Sometimes people say that wl1wvslc j05.m ater is removed from clothes in a spin dryer by centrifugal forswv1ljl05 .c mce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the si29742 ju/zf wycrduvlvt 5,rame when the car travels around a sharp curve at a constant l, yt2w4fv9ui 5v2zjurd 7rc/ 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alonmidy+5e9 .psine 5 ih5g a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a nye . pi5medhis+9i 55hill?

Describe all the forces acting on a child ridiz 11p7s( - izc,k jypfks/.-wnka ;wafng a horse on a merry-go-round. Which of these forces provides the centripetalznijw. a,1yp7 kzfkf kass(-1;-wcp/ acceleration of the child?

A bucket of water can be whirled in :.kavwvt/4 ci hn(bv ih1zw- +a vertical circle without the water spilling out, even at the top of the circle whev4 :v.z +h(tvka1iwc/-whnb in the bucket is upside down. Explain.

How many “accelerators”t .,*2p;k3i6: bh 0d vjts yu(pgkbwnj do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they p.k:g3yjtd ts,0pk vup(;nh 6wi *2jbb roduce?

A child on a sled comes fla+pqt d k5cak usxs/;462e-pd ying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he gasdes k- xp52q+;ucpadt / 46koes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inwasoj (mr3zg (3c 7dvlz48tj.3 oqh9 vizrd when rounding a curve at high speed?

Why do airplanes bank whi3e3-id7 iaa ben they turn? How would you compute the banking angle giv3i-ebd7iia a 3en its speed and radius of the turn?

A girl is whirling a ball on a string around her hebi s klgbc(.qmn0,(.wad in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target ong icq0bwb..,m nlk( s( the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, hof7 xy38hexu c5w large a force? Consider 8x xfeh7c 3yu5an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the M9+j3 ylhzk tp9oon’s orbit be difj9tpk z3+9lhy ferent?

Which pulls harder gravitational ne3cfg1nanrg(,q1n: r.1rc qly, the Earth on the Moon, or the Moon on the Earth? Whichq1rcqe(f,1rn:a 1.gcn gnnr 3 accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Y 2a ckcaeo:h lgj dyph/8vm/.04)sz5w et the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to 0 sc.m84k/ahgj lc: h) aoevw d5p2yz/the other.]

Will an object weigh more at the equator or at the poles? What two i8vkv3;vs0 m8iboj2veffects are at work? Do they oppose ea0i;8svi2jmokvv8b v3 ch other?

The gravitational force on the Moon due to the Earth is only about haly qo++c nz2sr6f the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?zsry+con2 + 6q

Is the centripetal acceleration of Mars in its orbit around the Sun larger 2x/l p:b)pp2fw r /b0zx)erdzor smaller than the centripetal) p)e/d z r2/zbpblx0f:wp2xr acceleration of the Earth?

Would it require less speed to launch a satelxw,q nj 6 je2wbg5q)v9lite (a) toward the east or (b) toward the west? Consider the Earth’s rotation directionvngj 5)q69b j ew,2qwx.

When will your apparent rugjbs4 ke 1i-3mg 3.nweight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upwag-jgekr3.b 43 us1nmird at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could 1ko)k2r7zq.bz xc f:6 ioqt y oxxrt.kg:643gbe adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shet2krg4bg:o6 qx6or k3otf) cyiz.:.xzqxk17 ll that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free falxa8vtyrd)6-y owa* l 8l” or “apparent weightlessness” betweend8ta8w- aylo * ry6xv) steps.

The Earth moves faster in its orbit around t;.m3i 7wbpd hphe Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of b7dh.p wip3 ;mits orbit.]

The mass of Pluto was not known until it was discovered to have a moon. qu3+vny 6qw,t 3 qv)ns50lfw cExplain how this discovery enabled an estimate of Pluto’s massfv 5n3slwn+ ,6c3ty0qvquq) w.

  The Sun's gravitational pi4hw r2wcs n6,4e ax;all4ovz*o. 4zh ull on the Earth is much larger than the Moon's. Yet the Moo i2as l46w z*o4vlw.o; ezchax4,nh r4n'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 19a fj 5t:m1qu8v80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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;; l fegy)zae, acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the gfa;l ye;,)ez 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 is exerted on a 2.0-kg di2 uh3ol0dco.blc ar:4 scus as it rotates uniformlcbu.2ld o4oa c03: rlhy 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 surface, and cir/7vr42vwqjue wi 2d- icles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your andw-2 v47ie2qw ij/ ruvswer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a spee0b qu7p)) txfck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is)u7e0)f qxpb t 32 cm?   

