Sometimes people say that water is removed from clothes in a spin dryer by cqa tsfp0 j/(fa7v5c6 centrifugal force throwing the water outward. What is wq0cj af(cv56as7f/ptrong with this statement?

Will the acceleration of a car be the same when the jb0qgqo40 j/.6 zus(aujqk t 6car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same sou.4 0ajjbq0s ztq6/q g6 ujk(peed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the caruy/fl*. 5 k;o9nxdg nwm(s ro7n2c 6s6pzm dv9 exert the greatest and least forces on t ornx 7569s .c flnu2/y ovsd;9m(*pnmd6zg wkhe road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forcedh 3p 0dwcs. la)v3fmni4g6p:s acting on a child riding a horse on a merry-go-round. Which of these forcesg.3pnmvp d:6 il4 3wd)s0 fach provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the w4ly.w/lvyv8b; bm wewiyhn87 wv9.b 0 ater spilling out, even at the top of the cir8w ;b/ wwlyn98lyhbyviv7. b w.m4 0vecle when the bucket is upside down. Explain.

How many “accelerators” do you hav.-a 4awb+ vcbee in your car? There are at least three controls in the car which can be used to cause the car to a cba-. wev4+baccelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smalli si s.6 ysmnq svp8(e5b /qvvt97,n-v hill, as shown in Fig. 5–31. His sled does not leave the ground (he q8 n6, i5vp sqvvt s.n/97s-i(bs myvedoes 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 l 65g( bznnhah4tz )xy;ean inward when rounding a curve at high speed?

Why do airplanes bank when they turnoujvd1rl4mbll6p 0g 9197sxg? How would you compute the banking angle given its speed andrsum6pv0b1g 9o xjgl l14ld79 radius of the turn?

A girl is whirling a ball on a string around her head in a horizgv* yjzy tfo .0q13(frontal plane. She wants to levgo0(q.f z*fryj3y 1tt go at precisely the right time 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, hh;dpp+ 0iejb0 ow large a force? Consider p0 0idebp;+hj an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double*9 l7o zu/tepk what it is, in what ways would the Moon’s orbit be do79*k u/lpzt eifferent?

Which pulls harder gravitationally, the Earth on the Moon, or t)awj/voi; l1g y iq2. fc2v*svhe Moon on the Earth? Which acce)q2i a lgv1fvj*iov.sy/cw ; 2lerates more?

The Sun's gravitational pull nl vr+lp+(: -j afg*puon the Earth is much larger than the Moon's. Yet the Moon's is mainly pgl+n:l-auf*v(rj +p responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the 8 r85q ajr3qhdh8j2fs;wm /alpoles? What two effects are at work? Dq3js /88 ;jw5alf hh qma82drro they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the hr3 fw)ecv k322xpix;-mew 3 y*m ;cklforce on txf3;3mvek x)y3lirk2 p m-2wwcc;* he he 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 larger o6tv0xgxt6 +p psaz 03lr smaller than0sp0v3t6 6xxzg+l ta p the centripetal acceleration of the Earth?

Would it require less speed to launch 888zki e o ju+p(mghd*a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation direc8j+zmok(* hig dp88eution.

When will your apparent weight be the greatest, as measured byr8bpz* my3vg/.j i-yt a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, ( j-y3i8v.y/m g br*tzpc) 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 couhg;r. j0bsl6u0*pcj xld be adversely affected by weightlessness. One way to simulate g gcr0;j*up h6js.b0l xravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “aaa4 hm5vrn l2b1fw* 7opparent weightlessness” between s2517 fwro4nbaa m hl*vteps.

The Earth moves faster i q;4n/ pml3n+sk6mo1lt1-h cpic e b-bn its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in Julc1b-i /nh1qm;+bpkl o csn4pt- 63me ly? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was dis5ee66 9 jettxucovered to have a moon. Explain how this discovery enabled an estimate o jt6eu5exe6t 9f Pluto’s mass.

  The Sun's gravitational p kk(uk8dhbktau nn9 pjey/r,p;)88*f ull 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 the center of a merry-go-round moves with a speed of fyrk8n9 /k*(8 k,tnh p8upkjd )ea u;b1.25 $\mathrm{~m} / \mathrm{s}$ . 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 .*fxjr b 1bd:brawx87 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelvh gdv4f 5 n7)c )4xed 2y*zzf 3z:2am1tpitrgeration 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 orbita4*dth r3 fyt)c:v v22e) 4x57zin gpdz1zfgm 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 exe2kd kfk/z jm vb*6i69xrted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m 9k6m2 dkz*vkx/6 jbfi. Calculate the speed of the discus.   

