Sometimes people say that water is removed from clothes i4 wfbi)z * 7rvv6efj 6cv;ru8hn a spin dryer by centrifugal force throwing the water outward. What is wrong with this statement?r;bhvzeuvf*rjw)v 876i64 fc

Will the acceleration of a car be the same when the car travenr/ ;*+5o 8(orysohuhcq /jfyk+g de8ls around a sharp curve at a constant 60 km/h as whenjrh h58cd +oosk(qr/uy*og;f / +8nye it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the 0 uop(thf6 f6 kahb.2zcar exert the greatest and least forces on the road: (a) at the top of a 6a6 thpf0z.h b 2k(uofhill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on rfr;j+-z7x fb 2nz7 vja merry-go-round. Which of these forces provides the centripetal acceleration of the chir7z+nf;j z f v2jrx-7bld?

A bucket of water can be whirled in a vertim,wwx,w m /nb4cal circle without the water spilling out, x/,w n,b4wwmm even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three contro *agu*bcarv9t gz,/z7j n t6o9ls in the car which can be used to cause the car t/t*gj,ta*9 gruz zo9a6cv7b n o accelerate. What are they? What accelerations do they produce?

A child on a sled comes flyingb;8 5 y /q(gl5tkfrcm8q damp; over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the gro gc;(m 8yfa5q8k;mbd p/lr5tq und (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 roullp:s,:5mhm ( h*bcmdnding a curve at high speed?

Why do airplanes bank when they turn? How would you comp:m1 3j3vkzuhcute the banking angle given its sv:3 c1 kju3mzhpeed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontp7v mjzx2z wqh;e zl+phh+*r 81 s0p7zal plane. She wants h+pzps e+ m;1hqxwl78pzh 7*r j0z2zvto let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force ou w92)*ex(0nh febuu rn the Earth? If so, how large a force? 0)bexr fu2n9 hu*we( uConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what x1kbc*c0; p xs7sl di/ways would the Moon’s orbit be differ 0x;1 sk/xi*bcdsclp7ent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the*fcwupj0 e3t av;*2ke Earth? Which accelerates wec0 tp;j*vfka2 3u*e more?

The Sun's gravitational pull o,xivx k43s rvkg q*u5i/:e9u nn the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for4r ,5vu:3n*xkqve9kii g/ sux 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 p1a pji 6+mo-yloles? What two effects are at work? Do thpayj+m-1iol 6 ey oppose each other?

The gravitational force on the Moon due to the Eac5j5h b e,dj*yrth is only about half the force on the Moon due to the Sun. Why isn’t the ,ybhc5e5 j*dj Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sunnxa.m- ewh i) pd5t6*c larger or smaller than the centripetal accem5e-c) 6ainwp dht* .xleration of the Earth?

Would it require less speed to launch a /1 v m:jf)iiotsatellite (a) toward the east or (b) toward the west? Consider the Earth’s rivi/jt f:1 )omotation direction.

When will your apparent weight be the greatest, as measured by a y02gkq 6xro5n.h 3wft scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the 60nwfok tq.2gy h5x3r same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lo c5+cswxg5o mi:sy3b5 ng periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we fwsc3 +b5goy :55xcsm ieel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betwee*)iopq i o qkl:12cbg5n stego*l2pobi:ic)5 1qq k ps.

The Earth moves faster in its orbit around the Sun in January than in July. Iel fk.;d t7fw4*wncd6 c.u* dks the Earth closer to the Sun in January, or in July? Explcwcten4d l ;dku wf.*k7 *6df.ain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was disk(l(w)w- mi yd98wbuncovered to have a moon. Explain how this discovery enabled an estimawy u8w9k ib(dn l-w()mte of Pluto’s mass.

  The Sun's gravitationu6cr ym 9 1* tuhbfnsncxt4k*2(:yn ,xal pull on the Earth is much larger than the Moon's. Yet the M:29x 6ttfhs by unnx 1,4(ukmyc** ncroon'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 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 1980 pm.2 0dtz(guz$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 j.hx yex:x(qp; ,hc4rin its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on thx(:4p q j;,rchhxeyx.e Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N . mib-ehxv;4wvpu58 g is exerted on a 2.0-kg discus as it rotates uniforml8 g.ibwevpx5 u-;4mhvy in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfr;9*m(yl 18vrmoin r jace, 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 gravitational acceleration at the Earth's r mv98 ynim*1lr;j(orsurface. $\approx$    g

  What is the magnitude of the acceleration of a speag st. r j85r0hjhoy j0s*yf+.z*nqg 9ck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if thezjjyos5yr hrq*8gs9f *hjt .0na.g+ 0 wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rapy - o/3+whe6w2/ pzutqtc3 wnte in a vertical circle of radius 72.0 cm , as shown in Fig. 5-36//uon3twph-ywc+q w2e zt3p 3. 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 speedbxe55 a8ai11yjnga-h b4y0 cd 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 this result independent of the mass of thgac yyda51e h1xn j405-aib8be car?   