  A ball on the end of a string is rev8pqdy b8zlj3( jfj1boh3e g *8q6r*q).at purolved at a uniform rate in a vertical circle of radius 72.0 c oj6b *zy313 urbegd*ar)pfqjlqh88pt(j 8. qm , as shown in Fig. 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 speed with which a 1050-kg car can roundj2xn.fhp (d8yp*pzp8 a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? If zhd *p8j(p xppny8.2s this result independent of the mass of the car?   

  How large must the coefficient of static friction be s6zv8o ylt0(fr -ze(ibetween the tires and the road if a car is to round a level curve ol t((oz08szr-vfiy 6ef radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate mwrx( ly( 9:3w2 sgmy+0vdzmna 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 wei zm(ny(:+vry0lg x9 dw3 2smwmght, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of varianm fo,msfr. 6yao0hj.r 3 5-hbydau5,ble 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 coefficie. yfmamyanofu0brh5r6 ,hd. 5-s ,oj3nt of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down am0fvi+v0c7e oc1 wcsz:vt+,; i6umsrt the top of a circlr++;c1z,cv vcoifm:usiv m e ts7600we
(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 dwul8lbx - f+ vkwi*o3,river) crosses the rounded top of a hill (radiusxvw,k-o i3wf+8l*blu =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 a k;5uyzvb5yd6 15-m-diameter Ferris wheel need to make fk5y;5zbu v6d yor the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertix*/371mv .f p-xldn)heqx z wvcal circle of radius 1.10 m. At the lowest point of its mo7/ dz.-flvp m nhv1exx*w x3q)tion 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 partictabxe;od5i: d4e r*z/le 9.00 cm from the axis of rotation is to/ *ded; zeab4:x5itr o experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricall4dsid6lhwzo2 8+e be (y walled "r2 eb+i zl dhw64(so8deoom." (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 a-+y m ,(iry6oqtjiqz z3.0h b) is rotated in a circle on a frictionless air-hockey tabletop, and is held ii yajmo +,-tiyq6br0(. z3qzhn 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, by not ignoring the w l-(x a8fjzsj4eight of the ball which revolves on a string 0.600 m long. In particular, find the ma(4zlfja -xj s8gnitude 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 6lusr;j9f5do veling 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 huwk2p8 svb7 g.+d(gxyoa g1:37qm pt$ 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 divn 74l-z- m5rfdbldt6(lx a4w ting 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 comp xn-/i8 .xls1e s1poqdit:g+konents of the net force exerted on the car (by s.ni -ox+g tdp:1i1 8es/lkq xthe ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 ac,+i gk.qs-a:t dki1z7 b.47zz aqva uscelerates 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 the turn, assuming constant tangential acceleration. If tb7i,d 4zaau+ q7 q zszvs.tigk1.ka-:he 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 od5;zcnhe.*.mpws )r7 lxy8 7ah/hor e f radius 2.90 m . At a particular instant, its acceleration is l8 dc mr*7zw/.)roh p.ay7h;5hes xen 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 Earth radi 2gwoh.gglzhufci6+ 81 6t2aaaa n99 oi) above the Earth’s sug ihh+n a6c2.9tg2zu91aowf lg6 8 aaorface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accee.jh s8e yk5m;leration g has a magnis5kj;.y he8emtude 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 rad c0q-tdsuw l3;ocmt-chk.(j 8 ius is 1.74 (k.8wcot u3hs-0tcc-l d m; jq$\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 same m0isl( z f)med v)xw(cb)q h59jass. What )f id)0s9 wmzj hv(b eq(lxc5)is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.6v 4b0t(zvx 4p0b x;ehy6 times that of Earth, but the same radius. What is g near its surfaceyvhe b4v;x4 tp z00(bx?   

