Sometimes people say that water is removed from clothes inwnxl. -:m (zya a spin dryer by centrifugal force throwing the water ouy:lz(n. axm-w tward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a srzyn /j.dat ,2harp curve at a constant 60 km/h as when it travels around a gentle curve at jaz2r d/t,y.n the same speed? Explain.

Suppose a car moves at constant speed along a hilly road72+) eryer8 hm.7arqvyj(s s6w0rpkn. 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 level stretch near 7kr0+ qsvm(2yhe.)wpj n8s7r 6rey ra the bottom of a hill?

Describe all the forces acting on a childua /t4ciah7pt .k3fe( riding a horse on a merry-go-round. Which of these forces provides the cent 4aefpk3acu t7h/ t.i(ripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the watc6* md so.n6rrer spilling out, even at the top of the circle when the bucket is up.d s*c6 m6rornside down. Explain.

How many “accelerators” do you have in your car? Therweeq4 km3;:g,4qcu dge are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations3g ;dkumq4 4w:eqeg ,c do they produce?

A child on a sled comes flying 6uv:2 umqa(gk*d97 p fyhdb7 oover the crest of a small hill, as shown in Fig. 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 sled decrease as he goes over the hill. Explain this decr * 9pm2k7fgud uy6:7b ah(ovdqease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve3ql+ f2j3-uvueims zj m.)t(ean6a8 p at high speed?

Why do airplanes bank when they turn? How wou /0geh)t( 2h asze0exnld you compute the banking angle given its speed and radius of the te nzast eg/0(e)h0h2xurn?

A girl is whirling a ball on a string around her head in a horiz asgf +q04ateej p-,2o *,icbxontal plane. She wants to let go at precisely the right time so that the ball will a,egb2*sa +- of4,tjiq0ec px 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 Ead3w6(q)vdvymh atcw)7 g mf2( rth? If so, how large a force? g 6m cvw) h)t( v2a7wfydmd3(qConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would tj-kx3tf5 q0 yz-l9a xz9+boh ohe Moon’s orbit bebf9 ajxz+-90 5l kyt-xhqoz3o different?

Which pulls harder gravitationally, the Earth on tfq89guzrm zt5v 09d v3he Moon, or the Moon on the Earth? Which accelerar5 t89fz dgv 0qv39zmutes more?

The Sun's gravitational pull on the Earth is much larger than the Moon's9kr*n j)3;tj;x qwj fd4frd1x. Yet the Moon's is mainly responsible forxx;)qr1jnjdd*fktf;3w r j94 the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the polekaj) -qh/ep-t *j *rkgs? What two effects are at work? Do they oppose each othjeq/**)g- hapjk -k trer?

The gravitational force on tjc0fnj4g*ghe ,4 yw 0t2*bxpv he Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’ , tpj2f44v n*bx0yg*ghe0jcwt the Moon pulled away from the Earth?

Is the centripetal acceaa 48wx:u +yayleration of Mars in its orbit around the Sun larger or smaller than the centripetal accelerationa8+4 xy: yaauw of the Earth?

Would it require less speed tfq rlg2) fud*sxwt.0*.,qgf co launch a satellite (a) toward the east or (b) toward the west? Consf2w x*gu tq.fs0.gdr)cql, *fider the Earth’s rotation direction.

When will your apparent phrf)) :qp4byuz3,*lq zeok(l(zv u 0 weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (leq (f:vzz(r)lo *0uup4) phby,z3qk d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer spacg46 zc*oy3p )dpmavghd7(u l; e could be adversely affected by weightlessness. One way to6 yd)pmv ;u coa(zgh4*3 7gpld 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 gravity you can think of.

Explain how a runner experience7 e/oie1qhx4rf zs;.bmzd8+rx* 8 pjes “free fall” or “apparent weightlessness” between stepipdhje+m/4 b;87qo18zxe.re z x fs*r s.

The Earth moves faster in its orbit around the Sun in Ja)uvd zhg kg)r6*y(c7p nuary 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 plane of its orbit.]vd(cu7k*gy) prz6g h)

The mass of Pluto was not known until it was discovered to have a moon. Exdv 7;o; hb-zjc4k*epaplain how this discovery enabled an estimate of pa;vc7 -d4* bkhe ;ozjPluto’s mass.