  How large must the coefficient of static friction be betw 1i 3r45 k3zq4zp+vyqrb6 ssbleen the tires and the road ifvi rp5q33zsz4yb1+ 4klrbq6 s a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotaanh; **auosv;y2yw1 n te 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 s*n yvwany2 1u a;*h;oweight, 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 g *)ghan2.noiq tiz/b)jemo9l4)x 1xz2zm k0 cm from the axis of a rotating turntable of variable speed. When the speed of the9mzh i loe gao 2g4z/n0.jqnx )kz1b*)tmx2)i 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 coin and the turntable?   

  At what minimum speed must a roller coaster be traveling1 ,d9q, wg elz5oxel4n when upside down at the top of a circle dlgq1,xow5z4een9, l
(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 mass5aygkbmnj9h:(- *libv 3 ggw8 950 kg (including the driver) crosses the rounded top i5:ng mvl3(9g-8hbjwkbag*y of a hill (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 pggna ;,by 1h *-cwhb:ser minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost poib;a*wy-shh : ngb1 gc,nt?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radiziys06tf5 g:-e xh+jnus 1.10 m. At the lowest point of its motion the tension in the feynt-56zj ish:0g x+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 63q;:t yc j la*mx3riaaxis of rotation is to experience an acceleration of 115,00 6* c;iqrt:3m3 aaxjyl0 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivj j78-7hmtl:n.-jabr fv iht0 al, people are rotated in a cylindrically walled "room.0 mri--bt vjjhltn.78jf a :h7" (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 rot7m ,xhms 4+ehuated in a circle on a frictionless air-hockey table7huh4s+m, mxe top, and is held in this orbit 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, bszji za6*1rzv:e16f s y not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitu16z 16 f* irzvssejza:de 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 travelinoe/7mmdq1g0c-: uq6ppa w;xs1,l dg k g 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 +t7zk yin6p9n$ 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 divk/0rt3/o2p ps fjvgsa*:6nxo rw+.lhing vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of /ut(/yng ir3i*ti v6 tthe net force exerted on the car (by the grou it/ntryu/*( v63tigind) 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 Indianapolircg; 3:5 0e3ky zff9kte*msuus 500 accelerates uniformly 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 thzmu0 k3re;ytu* f:e k5sgc93f e 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:i8v6daxp-,d1hh,h sm hnz /l particular instant, its h6 d:v/s,zph ilxd1 h-8hna,m acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Ea zc e6 f:e54y(v)vu+u tpx3xrdrth radii) above the Earth’s surface if its mass is 1350 kg.r+x vcv3ezxedutf( 45 6yup :)   

  At the surface of a certain planet, the gravitational acg:(8q.lyw;x axx zi3sceleration g has a magnita xx:iz yxql;. 8gsw(3ude 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 Mod/4 gg4 xhnw 6sh2:fsjon's radius is 1.74 /h n6gxj shs24 4fwg:d$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiqd3 /sks*xztust5es h992w+a b e,y.uus 1.5 times that of Earth, but has the same mass. What is the accelerationwe/sts b zu9e.uqd hs53+y9s ,ax*2kt due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times 7 r1i+ mp)xbxsmi)d; ,n t:ntlthat of Earth, but the same radius. What isb +d x;mn7 ripmtlxn,i)t:1s) g near its surface?   

  Two objects attract each other grsmabsz (l/9 :aavitationally 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 acceleration of gravity, at (eyb k gsf85-gdlmn-/5a) 3200 m l s-dmyn 8gkf5/5be -g   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whe5g qhuu v0b-+nby.m9ure thegravitational accnhb uu+qbym.5 u-0g 9veleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed int*8 euo) a)u7sw1 e oskle18iuuo a sphere about 10 km in radius. Estimate the surface graee)uo1i 7 k o8l)a8es*uus1uwvity on this monster.    $\times10^12$

  A typical white-dwarf star, whsh,m t3 l:-rbsich once was an average star like our Sun but is now in the last stage of its evolution, shl- rb t:,s3mis 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 orbiting in the space si a. xefz;qs+ ll+4x9bhuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in termxxaeb4.q + s9+i fll;zs of g.   

