Sometimes people say that water is removed from clothes in a spin dryeembh +wgp;o ni.x2* j l:ts(;gr by centrifugal force throwing the water outward. What is wrong with this stateme*jhb:; gin2mwp lx(;ost. +egnt?

Will the acceleration of a car be the same when the car travels around a sn9os/wd o0 da5harp curve at a constant 60 km/h as when it travels aro/odsda5o 9 w0nund a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a h t g p14-:0uvdvp8vqt iskr:v0illy road. Where does 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:tv:vqusk8it4 1r vd 0p-0pvg level stretch near the bottom of a hill?

Describe all the forces 0wwzmw bjl5 )l,/ mra5acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal accelerwzm/ awjl,0m 5rl5)bwation of the child?

A bucket of water can be whirled in a vertical circle without l2hcfxq ( *8gk l9i-uithe water spilling out, even at the top of the circle when the bucket is u-29lc*g8ilik uf (hq xpside down. Explain.

How many “accelerators” do w6swhh dg,z 2)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 are they? What accelerations do th ,hw6g2 )zhwsdey produce?

A child on a sled comes flying over the crest of a small hill,5 +3sgb t7j4gajfbr+d as shown in Fig. 5–31. His sledg4b g 5b+jfsjtra3d7+ does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve attd y;f 7o1-iwl high speed?

Why do airplanes bank when they turn? How would you compute the bandpo(c1n ko ,k6king angle given its speed and radius of t,odo6(1 pcnkkhe turn?

A girl is whirling a ball on a string around her head in a fp+e0 z )(txu7sje9xh horizontal plane. She wants to let go at precisely the right time so thatex 7 u) 9tjxfesp(+0hz 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 fo/fyzji g0; r7lh;p;)i(-jk ayfr j* zirce? Con/7 ;yfz zp f*j;; ry0airihi-j)jkg(l sider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’sgitt;5.87(syvbbu+0k rw/u 4sc i njo orbit be di+ j st4og(.bcwt 5b087siu; /yvni krufferent?

Which pulls harder gravitati8epu;l c7w .) 8 jmj6d+jwndkmonally, the Earth on the Moon, or the Moon on the Ear8n e)juj dpjwm+kw. cl6m d;87th? Which accelerates more?

The Sun's gravitational pull on the Earth is much larw5 hp(pyx dp*+ger than the Moon's. Yet the Moon's is map+ydp5(pwhx* inly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or atmr0q;kj9;t bi2d:r jd the poles? What two effects are at :dk;j 9qbm jrdr2;it0work? Do they oppose each other?

The gravitational force on the:ms be:y(3 gqyd5drfcx/pa 9 ) Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moonrmsp:ycxfd (q/5egyba 9)3:d pulled away from the Earth?

Is the centripetal acceleration of Mars hf;fz -6scpkd6s 4ff5 in its orbit around the Sun larger or smaller than the centrihkp6fd ss- 4ff;z6f5cpetal acceleration of the Earth?

Would it require less spn/tfcdt/+ ye/;du f3deed to launch a satellite (a) toward the east or (b) toward the west? Consider the Eartn def+//u;/ctyd 3tdf h’s rotation direction.

When will your apparent weight be the d 6(9 jjh1; 6ucaqepirgreatest, 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 be the least? When would it be the same as when you are on thj p q6u;6eh9i 1dcj(rae ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lon / fl +u0gqk)i9j4pwcxg periods 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. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of 0kfgil 49 q )x/ujpc+wgravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessnesipi27yff5fpq (1 hzp,s” between y1f,fi fqh7pp ( 25zpisteps.

The Earth moves faster in its orbit av1zspytn ( b6+round the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the planent +1( yzsvp6b of its orbit.]

