Sometimes people say that water is removed from clothes in a t9 qi+tt(+qz d,k9 -)omzq messw.m n;spin dryer by centrifugal force throwing thetqw;,+is nsetko-m99mz t. +m(q)z d q water outward. What is wrong with this statement?

Will the acceleratiosljaca 8/w8qmurau9yjq vj wf-(8:nb*/s-. kn of a car be the same when the car travels around a sharp curve at a constant 60 km/h as when asf.buvncqwyjj8 - as8maj q/u:/ l-r(wk89 *it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car exepc)h923f:fz0hfac ton:b-a y rt the greatest and least forhp 9:ohty :nfb -c2az)afc30fces 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?

Describe all the forces acting on a co *bmd j).-bqihild riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleraomqd i*b-b.) jtion of the child?

A bucket of water can be whcm-m v1)a 3jscirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Exs 1mm)vj-a3c cplain.

How many “accelerators” do you have in your car? There are at leas297 f(mz+p5tm -ldnrdvv+m o ft three controls in the car which can be used vl f7p -rz+mt9(dn 5f do2vmm+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 Fig0 ghgs1 u n5ak.dx;2kotm 7;ue. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the n t ug2o0;seadmu;hk5gk.71x sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curvzk54tto8 i d7m2:wkm n,x8qx ie at high speed?

Why do airplanes bank when they turn? How would you comot.;f c x:ncukwd0bp* f/s9.bpute the banking angle given its speed and radius of the *0 ckx/9.bcuots wfdp; :f.nb turn?

A girl is whirling a ball on a string around her head in a hor9 b86ye8rgyqo.f( yi pizontal 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 yard. When should she let go of thrgqoy by.(pi8e 96fy8e string?

Does an apple exert a vo3hh/)i :qmh gravitational force on the Earth? If so, how large a force? Conso q:mih3vh/) hider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, 3n5vh o7obvp0wz0vi- in what ways would the Moon’s orbit be diff3-7z0vi 0phnvo5vb ow erent?

Which pulls harder gravitatioakt5e* 83fvdt /x2dn,nn1,a uk;:qbej-h h c knally, the Earth on the Moon, or the Moon on the Earth? Whih/;8:31 cenk2,dxbnnfve 5 j hu-kk atat,qd* ch accelerates more?

The Sun's gravitational pultkl*u 79-8 riwnd -txzl on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Codu7l n8trz-w *9-itxknsider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects alnqs.vchr13. re at work? Do they oppose each othercv.r. qls3 h1n?

The gravitational force on the Moon due to ta+88iyztq5qp ;oq5 km mb 7x;mhe Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from thaqxzp; 57kq8y +t;m mb8oimq5e Earth?

Is the centripetal acceleration of Mars y:-zao5 0,mk,gavipcr bl 5/ +ux9rynin its orbit around the Sun larger or smaller than the centripetal acceleration of the Earvr yo :,l0ynp -aacizk+,m9bx /g5r5uth?

Would it require less speed towln(satc kng;*f4:8ong 0cg : launch a satellite (a) toward the east or (b) towardsc:gclnn*f 80g4t n;w g:( koa the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatoz0ei1mtn* l 8ht6y*cest, as measured by a scale in a moving 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 btc 1lh z6n8ey i0o*tm*e 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 cd-p ,vf4.hqi1a q htx-ould be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simu h-1, xv.hqd4-t fqiaplates 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 weightlessne+fb yaikz,9 :l7:ffra nj5e ;vss” between stb7ja:k i arfv;9+lfnzf e5, y:eps.

The Earth moves fast9nk ejqed+;du0m, d2p2jsr;n er in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not2qje k+ 2r,sdn dune 0;9dp;jm 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 untdmdp ze * x:o0,4mw/(rb bxfi)b ;td*yil it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s dbpxy(d zbf;** bd): xwmi4or ,t/e0mmass.