  Suppose the space shuttle is in or 0k, /ljj se:d5mbh/cebit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Expresj kcj ,/l/ :5d0hbesmes your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay; cca:* )vusi;fpxsv;e*,a/y ad )xfh on the edge of a potter’s wheel thuyf: *as;)s;px d) ,c aeviav*;/ fxcurning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a*wa 6g09rozqd vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed ir0 w ag9o*6zdqs 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 winn 7n:t dkvd6-th which a 1050-kg car can round a turn of radius 77 vdn7kn: -d nt6m on a flat road 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 frii y)a9*8sgfa wction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/h ?iya 8wfa9s)g *   

  A device for training astronauts and jet fighter pilots is da; qgu7fz2tf 69hj lr(esigned 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 weihu7 ; 2f(rtgflz9a qj6ght, 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 rotating turntable of variable sugu-/-iz..a m*o6 jnp vya:b tpeed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36a-omabz-n6 j*:.uty /i.v ugp 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 ) bs40m9:n7 /zkd ssufrk1 sddjq /vrzjy2 6*hbe traveling when upside down at the top of a circdr7nk2j/q ssmfd)z:9v bju461y sd*skz0/rh le
(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 (okb6qqr*yr fo//, t )wincluding the driver) crosses the rounded top of a hill (radius fr r yqoqb6k//wt ,)o*=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 Fer/ nuo.0f kq-mh4fqj a0ris wheel need to make for the nku4jfqm f.h0/a - qo0passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cig1qnnpf nap26vjx1wpc x8-h8 /3x(murcle of radius 1.10 m. At the lowest point of its motion mfv( uj13w 8/p hx6c8xppgaxn-nn2q 1the 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 axisln:0 dx ,xlk2ww yxjd78*2qc g of rotation is to experience an acceleration 0qjlxl wynkc d2*x: d8x2w7, gof 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cb d5y -t 1gc/ u6d:kjbh:gq492fnmncwylindrically walled "room." (See Fig.5t6: 9ncb2gnwqu1j-fg/d4:db ykc hm 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 x:mez43bku3zi rthn7j6 m b( )frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a d7xm3urzm nkb)zt (4bi:h3 j6e angling 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 tbo4,4wo; c +vbxnm+xz he weight of the ball wxmow4z+;x4bnb , c+v ohich revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m ick d*b;rw;2 5zq einc4s 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 masses 7h3muu:: es6u qbxod-) mmtx, $ 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 djnem2k8 k8+o,s3s tjmaneuver 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 componijyz2 3 j9do.f:hol g0ents of the net force exerted on the car (by thej: j3zl9 oiyhf0d .o2g 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 accej(jvk-d(afuo.x1 q:c9gg*,kuj ja8 c lerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and 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 avkkg (9 (j*aajg-u8 ucc,1fxo :.jjqdcceleration with no slipping or skidding? $\approx$   

  A particle revolves in pls,d69rb: gj8xb2la w*f7f/2vl qaja horizontal circle of radius 2.90 m . At a particular instant, its acca /pb9d2jbv 7lqa:s fg wf8r2l,*ljx6 eleration 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 sp/zbo bjd zx90;acecraft 12,800 km (2 Earth radii) /z b9z0boj;x dabove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g h 3knx +k+u8b-iphw o9kas a magnitude ofh ukp+ k-ixow+3 8knb9 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravityl ne4xx)rtqt (g)qt4) on the Moon. The Moon's radius is 1.74g)rqett)nxlx4q )t 4( $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet ij;wk.- arxc q8jt/,n has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to8k-,atwnx;i qj/rcj. gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, bu:ua 0:-qf,v 6 qcxcjqft the same radius. -u:0:fvq6q jf,qc xcaWhat is g near its surface?   

