Sometimes people say that water is removed from clothes in .wt: n;*cex v(eh+ 3tcalggd,a spin dryer by centrifugal force tcd+,ec * xv:gt wgl e;.n(3hathrowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car tra)us4uc k5 r*n)pmle b)vels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the sars5bceu) *pn u)m lk)4me speed? Explain.

Suppose a car moves at constsmcw4e:+ .n. h2 raz5h)xrw spant speed along a hilly road. Where does the car exert the greatera5xcn . wszm2:+ r4 hwsh.)pest 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 horsx h8ff 3d j-s22fvq3wl;tgwt 0e on a merry-go-round. Which of these forces provides the centripetal acceleration of the cqthf 3ldvw0g3t8 f-fjx2s2;w hild?

A bucket of water can be whirled in a vertical circle withg:z ia 5xyp(6iout the water spilling out, even at the top of the circle when xiyp(5ag z:6i the bucket is upside down. Explain.

How many “accelerators” do you have in your carxro0(y3 fl 1oq? There are at least three controls in the car which can be used to caus1of3(yo l0x qre the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in cd *we1 84ma5hodorm*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 t41a5moo *cd8rmhe* dwhe hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward whhnn-yzq/t *6 nen rounding a curve at high speed?

Why do airplanes bank when they turn? How would you coqfm)wi4hr0 m3mpute the banking angle given its speed and ) m4w3mir0qfhradius of the turn?

A girl is whirling a ball on q5 jqeyiv,u/etb +nfs3z,a */,xxm-ja string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of ti,*xxf35 q es tjmvnuq-,,+ aj/yz/ ebhe yard. When should she let go of the string?

Does an apple exert a gravitatio lwgau4i/v ,ha 9w+(sgnal force on the Earth? If so, how large a force? Congg 9u (,al4/is h+avwwsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wfp*uxi58m 3luh407f 9)ckg- ii sah tghat ways would the Moon’s orbit ii0 5u9uhff k ai7*x)mg 8sthl-4pcg3be different?

Which pulls harder gravitatilei.lle3p(nq6 wv r9zd:nh /5 onally, the Earth on the Moon, or the Moon on the Earth? Which accelnldn( 5/6 ew hezr.p: vlqi39lerates more?

The Sun's gravitational pull on the Earth is much larger than the Moo1juh0v1+ by rin's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consii hu1bj 0yv+r1der the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh morsy:) z5fe)hr xci izi49,gvx7e at the equator or at the poles? What two effects are at work? hc izg,fs7i9e i) x4rzy:) 5xvDo they oppose each other?

The gravitational force on the Moon due to the Earth is only about ha0bkqf eu./ 9pnlo *k*xlf the force on the Moon due to the Sun. Why isn’t the Moon pulled away/kn0k epu q.fx*b ol*9 from the Earth?

Is the centripetal acceleration of Mars in its orbit pc i/ywf(1qld3t/ y)rqeb- t7around the Sun larger or sma3p (e7)d -qy/tyb/q fcrti wl1ller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) 2ksqcxokbq( + 8bx4,ztoward the east or (b) toward the west? Consider the Earth’s rotatx k8q , b4qocz(bs2kx+ion direction.

When will your apparent weight be the greagmsls 5b26v; ltest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? sv 62gbs ml5;lIn 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 coulo16orjk md:0: abehx9d 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) tk:e: am rxo 9djboh160he force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free jf(j2 np4.pmd5 hcf .ofall” or “apparent weightlessness” between steps jmh4 .dj5nfppf c(o2..

The Earth moves faster in its orbit around the Sun in January than i mn;. q,u;h.qvnp,fgxn 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 Eafmv, hn;.u ; pn.qxgq,rth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to e 9j ws9o9qau8have a moon. Explain how this discovery enabled an estimate of Pluto’saj qou999e sw8 mass.

