Sometimes people say that water is removed from clothek 2kain 1fcpt2+62* wht; 2zzlcf3psbs in a spin dryer by centrif 6p knbkzft;cct 2+3* pwlf22sh2az i1ugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the cap omkgm)4s 8f8r travels around a sharp curve at a constant 60 km/h as when it travels arouns8opm4 )gm k8fd a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where do ebndy8i9m l10es the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hill8e1 lmndy0bi9s, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a emxrv59;fq n8)j q iq99t oov:merry-go-round. Which of these fje:i9vn mq ) ;o8r 59fto9qqvxorces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the wate f(hv2qgadc:p8cx8l:z4g k 5dr spilling out, even at the t85 hcdf:8 dzcp( vax4glq:gk2op of the circle when the bucket is upside down. Explain.

How many “acceleratorswbtd dgqg :h ,oe3z*46” do you have in your car? There are at least three controls in the car which can be used to cause the car to aczwt 3g,: 6qdbh de4*gocelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over tho2nelj. hpg08j4g4lq e crest of a small hill, as shown in Fig. 5–31. His jnlq4go40gplhj.2 8e 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 using Newton’s second law.

Why do bicycle riders lean inward wheg popih08*dxu 6:bdp +n rounding a curve at high speed?

Why do airplanes bank when +6 *(no**o m7kz9bai vlt bvu,u)yixithey turn? How would you compute the banking angle given its speed and radius of) 6okv, iamt*xyb 7o(v*uiub li+z*n9 the turn?

A girl is whirling akh7vur9fd .q+;vidp: ball on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hih7fpvvd+; k.id9uqr : t 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 th; )2fb /vn3a:zq ogxjzq)g+ khe Earth? If so, how large a force?) /hb:x)g3kn;q gjqa2f z vzo+ Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s or y cj.w8av 7otlaj.38/.clsgqbit be dtg7qvjj y . .8wsa3o.ca l8cl/ifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on(yt8 qd h:h 4)emc.as2d:kmpf the Earth? Which accelerates m8my4.dhc)( d q:faekh 2tmps:ore?

The Sun's gravitational pull on tcx vv*: 1fqw9vhe Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hi* qcx:v9vw f1vnt: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at tqr6en*5nefo2j20u m fhe equator or at the poles? What two effects are at work? Do they oppose each othj26* n eqrenof 5um0f2er?

The gravitational force on the Moon due to the Earthml g a mm16/vdp h,p/a6lcm8g* is only about half the force on the Moon due to/ a6ahc8llp*6gvmp1,m dm g/m the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration o6tb+-vuf5xh rf Mars in its orbit around the Sun larger or smaller thanb 6fu-v htx5+r the centripetal acceleration of the Earth?

Would it require less spe6di: hkt+ hkkaz-k+ (ved to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation dirh zta k:(d- vk6+ihkk+ection.

When will your apparent weight be the greatest, as measured by a scale in a movnv6mdcx:ytlnk38x3 ):pw e *fing elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall,y63:l k m :xefxnnvc3dt )w8p* (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 adverse- m.f.;pofz l 8qhupb(h* twb(ly affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the(zft( . -p *obfw;pu lhqm8.bh astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” bqn 315-rbse s rdg1ci,etween stesig n r3 sqer-cd1b,51ps.

The Earth moves faster in its orbit around the Sugz rmsf0j:4u jil6; t4n 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 th;ju4 zlf 0ij6mgr4s t:e Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was no 8 v z4 k2i1t,s0wfcbj:sy:nest known until it was discovered to have a moon. Explain how thise ,w0: nsjy81tszc:vk24 sf bi discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitationalkgt2fbq5w9a ku5n v+gca2,v( pull 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 tha2 qb25 v(agf9ukv5gw,ck nt+e 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 1980 +)1p6zzaegja3(k q hy$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orblmv44 :,m()ub:zprld nz* 8a qz ys)pfit around the Sun, and the net force exerted on the Earth. What exerts this force on tzq n )abp84lf d,:yvp4*zmms:) r(luzhe 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 s*pa nsef *a*+k8yi,wN is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s lewsi * 8sk*af +,*ypneangth) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orb/cnr5p9c/ bvj0 b 0ucgit 400 km from the Earth's surface, and circles the Earth about once every 9ungc //pbjv rbc 0c5090 minutes. 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 acceler0nbkm riatn: ag9 l*c. a9x((buj-voe6 jb2e*ation of a speck of clay on the edge of a potter’s wheel turning at 45 rpmji- *t*(lgxcn 0 k 9.nbvom b:ue62r9aa(abje (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform ) 6b k65vxe;twmz xk9+rn wt.yrate in a vertical circle of radius 72.0 cmtz. bexnr6 +tw)w9x kk 5v6y;m , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1xfz4ck7f 6m8k050-kg car can round a turn of radius 77 m on a flat road if the coefficient of stakc84fm kf zx67tic friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coef wf *c6+sypui o95zuwc oh;ke1o s(h98ficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m ai;s pc1w6(ousw9h8* cuooyf9hze+ k5 t a speed of 95km/h ?   

