Sometimes people say that water is removed from clothes in a sps8 h jh8fu 45j5qrdtg+in dryer by centrifugal force throwing the water outwarf4sh+5h qjd8tj8 ug 5rd. What is wrong with this statement?

Will the acceleration of raauae4u4x,l. bqqnrd 7,,; 61asxpza car be the same when the car travels around a sharp curve at a constant 60 km/;elxu1s,p.7dau6 r,a rzba,an x qq44 h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along alm7g- :f6qm da hilly road. Where does the car exert the greate f-67gqal: mmdst 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?

Describe all the forces aceow s8c qtgkb7 /e1 ),fesw -l0+s8nrgting on a child riding a horse on a merry-go-round. Which of these forces provl f+ws 8wnr k8 e) ee1,7o-tcb/0gqssgides the centripetal acceleration of the child?

A bucket of water can 2n 14j/n 4jyq5xvczw gbe whirled in a vertical circle without the water spilling out, even at the top of the circle when the bnyg42/5xn czjwvjq 14 ucket is upside down. Explain.

How many “acceleratorslslq zp;b9s*p f k:b9(” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What arsz p ;blkqs*pb9fl(9:e they? What accelerations do they produce?

A child on a sled comes fle +1.rvwa ae0yying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he doesaw ee+0y.r av1 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 le*,pog6ds9e )db tpo -man inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the ban5n5fsoi1jfcd4n +, yjking angle given its speed and radius of the scf ni5yo,n+jj 4f5 d1turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Shglgg c3sx0.c(x 3)yk ye wants to let go at precisely the right time s (xgc3yy)g0sxg 3l.k co 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, how large a.fh7m* vf 4xaiscn:,09cpali force? Consiaxisf 0c ml9i. 4nh*7a vf:c,pder an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, j /bb q: x7d7e4oor7emin what ways would the Moon’s orbit d /r7bem7 7:q 4oxjobebe different?

Which pulls harder gravitationally, the-efeyab o9n5dgd5, 5k Earth on the Moon, or the Moon on the Earth? Which acceler9 5g5e ,ybo -a5dfekndates more?

The Sun's gravitational pull on the Earth is muchwfw d;r,w/.ffa s;w;x larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gaxwfrwws,dw /;;.; ffravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator o* mxzj,ej *j1wr at the poles? What two effects are at work?*mzjwj,e1 j*x Do they oppose each other?

The gravitational force on the Moon due to the Earth is only u)zi4w jd 7/ k.pf,eyoabout half the force on the Moon due to the Sun. Why isze.o)f 7dj4 wui py/,kn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger o-r/rv3c m)hfh-tvro; r smaller than the centripetal acceleration of the Earth-vcfh;-mrr)rt3 o/ v h?

Would it require less speed to launch a satellite (a) s4 l.hts51jymas 2ua2toward the east or (b) toward the west? Consider the Earth’s rystj1 52aa hmu.sl24 sotation direction.

When will your apparent weight be the greatest, as measured by a scale is lobl)57m 8nw0gs8yf n 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 be the least? When would it be th 8 lm8onf5g)ly wbs7s0e same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long pehzqjd y6yrxi0 e-;//; x)xdj griods in outer space could 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 simulates gravity-0h;jyd)y/xz;6re xxjq /d ig . 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” ort* /rj3mhbbncuw-3)i6 z q+pl “apparent weightlessness” betweeqr-zp/ w+bi)n jm*t3ul6cbh3n steps.

The Earth moves faster in its orbit around the Sun in Janua 1)ttuovimq(u* 3 e1chry than in July. Is the Earth closer to the Sun in January, or in July? 1et*u (ocmq13t hu v)iExplain. [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 discove b,vhez +q9k7zred to have a moon. Explain how this discovery enabled an estimate of Pluto’s mash,be9z+ zqv7ks.