  The Sun's gravitational pull on the Earth is much larger thanmi.l+aji3nt 5q ldm6 .16jxfm the Moon's. Yet the Moon'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 jd3fql6mj5+n t. imia 1lx.6m 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 1gd8 0xk v k6h q oa8v7wch;c1d:t:jbf1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 t.oz oiuf)yk 9a29 (uuohe Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of rada iou2 ufou9o9z( )ky.ius 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 exerajalw6cz+h9kdvzn x( .(/ee (ntr7a0ted on a 2.0-kg discus as it rotates uniformly in a hor hn w/ zetn9acjza +(0r6x lae(dv.(7kizontal 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 f64d4g, jnq iom, /esovrom 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 youq/,o imsjo,g vn e464dr answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a b-n it.8i7z7p3c0 z amm y4radpotter’s wheel turning at 45 rpm (revolutions per minute) if .maz73c nzdrmbp7i y840a- ti the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolmd0y 0ze ikbrup58r(:) qtmp* ved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 dyputz08 r(0: r*peqi )m5kmb$\mathrm{~m} / \mathrm{s}$ 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 spee daoc,) ;xi sg 3uh0wck1qcjp,.o)9rwd 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 ,wgwr c)saxkp c1)u;9j3. iodc ,qho0road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefq-j;i qpq; pn0sv5s-m ficient of static friction be between the tires and the road if a carq i5m- ssj pq;nq-;0vp is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts andssp( e. ;gjbggo c b h)vzind.b2,8v;- jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the. ogh(s;bg)cj ;es-vz2 i8,.bngb dp v force felt by the trainee on her back is 7.85 times her own 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 a8.3bq fwhjv k,jcu 3 mta8 5sg; r3zj-xw4gn/e rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the ttk3wxbjsw38gm-54/8,.3 hrzuevqc a jnj ;gfurntable?   

  At what minimum speed must ax pu.i)3)picp roller coaster be traveling when upside down at the top of aupp3 p))x c.ii 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 the roef 4t6 p,al1idunded top of l,f6tdp1 4eiaa 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 per minute would a zgq ie -j(4tveby 6/oauu3/+l15-m-diameter Ferris wheel need to make for the passengers to feel “w+out/ /6e4 ae3qgu(vlzib -jyeightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circ/2iiqbxsax)3y5(q ylle of radius 1.10 m. At the lowest point of its motion the tension in th) l/2yabq(y xiix s53qe 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 u/d1e igb9 h:na particle 9.00 cm from the axis of rotation is to exh 9 idb1/n:eguperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wall1d om xgp.m,cj cfve9* ;vy) fvc+uf-7ed "room." (See Fig. 5-u,v.dv)-1cmc m+foxy fcv9 pe; 7f jg*35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a fri1g0mlz(f5t ,1kt;v1r v5vsuchli 4ex ctionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in ulis(ch ;elvxk1 v z0fvrm 55gt4,t11 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 n9qm7hkv; wm -7mgb)nmot ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magn9hk q7gwbn;m)7vm -mmitude 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 .7u(laxy8 ;*matpbsla 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 massesyt8s 7/o l+ro-3vwfaira.vepr2l;t+ $ 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 evap qzkfx-6:z .msive maneuver 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 componendnb 7 r9r+pp:uqmr(z4 ts of the net force exerted on the car (by the ground) in Example 5-8 when its speed is z 4:pq7pdmb rur( +9nr15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerak*o*ac5 6sfs htes uniformly from the pit area, going from rest to 320km/h in a semicirculs o*6afs* h5kcar 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 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 particulge uu 461,ghhrar instanth,u1g 4gruhe6 , its 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 12,5u oang+f)iz9f r( st9800 km (2 Earth radii) above(fg9r9sf5a n +t) oiuz the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitagotbs*b r 2t.:2lqsjz26 an(dtional acceleration g has a magnitude of 12 m/ro (.bt2 jq6*s: agd t2zsn2bls$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is6m7 xij,upx3f*iuk .+c2ww c h 1.72 .f*3uj,wc wi kch76xpx m+ui4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tim4.k)vt0jylyuhzkc ts,354 ;e rijk r/es that of Earth, but has the same mass. Wj /)0ju t5ry;t3 svk4i ey.rzh4ck l,khat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass vy8 6jumw;rd,) p*kee1.66 times that of Earth, but the same radius. What is geve8)uy mwkd*; r, pj6 near its surface?   

