Sometimes people say that water is removed from clothes in a spin dryer (ka8q4-fvz:bh 9 lc9 y3 ldqy9;i vpprby centrifugal force throwing the water outward. What is wrong with this state(9kf;pv9p-:l byqavhd8 ry9 l i4z 3qcment?

Will the acceleration of a car be the same whlk9d pfz; 90efen the car travels around a sharp cu eff ;99ld0pzkrve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does l g/7hx0ig-i,yhj5yt the car exert the great7ihgty0/ yxgj-, h l5iest 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 hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. Wxw8esh s+hy1s e,b5 k3hich of these forces provides the centripetal accelerati3sxy5 hw,h8kb 1ees+son of the child?

A bucket of water can be wh(bm ud -16q4malqi axp+c+9x dirled in a vertical circle without the water spilling out, even at the top of the circle when the bucketmd+(ia+ u- lm4q9pqdx 6a xb1c is upside down. Explain.

How many “accelerators” do you have in your car?o+:7u+ tezlzf+n 0o ej in1: +bdz+npl There are at least three controls in the car which can be used to cause the car to accd+ze+l+znon l 7t0en+:j+io zfpu1 :b elerate. What are they? What accelerations do they produce?

A child on a sled comes fy ximw4y aq2 /bnwj-75lying 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 goes over the hi/mq w 4w 25nxa7jybiy-ll. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high:(iwod,d cca0 speed?

Why do airplanes bank when they turn? How would 5w1o8x+zcra zq5 dh3tyou compute the banking angle given its speed and 518q+axcz h3o dwzt5 rradius of the turn?

A girl is whirling a ball on a string around her head in a horizontal pl1m kgu-po8iq2m - zu,8cf;blq ane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the ya,zo8u m1qkq-ubgp;8i2c -ml frd. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a forc unza -fd6jw,c*+x ss4e? sjxn +46 w*d,za- fuscConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wha j9v 8x yw1mh3bb6sdg/vv a32xt ways would the Moon’s orbit be different g9x3y a3b jh1 2svm/8bxwdv6v?

Which pulls harder gravitat(40 ii6r6plh8nmw; - x ) woe1qeppc+ak ya5yeionally, the Earth on the Moon, or the Moon on the Earth? Which acceleratex w4rc+;enyy5i60q1el ap() p ime8o6-hpwkas more?

The Sun's gravitational pull on the Earth is much larger than typ(oe,8,o v3aq z* qdthe Moon's. Yet the Moon's is mainly responsible for the tides. Explain. , 8ap3,yotvo(qzdq*e [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at ;y)sbx-j(s+m mblf39 sz9abv the equator or at the poles? What two effects are at work? Do they opp9s(xzy3aslf-jmvb+ 9 ) ;s bbmose each other?

The gravitational force on the Moon due to the6f 10mnsn +3jtfv ltm 3iyl:1d Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eartfn6ty :m3n01vt+ml1dl 3fjsih?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or syrx9it uy2n -jj+0*j6k(pyxs maller than the centripetal acceleration of the Earth?s+yrj- (j 0y *kpu6nt9ixj2 yx

Would it require less speed to launch a satellite (a) towg7 k9dt )pv4kmard the east or (b) toward )9gtkd7pk m v4the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a mglq .w6+phu5 kx)f y,scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fal6hp)ql wx,kf+ gu5ym.l, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space couls);a4j5 x;wocx7 aya gd 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) th g)ja 7sxo;caayx;w 45e force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fz9 g1 vb0opu8iall” or “apparent weightlessness” between step p0bg1uz9v8i os.

The Earth moves faster in its orbi4ia d5)gp6um kt around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not m56m4 dpi)ka guuch 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 discovered t2 x..vmp2b qlpo have a moon. Explain how this discovery enabled an estimate of Pl2q.2.b xpmpvluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. n.aar idm8u9zm2( cc :Yet the Moon's is mainly responsible for the tides. Explain. [Hint: zic um8a d:(rmn.a29cConsider 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 travelinga3yr k2e3ks 7j 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around armeht jh4ro-g7.6j 6the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? 76j g -6j.amthrehr4o 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 o +h59 itlh-+ xtc2ljlnf 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the2+lthlxtn-9i5c hj l+ speed of the discus.   