  The Sun's gravitational pull on the Earth is much larwy+u ixlp 9yk1*y b41jger 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 mo1y 1+l9py*ubij k 4ywxves 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 -4i6l8rv ul8 / dgxcdp1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its or l6to.m. h0otebit around the Sun, and the net force exerted on the Earth. What exerts thism.t0h .lo t6oe 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 2.0-kg discus as it rotatsk:4( jry8w b(px,zy ces uniformly in a horizontal circle (at arm’s length) of 8r :ywsb xz(pkj4yc( ,radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit:,3z3 0s,xovckr ,f e*d/qxhi2vs xay 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle inzq:3vkd,so02 ay , xr3hx,efx i*c/sv its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of q,3i;bk97 psrb+w8mczv ,gb i clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diamete,,b +bs;mqw3 bkc7p ziirg9v8r is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verc-fhz; uoz/w74n ee u.tical circle of radius 72.0 cm , as shown in Fig. 5-33. If it7owueu/ 4cf;ehn -z.zs speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car canpmr *k52 fqd8b round a turn of radius 77 m on a flat road if the coefficient of *rqbmf2dp k 85static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffic2: f xpypxm-s.--wct,i9 ry sdient of static friction be between the tires and the road if a c2f9t --s,yix w.p :-cxmryd psar is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter p1jto789ycyexc3. r h1q2 roiuilots is designed to rotate a trainee in a horizontal circle of radex2 y3h91 r .t uocjc71ryiqo8ius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    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 trcqf 2v.p2x +f kup1+phe axis of a rotating turntable of variable speed. When the speed of the turntable is slowly r2f2+1q. x+f c vpukppincreased, 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 tra5 xgd 62i43.6v5wrtgo3 ,wmmfc+t7 dsdg mdcbveling when upside down at the top of a c5ow d mg6 5+ ,.w x3 r2vd4tmg7dmcbd3tsifc6gircle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded :ceiu3f50*7ihe q d 9q6vjttatop of a hill (radius *c59ia6qv : jee0 3 f7uqdhitt=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 Ferri6p ra6:k kdrnq0* zx1a6z b)ejs wheel need to make for the passengers to feel “weightless” at the topmost point? a a k)0:zq p6jdrx*rkz 6e6nb1   rpm

  A bucket of mass 2.00 kg is whirled in a vertical co:gofr l yy+0f1rs z)4ircle of radius 1.10 m. At the lowest point of its motion theg sy)frrzl1 y+f4oo:0 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-w5egaicgv 26 ju:c r1 9.00 cm from the axis of rotation is to experience an acceleration of vi 51jrc wug: 2a6-ecg115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a r91 uar/ q)gojgkh-i((n rq/bcylindrically walled "room." (See Fig. 5-3rukri qg hb a1/q(( )jr/og-9n5.)
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 fun nsnj5t: g:*;w :+i1xki 2 krz7o:5cszppherictionless 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 hwztk:sg nz5s75kin x u:+ : ; i:nc*er21opjpin 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 thea/e,887 nt -tganr sdkc3np+j weight of the ball which revolves on a string 0.600 m lotdaj87enpnn- s ct3+,8gk ar/ng. 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 isni3;xt tv6go2 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 massewc.3 s vqk*(0, qqzplns $ 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 mat2,p 8n utsxs4neuver 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 centripeta,2pg4 eh qg in:.*xgunl components of the net force exerted on the car (by the ground) in Example 5-8g2 :nn i* gh,4qpx.eug 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 accelerates uniformly from the pit area, gol cp4zu0l8ce ay-l7;h ing from rest to ahz4 e;l0l8 lpucy-c 7320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius )gcwki: fi qa;5-dyf(2.90 m . At a particular instant, its acceleration 5)(fk c:fad;iwi gqy- 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 g*e-27 id 7 f4grdcxiruravity on a spacecraft 12,800 km (2 Earth radii) above the Ea*7 cxi2du7dre4if-r grth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitatt r m9o76bn) gixk)z9kional acceleration g has a magnitude ofrm7 i9)zb )x69kogtn k 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 Moon's n. 0bl;y4y9f1hzb* h4 ys ttxpradius is 1.7.1ty0 sy yn4hhxbflp*4z9 ;tb4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times tha8nz ab-;ves irnhkcaa.-3; yr/e*w r,t of Earth, but has the same mass. What is thw;,bscnaavih y-.;kn83rz/rer e -*a e acceleration due to gravity near its surface?   

  A hypothetical planet has a ma myqii1k6 l.m/hs9i/w ss 1.66 times that of Earth, but the same radius. Wl/yws6 m i/ 1m9i.iqkhhat is g near its surface?   