  A device for training astronauts and jet fighter2r d nc /ur;0z-jnjfrr*ho8k0 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 ba/orcnnj2h8 kzjr; r0d-r0 fu*ck is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotati2;pnmf7sy+ 0dogycy- ng turntable of variable speed. When the speed of the turntable is slowly increased, + n-ypf gosm02;7cyydthe 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 roller coastetbg+3i hqlrx** 9g6v gr be traveling when upside down at the +b grtg39 liq*vgh6*xtop of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mt,vv*)alef(c ass 950 kg (including the driver) crosses the rounded top of a htc* lva (),evfill (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 pcfq 5znf :kbc2 w2nd lo0s)zi44 77xjqwjs2*need to make for the passengers to feel “weightless” at the top4)js2i q cn* wc4xp b75qlf02z7nf z: 2swojdkmost point?    rpm

  A bucket of mass 2.00 o/2; dk c,r2fqz n)85wyu cxlr3vdam9gj7cz*kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting t7jl;xu ycf)r*vq3o5gzdm8k 2dcaz9 wcn/2 r, he 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 centrifugemi+t:f0 te 2ikiux,( p rotate if a particle 9.00 cm from the axis oiet2x mi0(:,+uk tipff rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled cu.nfh77 l zma ,on,.r"room." (S7m,,nuaz.o7c rhln f.ee 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-hockeu8r kpc63tsv 86d wkz. ci6i1: ku-grly tabletop, and is held in this orbit by a light cord connected to a danglingliw6 i kvskrkg:36-rc z8 cp6. 1u8dtu block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weiw3r*fe os6-z a(mmf (rght of the ball which revolves on a string 0.600 m long. In*( (3f ar 6rzwo-semfm particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a caybsr. *pg s)(dz ncnv/7dz:i*r 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 )ecu 2z;17moe l,j sk ef4kmz0*bkg3s$ 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 evasf -(dzqqxfb6xt(/3x r ive 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 tangential and centripetal compone1qml3vodl.2i*9cxkl uh r - q+nts of the net force exerted on t lv2clhu -x*k3.1 9ldqq+rm iohe 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 Indianapolis 500 acceleratm v0zes0z37 j 46txbstes uniformly from the pit area, going from 3sbst mjt607x0 e 4vzzrest 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 no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m zhp-uvm*4 k qg dht-( ar/z*.y. At a particular instant, its accd 4vm-/khrht.*-g( qa*z zypueleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km q r 7cyx-y(g6y(2 Earth radii) above the Earth’s surfa yc6rqx7y(g y-ce if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g hamj ehiq*mx2: z-5aa /us a magnitude of 12 mhj 2iazx5e:ua q/* m-m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon -fd:th7f lvp1. The Moon's radius is 1.7v7 d-1 pht:lff4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 cw;2 +lagnil* ,j.t kotimes that of Earth, but has the same mass. Whai 2*knl+w j gl.a,c;tot is the acceleration due to gravity near its surface?   

  A hypothetical planet has 8+kuj1+gcs7l0f m4ni*wyth .ldpof *a mass 1.66 times that of Earth, but the same radius. What is g near s 1k 4j8.nc d+lglof+ f i7why0t**mpuits surface?   

