Sometimes people say that water is remove8k;l6lngtpvzl+ ,+ ru d from clothes in a spin dryer by centrifugal force throwing the water outward. What is w n,ptg+6+rlu;8 lvklz rong with this statement?

Will the acceleration of a car be thllccg:v o7 *e* -rg0mumt)1woe same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? m0o*lemgc-u r*ltv: ) 1g7wco Explain.

Suppose a car moves at constant speed along a hilly road. Where r 90vv9av5vxodoes 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, (cav0vv5x v9ro9) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child rin n;:yz8(b ip25a m oyt/*;lc3y0plrhlru )widing a horse on a merry-go-round. Which of these forces provides the centripetal acceleration ofip au ;:0ht2yyc( 3/l oilb;)8ynnzmr5 r*l pw the child?

A bucket of water can be whirled in a vertical circle w m/f) zb5d-hucithout the water spilling out, even at the top of c -m hf/ub5)dzthe circle when the bucket is upside down. Explain.

How many “accelerators” do you have in : uy/ c17tabopyour car? There are at least three controls in the car which can be usedcbau7t1 p/o:y to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a s8vlw8*-b kr fxmall hill, as shown in Fig. 5–31.*b-8flkrv x 8w 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 decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a vx.2ihm xd81 uz7 swd3t4erk(curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking ang f/)may- pn;kxle given its speed and radius of)-/ m;xna fkyp the turn?

A girl is whirling a ball on a string around her head in aqq vryn2)uyy;,w5 q v7 horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. W;v qy7 ry5qy)uv,qn2w hen should she let go of the string?

Does an apple exert a gravitational 6gw8uzkcp ,s0force on the Earth? If so, how large a force? Cp 6suw,c0gz8 konsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wb 4-,msciza *eays would the Moon’s orbit be diffeamszb4i*c-,e rent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon 7 8c, m9dkgqvli:x+q jxb2p+o on the Earth? +v,xx7qc okglpi+j:bdq298m Which accelerates more?

The Sun's gravitational pull on the Earnoa jzi4v s5./th is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explainj/4 .azv5ni so. [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 poles? Whatibh4 rnb6 yz7q)un1 n3db4 y7l two effects are at work? Do they opposenbuy b7n4 id y1z7)4b6lq h3rn each other?

The gravitational force on the Moon due to the Earth is only about half tb+c; wrzok; 5rhe force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eak;rw5b rc;z +orth?

Is the centripetal acceleration of Mars in its orbit around -ncal*g)8lhvbr . -j xthe Sun larger or smaller than the centripetal accelerati.r-l*vanc-blxh j) g8on of the Earth?

Would it require less speed to launch 4rtc- vt7o18e wx9b-0j:j: xtxaakiva satellite (a) toward the east or (b) toward the west? Consider thecxxivtt :-:9 kat wj 07rvb1-8x4ajoe Earth’s rotation direction.

When will your apparent weight be the greatest, as measuredfg+8s bx,-h tjds: 0ic by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free:t8gs +0fxisj-h,db c fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in ouoawqa4 :7oe6x ter 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 forcao aqx:674wo ee we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” vd../uq)d( u r9-ue xtxm4c4v h0cyrmbetweend/uchqdx0t.v y.)ce 9v-mrm(xru44 u steps.

The Earth moves faster in its orbit around the Sun in January than in July. Isn6bpm x, s)0*oscjdh0 the Earth close xj bh,)dc 00pmo*ssn6r 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.]

The mass of Pluto was n6i:b .h a. *smggtubn2en1m30iicm( xot known until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s m1n:xu.n.gbgm ec 03aismb6it* h 2 m(iass.

  The Sun's gravitational pull on the Earth is much larger tuq0m*1b9j wj;e s yyrm6we93yhan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull fromr6wywbej93syyu ej m ;1 *0q9m one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane travelinz*8iw/mg )sof4vqd( * fs ;kjmg 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Eili)3yn s3t;k arth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is tl3i nyki;) s3a 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 /mw 7/hct ldokj.xs0v rvm 4e;y a-*b6N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus. 04detmr vyam c jox7s hklw -6*b;/.v/  

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and l3-i(unh0 b 73z*.bhywz yeuycircles the Earth aboh.ue wn -b*303y ihzuz(7y ylbut once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of (+ feea1g 0/i7qmnx,c:wd yq vclay on the edge of a potter’s nwydc0( : qeei1qgma,x f/7 +vwheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revol qcvf jo1t1)u+ved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If itsq 1+ fc1u)otjv 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 canfk4 9*pxa6gnwb) 9wnb round a turn of radius 77 m on a flat road if the coefficient of stat a*n) p f9wg6n9xbk4wbic 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 friction be between the tires and the)a o4vmhsxa c9fk0,5s road if a car is to round a level curve of radiusmxks o04f9s cv,a5 ah) 85 m at a speed of 95km/h ?   

