Sometimes people say that water is removed from crd3 e (v*aufd7lothes in a spin dryer by centrifugal for(3e aru7vd* dfce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travelsew/pnvfs3.n*e: 6iqw wwx fd3 ,l n.:e around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same ewwnne/ *x36ql3f ,f:.pnd. svw e:wi speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the e*qz pewd25w9 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 the bottom of a hi9ew2w z e5dpq*ll?

Describe all the forces a(brv5qm 1 n: ke1haf2 ywgww;/xw g8,ecting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration(geanrvbwk/xww5wmq;1 fg,1e y h:2 8 of the child?

A bucket of water can be whirle4e 6eh-3w7a k,.6okexhn hkb od in a vertical circle without the water spilling out, even at the top of the.w3 -7kh4obk nhxh,66oeekea circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leastlw3p4ybe mms+l:6o ,u three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they sue:my63+lmlpb, 4wo produce?

A child on a sled comes flying over the czy ude:pag detb-kn (.t- *24frest 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 hit-n. gf k*b(4aeyze- ud2pd t:ll. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward whe.onm:c ;sis 3x/.qwrfn rounding a curve at high speed?

Why do airplanes bank when they turn? How would you comps(do(h-d b id3ute the banking angle given its speed and b ds- dh3(d(oiradius of the turn?

A girl is whirling a ball on a strinu ,(-j,ivvtls1v0 o w7fii0ztg around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will h,s lvi t w01jf7-(ui,v vitzo0it 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 Ea0 qh5 i)e cqre3z(vc2qrth? If so, how large a force? Consider an ap cve qh023r5)i zc(eqqple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s or + *;5yhznh (f2y1w sg(dheglebit be differeny e5( znlg2+ys;1( fw*dhhge ht?

Which pulls harder gravitationally, the Earth on the Moe-ssi 6(d* x858fwmg yr/hj ugon, or the Moon on the Eajg5fxr-sm /dh8i6g 8we* u y(srth? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the) 9zdex,j lf1u Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the xj u1ef)z9,ld difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator ormf*ea+17odv+z3 sue e at the poles? What two effects are at work? Do they oppose each otu*7e zf 1v++3so meaedher?

The gravitational force on the Moon due to the Earth is v d) *8ej ,5xv7xqfev;kyqn 4nonly about half the force on the Moon due to the Sun. Why isn’t the Moon vk; qvjf7* yvndnex,qex8)54 pulled away from the Earth?

Is the centripetal acceleration of Mars in a pbwwtw5s)(l/ 3q-gvh2p b:iits orbit around the Sun larger or smaller than the ci glwbb-(phwpt2v/)q: 5a3sw entripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (bjtv)fr hpi1a l8-1+bvz m4 m+m) toward the west? Consider the8zf+j) ri1h- 4bma1vl mvp+ mt Earth’s rotation direction.

When will your apparent weight be the g-5swe.z zf jx;4.hhlrd e97enreatest, 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 woulz.ejs5rw ln.x-7 zh4 9eedf h;d 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 *m245k 9cnot+i xh ;kkduo8bvperiods 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 fmi nkxotk+8u; c b24h59*vkd oall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner 3gsee dmq2 .zi9 g4;izexperiences “free fall” or “apparent weightlessness” between st.g42; ieg3zmzdiqse 9eps.

The Earth moves faster in its orbit around the Sun2f r8kyy) k;rm in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much oy) kfymr r8;k2f a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. E 5oa6fvk33 wxjxplain how this discovery e3ov3a56jfkx wnabled an estimate of Pluto’s mass.

  The Sun's gravitational (1qen 7xfk:h +;-az oz/ njcjepull on the Earth is much larger than the Moon's. Yet the Moon's is mainly respo/h; f zxkn- a7jjco+ n1q(:zeensible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling w ,w9 lu)cb)msn5n(i e1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orb8yn++6 izn uaer l+x0iit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle ofy + ix6un8ein r++0azl 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 2.0kjai u+.4w8 gs-kg discus as it rotates uniformly in a horizontal circlw. i gs+uj8ka4e (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shutw4( cwhcj2ebj;8 sye2b/cls0tle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravita0b/elsbw js2ejc( y whc84 2c;tional acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleratiou27 w lkwxv3/jn of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revoluti3wwu v7kxlj /2ons per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolf.l5o 3 sin q- jj99e+oz2ceo:k-dcozved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig j-5f -z:io nzeolok 9 +csjd2co.9q3e. 5-33. If 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 os 7(qg2c;gvk speed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is thv c7ogq s(2gk;is result independent of the mass of the car?   

