Sometimes people say that water is removerlu) 9x/a yr6q l6yn jv-v*xv7d from clothes in a spin dryer by centrifugal force throwing the water outward. W6/x7)vru lvra6 ynq j y*-x9vlhat is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp .dzem .it r/2mu.pa8 pcurve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explai .ut. zipmm2a/red.8pn.

Suppose a car moves at constant speed along a hilly road. Where d) sxf.n 6cd p;4qia6zsr(tl-ooes the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill;for il s6act dq)-n.p4( xsz6?

Describe all the forces acting on a child ridirgc bsvzxc io:5;mb++x3a4 3j rlgu05ng a horse on a merry-go-round. Which of these foz ali:+ b3 r;c43 um+v5scgj gx5borx0rces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical ci,fcpc ;h*te x+rcle without the water spilling out, even at the toxph, c; ecf+t*p of the circle when the bucket is upside down. Explain.

How many “accelerators”7xk7fcn / c(9pmncg4e do you have in your car? There are at least three controlce4c77nm p fn(9 xg/cks in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig. g pzue ovjvo9-; y +ja85,/quj5–31. 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. Eq/,oujjvj98 y gu p-a+e oz;v5xplain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high m1 7klg7g )s/ jfl0pkhspeed?

Why do airplanes bank when they turn? How would you cw2c m v+dqjurf,s7jre o.:gz t3cc4; 4ompute the banking angle given its sjoqm4ugf.:7+v,j2 ertc;cs3 zc d4 rwpeed and radius of the turn?

A girl is whirling a ball on a string ar (*mxxr;mg5n0jr ( wfeound her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the m0mnj xg5xe*wr ;fr((yard. When should she let go of the string?

Does an apple exert a gravitation; cfrkv,7.eg*km6qpg al force on the Earth? If so, how large a force? Considev6 f*,;pq mg kgc7.ekrr an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double whacaeo vhe*094 mt it is, in what ways would the Moon’s orbit be o4e9v0c h m*eadifferent?

Which pulls harder gravitationally, the Earth on the Mw.(p1w4ymm/yjca-a n oon, or the Moon on the Earth? Which accelerates more(1/ .y pcwm ya-namj4w?

The Sun's gravitational pull on the(g v- w75kncto Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for tcw vktgn5o-(7he tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh morc.btr+1i87en/ jpsh3r ) yixo e at the equator or at the poles? What two effects are at work? Do they oppose eaihc)r ybos+n1p8i/x7 3te. jr ch other?

The gravitational force on the Mh+3j4 xb5oiq roon due to the Earth is only about half the force on the Moon due to the Sun. Why isnjo3ib45+ xqr h’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or s0 jdlp rh0kdz **(8oxemaller than the cen*z(rx80hjp lo de0dk*tripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a+ ;qo o/6.wfyebww *,uwiig9hld) v4b ) toward the east or (b) toward the west? Consideru)*6,;oiov b4q9i wwhdeg ./+fy blww the Earth’s rotation direction.

When will your apparent weight jqy.(l wte;p8be the greatest, as measured by a scale in a movin8tl;wyeq p.j (g elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversel) mn q8i)sf5sx.a mmp9uww g3)y affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how t3gi.p 8xm5 wsqm 9 ))ufm)wnsahis 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” b dkiqm60wj1: u c6 h3fby1xqq6etween stepcui :fh q m1 y6qq10djk6xw3b6s.