  A device for training astronau yn8ojsx) :067x 3k7dyzumuf ets and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how mxjo 7s )nu3k x6ed fyy708:uzfast 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 11.07mb /58 nkivh, yabfd, cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the ckvby 75, /nfdm, i8abhoin and the turntable?   

  At what minimum speed must a roller coaster be travelinec ,3-it/o0te12njs-l e :bqcb lrl8lg when upside down at the top of a circle0q3cj1:tsn e- r elb8l -e toci2,/llb
(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 (i7j+7z w) poohpncluding the driver) crosses the rounded top of a hill (rajwp h 7)p+7zoodius =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 a6v8 uuyt.vlil1u 1m z0lyw5x9 15-m-diameter Ferris wheel need to make for the passengetm90 .u x6l iyyllu81vwzu1v5 rs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg ipv(laq8k,/r 5vzr q k*ch96ivusf :0zs whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rop:8 v6/f svzk*q,p rh9lrqakc05vuiz(e 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 r*mg-ioc 0*; seokd u7iotate if a particle 9.00 cm from the axis of rotation is to e; ied0c o m*gosk-u7i*xperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "sejv/a6 w2as 1room." (See Fig. 5-35.)a s21vaewj6/ s
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 frict r s28:wn49ckza sp ft/3ieo(sionless air-hockey tabletop, and is held in this orbit by a ligh4es z /2 kcsrn9s(ti:3aow8fpt 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 , precisrpze06 +tkjg,ely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of zg0trjke6p+ , $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travel+ 51 )knnyo3tce 4pupding 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 7zmax 4 cxr3h($ 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 diving vertically at9x;18/a hz7 pvnmsswz 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 centripetal q vm *f;oh7t,kcomponents of the net force exerted on the car (by the ground) in Example 5-8 when itsf*t;ho 7mkqv, 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 uniformlyj4-i 10camt) jx gzi0p from the pit area, 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 cp maitj zg-)ijc14 0x0onstant 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 m66j(zfjml5 ssty -qe u*ynf6 7 . At a particular instant, its acceleratio6n5 tul6jezy m sy fsf7j*-q(6n 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.nz- 7pa gwo3 nkt6+ef Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 n.g-w6 kptna3f7 oe z+kg.   

  At the surface of a certain planet, the gravitational accele 1n0 5lecu1ey(rj f dw0bre+)w3doj:cration g has a magnitude of 1:jor0e3fc( 0re y+ed5 jn)dlbc1uww 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 tnhfg43)vzpk 8 he Moon. The Moon's radius is 1.748pz )3hgv fn4k $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hayyx8ql5. 0p)c mc9)mr muqj6vs a radius 1.5 times that of Earth, but has the same mass. What j y ) .ycur8)v xm5pmqq6c90lmis the acceleration due to gravity near its surface?   

  A hypothetical planet has a mxzfgb(5 ox(tiq7t1 89caf ns;ass 1.66 times that of Earth, but the same radius. What is g near its surfacef toagx(zs xt;c1i8 5bfq79(n ?   

  Two objects attract each otherv55)/6sl6q3j a.j v8auflqfh h 0ayjq gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acce 5 vghhuw9it(3leration of gravity, at (a) 3200 mhwi vhu9g3t5 (    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centermcfm1ty hq/yr /7;u)0y(hcw t to a point outside the Earth where thegravitational acceleration d1t hh)y;t(fmw7yccuq y/m /r0ue 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 packedc /wcq sw 2+h5iia9.lv into a sphere about 10hi .sw li59cvw+/2q ca km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once1x x8 bc( nup0q0o(qoe was an average star like 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 surfac0x8bx 1o qunpc q(o(e0e gravity on this star?    $\times 10^7$