  Two objects attract each other gravitationally with a foro38r(m koj,orcf( q p0ce 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 acceleration of gravi e/krr)2g;kiug(us+ v ty, at (a) 3200 m s u gg+v(ir;kre/k2)u    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the (vk)vlql3g + td+c tjdbd 3y242y(nnkEarth’s center to a point outside the Earth where thegravitationd)k dntjl4 d+t(g+v( lq cn 23bvy32ykal 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 mikro)tr3b ) ,tass of our Sun packed into a sphere about 10 km i biro)kr3t ,t)n radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but i+kmc1sws5 fmg4e4 jly 87 /gees now in the last stage of its evolution, is f7l/y+jks1e4wc sge8 4gmem5 the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spr xjz+2ukosgnhq 61 *3ace shuttle. Your friends respond that they thought gravity was just a u nhg3zxqk* 61+oj2 rslot 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 ap** n17m c tez0-zj9dw9rhb ov square of side 0.60 m. Calculate the magnitude and direction of the totv*c*9hjw1 pond7-z r m0ez 9tbal gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of 5)* tgxy9k kwdibo9e awo+)k: the Sun. Calculate the total force on the )5 oxwkw*)k9i tbkeo :9a dy+gEarth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravitykaf/3vp xjp1*k . 1xmnt6zi )vbi :4ln at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, det 1n4 ixxa.nkpl)1zt/j*ib3p :v6vfmkermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the perion6skf9 7rv 7thd of the Earth and its distance from the Sun. [Note: Co k shtrn96v77fmpare 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 the Eriidnh 0p po:98- y(bwarth at a height of 3600 km. (0hr:8inp oi-w9pdyb    $\times 10^3$

  The space shuttle releases a satellite into a circulartsh )-9- on7d9 ru6ks3tbjpxh orbit 650 km above the Earth. How fast rtb -hto 7s9xuk 3p)nj-hsd9 6must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occup7+*qhxm n.(iheys )kjcq yi,,ants are to experience simulated gravity of 0.60 g? Assume the spaceship’ss.my(k ej iq+hqi ,*y7xn,c) h 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 cid2 kp+)xm3eb hd6u*ahrcular “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 ebhda36 2+phk*) xudmEarth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity wv(4.j c *rrggulgy4g2 ould a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit aroun gg4v(4*g g2ryjclu.r d the Earth?   

  During an Apollo lunar landing mission, the command module cj*wh k fhxbp5:1u)e v+ontinued to orbit the Moon at an altitude of1xhuh:v+ep 5 k)jf bw* about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are c6qzouxdtvh w 1e ;,jn dn4vv7jc0)0 x-omposed of chunks of ice that orbit the planet. The inner radius of the rings is 73,000 7j16cw,v vhn )uet0;dx-vzdo 4q0xnj$\mathrm{~km}$ , 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 g/u8cqjxf- ,k4v, nwz rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s c48,qzw /uj,g nv f-xkapparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronav ,(zt,+kzg9vh)o qs but 4200 km from the center of the Earth's Moon in a space zbh t)kv(z9,g oqs,v+vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars ofyd5f; mq6n4nj equal mass. They are observed to be sefn4 qd6;nym j5parated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scpxynh 8u+ z6h wx6f76kale read for the weight of a 55-kg woman in an elevator that myfu 6+kz 7h6whxxp8n6 oves
(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 sudbwg ux/ca.6qi)+,er: -n ;kkf eys e6spended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s+ kdxs:/qeai,g uw;.6ybf-rce6k e n) minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits fitsh*lc/73l very near the surface of a planet with period T , the density (mass/volum *7ti/h3sclfle) 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 peyvius /bh* av :thh05/riod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near tthh5v ha*/usi0 /b:yvhe Earth’s surface.    s

  The asteroid Icarus, thou.v-ibs;(o(lf)y f) yair,olj gh only a few hundred meters across, orbits the Sun like y,)l(fljb-ryo vs .io)a(f; i the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of x:xz+w.xhs qm1h;+yn 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. It comes ve lz0y(5:yxmzu w w65czry close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s thi:yz yucw5m6l 5(x0 zwzrd law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the ce*1ax-t,y+ 5wqaialjjtr z p-b:7 6llz nter 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 four l+swu8n wz( zg1t7xr mikg-2 , lwz02ixargest moons of Jupiter (those disii,z0gnmz 2 78rkxx +1 2wws-(zwgltucovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the ltjf o( 50-rihMoon. 05 h(tl oijfr-   $\times 10^{24}$