  Two objects attract each other gravitationaea)d98 dj pvch i/qa)8btd 53tm6ft3l:blkz *lly 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 , m p/q3fn9v qw,;mwd( nthe acceleration of gravity, at (a) 3200 m,v( p q mmn3q9dw;wnf/    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Eart ,xu/8hllpx jml9jo8 / vm:w,lh’s center to a point outside the Earth where thegravitational accelljlluh 9m, xw/ovl8xm, :8/jperation due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun pakme8 m9ex(d5 j* -j,/z hdtkl0wyd9kdcked into a sphere about 10 km in k* jt5e -lxwd kj dz8dkd99/m0hm, ey(radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star lik54jpr.6 x h.9jo -yvcjddjp/ee our Sun but is now in the last stage of i- jdex45/6o.yjd j rvhp.pcj9ts evolution, 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 orbuq t3 0nbc2hi+ 08yczbiting 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 grav0cb382ni0ut +h qy czbity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locateag )c gqmu59n8d at the corners of a square of side 0.60 m. Calculate the magnitude and directionua5g)qg8c9mn of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the samlw klc,u:ux9o7 ml-, fex+)cve side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). Thoxml+-k,x 9wc )fllc7 euv,:u e 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 ol pfwcr/w-p,vhd.6 0rqy 1 p*jf gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mv0r*wl/ wph,j6y1fpp cr.-q dars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earthc4n -.d6e-wolm+m bym and its distance from the Sun. [Note ml+y4mmb6.nc-do -we: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable ew637y.f rrjej r-a. acircular orbit about the Earth aeafrre. .w6jr 7ja y3-t a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 kmvgm4n g+k8 +ik above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occuvg+4m 8kn+i kgrs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to expeptenl9)wuco:;si : s 7rience simulated gravity of 0.60 g? Assume the spaceship’wl)s;s:no: 7u9c ep tis 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 thn.i/k8koq b( j 5+1 kbpk-ydwie Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surfa-o1k(nqk+/8i. i kw5yk djbb pce of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from tjr6/zfco 7a )a4 irx*whe top of Mt. Everest to be p xiof*acwrr6a 7/)4jz laced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbibwh i6cyiojfe9; h4.n )7z*tct the Moon at an altitude of about 100 km. How long did it take to go around th6ebiof4 i;hw7 )yc.z9c*hjn te Moon once?    s

  The rings of Saturn are composed of chunks of ice that2 rmp0m7 xvs(c1tt/ cz orbit the planet. The inner radius of the 7 tct0 ps/mr2 v(zxm1crings 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 3bd( cb6*u qv : r4jryrw3a-hn*)sait15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at t3 :y3rq*b64c arwvsarbtj)hn( * d ui-he top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center o*rx6m9hdc 6amf the Earth's Moon in a 6* 6c9rdamxhm space 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-ste.uae 42;j,qkiiq mx3 w 2l5r .el1pl :xyhd;car system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to o kw,4 uqi2hlq2mx.dl1i.y5p c x3r; leaeej:; rbit 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 won7ib in2 jz0k32-aqmm man in an elevator that movesi3b0k7q2m zn2nm- jai
(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 amx0k*+d4qvjk,7- 3ytfpy b x 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 accelerati,kf+k *4qx0 ty p-7djmbyax3 von (magnitude and direction)? a =   