  The Sun's gravitationau:a:drz52su bt1ob -fl pull on the Earth is much larger than the Moon's. Yet the Moon's is oab2 tu: -u: fbd1zrs5mainly 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 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 198sht:r xs i0-v80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleratqrx-(g1 6nlam ion 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 orbit is a circle of radius nmg16xr(l-aq 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 g5lm4ah5 g2z ia 2.0-kg discus as it rotates uniformly in a horizontal circle (at armgih 4m5za52 lg’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttli m86vvr04ckhol5r 1f e is in orbit 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. Express your answer in terms of g , the gravitationa61i rro vf5lk 8h0m4cvl acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edbh bnj;*( 2cunge of a potter’s wheel turning at 45 rpm (reh;bcnb2n ( ju*volutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a strpxv( 4pd(-f y70jwplt nz, wpx 3qik87awb:4ping is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 0f:,xp( p -qpnwvwp p 48bw(at4jxi3 7 7zylkd$\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can r:inkt mr 62xyci68mtm*9vlefgy 5u v*zx 5z: 5ound a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this k5rx* t zzv5m86nmtc gil9u yy 5:xi*mfve:26result independent of the mass of the car?   

  How large must the coefficient of statiqr fqn,9tyfv2s)h f 52c friction be between the tires and the road if 5s2ty,qh fnf )9f v2rqa car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed toh4zzaoc 1*7jw rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on w7zjha 41zo*cher 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 rotating tur,x )gpwc szgop/,(,c8pve;aq ntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and tapvzwgo q,csx /pge, 8(p ),c;he coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaste6x)hgcs1tzafs p/p 66 r be traveling when upside down at the top of a circss/6zfx pph )g t6c1a6le
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the lwi 39irg;qb .driver) crosses the rounded top of a hill lrbqi;ig9 .3w(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 need toltdg6rij86 cp( a0f+( y 3anih,pg1og make for the passengers to feel “weightless” at the topmost point? , pgc 0hay(t( +dpjfin6 a8o 31ir6ggl   rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. ii6ycj0if;h7v ;y 1htAt the lowest point of its motion the tension in the rope supportiich7t; 0;jyii vy1f6 hng 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 to /w n8z1ntp(v9epenft)19r 9.00 cm from the axis of rotation is to experience an acceleration (wn/ont8 e919pvz1re pntf)tof 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in v:t v6w *bhi7ra cylindrically walled "room." (tivr:w hb* 67vSee 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 rotatev; wel5 j0jq texv7/3y9ms j/cd in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5- w 7vq3eet0mvc ;5/l9j/xjysj
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , preciselc:tp,g1n* qtf y this time, by not ignoring the weight of the ball whi,g 1*pfqtct :nch 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 mi9s;m z.kw ,j4w9cwv m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of massesntfl( x) r(,r ao8v:wq $ 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 ex 9tjgvn)r7jky j2i w- p,3sq)vasive 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 anwt1d8 a8,(5hoh g nlwid centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when h1(,l5 iwhw8t8ogand its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indiana kdl;. w wen*kf3).bzgpolis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangen*. ;w wkfkbezd)ng3. ltial 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 xifgj+sovx2h *7 t)c 4horizontal circle of radius 2.90 m . At a particular instant, its accelvxi+ oxj2th)4cs*f g7eration 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 Eartk ujd/ e + d,3ea3ijo10(flsvxh’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfac of0d/id lu3(eex,k a 3jsjv+1e if its mass is 1350 kg.   

  At the surface of a certain lskzj0s2 0 0atzg.rbx: ka3f)planet, the gravitational acceleration g has a magnitude oa: 2xz0s 0)lz k0skrba3gf. tjf 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. The t)8npohpm1b- Moon's radius is 1.7-b) hmno pt8p14 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical plane36cn, lskqhh- t has a radius 1.5 times that of Earth, but has the same mass. What is thec3s,lnhq6 k -h acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times thatbscv c9 z, ud3k:6rsm827brpg of Earth, but the same radius. What is g n8c,3 zbbrs9c v2u gmpr7k:sd6ear its surface?   