  Suppose the space shuttle is inr e7),o2aito q 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 gravitational accelerati2 rq)oae ,oi7ton at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay ijak2a4 m 5.s-cv1qqa8kpm ;2lp iyc0 on the edge of a potter’s wheel turning at 45 rpm-2mpayiij;v5mqp kca 4 l1ck0.8q as2 (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vu4nq na/;vu xhlnc06 /ertical circle of radius 72.0 cm , as shown incqx /anunn/h 64;l0uv 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 round a turn j19gqfor1r g1b-*bvg of radius 77 m on a flat road if the coefficient of static friction between tires and road is-qo1gb1gj grbvr 1*f9 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires + 8e5dtnuw; ;3z t*v ymu+ 8m-(wh0tkgfmh zmpand the roadht d8v5p*e g;mkz-w;+f h0wmy t3mzm(u nut 8+ if 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 fighte (.yhh*vh+cg ar 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 hay g*c.(h+vh weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotavcnzo42haa7.a7x5f n ting 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 vax4anhzo2 a5c 7n. 7freached 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 coaab;z uo 7h-p.vster be traveling when upside down at the- ;b 7vohp.azu top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses thel t8efhj-*l94 1wg*sez ,w1 psdxw/ur rounded top of a hill (radiu r94*hx-s 8jfwe wdgszl p*t ,/w1e1lus =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 -o)y8e msbwo n.0jz(mn+ lpq)per minute would a 15-m-diameter Ferris wheel need to make for the passengers to mnwqzej+) - m)nls.b p08o(oyfeel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. Ak ;pru0j -homvy 3lcuwd* p*)/t the lowest point of its kcj-u /p rv 0odwmlpyh3*;) u*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 centrifugr6)u 7nxtc1 9htst y.re rotate if a particle 9.00 cm from the axis of rotation is to experihc u79 ntr.s) 61ttyxrence an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a64w 7ot5im jny)5 vsot carnival, people are rotated in a cylindrically walled "room."jtvmio45 w 5 ys6t)no7 (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a cioadpsx3. srso2 5s1jgvs d94+ iql(,hrcle on a frictionless air-hockey tabletop,5s 2gv,hj+d94a( 3.xoriqsolsps1 s d 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 , pr;i.w * r+oy h,xtt4pnjecisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the maptiht+ony; wjx* ,r.4gnitude 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 perf4x 4hb, twir qsd6b(2gectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massesh)w k9;6qhm(:bc e h.k,s uakkh p/o8z $ 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 maneu qe3y h9:n9s dw:maiw0b mf;e9ver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal comn36ls h,/ imblrik :q+ponents of the net force exerted on the car (by the ground) in Example kis :lhri/36+ ,nmq lb 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 accelerny1 g8l,pj ,sjates 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 j,g js1,l8pyntangential 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 dl3uv7cy:n-wa particular instant, its accel :yd7cw uv3-nleration 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 Evzsv0*:x5 emmuh9 3m32k w a,afa;h acarth radii) above the Earth’s surfacw c 2fhe3 akasmmmxa 5u 3,0;9a:vvz*he if its mass is 1350 kg.   

  At the surface of a certay4)7algs q uyx+nb:mpkap 2y3 he /.u5in planet, the gravitational acceleration g has a magnitudeyylghuynq2/ppu 4sbe)37km. 5 a: ax+ 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 v(; /d lvjtiyj* 5tl(pthe Moon. The Moon's radius is 1.7v(vt;l *(y dtjjp/l5i 4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 )ljj33ub+ky nt;q1dt times that of Earth, but has the same mass. What is the accejqjt+)t31 3ld kn buy;leration due to gravity near its surface?   

  A hypothetical planet ho qycra4 t(+(das a mass 1.66 times that of Earth, but the same radius. What is g nea(ct oay4(dr q+r its surface?   

  Two objects attract each +mhfelegt. .i68 jw.sother gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective valoju*2) 6go tdnue of g , the acceleration of gravity, at (a) 3200 m jo *tuo)n6 g2d   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poin(yr7j7 erbem .t outside the Earth where thegravitational acceleration7m eb(ry7 .jre 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(cw(tfv3p5tyr f* oi4 mass of our Sun packed into a sphere about 10 km in radius. Estimate the s*f(w43 or (tc5fyit vpurface gravity on this monster.    $\times10^12$