  Four 9.5-kg spheres are located at the corners of a square ofh73 cyp.* f,-dv vmsku side 0.60 m. Calculate the magnitude and direction of the total gravitationamphfd-y3 *svk c,.v7ul 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 upi-dv6xy;rt ncsb-d-w0.xt/p on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, -rxdt.cx t;v0-idybp -6snw/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 whatek hkgxmy l4(7v.iy 9*f9. dda( u6ghf it is on Earth, and that Mars’ radius is 3400 km, determine the mass of d yl4ve*g hdug.7kf (xha ym6f99i(k.Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period off *(2 l:bfhe n/zk4yuw the Earth and its distance from the Sun. *42fuybl:zfkew/h ( n[Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed +2zh8yh n(h +zb eknd5ubx i-2of a satellite moving in a stable circular orbit about the Earth at a height of 36zin-+25kybb x8d2 h (enh zh+u00 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abovt +tp/ wizy ozu2iu32gz */bb7e the Earth. How fast must the shuttle wz3to7y2ip b/iu2 b* g+utz/zbe moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship 3fin9ef:myc sm8 1fc8 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 neeyci fmnfs3cm :f891 8eded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a sapdfi;* q0vd 9+ bx x/q* m4/fjrt1hrlntellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earq 4/n lt0vq*dmx * +b9;hrfx/1irpd jfth 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 w2nozi*8 y *zd 4fjbou:34r /lhowxln )ould a satellite have to be launched from the top of Mt. Ever dwfhn/ l on4o284*:b3y*olzj)irzxuest to be placed in a circular orbit around the Earth?   

  During an Apollo lun.)2bbg 3 jwto,syk5jxar landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it tbbjty.,go2x5k sj w)3ake to go around the Moon once?    s

  The rings of Saturn are compo1 pwjfo:l vx+6w0k,s m;k0 wobsed of chunks of ice that orbit the planet. The inner xv ;6koow f ,wm0:0lwb1pk s+jradius 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 mpy, fih2i 6q7f*, wips (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) pi,w62hp7ffiq, m *yiat the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronau;ar. qap 6;obat 4200 km from the center of the Earth's Moon in a space vehicle (a) pro.aa;q; ba6moving 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 equal mass. They are ;nn q,(:pw vje,(new ;jn:qp vobserved 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 each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in a g1-bcp+7od: u *r ozawbv,bb4n elevator thatzb1- pdr:u7oco ,4*aw bg bvb+ moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elengmv* +eo/5 c6 xpevkn4kwl ktn-. a)(vator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum avxcv ka )nmw(nnpo*5e46 ge+lk /-tk .cceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near t9jd 3z gcuu5590pt iswhe surface of a planet with period T , the density (mass/volume) of the planet is 3si9 5 duz0puwj9tg5 c$\rho=m / V=3 \pi / G T^{2}$ .
(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 th,hb6 ;mk sj*x)4vwcz ce period of the Moon (27.4 d) to determine the period of an artvw;,mx)h*6 zjcbsc4 k ificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Scgzjf 5ems) sj,3 k-c93jrj 28w3,7v jjmvjphun like)vhjrvc3pw jmgmck 87-3sjsf95 , z2j3jjj,e the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dful +t (7z3x9d8wp.3rht im jnistance 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 clr p-mgcajw:8x,ch1w 8ose to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar Syw, wmc1:jrcx 8-gh8pastem? 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 cente9lmq(30qhic)n(-lz lazhi,m r of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four larges l2bcn/oxy2v*j o+atd u- ;qw.t moons of Jupiter (tdb;.-yq+c *on 2o2vjawt xl/u hose discovered 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 the Earth from the known period and dist;qk47i, ufjq3in*t flance of the Moon. i ln43j;7qi*fqft k u,   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Keeau8j1uuu1j:v 1*dd aoph0*h tg3w f (pler’s third law. Use the distance of Ia*phgf(eu tv11 0o3duh1u adu j*8:wjo 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 many fragments (which s zcifns-e1s fome1e07 vh .v.;f*qyr6ome space scientists think came from a planet that once orbited the Sun but was d*mcqeef-sffs z ve.o7 6 nv.1y0;1ihrestroyed).
(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 afcu6s:pt. *ykrtificial "planet" in the form of a band completely encircling a sun sfyu6k *:c p.t(Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on 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 fr j*j2lajyoe;25y3jl x2 aai-x rvl*y2om 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 lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m* yxj yj ;ov 253a2la j-*riayllx2j2e long.   