The Earth moves faster in its orbit around the Sun inr.*;ksje42vi qgi,nf v5n(j d 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 pr ,g2ki s5n4 v*dnjf;ejivr.(qoducing 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 have a moondmtb99 52/nxn8 y dhxa. Explain how this discovery enabled an estimate of Pahy9m9 /bxnnt 582dxdluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the xf 4hmi(cm fse--j5q.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 .5scmq f-i em4h-x j(fother.]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 travelin :5m .cly lzhp8+5mc,tagw3lz g 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Ey;lj4hg 1 f (to8c,o*1vcli jnarth in its orbit around the Sun, and the net force exerted on thjh 1;8icg(o 4*jv,lync ft 1loe Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 6f)ou 2not q1an4qm.c2.0-kg discus as it rotates uniformly in a horizontal circle ) 2t6qf1a .moucoqn4n(at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 kdli b/ 5k qiv138js,knw,q gg2m 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. Express your answer in terms of g , the gravitational acceleration at the E b 2,nw jg1klv38ksgidqi,q/5 arth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a, 5zevbumqf la134m5m;)/n ti v lwd/x potter’s wheel turning at 45 rp)nuw x lb /lze;mm4fv,3 1vma5/t5iq dm (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 verticapf4 vy1 n0ievf/zw)6umq:1vn l circle of radius 72.0 cm , as shown p)6 0u1 4wv:ezvmfiv qy/n1nfin 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 s1pua g2i,g; dkzlx2i5ux k10bpeed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static p;0u2iz 1a g dxu5kx g1i2,klbfriction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of 25gh(t0niqx dzb1e5x static friction be between the tires and the road if a car is to round a level(5b25 zgx tihx10 nedq curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and fes8e6aznm-14umeyc2 zd9 j8 jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the foraeje1en24fsz 8 - mc6m9z8udyce felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rd3;gf92on x9f-q.osv,0.as cu0in ; rfmadusotating turntable of variable speed. When the speed of the turntable is slowly ingod -q0xds;v;.3uf90usmrna 2. faf,os9niccreased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at thite/jv+s4nm kf .+r+-eza: x yjs :ny9e t.sfvt +xn/rijs 9yze +k: ma+-: jn4eyop 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 mass 950 kg (inclxf3k jt6i at3m4 1pay4u s+i9iuding the driver) crosses the rounded top of a hill (1tait6+yj34mikp3xaf 49su i 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 btx2 +) t*uo vgt(37k nm3*uto mrvbl9would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost point? b+kx3mntbvmgro72t3t9)v**t o u u( l   rpm

  A bucket of mass 2.00 kg is whirled in a vertical cirr4+xznd3o5 h tcle of radius 1.10 m. At the lowest point of its motion the tension nrztoh3 4d x5+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 ax:1poq1f9l .dx pem: fois of rotation pxe.plfqmo 1f::od19is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival,q )9 z3q8xnnb.dyx ;h8be kfa, people are rotated in a cylindrically walled "room." (See Fig. b )q9nzbnhk .e8,fxy8 q 3xa;d5-35.)
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 frictinf9l :w0s8q .k0ykefby;bf )u x 6cl(zonless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a0uesffklq0 c bbxy6 fwy.z;(:)89l nk 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 weight of th z-h4g ggu l7 c/b+ p5rohu)7muzui0(xe ball which revolves on a string 0.600 m long. In particulpghlu /uz-u5hg4c7 ibx+u70o)gr(mz ar, 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 car travrm m. 6mteqslpv2zy /dy:2g6;qal 8 f8eling 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 masse)0vf*cqlnf(w ar-n 1ls $ 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 maneuverb4lj+kuf d- :o 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 tangenti*i *ldxts; )z6if2xav al and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 1 z*t ifxd 2l*;)vx6sia5$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 acceleratev.-zfjlsy9r/0juz p6-oa4ke+ c qf6h s uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. rluj+sv6hy4z fz-op 60 -/. ajq9ckfe 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 . At a particular iqi -a )r2hu4:*f +mj+b8r;ytjzbbjtinstant, )b+rj bq8fmbjza2;tjtr4+h:i *iu- y 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 a spacecraft 1)4kbr0j (lk/zsi/eo zn 2yys79tn k 4y2,800 km (2 Earth radii) above the Earth’s sur/ l7n sk/y y2noz4r9k04isjzb e(ky)tface if its mass is 1350 kg.   

  At the surface of a certain+nk7x*uz*) s-pnpwq vj qn3 ,f planet, the gravitational acceleration g has a magnitud*x npwp3knu qsq7-v+ *nzj ),fe of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. Th dldrj.7n7mg2e Moon's radius is 1.74 mj.l2rdn7d7g $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 *nmcud(pfmq5 8qf;*ch c /w v4times that of Earth, but has the same mass. What is the acceleration due to graq5c*8up(vmmw/c qh f d*4 cn;fvity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same7 qjwhvuf 7n:qe88,o e radius. What is g near w j8feheqn7o:q, u87v its surface?   