The mass of Pluto was not known until 6 l *z ab8m:z9pcgj8xoit was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’smz8zlx *p abc96g8 j:o mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yetf 481 zcmuhtn9 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-rou98z ncm ft41uhnd 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 5,h ,d.fr ij8-rmf 5b/imjyac,zr /cy1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orbit around te,-7 tkfopc f/he Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orb-c,tfeo pf/ k7it 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 lul xk-1un)0yis exerted on a 2.0-kg discus as it rotates uniformly in a ho) u1-xnu ky0llrizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit9scpl4fz n-t5 fv lt0* 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 ,fs-flv z594clnt* p 0t the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a spouht )0 tlq. ))- h;nlp+mfdz5f.t, :qtn crexeck of clay on the edge of a potter’s wheel turning at 4m, -nf ) ft.hqo:xq ut )t.dcltz phr;5e)+0nl5 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a unif+c;kmmh 0 jmaitaykpm 15t08:orm rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. Iamc+0:k m;p0ah 8ym jmt5kti1f 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 spee s4saf,rvnvfz86*v5 td with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction be *s4v8 snv5,tz rf6vfatween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of p a* 99vqerkw6static friction be between the tires and the roadrekwa9 v6*q9p if a 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-0 j gv6kmja ykst0bic+ *5yi ,8jwh4o is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the traine t,-m ik k0ojvj h s5460yjwyac8+gib*e 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 rotating turntable of variable )aqf a fk; 8b:,5hd,hrak g8udspeed. When the speed of the turqfg )fa,h k:bh;,ad58ad8kurntable is slowly increased, 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 o o,l,u muk;1zdown at the top of a circle uko1l;, m ,uzo
(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 drzzy4rb-rgb dg c8 w.;;iver) crosses the rounded top of a hillzz4wbr ;g8c-;.brgy d (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 pekgm 9f+iz.z d+7f)nz jr minute would a 15-m-diameter Ferris wheel need to make for the passengers to fekz++jfz9n.d 7i fz )mgel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of rah hvi1q16hl ( gjis0n dz93ir8dius 1.10 m. At the lowest point ofij9hrzh6i din1 g ls801(qh 3v its motion the 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 aru2jng dh80 +j particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,0 rjn0d 2uj8hg+00 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a c*8ou-)brik( 0krd kzg ylindrically walled "room." (See Figu*-o ( )bzd0g k8krikr. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated i0 aq;snl(id;m e0 pv8in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a ligh; (0;esmvdpqa n0l8iit cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely thydetg hnc,;yv a; 9x1:e1jv: wis time, by not ignoring the weight of the ball which revolves on ;gy x:a11dhj:n; eev w vc9yt,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 mup4 qej1g/m* . c hm(yh 4lmq2ish;su- 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 masses wt,cgtu (azq hn)4s, ip/x: v6$ 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 maneuver by div8g+k yfaui 4p7nrhukeq 3 -*+k :h6vdcing 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 centri7vho7sbb w+yhbs54 q8petal components of the net force exerted on the car (by the groundsq5bh8wyvb 7obs +7h 4) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit areasl gy.er13 fz(0 5qxqx, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential accelerationl3qg(xz .1rfxy0se q5 . 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 hor/.sek q haue.r92ff6a.xwb )tlo(fi) izontal circle of radius 2.90 m . At a particular instant, its acceleration is. hrfo(eas k9)fx2q .)w abu/el6ift. 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth9y6ci: ua/ssta e:s-+4bvlgl radii) above- uv 9ts/ sb:+caa6e:i yls4gl the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a mbe2 c;u qnkupqf*1 e95agnitube29cq enu*;fq u 15pkde 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. The Moon's rj5xbesk+gl /oi -0f (sadius is 1.7g s/sk(oe-i0l5+f xbj4 $\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 kaci49;knxvv.g a88y4 bs2z kthat of Earth, but has the same mass. What is the acceleration due to gravity near k4z;as2 c vv89ibky.gak xn48its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radffccu0zy4uykr s /25 :7w yx.gzj*0w tius. What is g near its surface 2f.jz50yu /sywzu : t7cx0 rwf*4ycgk?   