  Two objects attract each other gravitationally with a force n4vbr4l9cgv3 lpoyo9d :h2zl8 ;b pd.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 valp7(pd,mh9 *x i7 ch+cs 4ldfyjue of g , the acceleration of gravity, at (a) 3200 mp ml sh 7+dp,*dh9cxf7jc4(iy    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a pointhoq2la nx03-u outside the Earth where thegravitational acceleration due to the Earth is o-a q0ux2 n3hl$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the i)6x5: (6b o /gsiz sdjjr6cnimass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravi 6nj5ib d i):rgcs/z6ox(j6si ty on this monster.    $\times10^12$

  A typical white-dwarf star, which once wz+to f/ux qows,v 5,h*as an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surfaco /f *5zuohwvt q+sx,,e gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spa-lbp e nixeh0*5o dr99ce shuttle. Your friends respond that theyo0xbr*e9- nl ih9d e5p thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side xq+4 2vzx eo, smv8)eu0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other three42 z,sxov +xevm8ue )q.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years avw+2-8wkd ommost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four plane2kmwo8 w-va+dts 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 acceleraign m4o*wm:nptm +92wtion of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, deter no4 w*m:9ingpm+2mtwmine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earth2+;q truz0ky(v2osmh and its distance from the Sun. [Note: Compare your answer to that obtained using K ( tkq u22+z0yhm;rsovepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite mov k*j;*c) gkkk6a0grp jing in a stable circular orbit about the Earth at a height of 3600 g6c0*g;kk)rj kkaj*pkm.    $\times 10^3$

  The space shuttle releases a satellite into a circuh:yjlyyj9 1sa; b;af :/odi)mlar orbit 650 km above the Earth. How fast must the shuttle be moving (relative to /:iy9dy a;h 1s;om)fbj a:ljy Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occuysm 0t69+f niv1rix1;8psb ep pants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and givepvm01+ x9y s ife;i61sntrb8p 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 thh5gj t/+c*elte 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 you hjeg+tc 5/l*tr result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have towonjxc/ueik .-z))t ) be launched from the top of Mt. Everest to be placek)w)z/j)n e iu.c-xo td in a circular orbit around the Earth?   

  During an Apollo lunar landing mi uhdu r/.hoy9 rm0o32zssion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did itr m9yu oz0.dhu3ro 2/h take to go around the Moon once?    s

  The rings of Saturn are composed of chunks o.gfnlr 0 0iho2f ice that orbit the planet. The inner radius of o il0.ghnrf2 0the 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 podd0 gr6 yskmk bj;st3)z10s94(dmu Fig. 5–9). What is the ratio of a person’ 394;d mgb0 osmdj1 dk(0pysktu6rz s)s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 t8,2xgvr e+us km from the center of the Earth's Moon in a space vehicle (xtuvrg+, 2 es8a) 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 ma73z ma9tj.* ctgmv o1-ri ey0gss. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. t imcor g37 mgtz 09je.1a*vy-What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg womanq5 /ztg1da ep blgj ..frse6.8j/en;g in an elevator that//z1g5ee e;sg. 8r6jta lgj..nbpdfq 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 frq*gz; g1kps0 ir.(rghom the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the e z 0g1phq;g.skir(r g*levator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a plaam eys6a+9up*dx 0vx +,wb)j qnet with period T , the density ua+ xab+w9q6vx de0)pj*ysm, (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 o4b iqzg6unz+p4w6df n sgr: )0f the Moon (27.4 d) to determine the period of an artificial ws p:d4fnz0b u4nz66+gi)grq satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though rfg;( i7;2- jey dfhrhonly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distan-(er dh;2 ji7; fyghrfce from the Sun?    $\times 10^{11}$

  Neptune is an average dirn+*t3ypbsi v p)n.)d1z6r j wstance 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. Ikel+euu k,4dh3 8v*i,rhn 0rh, bew0nt,uq:ht comes very close 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 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 neareu4kqe ,8uw nd :,nhe,bvt,r*e h3rih00uh+ lk st and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about theen2*fv g6 32mhdnyi(90bu d cm 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, period, and mean distanc7l +st1rv9uy ry /sj*8w3 tarne for the four largest moons of Jupiter u8+a3tt r9ywn vjs /r1y*rsl7(those 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 Ear1dzhq)x i- 3evh ter98th from the known period and distance of the Moon. 1i)h9 v3qrzetd hx e-8   $\times 10^{24}$

  Determine the mean distayax j;l)xfy31p3+m(+lal /gf l)kywcnce from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to tyal3ykjg/x+cyflpl)l mx3 );f a +1(w he 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 eb+x il*8b e:aand Jupiter consists of many fragments (which some space scientists think came from a planet that once orbix8i+:* lbea beted 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 form of a band ce 7u)zf rhg+3completely 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 thec)7r ezf+ g3hu 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 from a hangingl8l g z;ex mxa8ku*xf62i;) wx 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 i;ife*)x l8x l 26uxzg wmxk;8as 5.5 m long.   