  You are explaining why1 d 3v1nkoj5ja astronauts feel weightless while orbiting in the space shuttle. Your friends reoa1kjn3jd 1 v5spond 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 ar.6rsj5 lyh hj0ygd0o-*t8 grsn m--oh e located at the corners of a square of side 0.60 m. Calculate the magnitude and direcgs gm ythsj d0-0l-ny. h5j6-hr8oro*tion 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 fpgqgg/*9 cf ;h g2u0m9 y.v)cdep wd.the same 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 uhg9 fdf;ymgdq p). gc./2we9*cvp g0(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 surface1p.fir 8/hlaj mo28w f0qz)l f of Mars is 0.38 of what it is on Earth, and that w8h.z2 pr1m ajlfl80fo)qf i/ Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usingm0 dg5ar(uk5xm : a,0i -l7h( rmzrjvl the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Ke-(m ul, z70air :j xh0r(k5rdglvm5ampler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about )p:eho/n pm2mthe Earth o hnemm) /:2ppat a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circula+as bi2 k3syx40pmlz8 r orbit 650 km above the Ea4380b +pai sl zmky2xsrth. How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship roqcck/hbg1 *u-tate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one k*b/u1hcg- c qrevolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Ear*ctakj8l;k g1(y ( *taju (nlhth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surfaajn(g( *1 ct*;uk ltjalkh8y (ce 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 msarpu(pck 72ojf5e8vz9 :,k have to be launched from the top of Mt. Everest to be p:p mazok,5pu2fes97 8v j(crklaced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, thhdn.y/ c.po0a6d9l qe e command module continued to orbit the Moon at an altitude of about 100 km. How long d9a 0hln.qd/oy6dpec . id it take to go around the Moon once?    s

  The rings of Saturn are com1 ijma07f0b73 le hevki u+m(tposed of chunks of ice that orbit the planet. The inner radiu 0uifl3b7v(m1e0 7e m+h tjaiks 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 diamet+yhr a)6/pg ijer rotates once every 15.5 s (see Fig. 5–9). What is thei /)ga hrj6+yp 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 wei: hdel4f:m b+sqq8+m ught of a 75-kg astronaut 4200 km from the center of the Earth's e8: +fq mh+s4:qlu mbdMoon in a 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-star system consist fc5 cfd/t+a;os 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 is the mass of 5af+ tcc dof/;each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator th;hs z 2 -brxo1z3+qtbwat moves tzwrsb 1x2+ -obhq;z 3
(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 of6(xi-d am f rmtz(15jx an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accelerat(d5 -rtxm(1a jfzmi 6xion (magnitude and direction)? a =   

Show that if a satellite orbits very near theybh d;b;.ymn1 surface of a planet with period T , the density (masy.y;bnb1hd m;s/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 q+ .vb0q ejrs 5sslns viv140b-5;wwdperiod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very0 ;vse bjr.+wqds1vq5li-bsv04 ws5n near the Earth’s surface.    s

  The asteroid Icarus, though only a few 1 gq :fs3zu; h-b4oogahundred meters across, orbits the Sun like the planets. Its periodg go4:;3-u1bzqfh aso is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averaglxy (mb9 kg7):w vrl0te 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 yea qf99bj,b2rb 3 jqmb6j;)lpzm rs. It comes very close to the s)qjj639 bz,9fqmm;blrb2 j bpurface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of v *oxt.gg0+i/nbg h w*8gqkk9the 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 ( r9zt dtbmw;3largest moons of Jupiter (those dis ;d9b mr(wtzt3covered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of u pl43vcv825vwpppvhn w-9n:po:: wathe Earth from the known period and distance of the Moon. : c 2- 3lovvp:4 :wanwvw58up phnpp9v   $\times 10^{24}$

  Determine the mean distance from Jux wqpehd(2; cv j/s: i;cts04s8yjq2 jpiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods i24jc8 x; ( qhtwceqss2jsvp ;0:dj/y given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between M,9f;2r s n1zj3jql9eccnct imm ;r7)vars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destrs jrt m97f )cj3i,9cnnm;r vz;qc12el oyed).
(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 ok.h: eo7l*sg-x :gb v6qij vq4f 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 t:g:hog -sq7vk4i .qex*b6 ljvhe 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 by swinging in an arc from a har xq6k5ob 0c3nnging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long0 o53rxkncq6 b.   

