Sometimes people say that water is removed from :p:(mbyiz9a dj l zv+*.kcd ;rh5pgs*clothes in a spin dryer by centrifugal force throwing the water outwad bk.c:+r(: vs*dm;p*5 zjilz gy a9hprd. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels arou6bz6yb: lwz ra56bkz;nd a sharp curve at a constant 60 km/h as whebl :bz 65y6zkz6a bw;rn it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constanh 0y8.nm27n5 llvgyxxph +fs:e qpg.*t 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 n+sgx.2 ph7 5nxlqmgy*:ev0f8lh y .p dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding adz gw */3mf6+fet/ czn dku*.c horse on a merry-go-round. Which of these forces provides the ceuz dcz*w6edg *f3n/ t./kmfc+ntripetal acceleration of the child?

A bucket of water can be whirled in a verticzaqz1 3 owns+3al circle without the water spilling out, even at the top of the ciz sq +nw1oz33arcle when the bucket is upside down. Explain.

How many “accelerators” do you have infm8frc un,-.31d1 pamz 7s 7flwgdha . your car? There are at least three controls in the car which can be used to cause nmagw r17c1mha.3fld,f.f-8 pduzs7 the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying ovep /0k2g:+wbf ( 00jhcwayb epbr 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. Explain this decrease uhfypgck0/ we j0b+(0b2p b:w asing Newton’s second law.

Why do bicycle riders leanrp4lo6hj*l x 1 inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you computeg9fx ooguz29 0.uy)p j the banking angle given its speed and radiz 9opo.) 2fuygxu9j0 gus of the turn?

A girl is whirling a baz5ryuz;( -bbop -xzx,ll on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that thyb,5zub( xr xzo-zp ;-e 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 forcz t4q(sb.fcdgp) z1 5qe on the Earth? If so, how large a force? Consider an ad5(pzsg q 1f.b zctq)4pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’fh 0opzxtk73ymmgn )r 0xhc3* 7b 5,zis orbit be differen,hi t7mx33 c*zf5k0brz n yohmgpx7)0t?

Which pulls harder gravitationally, the Ebv r29:0xewxhd)6-3 hc odkox+mjc 7oi.- mc darth on the Moon, or the Moon on the Earth? +-d:om orhj.0xvx3cbk oicxh )d27c mwd9-e 6 Which accelerates more?

The Sun's gravitational pull on the Earth is much larger thanlokm23fqx.bilw5 79a the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider th lkm7x 2a3owb. 95lifqe 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 twst59 /l9hdey) k5cz nhkt2t 4zas ykl o)d3*6do effects are at work? Do thekh*)595dt z2d edy a6ohn/lytt s34 zs 9kklc)y oppose each other?

The gravitational forcezqr2chwzs 0 19 on the Moon due to the Earth is only about half the force12 cwzrsqh9 z0 on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun largercfw6 rl1:mu)i or smaller than the centrifr)l6micu: 1w petal acceleration of the Earth?

Would it require less speed to launch a satelxp,vsz 8cl;- hlite (a) toward the east or (b) toward the west? Conside s-hzl ;c8vxp,r the Earth’s rotation direction.

When will your apparent weight be 9ru0,ag f:wd jthe greatest, as measured by a scale in a moving elevator: when the elevatdua9w0 f:gjr ,or (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 adversely affectcg(g(.qhv d (ued by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on ((g.qch(dvug 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 experiences “free fall” or “apparent weightlessness” nz p5r tj.vf/-between stepjvn p5tz /r.-fs.

The Earth moves faster in ilb o,sbz5b c*txl;gd6bdqt5cz7 ofwk8(;1d 9ts 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 o58gkobz flq wbtsd*;6bto,dz dl1b9; (c7x5c f 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 hag 5eb,rwhk7tk+9 k xv)z4zkr1 ve a moon. Explain how this discovery enabled an eszkkw 79xtzbv5r ,k1h g)k +er4timate of Pluto’s mass.