  Two objects attract each other gravitationally with a force of 2*/ox4c sdv 5x1g/t1i tcqq8ny.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 , krh6 a9kw1 lea;5)a5cf rn vm)the acceleration of gravity, at (a) 3200 mvh 5kmf6) ear 1)w;lkca5a r9n    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whe;nw ifk 14gbh/re thegravitational acceleration due gkw /;bfhn41 ito 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 svffy./6p h6rfdzx3 2Sun packed into a sphere about 10 km in radius. Estimate the surface/f6yrszdfh6p2v3f . x gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average sta+dqr*hcu4 9z/s ux)r7bgqmp0ez:p h(r like our Sun but is now in the last stage of its evolution, is the size of /9zg(cr 704)pzh ms puequr+dqhx * :bour Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astron5k 0j lmrmleeow oubj14j6h58 l/u.f+auts 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 acceleration of gravity 250 km al e+k5bjjh/ e01oj u56.llum rmfow8 4bove the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m*8dv11e;mz/knce/1v q ip4ps yzu0 nb. Calculate the magnitude and direction of the total gravitational force exerted on one spher;ps1eqbn/ *p 8zve1 kc1 i/dz0n4ymuve by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the S5twimxo )*zst87 ;6vxv/ l bwtun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assumin/v65z7bm txt;wtx8wi ovl s*) g 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 o0k6 8zfngnaxb;08y a tf gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass0a yzfbg8;0n x6ant 8k of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earth 3 :vsopr5*aa fa4/kzjand its distance from the Sun. [Note: Compare your answer to that obtained usjk:/szpvar 53a4 f*aoing Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular lr.1i67g -y- pigf6yf9 q(te.olby xyorbit about the Ea. 91 fbpyligel.x-qfyi6t6 7 gyo-r( yrth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases 72sxo +l9aiol a satellite into a circular orbit 650 km above the Earth. How fast must t oi92oxs+l7lahe 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 expxu)o orra+ g((no(uc;7i nig4erience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32i+((og(7iu;ua) o x4ogrcnrn m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time iajstl .eb f5s)t16u-.yncae8 t takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of )tnseaef8lcbs5 ja .1tyu. 6-the satellite?    s ~    min

  At what horizontal velocity wouldqyd(oa/a+:dwh9(fq iek vx21 a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Eartkaqhe9o :2 iy((fqd/wa +1dxvh?   

  During an Apollo lunar landing missie )j/f2-kbccron, the command module continued to orbit the Moon at an altitude of about 100 km. How long did ckf e/2cbj)-r it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of (m( ,,l yhqhne,qr;o :-hri opice that orbit the planet. The inner radius -,hhrpe:o( ,r ,;q nmilhy(qoof the 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 rotates once every 15.5 s (see Fw8je8.g);f a8 a bmjquig. 5–9). What is the rj;)wj.meqb 8a8g8ua fatio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cente0/s xqwljt*aup;*ed ,r of the Earth's Moon in a space vehicle (a) moving at constant v xjqeu;sdtw,0 /lpa**elocity,     ----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-sth6:ujoqk z : ,uk9+tbhar system consists of two stars of equal mass. They are observed to be sepau+ 6okzhku9:j:,tq hbrated 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 scale read for the weight of a 55-kg woman in an elevatorg e/l6ub,.tx q that meq/x ,lgu.t 6boves
(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 cfwt(o a0gs2vnhn y+8 ,ord suspended 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 minimum acceleration (magnitasnnt 02v ,h w8(yg+foude and direction)? a =   

Show that if a satellite orbits very near the surface of a plan:c2zftij6ue geq:1 2t et with period T , the density (mass/volume) of the planjt1:eicq6z 22 ftueg :et is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the period; nym7xlgs/+2 l,6fka ru.ercli- m )r of an artificial satellikml /f+u 2y;r6- grrs.llmc7 , inax)ete orbiting very near the Earth’s surface.    s

  The asteroid Icarus, thixkjrs+75 /ewough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its me ew/rkj7xs i5+an distance from the Sun?    $\times 10^{11}$

  Neptune is an averaga9i0i*z+qzts.b( c b r7sq5q6ok- fwd e distance 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 tcgjoe;x8a7kqto- h* 7yq.o)*p r0xe -o xbx,every 76 years. It comes very close to7o 7-xo.e*,ok0jcx)t8tgepybx q oh;x *-q ra the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about they xdcj3r 06r8+cn8y 35k tzaeu center 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 foutf.) q6rqg+u qr largest moons of Jupite6qfu t.g+q )qrr (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of 3nd uq o z:wdkdx5y5(+the Earth from the known period and distance of the Moon. 5ddk qu:(oznx 5y+ 3dw   $\times 10^{24}$

  Determine the mean distance from2 y9b l;rn4ukd Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the4ry 9; dukb2ln 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 fragmentpn8.ze,qym w )s (which some space scientists think came from a planet that once orbited the Sun but was destqp)mze w,. yn8royed).
(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 arti cf7(e6 dbo8sxs**;yq/dw zkxficial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to mxsqb*6fskc dd78 o zwe */y(x;ake 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 vine (Fibo59lv8lecc2 4 jzd5 pyk d10m+;s wngg. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine isvcedzw ydbmcp5lln 0+2oj8sgk59;1 4 5.5 m long.   