  How far above the Earth’s surface will thnciytvk 8;x /)mdxpr wn0*t9; e acceleration of gravity be half what inxkdt; * 0x rmcnpv;)y/t 8i9wt is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cia4k 7zvgryz 82v:bo(crcle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses arz:4k78v yz c2(vao bgre 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the ap.-jrbr:;t)oo5 ) eo5gjexw* g -z mm-k5dgaeqparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude ow):xjr- ) *ezmg.-tgode5 km ;5jgo e5ba-r oqf this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling t wm)z eta:z8*directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equtzmt)w*8ea : zal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom ye-,1wy+d( a4,uff c j .cevwsscale in an elevator, it says your mass is 82 kg. What is the acceleration of the eleeu(se dcaj4,+,fy1yc-vfw . wvator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a cir2pwtghz/v( f;p ;wk, ecular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diametv/,w;2gkp pet(hz; w fer of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Figq wip::m2r-l b/m* cds. 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 in terc(sn(ko z ii4(ms of its radius r, the acceleration due to gravity at its surface i4k z(s( (nociand the gravitational constant G.

A plumb bob (a mass m hanging on a string.osyiph y1,/u s*vus6) is deflected from the vertical by an angssuvsy*/6 o ,uhpiy1 .le $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of Ifsgc+,a;zso6mzl zat , 315bjg the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle th z3+g,z1gs 56asc;tlb,joma z e curve?

  How long would a day be if the Earth were rotating so fast that objectz.ip 31px. ufj2zjy)t1g b ,wfs at the equator were apparen121zp..i p buf zjfw3tj),gyx tly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 hc*2rpoc7h rod( e*6u5 lu1of$\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 lamfz 41:qkk:qm f roem*b.g+edz) *o4vtp suspended from the ceiling swings o+ * o4gq1 q.vk fkmfberezod):*:mzt4 ut to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massivezpl5 w t2w/-macwy31, ptvc:k as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of J 5c-3t 1c2ma yppzk/vwl,t ww:upiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Huph o duid4:zqsb,m1 ;*bble Space 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 measuring the speed of gas clouds orbiting the core: *d ;pduz miho,14qbs 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 e,n; 2o,wk7j+drltknpr 5, td as it traverses the hill and valley shown in Fig. 5–45.r,j+en pk,7d 2t5lrn, wdo ;tk Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning pcpk6x6h 8vzp,+vta+ System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determin +tvz6pxvp6h+,p8k aced 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 satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR0ppf2mpg x4x b*5d.g s), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughls5g24x mg*.0p fb dppxy 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 .(sz aj31qslpthe space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth)pl(q13zja s.s, 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 ,ue7s4 c9 ju)qw/;f2wdsmpx o is its mean distance from the Sun?cxf; )q,m 4euws o/sup97dwj2   
(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 actuiyubz:.c1 wm9 ally "feel" yourself gravitationazw.c1iuym 9b :lly attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the M.nk: /y+psl hh 39/hgiaa7dyqilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-yesh n a39:yg/diah hq/ y+p7kl.ars from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are locat.p ql1/u8tabted at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom qt8pbu /l1 a.tside of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earthah3q1mw6gbwq+o vb 04 $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm mh23n5/p,rww )s5pgoaiay+q-long sweep second han,2s5/wm)r3anq5gp howa+ iypd on your wrist watch?    $\times 10^{-4}$

  While fishing, you getj*pda ty 9dkj.*4f jh* +clon0 bored and start to swing a sinker weight around in a circle belodk*0. fcal*9t jn*4 jpyo+jdh w 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 Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so t-tng.n aavz;/w2f q2al,uz 9shat a car traveling at qgan slvn2;a9-utzaz/f 2w , .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, util1 edt p6v.4ps .h3i2l( ;bbqol hpzbq(izes 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 kzq ; sb2b bdtp.lh1(h4vi 63.(pp oelqg 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.$\approx$    $\times 10^2$