  How far above the Eab(-ny*f/fk1 ux5rk o jrth’s surface will the acceleration of gravity be half what it is on the surfaceon1 f j-y/rkf5xbk *u(?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands azokf5w sdvqz/e /),yjf m- -*mnd spin in a mutual circle once every 2.5 s. *v/ de)ow z, mksy-zjff/mq5-If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratihuypa*7cr cjja;2bzw2 ;d58v6v -b unon of gravity at the equator is slightly less than it would be if the Earth didn’t rota b8 u; z*n2bwrpaach du-c yj2v65v;j7te. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travy.rf x(+sjbo8 eling directly from the Earth to the Moon experiesobyf x+ (jr8.nce zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scalercv5ea0l( q6q6.f 8 vb ilqd)a in an elevator, it says your mass is 82 kg. What v)i5q0arb8l qe6l a (vcq6fd.is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consis k dv8dqgp9x-:r*str5 * x1srsts of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotatipr- d8 ds vx9xt*1rs5:s*qrkgon 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 n4kv; kp1bc1 w;sw1vv a vertical loop (Fig. 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 mass of a plafzkp 6zktuy7x1 4 rd/:net in terms of its radius r, the acceleratiktfx yr41 z/dz6 kp7:uon due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanrtmkg98 ;dw .9a,ek3s h( cjksging on a string) is deflected from the vertical by an angle9;mc wak8r3k .(s9 tg kd,jhse $\theta$ 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 f pne)xw ;-e xb0:0dqdcoefficient of static friction is 0.30 (:qx)be0;dp w fxd-ne 0wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the9ho7k3+heciw d t1m7 j Earth were rotating so fast that objects at the etm7w1ed+73h o cj9k hiquator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a confo2o .;/csa6t :o bzaggmi7 d4stant 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 speed rounds a curve 6vy g)-5 gta.s xx s9xb5,hrreof radius 235 m. A lamp suspended from the ceili9ex -txvghg,r ).b5 y6as xrs5ng 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 has been claimed th;fysh/ mfrv+jg b8 ;j0at a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =h r;;/g b yf+sjv80jmf1.9 $\times 10^{27} \mathrm{~kg}$ , 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 Hl ): lh*iw6u8epun:joa,+ o iiubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense tha:ol +ilwpeni,:hj * u6oa8ui)t it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and v:z7h qnput9 )jalley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) :tznj9)p hq 7uHow do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group osdam.ys m8tic. 88l (af 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 altitu(a.c m8.y8a i8st msldde 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 billion v6*t j edx2bs:km, is meant to orbit the asteroid Eros at a height of about 15:6 vtdbexj *2s 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 of reu:ab-f52; 6of-vciv9e3kqxzdt cde9 pair. You are in a circular orbit odqo -:ftuk 2c6eib9-dcev3f; 9z x 5avf 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 p b,px io-edn.v 5 g426ynls*wleriod of 3000 years. (a) What is its mean distance from thondg *v - w2s y6ieb.,x5n4plle 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 izsz);hd ;fnza:c.v 2df you could actually "feel" yourself gravitationally attracted to someone near you. Make reasof:anzz;hc)s2 dvz. ;d nable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center oh s ig7a;atfm9+8a 7jpf the Milky Way Galaxy (Fig. 5-46) at a distance of879pfag hi7st+m;aj a about 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 0.50 1ql wzqqju.pg( m+tin36; 8g8bi n+ewm on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of6+ mqt3 bpu(nn18+qwl;z gi. j weg8qi the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eartcox)sy)l8 8*dnj k rj*h $ \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 6.aappt3ynbde1a :g q bd7,: eof the 1.5-cm-long sweep second h.n :3yd q 7p6aeged1baap:bt, and on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and stz6 h3klf kt1si +- egzee:2vk.art to swing a sinker weight around in a circle below you on a 0.25-m piece e:e 2k3kev 1s+l6-h zgiktf.zof 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 radius17r e(*fff,mvg2o - drw lew2s R in a new highway is designed so that a car travelwsm-v,fl we(gr *2de71of f2r ing at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiati)b2*ky/shqgu ng curvek2/*)qyh sugbs. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction 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.$\approx$    $\times 10^2$