  The Sun's gravitational puofj+i vne: 44xi2,pv zll on the Earth is much larger than the 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 +, xe:i4j4 f2on ipvzvthe 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 1980 v 5mx ug g10syp1 3czypgs120qhwm 89l$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelera4y9)oyn c(fz oj0vi 4ption of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's oy c pfo4vi9 (4)zn0jyorbit 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 )oncqr cl7r00 is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal cir7o0 0n)lcr crqcle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle az ft1(m*b 0qo33rs zlis in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutez1 b q30t osarf(zm*l3s. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a spl, un4*13ujnm*9 iccuyg nfqb 3hc+q*eck of clay on the edge of a potter’s wheel turning at 45 ry3b *ngf4 *qn*c,uunlc9 1qj3m+ uihcpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform r9tgn +9rarrcky +f3n4ate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is rk9nr ca tf +gy+4n9r3 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 w .u (4magsy+ixlk 7s7which a 1050-kg car can round a turn of radius 77 m on a flat u4.si(mk7aws y +7lxgroad if the 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 the tires u2p m6xje)zd: and the road if a mz2p exj:6u )dcar is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and je2oo.d h f8xl4ftnd77e6p t2m 6x,eeh ct fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating? m hfe.no228,tdodx ft c 47h6e7epx6l   rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 5ye5lfd5cy1ze* xrg : c/ew *hcm from 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 d/f eezyyglh* *ecr5:x515w cuntil a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at u6 zdj,xlm(+othe top of a cir6zo+x(lmj, d ucle
(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 rounf rl*tos )3*x g9bngl4ded top of a hill f4rl lb3xgno)sg*t *9 (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-diameto1c .6wpoq1 w8q5iog km0 gy1uer Ferris wheel need to make for the passengers to feel “weoo101q.uq ygk gc 8ipw615mowightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10/ c;xlrht fj7s4ph.b: / gwd:w m. At the lowest point os/f/:.cl:hbdwxph7g t 4w; jrf 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 rotate if a particle 9.00 cm from the axi, wxe h 19cc)jbl;aqg+s of rotation is to experience an acceleration of 115,000+lxhq cg9,eaw )1;bjc $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carn2f,2qg.t*z ht6mz .-o5ym c4sultbjtival, people are rotated in a cylindrically walled "room."m ,yuhjmt.- btg6 lo zt4f .st2z52*qc (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockex8gwn.96yf vby tabletop, and is held in this orbit by a light cord cov8 gfxbnw 6y9.nnected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely -nmeci0znxhs;t2 /y . p,hh 7uthis time, by not ignoring the weight of the ball which revolves on a string 0.600 m l h2e0.7zn-n, thsu mpxy;ich /ong. 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 ban mflva 0x,0,uuq4c5khked 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 masses h2,aq /zdtf* u$ 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 vertically at 310(t ia l/r8(sypa9t 0iw $\mathrm{~m} / \mathrm{s}$ . 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 ce7v n- ;kmi* a,ufwxea)t-rc8intripetal components of the net force exerted on the car (by the ground) in Example 5-8 whecxi-nk r vaiea*, mf7)8;t uw-n its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, goingd/;se,z (qnq p+2+ewk e5tzvd from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with nd;n/5,ewpe 2 +t ek+ vdqzs(qzo slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius l h0wkp+tlv xc5* -yg14**u knwu+s0qj6 o sft2.90 m . At a particular instant,scokkvj 16 yt 4xqngtp+ +w0-***f uwh5sll0u 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 ;ng)e d7-vk.an c*l.stlpig,a spacecraft 12,800 km (2 Earth radii) above the sgvl*pin g- 7ak; n,e..d)tclEarth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acce)lj/y 9dy wnu)2u q;c.hdcv8lleration g has a magnitude of 12hcu9uy8 2;))q y.wnjd/ lv dcl m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity g2ef /r61essq lll1)y on the Moon. The Moon's radius is 1.7sf/rl l1gesyqe 1l6 2)4 $\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 thatglfd( 2jbe.veh63 ky5slxl2 6 of Earth, but has the same mass. What is the acceleration due to gravi32blhe6lx fvl kd (.jg65y2esty near its surface?   

  A hypothetical planet has a mass 1.66 times that of Ear0c eu33)gbyfn th, but the same radius. What is g near its surface?33)gu yefbn0c   

  Two objects attract each other gravitationaler5zc;7rdjw vae;q; 1ly with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , th82-o yr)9mzfg 4cem spe acceleration of gravity, at (a) 3200 m fos z mmpc4e29g8y )r-   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance f/bvwc3jt gbqgqt. z. x,3dn0q8i4v ; qrom the Earth’s center to a point outside the Earth where thegravitational acceleration 3tn;.q ztiwq38 b.j/g4v0qbvg,x cqd due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a spre7 oemoob3)4qv xuyr/)* +6do jl1 ybhere about 10 km in radius. Estimate the surface gravityurlmeby jo+71)dx/*o3 4 qv ooyrb6)e on this monster.    $\times10^12$