  Two objects attract each oks3** y5 zhs38bt ylre4 4,rq9owueozther 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 acceleration of gravity, at (a) ljv9cd 8:b: 6:+(5unzfzh.jlg v hqih3200 m zz65:lu j+jh:clf hnb:d(g8qv.v9hi    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where khyhgib; , e14thegravitational acceleration due to the Earty1h;ib 4,hkegh 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 vn i-)r:svuub,u fa-6packed into a sphere a6:s - n-urvfaubv ,iu)bout 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, wtwk e sywpb2x5nua)znpps+;1-2ss n 32t8 t5khich once was an average star like our Sun but is now in the last stage of its evol-53asp)ttesyn+22x5p;2kszn n p 8u1s t wkwbution, is 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 orbiti)sgakd- b n-2v me3/*y jmws)rng in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up therek-wv/me*))g-3ndyajs r b ms2 . 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 aslz9il e)(fe6 ze5 8xu square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exeslxi8ef z)z9le(u5 6erted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of th 9,ho4jf *g9qjww ,mkee planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assojegmfjwh w 49k*,q, 9uming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surfacemp1b2q- uo) cv of Mars is 0.38 of what it is on Earth, and that b)ovuqc1m -p2Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knqgu6x e-iihc. *fw7 kc 6b,7mzown value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’k6w.i,-6ch beqg *fzi 7c xmu7s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable ;yug;.t ;v+n nc b2qrrm2bqa7 circular orbit about the Earth at a height of 360+vynbr; b a; qg;2cm7rtu q2.n0 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 xbf 4ze6sfj:w)6vs28 i esb2pkm above the Earth. How fast must the shuttle be moving (rewv 2bs6x :zi)sb6jfp2s4ef8elative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical s;v/wqec* v5bx paceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for onewv5* /;bceqvx revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit 38ichnwi l5 ,uthe 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 ou5l,cinw3hi 8 n the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite s8 cgbvmcbr 5dw45z+) have to be launched from the top of Mt. Everest to be placeddbcv5r )4z+s8mg5cbw in a circular orbit around the Earth?   

  During an Apollo lunar landifcd,078y*atf jdi7 nzimeb+0 ng mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around thif870+mzc7 be,*ddjfnit0 y ae Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plane;x( 89v2c uxgyh ci6fkmy03udt. The inner radius of the rings i( u0v;ux83md fy62 9giyhx ccks 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 Fidq xfdm/i-csqb4f1 :/t2.xjh.4 s xdb g. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the hfd4d.xm sb2x:b- / cj1t4qqsf. x/id top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center ofdm t- 3moo-64wx;bw3kp wor1t the Earth's Moon in a space vehicle (a) mobow;1wx otp6 -wm-ko 3mdr3t4ving 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 of equal m ::esynkru*g:.z2-nmz 8swt sass. They are observed to be s 2 ksy*.umw::ztns8z : er-nsgeparated 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 wg qg6. l x(6lyt1 +),sq.ulx+txfmmoqeight of a 55-kg woman in an elevator that mo xxm1,x .66lg)sl lt(qqomg . u+t+qfyves
(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 frjde vh4ejg a7*73+bkh om the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the 74e k7 +hjagj edh3b*velevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits z0-ykrvcgf:fcea ) + ttft06+ uim8;w very near the surface of a planet with period T , the densitr-uaytc0te6;k+gt)ficw+0fvmz: 8 fy (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (t( :d:0wb/ 6hs xs5 8gcpvvcc-hi8 rvuy-.d lk27.4 d) to determine the period of an artificial satellite orbitinv: pvx bcitld cu08d/68k r-h(yv c5hw:g-ss.g very near the Earth’s surface.    s

  The asteroid Icarus, though only ,ebn fqhb; d7ba0b) 8la few hundred meters across, orbits the Sun like thbha0,7n; ebl q8bbf)d e planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagev1h;6jqaax )x 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 every 76 years. It cqa; c4okaq3en 2i6 eb3jc)o)aomes very close to the surface of the Sun on its closest approaabaco)aq ene iq43ojc;3 )2 6kch (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 the cent f+d/gkb0bw0rer 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 fobo* 8 tydkqj8pz4p+ l1ur largest moons of Jupiter (thoset y41q8*jl ppbkzd8+o 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 the Earth from the known period and distance of the M (hug(thuoup/sd9b (2oe rw6u 2tv ze3c 3t:9boon. r2/su9dpot t3(3 ucoz:9v( b2t huw uhgb(6ee   $\times 10^{24}$