  Two objects attract each other gravitationally with a forcef:g os(,jlwbv t;qr:t*f:t m 07a)qis 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 , thef ,r6)fzg ei9;*kfivt acceleration of gravity, at (a) 3200 m eg) tffvi 6fr*9z;,ik   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center tokf, sy p;f6eb1d0xxogmp(o0- a point outside the Earth where thegravitational acceleration due to the 1op;mxyd-(0fks f6 o0 exgbp,Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five t; p9le7dgo2rc imes the mass of our Sun packed into a sphere about 10 km in radius. Esti;elr p2oc7d9g mate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf5zay+j hi) 76k9ifn f hx4t9tb star, which once was an average star like our Sun but is now in the last k i64hf5f 9tx+yztia7bh n9)jstage 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 orbitib4w4 l:rw1x4ig w,fcl2 ndnq(ng 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 lwnr4qgw( f1lx4b,d4: ci 2nw acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locatej ir5xn+v2krgg ,- )adfgt *-ad at the corners of a square of side 0.60 m. Calcula5-ka ng- jivf)drag +rx*,t2 gte the 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 up on tls 1v,yr2h/dytq3s7 o,n lej3he same side of the Sun. Calculate the total force on the Earth due to2 s,l yvo j,eyh1rts7 33qln/d Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the accelerat)ct 67cb-eyfwz-vd0b ion of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ ra6c7f--w) vcb byde0zt dius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the pem(lvi; )fx5v k8uuyy. riod of the Earth a(8u)5ymu; x yiflvvk .nd its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about9aiy66dp1d+orj, mm n the Earth at apa mmiy1 rdn+9j d66o, height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular //o 1f6i wj ) zgr6.rdummdr;yorbit 650 km above the Earth. How fast must the shuttle be movi.mjdigor/1fwru /dz6 m;) y6r ng (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if q-yat c 8os1vgx 16a,qoccupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 8 1y6ta avqocsg,xq1- m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a sate1.i6+oprf,u wug7pc 3nycg.rouy3 j7llite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of thu6f+ iucy1p ggr73pjc.nu3,o r .7 woye satellite?    s ~    min

  At what horizontal velocity would a satellite have tofi cy;abag*y (wd -w/wo5 ++ln be launched from the top of Mt. Everest to be placed in a circular orbit around oc awbw-/d 5+f a+lygy(*n; iwthe Earth?   

  During an Apollo lunar landing mission, the comcc wma ld(*pdjn6aed,7 .o88o mand module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Mwccj8 ,m6*deld (oo.pn7a a8d oon once?    s

  The rings of Saturn are composed a.k )3imnro+o of chunks of ice that orbit the planet. The inner radius of the rings is 73,00om3raok n. )i+0 $\mathrm{~km}$ , 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 ro d(s gx-q8-r+q6p)di4noy eeul c:j)itates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’sicxyd-o 8qdqnpjs4 (rg)e+6:l )-ui e apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weiadr6fq ( rnb4+cnlu/,ght of a 75-kg astronaut 4200 km from the center of the Earth's Moon idqnafnc r4/ru(+6, bln 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 consists of two stars of equal :qpo0 m mnmc+m4:h o-bmass. They are observed to be separated by 360 million km and take 5.7 Earth years b n4hmo 0 ocm:pm-+qm: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 an yyq6ap+n, l1selevator that myq6 n1+ays, lpoves
(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 suspdz xf( o)tq+21r cj,qjended from the ceiling of an elevator. The cord can withst 2( q,ctzx+j1d orj)fqand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with pe 3bno4-rz 8esc u4g)dyriod T , the n83-e rbc yd)uo 4gzs4density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the period dg4,)e jdyxr7z p-mmse s 089tof an artificzeym,r490 pd js)get -d78 xsmial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only al:(di ,tuxx+ac( t-mi few hundred meters across, orbits the Sun like the planets. Its period is 410 d.-,tx(uiixm a c+dtl:( What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4o pb*3o7vu1ot.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 closel+ bk9;yawgxo 4qos t09m rf 4p3:4qfc to the surface of the Suq orb; x4w3 fyap+0s:tlm49g9o qfck4n 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 t db80x9uh0d9( zm jabxhe 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, periodb3tz cj 85mxh 5bk99dr, and mean distance for the four largest moons of Jupiter (those dir mz h8k3d b55jt9x9bcscovered 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 pw7/oj,p) .haewt3lqvm19 et teriod and distance of the Moon. o 73 ajtm.qe /tew)l1p ,hw9vt   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of fphh 5yowje:d, 987ut Jupiter’s moons, using Kepler’s third law. Use the dis5f,9e7uow8jh h dy :tptance 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 m 8+;79fsy,t t i nwaemcf+/vpaany fragments (which some space scientists think came from a planet that once orbitet+t ,8e+p9aa 7/vs; fy nmiwfcd the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the 2r n7ts oi/vc7form 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-Su2r/t7vn o7csi n 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 hanging vine (Fig.x kil;jo2i b*( 5–41). If his arms are clkioi (*2xj ;bapable 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 long.   