  A typical white-dwarf star, whi7 rynie yf b;2wgsd5 (d+5g4kxch once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravk7 ef+g 5wb(5nd2r syg4x ;dyiity on this star?    $\times 10^7$

  You are explaining why ast(9nl3bn:cd kd 7d9zih ronauts 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 it isn’t so by calculating the acce7l3kd9hdzdcnn( 9b :ileration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of xy6rk rty8 g0.df0i-ja square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere r0-0t8xk yidfr y6g.jby the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years nw6p/qk1 5cn;y5w)c kzn 6iwn most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, aw5zp6 / y6nc;n5cn w)nk qikw1ssuming 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 surfaq,ki4 aq2+a.vc g61z9mme ftace of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Ma azg evq+mf4i 129kacm.6,t qars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of t(nszt29 z rt(qhe Earth and its distance from the Suz2rt t(s n9zq(n. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about thez ;yp9 sv ya;ak,t0fl1 Earth at a height af,a01yk tl vpz9sy; ;of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a co0r fd*a3 x4k*qgy9huircular orbit 650 km above the Earth. How fast muh* 9uof d3yaq*x0rg4 kst the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experienceka/gjd28f)-oy9d g1mop eoo)1 p fq (j simulated gravity of 2 )yo jo p)mpk1/ojffq-(a ggo9ed8d10.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circula ou2ux.h:f91 tiqo/l dr “near-Earth” orbit. A “near-Earth” orbit is one au ht2o91fxiu.o /dl: qt 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 launched from the eyik0 u j./k6u5y o951 qqnkebtop of Mt. Eve6 k5oie5n/q kyejk y0.uu19 bqrest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landinu/r 8 9om75nf0 vahlgwg mission, the command module continued to orbit the Moon at an altitude of about 100 km. How l5ur/a 9ghn0 vfolm 7w8ong did it take to go around the Moon once?    s

  The rings of Saturn are composed of cf)nz+5nv lm( hgb/e 2vhcz0v;hunks of ice that orbit the planet. The inner radius of the rv h;0(n+/bfvhecn )m5zvgzl2ings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5-e+co)agl;e o3 qsh 0e s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at oh co+e; )q 0al-e3gesthe bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronfjt wp7j.gbye3)t 4/a aut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at c3ae)4tj7tbf pw/. jgyonstant 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 syste2yue bwyak g geprw*+h 2-;s.+m consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between+;+ybp rw .y a-ew2e*gkghs 2u them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for thufzxk/ * d2:bde weight of a 55-kg woman in an elevator that 2fdx :/*zb dukmoves
(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 elevatorew;vnf7-/in1qi 6p vm. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude e6m vnnwq/f7-vi1i;p and direction)? a =   