  The Sun's gravitational pull o-nl i d7e ;(q5o,m0oc gonb:ld7o3q edn the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of lbn enc5qo(om,7: -oq dd oei;gld073 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 jp9-ru qb kgxkv:a7. 87q, t sfw93skn1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 the Sc*mhv64 (yct dun, and the net force exerted on the Earth. What exerts this force on the Eart*mc4 6htyd(vc h? 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 rotatdm07 b9 8ygnzz1+qnnnv;y. apes uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calcnd0 n7+q1zb 89nyn.z y;apvm gulate the speed of the discus.   

  Suppose the space shsunk9uylhn* 82k) )ptuttle 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 8usy* ) nh9 tu)l2kpknin its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of 4 ljs0skbym70 the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolub0 ms4sjl y0k7tions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end ofb;5,q4 spqlin a string 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 s4q,npl 5 iqb; 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 can round a turn of0 5h az2m 31g0zmy fyi2,x0*)han (bjrydwijv radius 77 m ohz0rf i,)mz*yxynyw v2 (m3gdi0ja205hja1 bn a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static f8mbchd):mi n:hr;y o)riction be between the tires and the road if an::)b;orh8h yi)m dmc 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 desig0+upiarmy g3 9ned to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by theiga03+y mr9up trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a ro3zr q : i(m6(cen(*qfzq/r tjdtating turntable of variable speed. When the speed of the turntable is slowly incre:eq(r6mfcq tzj/ rn( d(i z3q*ased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down atgtif-r9;*ffh the top of9fi*f; g-tfh r a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (incim-j/vsd7l+z luding the driver) crosses the rounded top of a hilllmzv+7is -/d j (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 minu5)jhk7 eylo9q 1-ogz mte would a 15-m-diameter Ferris wheel need to make for thk ylmo71gqe joh5)- z9e passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. A;-o3z4xpa*8xo xjrgk t the lowest point of its motion the tension in the rope suppxzp-k*agxo ro3x j48;orting 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 0l(8reuue/l8lhm*;yl8w ri zvd4 o.ga centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accegeh ulzl8i8ro u;8l4d. * (yrew /0mlvleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peoi attq-q j-3*hple are rotated in a cylindrically walled "roomtq i*-thaq- 3j." (See 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 rotated in a circle on a frictionle cj*jer p6,sm, pbu((dss air-hockey tabletop, and is held in this orbit by a lp,,us6 bp m(*rje dj(cight 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 okyd,ev ep3:cq2 +fn1s kiu20this time, by not ignoring the weight of the ball which 3dk:nof ci,vs k0+eu 22yqe1prevolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is9d94fkjl+h b)ejf n-gz z d0x2 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 massel ay6j1r* vjgu,. wnk/s $ 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 e ppo21+ l.zxgqvasive 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 tangenhs (vl1w07srcdj:o0f xv1 pc5 tial and centripetal components of the net force exerted on the car (drjp 50(w1shf:x7o0 l ccvv1 sby the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, goinw1bf zo.z) l:(mxwx x0g 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 t0l)zb:x. 1m oz xwfwx(hrough the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a partioeviw0v3 az2 iym.1ezqey2) 1cular instant, its acceleration is 1.05 eiam)2 vy11 .3 qziwzvoe e0y2$\mathrm{~m} / \mathrm{s}^{2}$ , 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 gr5v /ipa) kqv4sewes7+avity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 135s )w4pv5+ e/avkqes 7i0 kg.   

  At the surface of a certain planet, t1,cb c 2l8spqf*3ymff) p:gddhe gravitational acceleration g has a magnitude c:qm b8lffd1)fpdcs* py 23g ,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.- it e2) kpwah b;l2q-nyx;3cl The Moon's radius is 1.74cbakeq 32x ly;);twip2 -h- nl $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tqbgr(b(+p5h :td :g 2ulxch u1imes that of Earth, but has the same mass. What is the acc rp (+t gu2dgql1hub(:hx:5b celeration due to gravity near its surface?   

  A hypothetical planet has a ma44du).nxj1, . uk n)njk ycgxqss 1.66 times that of Earth, but the same radius. What is g near its surfa ,kcyk4. x)njdu 4njxqu n)1g.ce?   