  How far above the Earth’s surface will the acceleration of gravity be hmsx7 -7nj sb+ealf what it i-+7 xsejmsn b7s on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin*hvj zo(0i ox6 in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard vi0*(6j o ozhxare they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gramp 3s *)c+ape1rqzrzz y;(s z+vity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction ofzpq+srcza1 y(zp3e zr;s*) m+ g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling direct 95li.jgeti :mly from the Earth tt igl5:j.mie 9o the Moon 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 baqe87s )idke r7.v kwx-throom scale in an elevator, it says your mass is 82 kg. What is the acceleration e kr.kew )7 i-vq7x8dsof the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about mbia3u bfv, 6o1y g2.m2nzbs3its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per 2 6u b,moma f1y33i2zsvngbb.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 hisbq-em+2ag myrak /u.r5c 5,y z aircraft in 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 planet qh5;i q./owl jin terms of its radius r, the acceleration due to gravity at its surface and the gravitationa h/wl5ioqq j.;l constant G.

A plumb bob (a mass m hanging on a string) is deflected frox74 ic6 -qvi6e bqb1muwd3ai,m the vertical by an -qu a1e6qii imd673 ,w xvbcb4angle $\theta$ 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 banku)4v+*m )ofax a izui3ed for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of so)i4afzixmu)+a u3*vpeeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast vw)gire0r:4 ag (tkpj1-,vqg/vca;l that objects at the equator were apparently wijrv ga )g;: re/vlqa v,wk4 p1(g-c0teightless?    $\times 10^3$s

  Two equal-mass stars maintain ul az v039xz,gp7c+sy a 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 2 aqf.g.lj-1 tw35 m. A lamp suspended from the ceiling swings out to a1taw -ljq ..gfn 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,d8 *u 4d4dsl8rpbntsu-sge + 2 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. Calcub d*s8e+t4-8 ud2u rsnsdp gl4late 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 presence 1.rzdj.e0 jh mu+d0gyof an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measurizye0 u.jhm dd0gr. 1+jng 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 speedo4ci: +vj ps(c as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heavies :c4j s+vcpoi(t? 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 of 24 sat-sgdbzcp4*pv.) u c-kx hlyr /tnopg 2d)0s3-ellites 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 evk-odgp0 std) h3xvzgp.c-c n-)r py4u 2bsl/*enly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEr,9 6a npz5qms4l;apbAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros asa q4znmrl b,p9;pa65 t 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 satijnkhqz 9 ** gauy:rutvq4;f 2ko,+2pellite in need of repair. You are in a circular orbu, yjr ztakni4gf;ohup k*9q:v*+2q2 it 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 yeax4r6n-7w ppg-eyu(h wrs. (a) What is its mean distance from the S-x6 gpyn hre p4-(7wwuun?   
(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 8;wj3j(hro 5kc(stlo G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make wol8o jrkth3;((cj5s reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milkyjoxtt/j)r7ro y( 0c7y Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from th7x)ctjtr 7 0o(o/yjy re 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 ah8ros.u:) utw+y gyi3 square 0.50 m on each side. Find the magnitude and direction of the gravitational forr go :twyiyu) s3.uh8+ce on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth . p-+pd bqbab)$ \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 1r*s.;gwdd s j z;i;3yu.5-cm-long sweep second hand or3g js ;.dzuyw;sd*i;n your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arourt:c540yd dfn *e9bypeg3 dp/jzu lac;u, 2( and in a circle 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 Fid jy4 ;t0eaz(ud5cdp/p ce32nfla*u,9:bgr yg. 5–10.]    $^{\circ}$

A circular curve of )9ht :sf+ll+ sdw/eu4xm3l hcradius R in a new highway is designed so that a car travelinxst/+3ell4m:d c l9huh+w) sf g 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 negotiat ksh46- xvrtf7ing curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide thefs-6h7 krt4x v 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.$\approx$    $\times 10^2$