Show that if a satellite orbits very neilifjum5 f 8:+ k:z+xohe.st: ar the surface of a planet with period T , the density (mass/volume) of the planet 8t:.5+jl+ i:o im k:ffsuhexzis $\rho=m / V=3 \pi / G T^{2}$ .
(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 dete*xf,i jw. iysejhoh 9v k9709armine the period of an artificial satev9wxsykih0*7fae .o,9h9 j jillite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though ojnpog- 3tc; z5nly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its me;- gzncpo3j 5tan distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of99zjmnd b l12j 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 thntzx1. )pen7d b;gjzge js10,9j3f gte Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is f,tj 9.xtd3gbsnje1ggez7)p;0 jnz1 out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galab hab5ahn 7wrj x3(t8,xy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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,*db. 7vyvd4 or8kl7: ). mtoyjhctzu) period, and mean distance for the four largest moons of Jupiter (those discovered by Galilymv.*:ut r4 dz7o h78 y)bd.koj tlcv)eo 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 fo7zsle)4vf w :rom the known period and distance of the Moon. of7l) :ezsvw4   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupith r(z*t,n4y53tv xvhger’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to tx (yz *tr435gh,n tvvhhe 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 mtb+.n.s2 udyen:*huq any fragments (which some space scientists think came fromns+ bt:yuu*dq2..hen 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 descrir )e6 ez/i yunubph7b.1:m2r qbes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the ba)7ubqin6rzmbypru2 1e:./ hend 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 b*jm km7+sazq 7y 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 thj7m7*sa +km qze 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 of gravityirlognm15snq; khnc, *v(mv -e-;e6 h be half what it is on the i vehm 1o6(5- knnv*ghlm,en r;s ;-qcsurface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands ab4e0f/ nir ey7nd spin in a mutual circle once every 0f/b e 7yirn4e2.5 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 royc.z:irnp qc 3 r0-dx9tates once per day, the apparent acceleration of gravity at the equanxr:pyiz0c.c -9 rqd3tor is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from(d(,2l1vzfljmzx hf- the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon xzvl hl- fmz(2fd1 ,j(pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, iewt*y -m3d1a/bubkvmwf +-9 but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration omi+e9d-y bwa v3/1u*m-fkwtb f the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tud5+3u)x 0vbfgaf*sn qe4uzy1m 23 lqhyn3p -ibe 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 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravi12li fz5+s)3epy quan *vnyx dgfmb h34- u3q0ty 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 (Fm54-5vho,e,ph:n0urmt4zp gqcw x)c ig. 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 ma2k e +cuyt/iu(ay17ikss of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational constant Gaeuiyy1iu2(+t k 7ck/.

A plumb bob (a mass m hanging on a string) is deflex8z. 9llt c.gscted from the vertical by an angl9cxz.l .8tlg se $\theta$ 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 oo 6k0 csnxzx71f static friction is 0.30 (wet pavement), at wn 6kxs1ox70zchat range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at idw0cd(2le*p 0l /anyxi) px 05ef8nuthe equator were appa ypceed)00di0 n/i58u p(f*lax n2lwx rently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant +mqeofyy)-:v3u s9uq 0oxcs5 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 speeg gppr7,8i6vy d rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out togry 8i7 ,vg6pp 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, it has been claimed thcdutwo0mbcb/ 6 63o o (3am,awat 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 th3w6uac3o twd b /ao6ocmm(0b,e 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 presey9iw9o0msz+8m 9z5ihd3k mjqnce of an extremely massive core in the distant galaxy M87, so dense that izhqs 9dmm3 iz+9wi0 jk58yo9mt 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 spe3qhmfx*;- lfted as it traverses the hill and valley shown in Fig. 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?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at Atqfhx-fm *;l 3?

  The Navstar Global Positioni wt,;jstx6f )gng System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of at6 txw)g,;sfj receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 bin c3)8qn(mfwhr p:x:tllion km, is meantrhqtpmn w: 3x :(8cf)n to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursu-tfq,ks 8lg u* z(8cqcing a satellite in need of repair. You are in-(tkqq s ulzg, *c8cf8 a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (padhh ;z r-82ba) What is its mean distance from thz 2adb;p8r -hhe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feemiq d*md*0n-27ok5 z hzg.e,smv hnm6l" yourself gravitationally attracted to someone near you. Make r50*nig7mh,s k2*h-dn 6dmqm z zoem.veasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky bw5gps vz8ruxszy 0hb/umw,u*2 +: :g 9 hg3ykWay Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cenk 509:gurshb+uyyw z8 b32 ghugx,pvms/ :*wzter $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.5 f12cu zv5ptpchl j+0x/49 lko0 m on each side. Find the magnitude and directilcc4 91/pjfkt+hluz2o0 xpv5 on 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 kghb0tko5y raj 5;-(p ny 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 the 1.5-cm-long sweep uqr l o074r4dqsecond handd4u rrlo0q4 7q on your wrist watch?    $\times 10^{-4}$

  While fishing, you get borhh* i sr+2i:ktc*xa9zed and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The w+:*hx c9k*2 asiztir height makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so th5hlbu9 j; zt3rat a car traveling at sp 35tjhzb9l;r ueed $ 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,x +no3p,pm z1m utilizes tilt of the cars when negotiating 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 pxm+oz3m,p n 1 (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.$\approx$    $\times 10^2$