  How far above the Earth’s surface will the accelerat6cx44 c52jvxgo/ qqhiion of gravity be half what it is on/iqh46 4c2qxvxgj oc5 the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass fgb8 79fp,g csgrab hands and spin in a mutual circle cfg 7 gf8s,9pbonce every 2.5 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 p,pcecm9ua* 6z er day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Es6p *, acem9zcutimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling dh 0owtfosdi7 h7r)e teky:3w58+u /qf irectly from the Earth to the Moon experience zero net 8q wk hr:7 e57utsf03yf e)withd+/ooforce because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in b6k(xibjngtl* x6 6 jt8i 4xe4an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directib 46bx g*6n4xjxjtt8il eik6 (on?     ----待选择----upwartddown 

  A projected space station consistsqvxd j(n:zu e8*nx4(4) qi evc of a circular tube that will rotate about its center (like e *x:cn8 vxein)(4qvu qj4z( da tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43). 7*: (cf3rn +jrx htvmg
(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 dj *qo/f js/gc20e mq,5im*hiradius r, the acceleration due to gravity at its surface and the gj ,*ig0m iqf//ehj *do2msq5cravitational constant G.

A plumb bob (a mass m hanging on a string) is defleyz g;wocu(4*ep(mzwj , f .0qycted from the vertical by an angc4e mz;w( (*jyopq0y,w zfug.le $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient of sb4 hsjw8r8k 4la/; tbm-v5chv tati;4s8 lb 5bcj-t mw/4vh8kahv rc 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 objects79rj0m 8k/si1zq dlst at the equ807rqs lkst9m id1j z/ator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apaw9vj,r )b, t5f 4dtmaart 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 roh0xq8p 0j ao rh8b 4olxdcd7go8 3n,l73(vbo hunds a curve of radius 235 m. A lamp suspended from the ceiling swings out to8h3h8cn8b o o4lp h(37roqd0 7lvjg0xx boda, 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 Earth. Thus, ity c73o ivp cx:f71th2t has 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 per7o: 71ttf 32 hyicvpcxson 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 Telescop: akvjnhjhiw(: 0++z be deduced the presence of an extremely massvh jhjwn+zk: (a b0:+iive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 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 shown i7hbv1n.j +/lbyl kg( gn Fig. 5–45. Both the hill and valley have a radius of curvature R. (ajlgknl(g.1+yb 7 /b hv) 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 sate(w 3fys)x,0 kr cchzo(g 8j2vzllites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The 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 eachg xf2ky 3,0v)s zczc8o(j wrh( satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), ayb p wjftbg/romk/* kb0*800u fter traveling 2.1 billion km, is meant to orbit the asteroid E0k8m og *j uw/yb *bf0bt/pkr0ros 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 thenmrl s p42iqn b3d l*-/lath1/ space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25/blm q4 s1l2atnrp dn3l i-h/* 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 itsv m;pcpy;7ur gj,w hz c4:7ep3 mean distance from j ym r7,zppwg3c;4:vh u ;7cepthe 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 wouuyyo7 -pgp.g vz4 2k mh243qxpld need to be if you could actually "feel" yourself gravitationally attracted to someone near yo2 2oq-k7py 43xgpm4 .pyzuhvg u. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center o 15q g-euai.vyf the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,aq. i ge-5y1uv000 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 apgvwnx k2e h5*g.1k,f-p rb8 dre located at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the mdkge 1-fg,x*bn w5v r8phpk2.idpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 55(3,i;rolm 9qd0/tolvygyki7r wg; c 300 kg 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 ta:.ir14 tcy 9 h5awmbphe tip of the 1.5-cm-long sweep second hand ohaatb9514ryw m. i:c pn your wrist watch?    $\times 10^{-4}$

  While fishing, you get boret bjx6z1dd rkk5zgj0v k/2o;3d and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes jgd / k05r2tbzv1k;okz3jxd6 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 xzdg)t ewr o5rw)q56)radius R in a new highway is designed so that a car traveling at s6rzx)t))oqg e w 5wr5dpeed $ 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 nego0vat0pu z*d:a tiating 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 forced0ta*ua:zv 0 p 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.$\approx$    $\times 10^2$