  Determine the mean distance w6/sz1b g qmge t+9t0,gf *czsfrom Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given i9q,f *gszwems z/gt10g+ ct6bn 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 mtad h/vg eh/8 30izzph; o(cr;any fragments (which some space scientv ecp o0g(8 tzrhhid/h/3z a;;ists 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 " jm,x :z wb(0hppt--boplanet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly en -b(-p t:opbxz,hw0j mough 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 gorgehyc-. eyq hp w/mfya1j(54a q6 by swinging 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 tolerate at th- yaemq. 1a6 hc/qyjp54wf(hye 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 accelerati;js*, dappqv 5on of gravity be half what it is on tj;s*p d5vpa, qhe surface?    $\times 10^6$

  On an ice rink, two skaters o 2e ngdw.te2hm5qh.7qx+g pl.f equal mass grab hands and spin in a mutual circle once every 2.5 s. If we asshnx 2g 5+pwqm. 7 el.2hd.gqetume 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, trj1:t4 3f kzpdhe apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotatd j3t1r z4fp:ke. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a snl. uwqj a),gde eq.;ia;./s fpacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and o .f.a/a) qugeseqiw,.; djln;pposite forces?    $\times 10^8$

  You know your mass is 65 kg, b 0ts )5,ipjbtxc0 u.fvut when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of thu5j x)0 vt. fpst,icb0e elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists ofbjk(9t1tp ) vu a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1v9p)ttb1 ujk( 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. ;6qf;wt)dx nj5–43).
(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 terf4ckw o4 -k2ztms of its radius r, the acceleration due to gravity at its surface and the gravitational constaco -t4zkwk 24fnt G.

A plumb bob (a mass )p n(fm7 ecy+fbys1c. m hanging on a string) is deflected from the vertical by a)ymbs cpf1y+ncf (e.7n 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 67 m is banked for a design speed of If the coefficc a hp7kknvjqc r1e8gs-,uj270dq( b8ient of static friction is 0.30(q2a0q7 h-c8psn1g k7u rdk,je cv8 jb (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 objeqi;u x(dh+bcnq33 c h0p, xj*hcts at the equator were apparently weign3u0b( xi; hhqj ,hcpxdc+ *3qhtless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 (0ye m 4x, ;nylsekya1$\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 speedy-. /*ybbcsbb(jh f,p rounds a curve of radius 235 m. A lamp suspended from the ceiling *jsbyb-(/.y b fbcp,hswings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the E1b k( h:n3bpcsarth. Thus, it 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. Cab:(1 skpb hcn3lculate 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 h dq-dmvj5/1 mof an extremely massivhmdj-m1vd q 5/e 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 in nx4-d0yy 5il ad ww.-yz7uj+ rFig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) da4yw0yilrdy.7 x5 - +-jwnuzExplain. (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 satgzpvd s f:y6(3 agke (s2c3z2nellites 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 fezsskag(y2 2 :(g evzd6f3ncp3w 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 billi oa)26x* v g9lj8 kqm8j6wowxzon km, is meant to orbit thqg* lw9) 2mkvax6 8oxjz6wo8je 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 a satelliz e(2sab. wm9lte in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above tmzb 2 ewsa.(9lhe 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)lgd6* (0s ezvrx,1x cikwsp: * wy0:olsa q;0f What is its mean distance fr z;x : i0cswwerg0*0ql y*l:ap o fx,sv(sdk61om the 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 woul1ovi a(d;-phjz:8q x sd need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reov8qhd ( s:aizp-; j1xasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milkp u:fohg 4.v0vy Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the ceg0u 4pvf. o:hvnter $ \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 oqn/ruled- k5 re)h5kj0 00(ldo)g fft f a square 0.50 m on each side. Find the magnitude and d5/l)gdef50eukq ) nflkoj(rtd0r- h 0irection of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitje* p,q7z btn 5.,o jvk2cj8rfks..yfs 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 exper(qdvbb dji;p3 5lg(60 evi1 vlienced by the tip of the 1.5-cm-long sweep second hand on 3(50lie d(6pbij;dvvl1bqg vyour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinwp-o mn :f6:kbker weight around in a circle below you on a 0.25-m piece of fishing line. Th:pow:f nmb- 6ke 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 (d )cv2h+ q,eyr j/rit in a new highway is designed so that a car travelinej,(d2 c qtyv+/ h)irrg 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 negotiating)49gmow o-qzo 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 (approximatew9oogzq -mo) 4ly ). (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.$\approx$    $\times 10^2$