meters across, orbits the Sun like the planets. Its period is 4 jwu,eit/51cku7+lhc 10 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance o j0fflz(/(kbrc jt;tkv5yv+kcr( o62 f 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 roughvk4o kc ) oft+cx3hdz-51blc+ ly 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 comet from the Sun. Is it still “in” tkflvcc1oxc d-5) 3o +t4b+kzhhe 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 l (h7m+o1or;e4tu-)p:r 5mkcf mto kq 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( a .i vb+qu.17iyjjya the four largest moons of Jupiter (those discovered by Galileo in 1609ubya7v.aq ( 1ji+ y.ji).
(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 thezr6:nq;z qk6ax3butz .t+ 6dg known period and distance of the Moon. 6t3kgqx:azrztu.+q 6dnz 6 b;   $\times 10^{24}$

  Determine the mean dist 6o;k7( m5b yzx 4ldqge:/bajsance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given d/4( xky m;obg: 6q7ezj 5lasbin 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 betwe ek/706p4mje :z)wd9pe wfohken Mars and Jupiter consists of many fragments (which some space scientists think came from a plaep0 pmk we/)zhk e9wd oj7:64fnet 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 )1ifaj-o e d) kr7an0*a;mxk o"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. Whx*aae 7am)do 1 if-)0krkn jo;at will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. rl,f2 788yxav,(e )fu lybe lj5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is th2 f,u,vl e(b8f l8y)lrxa7eyje 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 hg;lbi *h4oh+ u8rd..lm) uy wlni43l2i*nmx falf what it is on the surfacm.lmwbnu xlld)4h2n8i3oy+ 4 h* *ifur ; gil.e?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands an3vyy79bul/yt29vn bx d spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their indivi ybbtvl/nu2 yx97 v93ydual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rot ixbdnftv3cr;qw1c+ p ()au0+ ates once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the ma;ifxqnc0( ct+ a3v+bpw)1durgnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the Es3zaz 9t0)zp 6 axy5dwarth to the Moon experience zero 3atz 05zwz axydp 9)6snet 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 a bathroom sctlm rnak7v6)7e i4*ym ale in an elevator, it says your mass is 82 kg. What is the act*nlke) 7myvi rm67 4aceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circu8 6ch0ewi1-oql x+ lajlar 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 of -c0xe 8 hjil61+ qoalwthe Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical l1(jxr cd5o 3dmoop (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, thu 1,,genum:t+* lgjebe acceleration due to mj,:1 * neut,+egglu bgravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vp xk;ae2o7sv5r1 vui27d7aw yertical by an angle aav di72eoxps;71 rv7 wuk5 y2 $\theta$ 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 od ldgyn c/;93 o)mymhevx8a 1 the*,t6f static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the 1v369 c ahmdtnyx;e 8*y, /oeglhd)mtcurve?

  How long would a day be if the Earteh6wwwn5f 4,a qv 6 3 bmlplo/aaa( lbx0ie4*4h were rotating so fast that objects at the equator were apparently fei5 e b(3 mw0l4 6blal*aon4v4,x6wa paw/q hweightless?    $\times 10^3$s

  Two equal-mass stars maintain *i.juz/3fesi gwhq98(tcd u:qwct-+ 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 curve of e4cj9eu haxg/bv*;nll0h aq9u 70/xfradius 235 m. A lamp suspended from the ceiuxch0n/hxue 4/l v9g0;belf* 7qa j9 aling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timg61ax)hrr4sa 0 x fsb/g6uv5hes as massive as the Earth. Thus, it has been claimed that a person would be crushed by the shv5x)1agrgx s 6ah 0/f u4r6bforce of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubblnwti2fjvmu5-rcc(d2 t161g1sm6e t k e Space Telescope deduced the presence of an extremely massive core in the distant smw2t6fvc6rt1(em1tdg u 5ij1 2 cnk-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 constam5 :gg)7wtf kkqbf+( bnt 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 is largest? Smallest?) Explain. (b) Where would the driver feel 7bf5 +fb ( tmkqgwg)k:heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPSlcx zs3 ,gsi3 4l1ekr;) 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 satellitzsl3;ser3x4c k 1g,lie 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 billp01 -d uw8sz ) ;rxj9,pxadlkgion km, is meant to jux9wdz )0k8pxg,;sr-lp1 a dorbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the): bom+ su16eh2(qa p fsqav:w space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satelli::h s b6af qma(o+wevuq12ps )te (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 ppzu: *ef) .kdx2k ca*zeriod of 3000 years. (a) What is its mean distance from the Sun?pc ue2zakdf *x).:k*z   
(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 neednn:je7*tu9-ig by4jte/jz3i to be if you could actually "feel" yourself gravitationally attracted eiy jnz t34itb/ e9uj7g-jn:*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 Galaxy (Fi/jevpk;glr54(nqa 1vzl4 k, vg. 5-46) at a distance of about 30,000 light-years from tha1p; n v(k/lvrq z 4kj,54vegle 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 6giq7qt-,f hg x3uqew53lkv 3. Find the magnitude and direcwe5h3 6 u v73qxti3-gfqqlgk ,tion 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 tst+8zn 02 wjilhe 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-cdx.0n/7671ezy bh mgw ut7eilong sweep second hand on your wrist w 7enw6mtcz1 heg7dyx/7i. u0batch?    $\times 10^{-4}$

  While fishing, you get bored and star y7:nu8so.vs ot 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 the vertical? [Hint: See Fig.vu .sn8: yoo7s 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so thaycdm1zq+7 /9,bx4 kddqcnf 9ft a car traveling d ccbq y9m 7/fz+9,nddf4xkq1 at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiatingi 7nv-.a2rs-htxhclgq+ 9 )a j 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 curve .j ) l7shhqi-axv2c-gn9tr+awith 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.$\approx$    $\times 10^2$