  How far above the Earth’s surface will the ac:sdpi 4g3;jq kceleration of gravity be half what it is os p3jkdi4; :gqn the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass gr:h.;p8em 5 k;vpfskeiab 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 massph.;mfkpi:;e85evk s es are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates .qa vhl5zmaidd4f25 4 once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. Whatzf25a hvq 4im4da5ld. fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth w0h (:at hno.evy(iwu0ill a spacecraft traveling directly from the Earth u: e .now00((vihahytto 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 bathrewq/+ r)cm(8vm ty e5l)4 eysooom scale in an elevator, it says your mass is 82 kgt5scqewmy 4e( )/r)+evyo 8l m. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a c30pr+wco5wxy ircular tube that will rotate about its 5po+y rcwxw 30center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical lox5jul ur :d--fs8j.tc op (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 j:gxen ),2f stof a planet in terms of its radius r, the acceleration due to gravit,:)tsxjengf2 y at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected fromnae gqh00 09u/iw ;n 1j3 8iemg1ct:sz*zkvt n the vertical by an anglet e ;thv /iw c3ns kza:nu0*0qmzng911ieg08j $\theta$ 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 sp+k sru69js 0jeeed of If the coefficient of static friction is 0.30 (wet pavement), at 90jss+ er uk6jwhat range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objesxi6o-9qp/ n3kcm5oe tjk0. gcts at the equator were apparently w c jnxe9 p-6gm/30t kq.k5osoieightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 l nlqd+q-37ur 0-dwa:4 fewii$\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 lamp sh6 .l lifs :pj(ne0m1pkk+x-zm)ey )auspendeea 1) k:l06l n( -mepp)zhj.xkfmyis +d from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has bujb+kw.aw(bqx /:zam40)k4 nos dod ;een claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the nu(/ .04)wdm osobkk+a d qw;abjn4z :xumber 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 of an exjnl8s- pd.hukd89r) xtremely massive core in the distant galaxy M87, so dense that it could be a black hole (frdhrl dj)n. -88 pks9uxom 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 cooa7/ cdjz9 w3wu qoop,a d+5g)nstant speed as it traverses the hill and valley shown in Fig. 5–45. Both the d o+w/z 3oo,5 adj7gap ucqw9)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 losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a gro u7 w4hgg,rk3hup of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of apprug3hk, 74grh woximately 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 billionljna* ahfnf/2w1sod. d2 l51o km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rou2o5nhfwanlj*2al/s .d d1 1 ofghly 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 nere0+ n d sc)1,xuej8wszj( dd1ed of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it. se1zc dsj,r0w(d 8d )eun x+j1
(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 periox; p5oc*zps4y kqx5d2y: rn0bd of 3000 years. (a) What is its mean distance from the Sun? pyyr5 c k;42 nsxdx0*5oq pbz:  
(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 could jk ,inm x( dfp6 .ctpc21inx07actually "feel" yourself gravitationally attracted to someonexn p 710f,2(ipmjnikcdc.x t6 near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a dist;r x4zoc/ ab)uckv *m;ance of about 30,000 light-years from the centerc4 k; /xaumrz*v cb;o) $ \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 ci ki*.g j9scv xcu+uz)b3n7e8orners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational forb .+ixs3e 8g ukz7i )vcc*nju9ce 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 gb sz:8s8mjn:w+y(u gthe 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 eh1mdkr,b mo38 xperienced by the tip of the 1.5-cm-long sweep second hand on you8 1,khb3dmr mor wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around i *(gcmzc(l jf4n 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: Sl j(gmc(f4zc *ee Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is desjyio9 +)r+ wemo+i+.ggw8x rrq( 5 abaigned so that a car traveling at spgo5w+)ea j8biag 9x+.i+yo rwr + rm(qeed $ 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 Ace .;jn s1.1 d du5zdapb -ajire7ml/0ixla, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide thb jddmuelx sj5.z/r-n.0i7 aid p1;a1e 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.$\approx$    $\times 10^2$