  How large must the coefficient of static friction be between ioq jumv-/ i (ivo.z07the tires and the roa7.vimuo/zov - qi(0jid if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training q9tluif*4 lm t(ah 2y2astronauts 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 w2i(ut*2yqhl la fm t49eight, 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 r(9a 9adj9s ay,x3dkoc otating 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 coefficid9c s,a aojy(3 axdk99ent of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be tb:;o poe9lol1b1s 0wtraveling when upside down at the top of a cir10o1e;ow:9bbotl ps lcle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the3w31qbu 2 e y dx4q(o*hak*hyu rounded top of a hill (radius =x3 ah*o *uy (wb2qdyk3u1he4q95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter F) +5tn- 0g6 zc/gnqupteyf w(zerris wheel need to make for the passengers to feel “weightless” + qgp60cz-ze/fuynt( ntw5g) at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circleppxdbf4;,y 9t of radius 1.10 m. At the lowe4p;9 dy txbpf,st point of 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 a particle 9.00 cm from the axis 9 y4 75rx p1ktsm nr9:ctxub3cof rot xs9t 4y9xtnr3 b5:7cc ur1mpkation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at aaybqj22 33i owbsd -d az7 20c3zylbu* carnival, people are rotated in a cylindrically walled "room." (See Fig. 2bcb2zyjy*du3zbol0- aq3a si 7w32 d 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 frica)y-sm6 jwm*;phmeo8 e( pb(ltionless air-hockey tabletop, and is held in this ohm-m*op(je)amb6p( l 8; es ywrbit by a light 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 this time, by not ignoring the weight of therry(l :,nqgc) ball which revolves on a string 0.600 m long. In particular, find the magnitude(qngrc, rl) y: 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 is perfectly banked for a car tra d : m2.ljvzx9luixot-7, ux:aveling 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 masse+bq : ylbu9o5 nmv9ka6s $ 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 at 310p/:vlcjxym 0tgoqb n3+gg:u ;), j;pi $\mathrm{~m} / \mathrm{s}$ . 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 a4v7iwife(t2j m-z0+xe)t o kgch y6i+ nd centripetal components of the net force exerted on the car (by the grmv4t+2( ho-cgeijzx 7iwy+f6tke0 i) ound) 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 thexvmkhs1q5/v t; 8 t5ff pit area, going from rest to 320km/h in a semicircular arc with a radi fkx1;t5s5 8vf/m vqhtus of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular0x f 4riosd+axkt ba1 a+l mhd,,39jp2 instant, its acceleration is 1.,fmhdop+ab1k 9x d l,s+ax2ij3t0ar 405 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 spaceequm2 alytz4g7 d+1j (craft 12,800 km (2 Earth radii) above the Earth’s surface iltdgaj2u m(14+q y7 ezf its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational mu25 ixfb; n,y q7ps0iyc7 9kek4 gm*macceleration g has a magnitud2y74ekgq np uk;i*yi509b7 mx, msf mce 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 radius isdi luojl8pn ,jgyf98h/b4j-8j30vo w 1.7 un hj9,ji vb 4 8df80gpoj8ojyl-l/w34 $\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 that of Earth, but has the:foz6ink/:xl.g 3hl j same massgj::.k3/z 6fiohx lln. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times thx uxyqp5t f/o/;ket 7:q-r+h rr:(ymg at of Earth, but the same radius. What ishxo;+ek7r-x/ ryqgf/u ttm::q 5 (r py g near its surface?   

  Two objects attract each other gravitational, l;h6jc0 7grkx7)sub/j zd c8ymq f:ply 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 vanrffd-z dzk5ri7+i u/sb 0;f*lue of g , the acceleration of gravity, at (a) 3200 m ksrfzb+ /0fifddniu r5-*z7;   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside 1dw*ofb8bvo1qu;p 3 xthe Earth where thegravitational acceleration dubxwf1 1b83q p;ov*doue 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 packed into a sphehunj);n, atp(muza,l;r l1 l :re about 10 km in radius. Estimate the surface gravity on this mr:hlnl( aump z)tn,,;ualj;1onster.    $\times10^12$