  Determine the mean d+ w5jiywbm+y-istance from Jupiter for each of Jupiter’s moons, using Keplebw mjy y++-iw5r’s third law. 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 fragments (w0 9hbjrzsghir +cy hp 5w5-a(2hich some5 jcrr2w +(sz0iy g5h-hhb 9ap space scientists think came from a planet 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 "planet" in the form of a band co.)ol .l,hrm znmpletely 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,o .n zh,)r.llm 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 swinging in an arc from a hanging vinb.7r /jiq2 f8ijhih4s e (Fig. 5–41). If his arms are capable of exerting a force of 14i/ shf 24i87bjj .rihq00 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration 8peb57jin(p jof gravity be half what i 75bpnp8ej(ji t is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equaa)u85js a,sa(vta. qel mass grab hands and spin in a mutual circle once every 2. jst)aa5,8a .svuqe(a5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceq0gm*ees i a;4leration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnii; ams*ee4qg0 tude 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 pw q78s1 m l)+w-o)d z0b uowi-q+wezjEarth to the Moon experience zero net force because the Eariz0- +w1 w )uwolo q dmwqs7+bj8z-)peth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you st6iyepcdmj4*3w,hh7 30y ivi qz6/s gqand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceles v6z7/w iip ,q43hedy*6yi 0gcm3qjhration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abou8 tng9v(p8 4fd1zstd6r buwy5t 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 1g9bzt6sdy4v8pt r f un8w5d( 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 a x*n4o xuxhr4-ircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the aco wy rvf2 t-*h-t w:m08kj.bket ;gvq/ j1csv2celeration duesro vtgj t2tm1w v-0kq2fwby. -*vc: h j;8/ek to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical bo;hf mgo1e 7*kx5yx1 fy an f mf1xh7;*g oxek51 yoangle $\theta$ 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 2p+or 4,-seac,f lydm If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car slfm2-ro,syp ,+e 4cadafely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects3g83gyoh p1lt; ct+zo at the equator were apparently weigh8o1o3zly3+ tg tch;gptless?    $\times 10^3$s

  Two equal-mass stars maint 5)0hfk m7q ueib;,o csjr4 rfzf/m);oain 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 radiuxy4)hmnk6; wyvdwf +o 9eodg2 zp3r7+ s 235 m. A lamp suspended from the6w 3ehor4+ 9 y +ny7odfwzv2km;d) xgp 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 ekhza l0o)f6 ffw/c 5en ll 0;g+jur-:;dke( kas the Earth. Thus, it has been claimed that a person would be;;060eku( g)e+l/ fe-o 5wkka jnzlf:ch fdrl 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 data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an ex:8uiwq i x-jxe r*a76wtremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). Twui6e7x*axi :w8qj-r hey 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 th,zqxmghd0-+ l.+s r m2w 9havce hill and valley shown in Fig. 5–45. Both the hill and valley have a radiu+9czha- gl2qh.0 vds,r+xmw ms 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 (m8q.luj)/ 2umj wl t2(k 5dczeGPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by thj.8/zkw cl)5t2dluj2uq(emmese 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 Re;vmlfrj6gtyh1 f+ vsi7,; e9zndezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at m f,+iv j7zegysvfrh ;1l69 t;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 a satellite in need of aw,7bjk5 l0jv6p ng gj1e:8ejrepair. You are in a circular orbit of the same radius as twkga5nv j j: 0j8jlpe 17,gb6ehe 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 distawvd60 fz8jag di:b4h2nce from the Sun w0h 6j2v8fba ddzi:4g?   
(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 zl+8(+y seas96z8u.vpea sybof G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. M8pa+y9 s.zul (ayz6svsb 8+ eeake reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a d pbi )0a(jiv4qistance of about 30,000 light-years avipqi4 j()0bfrom 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 0fr dk)nk0oxrb0ld*5: v /i3vl.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom sdl: fxi r0b5k3ovv)*0 /ndk lride of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg.z0)ob9 skot r orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of therq* 5+b 3fbscq+ a.oai 1.5-cm-long sweep second hand on y+. *aq3boraq5 b+csif our wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arour,tmpttjftd buar)s 7n8b5 u *b;/q4) nd 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 Fiu)* /tptmrfs;ntq,ju db rtab b475)8g. 5–10.]    $^{\circ}$

A circular curve of radiusp t .wmtkalz) 9/rms(,-y6xwp R in a new highway is designed so that a car traveli/.yp(z xpkmwatt sw,)-6 r9 lmng 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, utilizeha8. v -9(uit, xe/yzmhus aw(s tilt of the cars when negotiating curves. Thev ./i9x(mhz , t-ewu8hyu as(a 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. $\approx$    $\times 10^2$
(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.$\approx$    $\times 10^2$