  Two objects attract each other gravitatiohhuv,98hrc8gds :d z 0ath)m )nally 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 accelerationftb g .(4mx ly5n2a* e2pt3egp of gravity, at (a) 3200 mea(peg2bg2typ3 4 xmf*tl5 n.    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wherev 5u r-,err0 s+r3 kounku4-3:irzktf thegravitational acceleration due to the Earth,e vuor5+4frr: n3 3 r-k0-kzsrkitu u is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron st:lf n+efv4kq3 ar has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gv3+ elfk4fn :qravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star lk 8cvwhuf:r(5zdx9 n9ike our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface grav9w dunr zchkv(x59 :f8ity on this star?    $\times 10^7$

  You are explaining whuiykp4;j2h/en //o v by astronauts feel weightless while orbiting in the space shuy; //oh4kbjv/pn i2 euttle. 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 above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of. uh9 mo.) i(mpchew3q a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere b 9hmi(.e3q )mhwo .upcy the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mojp/a32q:zaz aq2v* u pj3y6e wo7a5dist of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assu5ja:p7ov3aqy/ q*z2uzdej3awp i 62aming 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 surface of Mars is 0.38 of what it/zh sr:y3*an rr*q5dh is on Earth, and that Mars’ h*z3qr / y*sa5hnr :drradius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of th*/va5;he. tmlqf1 jl be Earth and its distance from 5 hvt *qe.1;l fbjam/lthe Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abnidr o. **55 kdy i2d6lcwtrb+out the Earth 5ddr2ib 6 5d+i lrctkyw *no*.at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the8pjs (,i*f,7bw(pcug xrs3 6z0y fzdck0i 8aj Earth. How fast must the shuttle((p, sy,frcg0 z8f*db wcxzaspjuki7i368j0 be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experndt5.q1 ywy,cience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the tq.tywdy n c,51ime needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takeswyi mt 9/0dxn0 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 whictd/ 0mxin9yw0 h 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 wod8s mh;v:/ o(3nrmux ek)tdh:uld a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth?h 3;) v/m( kx r:8:nuohtddmse   

  During an Apollo lunar landing mission, the command module continued to orbit 49tn ai58sf4t oq m,pivkx,:h the Moon at an altitude of about 100 km. How8i44:h tk,a5 tmnsp9,vf qx io long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orea/5/lnef bbzi-5 ,1cj ga-mibit the planet. The inner rbej1n5f -calb ,az iegi/ m5/-adius of 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 on/najaf;0dk41axgyo7, ari8k :w)ca dce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bot/a ca d) wa nf,17i;dkjyk:4r0oxaag8 tom?
(a)    (b)   

  What is the apparent weight oh kkz0u02 kq8vf a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at c2kqzh8 kkuv0 0onstant 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 eqo ;s v5b5ksnx9sujl5n )qe8 j*ual mass. They are observed to be sepavsb8)nlosu k 5n;xe* 5s9 jjq5rated 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 aiukhqf-,+ /.yo/hvjl ;+ jene 55-kg woman in an elevator tha h-/jv fuo;e. e/hk+l+qniy ,jt moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. 57x w spmi4zxhq.f1ef m4yz,* The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accelerati4mxpsefi * f 4h7m1yz xzqw,5.on (magnitude and direction)? a =   

Show that if a satelwuwo8 bye/v)8u/waj ) lite orbits very near the surface of a planet with period T , the densjba/)) uw vyw/8e w8ouity (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 (27.4 d) to determine thto q(v(d(+ bxye period of ox(qy+( dvbt(an artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acrossixl .6lir( f d8s gv0mc./s5mc, orbits the Sun like 0sd5 /slvig r.mcxlf.68m c (ithe planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of+(hzhhtv,6wdmt /sw* m uxi43 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 oncbkg vbz+b7pg(g7a p79e 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 out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from z(gbbgp vk9+77 bgap 7the Sun.]    $\times 10^6$

  Our Sun rotates about the 30bbp. /gczfq 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 four largdfxyh /; .bl.11tq vrxest moons of Jupiter (those discovered by Gtfbxxd y/l.1v;.rhq 1alileo 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 dist .2 koal7+h86sqlq xsuance of the Moon. s.8aq+q2s7oulh 6x kl   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupitonqr3s3hxx 4vk 7aj,k39ebr7er’s moons, using Kepler’s third law. Use the distance of Io and the periods g j7qv9ax33ks exro7 krn,4bh3iven 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 Jupi o,z7:a x4,4s cvtmofeter consists of many fragments (which some space scientists think came from a planet that once orbited the :mto74 ,,c s xvo4fezaSun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form u 3ghe4 mrg(w d4mp,:zof 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 enough to produce an apparent gravity of g as on Eartgp rm,muew( 4:d hg34zh. 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 (Fig.td 1 x ;k0okknl4-ea*j 5–41). If his arms are capable of exerting a force of 1400 N on kejtkl; 0 ok-an4*dx1 the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be ha6q7qkbhk) d y.h3ep ,qlf what it is e p7yk.qhb)q, qkd36hon the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual vngfr( 5p3co1jk (-ti circle once 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 ano315 f(vr k- pcj(giontther?    $\times 10^2$