  Two objects attract each other z;4ec1nuvyn.2 p)h mr 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 effectie 4va0p50:ox rztou 1gve value of g , the acceleration of gravity, at (a) 3200 mg0opuzra 05e xo4:1vt    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside l(6iwahq)kcw6v9*n u the Earth where thegravitational acceleration due to the Eartiwu(c n)k w696vhqla* h is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times thev mi39al43f ii3;y tn/fv)nty mass of our Sun packed into a sphere about 10 km in radiusli 33)/ntmiy4f;n3 vf9iy v ta. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun b;hqqizdp trzb ;;f 4v:hb/r;+ ut is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. Whatr;tr +;bzfv pib;zqqh:/d;4 h is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel :45 8zgqna+xbcxq: b5 .mz) ssk5oyzxweightless while orbiting in the space shuttle. Your friends respond that they t+4c sz xzq n:zsaq x8:x5)bb.mgko5y5hought 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 loi*xh zr-kb0k5 cated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gr-z0bixhr k5k*avitational 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 sd.8kgt c24emdq ;a1neame side of the Sun. Calculate the tek.g 82 qd1;td cnaem4otal force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of what p1szyb z5c)/ul o)bo)it is on Earth, and thzupzb)o )1clso5)/by at Mars’ radius 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 tz9cq2l3pdmby 50 hbw o 63/7wxub t,aphe Earth and its distance from the Sun. [Note: Compare your answer to that obtdb9 mal2 06owqxhc 5wz7bp3,yt3 /ubpained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in bia80-y;miw.yxk( hr iwz- d7a stable circular orbit about the Earth at a he-ib ;im kx-y7z .8 hr0y(wwiadight of 3600 km.    $\times 10^3$

  The space shuttle releases uu/lhja1w) b 3ms;6bd a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relatjam/1sub lwdbh u);6 3ive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaz.5c39rm wenndi t9s-ceship 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 needecs9 5z -rtd3w9nmi n.ed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it take5xlsgne 6il;- ymnu3/p :5ikxs for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellik;m6e:x/-psng 3ilx5yin 5l ute?    s ~    min

  At what horizontal velocity would a satellitswb6waagv/ (hmie.o,c4qet5u42 m8e e have to be launched from the top of Mq5e./,uww e 4mso2batmi4e h(gavc6 8t. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued t c*r,* c/gju) lpmpty;o orbit the Moon at an altitude of about 100 km. How long g c;)p*lm,/pjrc *yut did it take to go around the Moon once?    s

  The rings of Saturn are composed 6pw cvtsjf4fc+q. **wof chunks of ice that orbit the planet. The inner radius vjsp+.ctc*wfw* f64q 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 once every au(dj d.nsq8 715.5 s (see Fig. 5–9). What isn7d qadujs .(8 the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cfz p rh 7o5x.7(sa v)imy7, syg32oiucenter of the Earth's Moon in a space vehicle (o7v7 c,ioyxy5h i 3uma.pfs) s(2g 7zra) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system conuq6 +rn(9ynlw , dm3vhsists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What (3+,6hqrvly9 mnudwn is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg wom 8k:c1f pi+ -iz8rlwczan in an elevator that1 c8l:+ ck z8-rfwizip 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 nw7q2)6zlfde of an elevator. The cord can withstand a tension of 220dz6 7qfn2lew ) N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite or. 6n n6 iyqd4rlv-ha v+pi8j7ubits very near the surface of a planet with period T , the density (mas 6-8j npdh.7vuy avl+r4niq6is/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 Mo--b8/o 4 cziov8 ikx(i(pab rnon (27.4 d) to determine the period of c bior4o/ -a -x8(iv(i kpz8nban artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred.m0m8+5atm2a2;hs zhwqq yr: h pw; kd meters across, orbits the Sun like the planets. Its period is 41w2h 8;.2hm5ktqyw;h0pzq:d + msaamr0 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagemr/bx2 j-w/d , nnch:q 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 comes very close ttn75+e g.a.y-/psko gc mka zkm2hc- .o 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 fart/ a t -k.zhc5n2 kgemmac.o+.k-gp7sy hest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxjpfr qt7w 8oa*6.xt:2sq3ugrfr 7r s/l +n1twy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 thps,6cpxh9 0zb:i u2(nbdao (y e four largest moons of Jupiter (those discovered by Gapnh9x pz(s oyu:a206( bb ,idclileo 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 kp:5w 0ag 5 cv1yq vxs5p;hk8dpnown period and distance of the Moon. q0;pxhg1k y 5pc avd5 pv:5sw8   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kdt q9: xxh w+np)dvs+1x +ud9zp fs9du a).a;depler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tu;d19 +n:aadhsd9xz)q) +uvxwfx+ 9sptpd. d able.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt betweer9)k:h cxfd2m n Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once okhf2x mc )9r:drbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet.mabn ) ot4 ;oig0bvz8" 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), g o84bazb) tm0;.niov and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hqx 6e ypogxkcm7f k6h42,m/ rsmw7)0ganging vine (Fig. 5–41). If his arms are capable of exerting a force/g74 kqo2ms6c06yfr 7kphwm,emx x)g of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleratim;cqi9n.af b:yso ;b 8on of gravity be half what it is on the surface?9acbfsn q.; :myi8b o;    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cir;i gy 3vbv.9ptb(zc8rcle 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 anothe3vy zr9pcbv i8;t(. gbr?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelc ub8t ft 5 nvt),ge yyy7 aj2v6;-sgkx4q,4jleration 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 y4u;5, q ttgen,cg-fkblxy 264ajy vjvs7t )8of g is this?    $\times 10^{-1}$