  A typical white-dwarf ml* p9.(,ix i ./rooeedvn 3 xpsy;e(vstar, which once was an average star like our Sun but is no re/l 3xyo;..(9 *vevi io(ep,x dpnsmw in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orfy 8;khw .,-a7cd( v+bkikies .fe /rmbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 2fbkk-r+m;7hev/8,.di( c iwys.fa ke50 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0. ea*s/;bu0 xy un pbj8p5-d0xx60 m. Calculate t;8sde0*0 upx x/ ajux5ypnbb-he magnitude and direction 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 up7x.7faazw 9oibd 7lw. on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Satuxl7 7 .af bw7zw.iao9drn, 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 unq1 ox,t5sp91p 0q-jplfu pqv;xg(6of gravity at the surface of Mars is 0.38 of what it is on Eart5toq ql9sfxgu1,p (xn6; pqj -p 1vup0h, and that 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 po8 m, 3w6- ,+rvqg6euvvzvt7ssns m9period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example+g3p,r9vzmmv 6ss8vnuqtv7w- o e,s 6 5–16.]    $\times 10^{30}$

  Calculate the speed of a satelm *f -x z.yhcb4x 132lmb jeinont6v3+lite moving in a stable circular orbit about the Earth at a height of 12mnjozy3l* n xbbex 6.t3h+i4 vfcm-3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 65ln c,m08s7qxf 9 + jp)zt8kbge0 km above the Earth. How fast must tb x8m,jpl+n9gf 8ts0 czek7q)he shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupan bf a7bel/xi q2n)ql)t0xln+,ts 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 re xb/2l)t fb ),x70 nleqqn+alivolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “ne;9-g0 qcynzprar-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared togqn- 9ry;c0pz the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be l: wv+xlnv-p9r4smd t8 aunched from the top of Mt. Everest to be placed in a circular orb pwnvrlt s8x+m9d :v4-it around the Earth?   

  During an Apollo lunar landing mission,/c1zm , j 4l+te+jashc the command module continued to orbit the Moon at an altitude of about 100 km. How long did ietmc+jj+1/sh, l4 c azt take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planei3ts:t9 vd,p epoz8k/ t. The inner radiu t tvz3k8,/ oedps9:ips 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 15.5 s (see Fig. 5–9). Wh6) c5sl os27 uyibxps9at is the ratio of a person’s apparent weight to her real weight (a) at the top, ansol x5y 7ip2u 9)s6sbcd (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of thcm6 yb*el2fxkryoz,-d gty- 8tpp 3 ,3e Earth's Moon in a xd-z 26my83pktb*3ore, pcg,tl -yfy 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 consists of two stars of equ7t. yv85qxfqx al mass. They are observed to be sepafyx5v 8qtqx7. rated 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 rea c4q .:h(iwscxd for the weight of a 55-kg woman in an elevator that moves wx.4:( ccsqhi
(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 elj9nyu +.6z-)xe ssia fevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum ac.s6usf9eixna+ )j-zyceleration (magnitude and direction)? a =   

Show that if a satellite orbteu*-p/vwq x5,g xci +kvp8u5its very near the surface of a planet with period T , tv8ig+ up/*u5x,x5 cvtpkeqw -he density (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 determi.3qom b; cjyq oj.7dwb.l8k: dne the period of an artifc dbb.q:.q; o7kjj.mwdloy 83icial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundxg16pq /ujs4 dred meters across, orbits the Sun like the planets. Iq/1jg4psu6d x ts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distal lk9g8u4 2 .gop-4f ukahz.p/uc.g jhnce 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 roughlf csqzf tz ah58m;gwy, .66x9fy once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39wa6,c f.gtfms69h; f5q yxz8z). 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 aboutl 69ux/ uwst:pl-a00u t +9v0: hampqywbno)f the 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 mas jr-*to+ phim/f(y rw)s, period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 1609)r * f-pwmy+to)rh( /ji.
(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 periodfatfp8,csc t4x-di p4 )x:oje8sqkx6 48k5gm and distance of the Moon. o 8e iak -m4s8g) pj4pfxf,8cst6c:dqk5x4 t x   $\times 10^{24}$

  Determine the mean distance from Jupiter for each ofjzs-5l,owx k7 Jupiter’s moons, using Kepler’s third law. Use ths7kxol ,5j -wze distance of Io and the periods 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 Mars and Jupiter consists of man n:t 6jh9l75kvrqs p-my fragments (which some space scientists think came from a planet that once orbited the Sn: -9ktlp q5j7mvr6sh un 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 dej4zd cop2sr ((perv3-scribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly encp(2sv r z-d3 erj(p4oough 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 swingi g/jdr(;.n( n,mjujmeng in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowes mm ,n gnjr;/e.(jduj(t 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 gravityplfkb-r07 mxx2 735t ck8 (e sc,grq wczl+kv: be half what it is on the sus7xv tqcmrx 78+-kb320z(ekk:r fwc,cpl5 glrface?    $\times 10^6$