  Two objects attract each a/)3kd uv v1t4un gy- zmwq:2jother gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceler87y06n /la - a;te+ux/sxanmclmx,gxd 3v pg5ation of gravity, at (a) 3200 mp8 ,gmyv-6t+ m 3 xx/xgax05dne/nuac;l sa7l    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’qcnrd(ek i :++s center to a point outside the Earth where thegr+(qn c+ekdr: iavitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphere a.;ytl / r2+c izo6l(jtuuas-nbout 10 km in radius. Estimate thctly r2ul(6j .z-+s ;inut o/ae surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was9 ke +ug zv9kqax2s-i-4t5k kk an average star like our Sun but is now in the last stage of its evolution, is the size of our k 9kks4ev9t2+- kiuq k5zxa g-Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts fer-.tzd5(cht l 3 gt/l5bnf9dqel weightless while orbiting in the space shuttle. Your friends/tg ct-(ldzn3r9. b f5 hdt5ql respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a sp/ qib1e bkm- n29-mcmquare of side 0.60 m. Calculate the mmc9-nq bi-2e1 k/ pmbmagnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years q82qwft7 rf;z9s 3i1dow v;svmost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and 8; z vsv 9f7t;r1idoqf3qww2sSaturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravitb5*ek4r526/ rlypsvme v0 ys1jitt 9w y at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determin*5l trv/eske y tp4b6s09rw5 iyvj2 1me the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the periodb gkeoy1 r/r4, st(dk, of the Earth kdt/e,b,rg yok 14rs( and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about t wtcz+pu:,(3 hcl j6qkhe Earth at a height ow 3kup z(q jl6:htcc+,f 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbi4:gqqx l +9izzt 650 km above the Earth. How fast must the shuttle be movin z4 9qzq:+iglxg (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to expers+-pd;j50d .vpo4 cfci:0xdjf 5 dzhj ience 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 5–32.) if0:x.djc5p5o40; fc -pd jvsjhzd+d  

  Determine the time it takes for a satellite to orbit the Earth i gl 4f5,-;o askxit/fnn 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 xtsfo,i g a4/f5k-;nl on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top ox.;t:jnsz 5bn: xqx+ 0 bjngv4f Mt. Everest to be placed in a c;x.s q:t +5b4bxg:j0j znvnxn ircular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continuedo 5tu,vggwt5 2 to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once? 2ogg,t w 5t5uv   s

  The rings of Saturn are composed of ch;n5b g/xjm (; zti,rxqunks of ice that orbit the planet. The inner radius of th( n; x ,bqrzj/t;mg5ixe rings 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 rotatgojm5v 62k5h1 2x,puszxl*u i ax5rp* es once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at thevxs2zp*g,5jkm 6lr o5xh1 iu5*u p2x a top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the c4i 7he:.h+xc32j uev r kisn.fenter of the Earth's Moon in a space vehicle (a) moving at cxki si7ef3:er4..hcjv +nu h 2onstant 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 lmd hd: znwqex: ) ebzsd.a,;wa/1z09 two stars of equal mass. They are observed to be separated by 360 million km anda:1:;xe0ez9n)zdh. zdad lb, qm/wws take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for thrnixvb75, sxa8zj1;w e weight of a 55-kg woman in an elevator that movex8 a ;nwj1brvx5 ,sz7is
(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 elevator. Tr d 6bw nr.zzlvkdutk(i+5 *0/he cord can withstand a tension of 220 N and breaks as the elevator accelerkb60d l zwi/kt5v*(z rdu.+ rnates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period T3 m4x-j slvb r611ctpv , the density (mass/volume) of the xv t4p3 1s-r1 bl6mjcvplanet 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 andmiobc)8eh( - 3oj)y yr the period of the Moon (27.4 d) to determine the period of an arti8i3mcrhje )-)oyyb (o ficial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the)gu j t4)kl;q owyv:0f Sun like the planets. Its period is 414v:ft))w0oujqk g;ly0 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanpv62y2e1s u 1 y,s7zhvfh xh,pce 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. dvukw 0y:35af,2c iwz ks8r0 yIt comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comecf0 ,:yr83w0w2k szkad iuvy5t from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cente .o,hk0gtgg5nr of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the fo( 6xg/e-ztwsa ur largest moons of Jupiter (those discovered by Galileo in 160 ztw-/x6es ga(9).
(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 thev+q: 7birn s8n Earth from the known period and distance of the Moon. nbiv:7 s nq8r+   $\times 10^{24}$