  A typical white-dwarf starqx a+2uouot,.c.ztf3, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon butuf+, zuca3qot2 .. txo has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts 4j4eas+d)bn1edzcn0 f7z atkgbxf( 431p(mw feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. +ezpkd0z )sw n1ctedg xj1f 4(7(bfa4a3nbm4Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 ll5jv7t*c y mz-wrx7k4pw8.g m. Calculate t8ljr w7mygt.pz x-ckl* vw475 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 up on the same side of 4ct,iyl /-d 9yqnf km3the Sun. Calculate the total force on t3k n c9lfq/y-iy,d 4mthe Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at lhnakbvj/ud 6l(;vd u 88nt(u 6*9yig mr83c xthe surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass 3 nk(9ij8*;cguram/(u b 688t dlnvdlyv xu h6of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for th/jhhgl(c;tt+ cy;fq( e period of the Earth and its distance from the Sun. [Note: Compare your answerjt(cq+(y;h/gl f tc;h to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed o. n :jl(o9 lg4qnxhm)nxw ca++f a satellite moving in a stable circular orbit about the Earth at9+x:jxno(hg. n naml4 l cwq+) a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellitwrztpc7kv*+i8 )z lqiqj:,4n e into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (rel7irpjtkn zz i)vq8w+,lc:4q* ative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are t,pgwp-c0 tj b 0myr7h *u/y8qqo experience si-w0m8 tb 0ryy/q*ch7 ,qppujgmulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 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 satellite to orbit the Earth in a circular “niks+:h,xri15 ;ju k ayiy:/ vdear-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 ofyxiu ya +kj5dr:;i :s iv/,kh1 the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched frxb3 s45s cxco4om the top of Mt. Everest to be placed s3c4xb5 sc4ox in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module cq8xwg m6,m s eq ):rm2zm:sorr65fp2 zontinued to orbit the Moon at an altitude of about 100 km. How long did it take to go around 58q)mo2 wm ,qs6 :rrse:gx2fmmp6zzr the Moon once?    s

  The rings of Saturn are compo cfah enf-+r(:u fs.cq yi/l0:sed of chunks of ice that orbit the planet. The inner radius of tsci+hec nqu -f(y/0 f:l:fr a.he 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). Wht o) fgi9l51s8qg bfz+at is the ratig1f t5s izq9gl)8of+bo of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent we1ylgq (.eoe7j 8ooyk0ight of a 75-kg astronaut 4200 km from the center of the E0 ljgo(. oe7ok81y yqearth's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consist5xvy xmvs rlj,l5o01(s of two stars of equal mass. They are observed to be separates ly( l5v xj,0mvx1r5od 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 wo0tr(wm kn )ox6gjm;mla5cld5 tq08+ yman in an elevator that m 5ngrkd; mc +j0mttx) q(moy658wl0la oves
(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 el5kaq (i mx*xmmh2;tv 4qrem+9evator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnituderm ekmivx5mqa2(+mq9t* ; 4 xh and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with 0dztjaj5 f5w5 period T , the density (mas0tj j5dazfw 55s/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 pexxs5bb1/g /z uriod of the Moon (27.4 d) to determine the period of an artificial bu /x/5zgs1bxsatellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred i5 cz:59s0:q tmqjydsmeters across, orbits the Sun like the planets. Its period is 410 d. What is its mean discj qsz0i m5t9:qds y:5tance from the Sun?    $\times 10^{11}$

  Neptune is an average distance og l3t)bbl jos/+ jb7.if 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. Itj (qjz; ).,p2zbq fehn comes very close to the surfac ,e.f(hzqp ;jn2)zjbq e of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about tp4aje w-p5 .gxfcajv.91f-nnhe 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 mass, pr. vt (8au oq zu(**6oos /8iuseyjl5weriod, and mean distance for the four largest moons of Jupiter (thou jwir8 zu(6o oqsov 8t(*e5ls*y. a/use 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 knownn.1 ozuo khw254ypif *r-jh: e period and distance of the Moon. zyo1u2j .hfeh*4r5wn pk -i:o   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usiu 44c0ln xbbpaxfh 55:ng Kepler’s third law. Use the distlbha04 b5 x:px4fucn 5ance 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 c k.b.ent-vlb-b)d8kwj + 1a ilonsists of many fragments (which some space scientists think came from a planet that once v1-be.jabk il d-wtn)k b.8+l orbited 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 desp bkj ien;49t-o zcrt:z),k/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 enough to produce an apparent gravity of g as on Earth. What will be the period of revoluber,ks - ozjtkz9n: t4i );c/ption, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig.j5k.b ymqkd7,dfu4bm:j 6k3mv3 ye5g 5–41). If b7b,5d jjqk6 dmvy.k 34f5y:meg3ukmhis 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 long.   