Show that if a satellite orbits very near th24qcmz:tm,z ye surface of a planet with period T , the density (mass/vo4 zqtc2,mm:yz lume) 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 perpp6 a)j6nft +xn r2)lqiod of the Moon (27.4 d) to determine the period of an artificial satellite ora62tr xpn+jflpq))6 nbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few4dhkos *2 :vgab1*zvw hundred meters across, orbits the Sun like the planets:2a* vb ks4 *hogzwd1v. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanfr(ulvbdc86hjft2. 8 ce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. Ibov sz q52lw8l 1v2p6kt 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 vb8s65oqpk1 zl 2lwv2planet’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 of the Gc*qei7qh0gns3 d0vy) alaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 3p9wpk0iftw5fg 67y kz .bb3gngv- )kmean distance for the four largest moons of Jupiter (those discovered by Galileo in 17yf3bwzgkfk v0b6gp-ig3 tw9pn)k . 5609).
(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 M6k3t 5qco*eyzx,n mlhk1e2e3 oon. e13kcnlkey3,h 5mqez6 2*tx o   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moobkosr44kbl ;8pfc/)dpa mm+ pg:6. skns, using Kepler’s third law. Use the distance of Io and the perioppmrs4lb f8obcmsp:+ ;/kk d) ga .k64ds 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 betwehjv v;x5k 00nven Mars and Jupiter consists of many fragments (which some space scientists think came from a planet nvj 00;k vxv5hthat 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 "pvuokijh( .e44 lanet" 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 revolution, this planet's year, in k4jh (v ue.4ioEarth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fip oex1 td:/m)mg. 5–41). If his arms are capable of exerting a forpo:m1)m /xdte ce 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 wibxqjf n5r9nkyec q7689pyj*m;0k. g a ll the acceleration of gravity be half what it is ony jyk bq;ej97*0p nkqa9xm.6 5crg8nf the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spinpqvor*0 9) ioj8 kx2np in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masse0ijr*p v9xoqno)2 p 8ks are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravihou)v g *qq.xz80pz1d ty at the equator is slightly less than it would be if the Earth didn’t rotate. E1dvx).zp0gh u 8qqoz*stimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will x9jh/o v/x.(ui tz8 0fvoxqsn7 uy,ent0 9-u sa spacecraft traveling directly from the Earth to the Moon experience zero net force bev0/ovx 9,x t-on .i/ hj0 qnstuyf8ue9x7s(z ucause the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, ls .why 7v6ih1but when you stand on a bathroom scale in an elevator, it says yhs. 1wvi yl7h6our mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stationd59fz vy +uk6,jph o1q uetc0t7 g*/pi consists 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 diameuzv t,fqhigy5c+ pe ojt1*7u9 60pdk/ ter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical 4pw9p xy7:t; ,19nz;pl mofbik os3yoloop (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, /(kd ei1sx9v mthe acceleration due to gravity at its is/v kxmd9e1(surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vepirli)c1uukq c;.2ln ipz2-/rtical by an a zr;p-c 2lil.1/ 2pn)iqkcuiungle $\theta$ 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 desigf ajbbrtwr)96x9d fo6q.z p;- ;gqid2n speed of If the coefficient of static fricz;9 d grf- 9fq2dpb.ojx; )6rw btaqi6tion is 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 were rotating so fast thatc.wyn, euux tts8/ uvwj4k(w.y(y:o* objects at the equator were apparently weightvu,4 o.wt*(ek. uy /s xtj:8 cw(yyunwless?    $\times 10^3$s

  Two equal-mass stars maintain a consh*9hu3fkgicg;ybx ; yz/(d8ftant 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 cnos,+ d2u:,zand 8t+.xg go lcurve of radius 235 m. A lamp suspende+szndoc+u2 8a n,x:og.d ,ltgd from the ceiling swings 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 Eart ws 2re-c2,rwskb9g 1vh. Thus, it has been claimed that a person would be crushed by ts2ew9r 1s2,bcw-kvgrhe force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data 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 h 6bjv4jf*y jiu -y( zl1jx(2tHubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hovfuh tj(yl *jxi-jj 1z6b4y2(le (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 s .j* +viyssbo+hown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces ojs+ s*y+vb.i 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) util ,gh*zc0d00hzyh r9 s2+bhkmu izes 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,mk hr0b *0d9z zhgch+u0h sy2. 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 Rendezvo)jez12bhj saqm65u x*us (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 keq6z)s 1ajb u hx5*2jmm . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in needlk +0c/f bg+bt9wvtw ( of repair. You are i0+b(t+fk9tgwvl w /bcn a circular orbit of the same radius as the satellite (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. bdr/5s j3* 5 m jl/mspmb.o.j(vpcg x:(a) What is its mean distance from the Sun?5 s(gpbs.c / ml jm5p.r:mojvx/bjd3*   
(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 wozygfdm -73d4 ;qv62e d cjk)vvuld need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonabl dvvydc74q g)v;j-fz6 edm23ke assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy 6puw 8x6ztha-:s8r ) ocy 1acc(Fig. 5-46) at a distance of abo88p aw cc-cyr:o6)at6suxh1 zut 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 sy 96 p7b*y(brqjcn+gaide. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass plab* 9aygbn+c67pjy q(rced at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earthq d qaf*.6roaop /n80 fvfr*o. $ \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 sweep t-ym1k 3d9 jkl0rqo v)second hand on your y m)tkr-3k 01 jloqv9dwrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around zqju6puwp w3 3czj4m kc2)g f41v:b:tin 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 j:wvc kqz wptuu:mc)pfj6g3 342z1b 4vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car ts0kiv0q;(85shnt s uq(ozd )lo 1k4pn raveling hnpis)8klu004 (qnzvsqk o so;d5(1tat 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 negotia bxfdig6s. : )dex4( s.ljkz,xting 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 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.,z 4 j6fbi):skldx s(. .xdxeg $\approx$    $\times 10^2$
(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.$\approx$    $\times 10^2$