  Determine the mean distance from Jupiter for u txc2)nop-5)lnz1 xq each of Jupiter’s moons, using Kepler’s third lc)u z)x2tno-q lp5x 1naw. Use the distance of Io and the periods 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 many fr d/ oiy fwdw8-pieoc gx1 *192xi4x5azagments (which some space scientists think came from a planet that once orbited the Sun but was destroyed)o*w 1dfpi4o298 z xycwa1ei/xdg5xi -.
(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 awe0 t vk60+5p,tfcdvehz)m s3ek9 jc6n artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is cptee5v6c3t 06+kj m9 d h)ezwv,k0s fexactly 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 swingin5 : xpo,g.3dl p6m tgch7sfkv,g in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolex6 vpskclp, m5gdtg .of7: ,h3rate 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 surfacinjx:h u1 810nq6k.be6gfa bve will the acceleration of gravity be half what it is on the surface?nn6xbeq 01 k.u1: 6ijvbgha f8    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in1n:sc nk)-pxpi ol3g2 a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.01x-o si3nl :npc) kgp2 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gra91f 9*dimnyoo9y . ffpvity at the equator is slightly less than it would be if the Ea y*nf m9 .yi9dpffoo19rth 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 ki0p9mad59 jyrs+y3 v from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposit9jykm9+d ryps05a iv3 e forces?    $\times 10^8$

  You know your mass is 65 t gt4dm0(h a.w(tk025 ijhfsd kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. afg( wjh04diskthtt2 d5m0(. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consw vi88h8h 1zw/5np c xwyary:6ists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle for/zrhpc58y8w w8yi 6wh: nx1avmed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5xvrh(701*k j qpu)phu –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 planz r hggykn/yoe5h-tc x96 4(x)et in terms of its radius r, the acceleration due to gravity at its surface and the gravitational conk-5yner g/x(tz yc)4x hgo9h6stant G.

A plumb bob (a mass m hang v7,bup1fze3waqqsz+2g)rucd l-0+ o qw1x)b ing on a string) is deflected from the vertical by an qwqb,bcqs31v lz)wr 0)fu u7a1g 2++zpeo-xd angle $\theta$ 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 67cs0u3x6pfi j24 pnz; y m is banked for a design speed of If the coefficient of stat uy64p30 zjs; 2xfpicnic friction 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 that objects at the ecvl:/ 4jqfcn 2quator were apparently v2/f nc:lcq 4jweightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart ofe +z(pa8qt degx5- ny4 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 rocz54g31 tjr rpdo)1nsl*g6dmunds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an dgg)6z 1pnr 4s3dt* jlo5crm1angle 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 hia-hc)sfdw74azc ; 0 been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following datah0dw4a7;zhs-c ic f) a 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 presence of an extremeb0dtqhm8 / lc3ly massive core in the distant galaxy M87, so dense that it could be a black hole08cdl3tq/m bh (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 +pujxpzo8k 7y c,tr 14speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley r +p8pk ,yt1j4x 7zcuohave 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 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 satellty+c ett5(t+w ites orbiting t5+t w+ceytt (the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical 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 billion kmuz5npp lc71 if2xg.( n, is meant to u x 72n15ni.pzpfc (glorbit 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 space shuttle pursuing ,ns nw(zt+ iv 8 yi0c,ie;4jmaa satellite in need of repair. You are in a circular orbit of ,4 0ai +zi8jnv,nmwc eitsy(;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. (a) What is its mean distance fvuh :+ ,yku)mo/ayk:srom theoy),k+hya:uvsu k/ m: 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 would need to be if you could actually "feel6l 4q p5;wy/pecnx0 z)f1wdh+mgyjd+" yourself gravitationally attracted to someone near you. Make reasonabledj1y50+g64wqc xmwh )l+ey /;fp zndp assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxj3qr.ff, ;zukq :wh/by (Fig. 5-46) at a distance : .b,fjqr zfw/q;ukh3 of 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 siy2m6+bateg9y de. Find the magnitude and direction of the grava6b mye9t+y2g itational 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 the Earth ) v5vfxzwruf fuw 7gu : t3o9zc9,qs5;$ \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-lo p6;4 7z/ mk3bwqe)d) rwb4 ne-wzryczng sweep second 4 nb7zm4)z ydqb-kp/;rcwr3 )ewwez6 hand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around t)h cm2rmo3c /in a circle below you on a 0oh)/rc tm 2m3c.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. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car traveiu bi1 7,4gjux 2o rbm4wqua/1lingi a12ouju1mi4b47qrw, gu/ xb 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 n:4dfzkk cjvpft8ra9h 15;l-oegotiating 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 k49v1 alz-8:p c5 jodfh;t kfrtrain 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.$\approx$    $\times 10^2$