  At what distance from the Eartku x+irc 35 h,nvp9c-th will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull ci-vr+ h59,x untkp3cwith equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand jik rk54ol0p+on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which ri pkj0lo54+k direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about itzxoj 2 cucxhe5.4;uz(nh1 ,los center (like a tubular bicycle tire) (Fig. 5–42). The o nzxe(u.z5 ;c2j 1co4hh l,uxcircle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43)l4jh .ea63tit .
(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, thq: jxv1 da8s6fe acceleration due to gravity at dxvq68sjf:a1 its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is dee *uku:t 4uuo+.h c*tjflected from the vertical by an angle . ueo 4uh+uj:tcu* *kt$\theta$ 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 babs)dr n0.*r6mpmkfh*cbbz , 8nked for a design speed of If the coefficient of static friction is 0.30z *rncm f0b8k) hs*6b pdb.mr, (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 k/zu:hio8n5n(b 0m am that objects at the equator w5nai z mm0nh/(:kobu 8ere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance aparto b8 lgm t5 4+dglb2grg32b9paa38ge w 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 235 m.fip8bu hqrkzk636 bzi9 14(zm A lamp suspended from the ceiling swings out to( b i361q4fmr8 zhpu9 k6kzizb an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive a r ootoa*+mgats01n2:( hpwx)s the Earth. 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. Calculate the number of * ar o s)o2ntt:wp1(hxog+a0m 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 H 5i4l *pf 9o sh)ehy:kw+0sqrhubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that ishqw *ys)ke+: hoprf0lh 594i t 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 h/4qmfsdl 5j3lill and valley shown in Fig. 5–45. Both the hill and valley ha3fds jml/45lqve 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 A?

  The Navstar Global Positioning System (GPS) h:3pwnz3 z*r xutilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of eachxr3n3z :*h zpw satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after tr*d z7qwavm 5yf mi.91qaveling 2.1 billion km, is meant to orbit 1z. vf9qmdqi 7m5 w*yathe 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 satellit ri( gi4ks8o+s-+lvvhe in need of repair. You are in a circular orb4l(sio vkr-ig+ vs+8 hit 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 ydr xcp6jb* wwf 0 h71ob7(mxc +sr:kh;ears. (a) What is its mean distance from theo1h6fs (xdc;wkr7b:cr 0 pbhxj mw 7*+ 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 *jsggf0f4f5 c )8obln G would need to be if you could actually "feel" yourself gravitagj0f fs8b)on*g4f cl 5tionally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of t:fh +pyjz24bav+c 6mdzlnvgi6 h4:2fhe Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the centepn+ a42 4+l2:hzivz myjffd6gbv:6 chr $ \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 n6-bra0ow8u5q 1m(hg rqs , nxpeos39of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom bm-(9wg1ns8 6quo5,pxrosr 0qna3h eside of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth d9 dq(y,bt91kgnftvy6*i3gh $ \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 secong w*)m* nijzwb-(az )hd hand on your wrist wat *bz*w))-zwhagm ( njich?    $\times 10^{-4}$

  While fishing, you get bored and start to swy(edn 2vi.t fe7.*4k -wl pbrhjpk y2*ing a sinker weight around in a circ.ehyv k.- dnb4ptr le*w*7fikpy(2j2le below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so aa sj9 364sqg 3vasym7wcp;1 uthat a car traveling at ;a9v6jucm7 pwsqsyg 3sa a 143speed $ 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 nehhd f 1zha,wh )x5s ab0eg--5zgotiating curves. The angle of tilt is adjusted so that the main ) fzeh5- hzbx,1sa- ag5hh0wdforce exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$