  Because the Earth rotates i-0gdo zql o57once per day, the apparent acceleration of gravity at the equator 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? 7o5i -qd ol0zg   $\times 10^{-1}$

  At what distance from the Earth will a spacecraft tbyc2):- wp6,tb jeyj mraveling directly from the Earth to the Moon experience zero net force because the Eyt6 ,c:jjbbpyw e -2m)arth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you p3q0, *sr nswhstand on a bathroom scale in an elevator, it says your mas rs0q,wnsph* 3s is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will ro f 4)t:qox/dimtate 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 gravity at the surface of the /:) miqt4fxo dEarth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–4/ w kqe5d99cnh3).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accel2) g6acp(u crw*xfz+cb0bw 5ceratz*5 b+b)w 0pw(guccca2cr fx6ion due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m n3n is+lk.q/jgoqsmhcl;wj 5 5b5 pn+y on ./2 hanging on a string) is deflected from the vertical by an anjy 5 sg/oo5s/n+i.mlwk2 .ph3n bq q +nj;cn5lgle $\theta$ 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 9i5 9dpzlk :7n ,wjvdkm is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can pl,9 ikkdvwzd :nj597 a car safely handle the curve?

  How long would a day be if the Eau x.s qf)q+fs)rth were rotating so fast that objects at the equator were apparently wei+ suq))s xq.ffghtless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apd6kkz. ) x;nohsckd6 +art of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 22 ry7jhl;k1gi 35 m. A lamp suspended frglyjk;2r i 1h7om the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it ha2g rfh/nw( g-js 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 -ngw2r g/(jfh g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Tel*z 1ihvt4wjmf8ra9r 7 escope deduced the presence of an extremely massive 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 speedzwm arf7h19rvj t84*i 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 valleyxkql4e 3 uab71 shown in Fig. 5–45. Both the hill and valley have a radius of cuel4xq1 u73 bkarvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Sy 3f fxr4241k8c lueelhn;ph,z stem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earthn le huk;3h1f2x4fz8,4cr el p 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)woevs-p mv2)d1 kz10+0mzkk l, after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height dz-+0v 0 )kvmk1eowp1z klsm2of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need 0u b)kwjb u/j4of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km bk)bjuu/ jw40behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distance frv.k-oay*2 zxwp gi vtpf b14i+uav: k+bbx,:* om th iu-o*ivxv ,w +4pak:b2zt g.xbvfp:b1y+a *ke 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 b 1w(s.vc yui8ge if you could actually "feel" yourself gravitationally (.wiy vc8ugs 1attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centen tmm;j2u 9yiw2cb*2zr of the Milky Way Galaxy (Fig. 5-46) at a distance of about2tu;*2i9 jc ymmbnwz2 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.5t-c u*f0xc,ifa:od +b 0 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0a-+u,0 c*d :bcf fxoit-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the u6h+fwx09xdwj1 jf f 6Earth $ \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 accelera-x* vy0* jm;rbv7lksm tion experienced by the tip of the 1.5-cm-long sweep second hand on your wrisj;mx-7svrl0*my k * vbt watch?    $\times 10^{-4}$

  While fishing, you get b/yzn;. ,d0bq+gxr f f3lhc2hyored 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 a comple/l+.fhr bqd gxfz2yc0 hy,n;3te 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 ;wu*v s3m bc1e zj6s;vin a new highway is designed so that a car traveling a3 swvubc;es m *j1;6vzt 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 negotiat* cexhf dv6o;viq-s l h. y;o 0fs4gp83cjqk+3ing 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.jh*c +h4s v83 -6gqcfdivxeoq0ysk.fp ;3 o;l The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$