  How far above the Earth’s i5o7wt, ss*pa ,jvmk0j auo+) surface will the acceleration of gravity be half what it is on the majo*07js+up ,ia5 )vwok,tssurface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mut989zpp hyekyd4 l0 w*bwi8e ,bual circle once every 2.5 s. If we assume their arms are each 0h0d,9 4pwy98iw*ykb ebe8 zlp.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, t h6inb2xpo-ft7 ,/qmzv xsp: 3he apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude 2hbt:pmv,3z i fnsq xox6/7p- of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacec+ 6)b wxrh*nj:qve/,3uy7htif+e yubraft traveling directly from the Earth to the Moon experien nbf 3 iqwt:/j ,+u+7yehv)r*b 6euyxhce 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 y2;c ukk3 s(h3yzh3 jwwhen you stand on a bathroom scale in an elevator, it says your mass is 82 kg. k;2wcz33 yh( sk3yhjuWhat is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that wsfh 9572kpfh m ayp;l*ill rotate about its center (like a tubular bicycle tire) (Fig. 5–4s972yph5 h ;* lfpmkaf2). 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 hisbm:a(m:i auqjo4 gid 5li*n0- 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 th4b wc 6fa t4jffxe11p+e mass of a planet in terms of its radius r, the accelerati a ebt x1f4f46pj+w1cfon due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) i0ks zjm. z6h4ls deflected from the vertical by aksh 6lm.j4z z0n angle $\theta$ 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 bank0vsj9xc;nzk 8we ,md 9ed for a design speed of If the coefficient of statiz,e09v nwd;xk9cms 8j c friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fas la nq-ne+zkldpp79w/lrh9v*l779j yt that objects at the eld7qenzl* +py/ 7rjkan- h 9wvp 79ll9quator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain 2smi e2jl1yk,pzx); xa 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 k tcfbpvjv6b7ek3n1 w.d ; st+x6xc. ,rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out t,wbfv67tc1;kktv x senpxb+c.j .d63 o 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, ib9i+gkq/ahe, 0s .mr7 oqk4o(r*pngpt has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter sokp*+ g7 n ibpq(ehmkgs/,0.qor4a9rince 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 Spapd0i453otx9*/ ywo kynob y) pce Telescope deduced the presence of 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 0 oytw*k pb5 9xyyd3pno4 oi)/measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and vall aw0 :)3gtaivs6,ghp ,vba wz,ey shown in Fig. 5–45. Both the hill and valley have asv awgb0tw ag,, a 6,:3zpvi)h 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 group of 24 pt1ji+ q0)qae satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellitetp qqi1ae)+ j0.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (e y)gmmp 41yd1NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 1mm)p y411degy 5 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 purs3eb m(0f)uusluing a satellite in need of repair. You are in a circular orbit of the sameu sf l)bm(3e0u 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 years. (a) What is its mean dis ,*ms6 tvlxk s6q;dthy( vcc:tuk ,o1.tance from ttvv*(t;kx,6c 1 k6 s.d,s um:ty lcqhohe 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 oh 2j)+jbm( -liu/gpvux4 d 7cvf G would need to be if you could actually "feel" yourself gravitationally attractxh )v7(+ jblm4-gv/pujd uc2 ied to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arou yc(ww v1pg4f w4tbwnk6n( g9:nd the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the ce wpn(w9 g ng46 kf4(:w1wtyvcbnter $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on ehv(o1iyh s q03qgnb 2 v3*m0kfach side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpointmo0 b*3 0 hfhvgsqk1y3n2(viq of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 /4n 7vttb;hbwkg 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 bpdt:m2 eueta 3/.3ae experienced by the tip of the 1.5-cm-long sweep second hand on bt3datm.ae:u2e3 p/ eyour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weig beu6if37vk +todce- 1ht around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circlecb67e -e ofdkiuv3+t 1 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 a car ;wkn+2 r:heuk z y t8:*9dniqzfu;-irtraveling at speeiu qude; *+92rznf; wtk8hykzn :i- r:d $ 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 Acelu(b4a ykt.1n va, 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 the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is noty(a.4kt 1 nvub 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.$\approx$    $\times 10^2$