  On an ice rink, two skaters of equal myfze8fh)o*pt . 5dce2 -1gko:q4jn c mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual m-e 4c nj1d5 ):*cy o.z8tpkgfoh mfeq2asses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparenho-*ncl32*7 z i4inde tb-umdt acceleration of gravity at the equator is slightly less than it would be if the Earth di znn-ot3cldbe4i 7uh*d *2m-idn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelin xpxx9eetg h2i zj814,e7 /hehg directly from the Earth to the Moon 4t ejhp7xix/2ehe 9 xezh,8g1 experience 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 p904k4h9 ry ikd)x7/nbtfx pascale in an elevator, it says your mass is 82 7bi 9)nk49t yf4 rxpk/dha0pxkg. 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 rotate about9 cygnn 4w5g;isazk23 its center (like a tubular bicycle tik;sw a 3 9g4y5n2zcginre) (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 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).3bphkx;o e i wd-z:63v
(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, x9sw+*3mw . qyb4s(shfujns)the acceleration due t s.jn4*(3m 9y)w+u swhbxs fqso gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) p . rddpjl ;ma2lj;e99is deflected from the vertical by an anglmpd2 el.pl9ar;9; jjd e $\theta$ 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 coefficid*tc/-qpb/p4x* :een mh7 sg-fs+wup ent of static friction is 0.30 (wet f*xsn t:bem/*/d-p - 7 phs4qp+wgeuc 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 tha2-9d+dkept 1lz8nk sq t objects at the equator were app9pk t+kzq 12n8de -ldsarently weightless?    $\times 10^3$s

  Two equal-mass stars maintain aqd/kg*ral *(r constant 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 of radius 235 m. A lamf3; tftx odd( n+uw/isxi+b5 6p suspended from the ceiling swings out to an a fxo3 tsfw6tiud/;5n i( b++xdngle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earthkz/+ylm(9ry qp;0j1 1z n yzyc. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size zk;ylc0rqj 1 zy/zm9pn+(yy 1of 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 =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the .e0aat nkd) o(presence of an extremely massive core in the distant galaxy M87, so dense that it could bekea dna.(0)o t 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 traverxbq8ra -s./ze)4mrojses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losqs 4)xr-/jrbao8me z .ing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satel4 oz) fgvh7qetjslp: w 2 .uqu8/2vy/llites 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 each sate4v :os. tjw/)quv/ezlq82 pul7 gf h2yllite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billier o9m9 m.k/zeon km, is meant to orbit the asteroid E9r/.e9zk m moeros 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 sf fi4; (br3i sl.uosi,atellite in need of repair. You are in a circular orbit of the same radius as the 4(3u;fsi o,r ifli.sbsatellite (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 q876ugos617 ke1o; +msvvdur gxw7 yoof 3000 years. (a) What is its mean distance from th1exs goq1g+7w7s6ko; 8v md7uyr u6voe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you bf3rtj(s 12 ffcould actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptf 3(2 rsfbtj1fions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way cy4 xhwc;ic h0w*lxam4k99v( mx t58vGalaxy (Fig. 5-46) at a distance of about 30,000 light-yea *x8xw(0ic hay 5lmmcc9t 4k9xwh;4vvrs 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 0.5/9, d,y.d wmfhhv./s a*x lclx0 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.d/f,9x d*s wch,xhamy .. vl/l0-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 kg8 p ndvdsqp8:082xwrmmk3 nv / orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-longub4 yb*imj+h:xz g6 tqz5f9/y sweep second hand on your f:+zbmy9*bg j4u 5xzqh/ ty6iwrist watch?    $\times 10^{-4}$

  While fishing, you get bored and st pp.v5+sq39rdo stz8z art to swing a sinker weight around in a circle below you on a 0.25-m piece rpq3sdz8 v9pso +5z. tof 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 that q5g it(a uwuxs +8..eja car travelinw8+ug. ti.uej( x5sqag 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 ca owk q3h;of6o:rs when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed6ho3kwqo;f : o 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.$\approx$    $\times 10^2$