Sometimes people say that water is removed from clothes b7gk0 +dvw k(-s.e(9za lbqdpin a spin dryer by centrifugal force throwing the water outward. What is wrong with thisapksz(9kl+bq0d7vb . d wg- e( statement?

Will the acceleration of a car be the same when the car travels around a sharp mr:x:lhd.:s ucurve at a constant 60 km/h as when it travels around a gentl:mr:l.s d: hxue curve at the same speed? Explain.

Suppose a car moves at constant speed along a hik xa2xx5p/f77lxp /d+s8wpry lly road. Where does the car exert the greatest and least forces onw7lk r7x+xpf p dp/yx/a52s8x 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 mert wn ew4v3p93rry-go-round. Which of these forces provides the centripetal acceleration of the chil3w4n3twp erv 9d?

A bucket of water can be whirlen4q 3)fvp.,y(hes zv e7 h,otwd in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explaivyovpqhf thzn w s)3ee47( ,,.n.

How many “accelerators” do you have in your car? There are m5oqe1w 91u pua. (,x:i jfiwlat least three controls in the car which can be used to cause the car la5 xjqep1: 9uu,m o(.1wfwiito accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the c+mcllnb /6af*i39e yhrest 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 c6l93/*am e n +lhiybfhis chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at aa9ku x,r 0vvf3k;j *y qh;(bxhigh speed?

Why do airplanes bank when they turn? How would you compute the banking ,iau *a(cpmz f xct:q5-fd p9+jtw( ;mangle given its speed and radius of the turn ium(9dj *mf:cpf ,pxta5a-zc;(tw+q ?

A girl is whirling a ball on a string around her head in a horizontal plane ,jc a5iaaq jhmyw.wuld5g.7r0k03*q. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When c hg*d jk q.y03i,auwa0r5q a.l m7jw5should she let go of the string?

Does an apple exert a gravitational force on t;i8 s5zxwsg5rhe Earth? If so, how large a force? Consider an ap szg5sx r8;i5wple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, of wyx-w/x+no nsi;5- in what ways would the Moon’s orbit be different?wx- -iyn5w/o; x nfs+o

Which pulls harder gravitationally, the Earth on wl4-,hud q8l)zi)w g:sen2 t cthe Moon, or the Moon on the Earth? Which acce w ql482)gcznlh,tes :)dwu-ilerates more?

The Sun's gravitational pull on the Earth is much larger thao zyd1 q4brac65a0 /q9eylr4,1yalm gn the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider t 4r4y0,6yolyc lde 5mzr1q a/1bg9aaq he difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Whatp3k juw l2b (8i)qdzn4 two effects are at work? 8q2u)d4k iwj (zb3nlp Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the 60l - vsk,fkipm (kezj/sz.m8egf0 q4 force on the 6s80k/-,j4e qgkpivk 0 mfzefms(zl. Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around thwba3-czxvy oiu7v16 4e Sun larger or smaller thu7x1vvba zy 64 3cw-ioan the centripetal acceleration of the Earth?

Would it require less speed jvy+g pcg9 94(cqj1csto launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’scs4(1 g+pgv9c 9 jyjcq rotation direction.

When will your apparent weight be the greatest, as meavqw+0+2 oic: zizw+idsured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When woul2+wqz vcwzo i i+i+d:0d 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 b 1vo *mfyl,q/rqe8zy6 , ws,wspace could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shellso,16q8 z /,vfby, *mwe rwqyl 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 “frunrh u q-u t7:fp-)dl+ee fall” or “apparent weightlessness” between steps.)u :-ql7p+uu- dnfrht

The Earth moves faster in its orbit arouey,jb fr5k94i nd the Sun in January than in July. Is thj59k ir y4feb,e 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 its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explair hp x8v npb1xu6w+t6.n how this discovhrpt6v bxwun.8 1p6 +xery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the M9l/.ru0b 5sfykfsx kq)* e2q7el/n cqoon'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 sitti /sxq ueffnlb y0rk* 9q.)l2 q5cske7/ng 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 c9ij(g2qj3pz qu3 ju; 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 aroundd7u yvb+2 pqj7gxekm,p)w)j( the Sun, and the net force exerted on the ,md7(we2u bgj+yp )7x v) kqjpEarth. What exerts this force on the 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 discus as qe0m8 ztrk,.v it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Cm ,.08e zrktvqalculate the speed of the discus.   

  Suppose the space shutyfu3;i qh5 xx n21kt9xtle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravit;uxxqkn9 ty5 xf 132hiational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of theqh6i1gj uildi jf(t* k)r0qi(63uwg;bi( jv + acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per+g6 6l *d;g jh ijtkw)i(u0qqviir 3 fji(ub1( minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in hx/ ae.ri ruc;8xzo50a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its sphx 8c.a/ zixueor05r;eed 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 of98d8a:k x i votf7p2pycgp*5ty xr6. q radius 77 m on a flat road if the coefry2 .xtqp6c igkp 98v8:yx5fp*ot d7aficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of staticms;,l jd.u ;ts friction be between the tires and the road if a car is to round a level curvl,mst ;.j;sdu e of radius 85 m at a speed of 95km/h ?   

  A device for training y5fwluyk3 12wnztka 0f+w9 0 yastronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fasfzykk wfy +a2n0 5tu3w0 lwy91t 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 2xpnw /wbki675r.eibq x 9* lvvariable 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 coeffi7b x w9w 2nxl6r5v ie*pkiq.b/cient of static friction between the coin and the turntable?   

  At what minimum speed must a roller co/sj6 :dcq -9o3 jpwb pp-3yvgfaster be traveling when upside down at the top of a circle 3bvj:wog y-j 6pqfc3ds/ -9pp
(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 tme +o1 .fqp :/oa1s4aw r.r. sanj:sxzhe driver) crosses the rounded top of a hill (rad /a1wsfema :1z q.xs.4or .pn o+:rasjius =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 15-m-diameter Ferris wheel need to makeih 71z.f+h o :jb0lmlw for the passengers to feel “weightless” at hh woijb.1l: mz70fl+the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in aq6lpzcym-, m-ao1( 6nps;j r o vertical circle of radius 1.10 m. At the lowest point of its motion t alq6-p6cs j(z,opm yn1-m; orhe 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 part0pi uma iq:;*n7os p86avc 8jticle 9.00 cm from the axis of rotation is toji8t umaan c0 vp6;oi*q8p:s 7 experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walledvl 99ehlu; tcjlc 70zf ,2ksf2 "room." ( s9fv2h7l c 0tfzu9e,jl;2clk 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 circle on a frictionless air-hockey tabqdur/p7 -d,ziletop, and is held in this orbit by a light cord connected to a danglirudz i, pq-d/7ng block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weight of theds (j tpmqc7i(*v*0dd ball which revolves on a string 0.600 m long. i0j*p(d d vm7(dtcq*s In particular, find the magnitude 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 ofds97 k :*m3ddpvsacj. 88 m is perfectly 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 masseq4 ekdhn 8b38ps $ 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 maneu5k8iy0rm-ab, dd :dja/f r.znver 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 comp;p ar 6))yrxoj-hklwcrai gs* )d2 *0conents of the net force exerted on the car (by the grounacw*gc;s*6xir)y ) -dpj0l2o )ah rr kd) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area:bbrt)-zzbi-fv da9 9, 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 the9 i-)fz-dvbbzt:a b r9 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 particular iqs4c j+u4oma4na;l k +od 6m r*2-tyymnstant, its acceleration im+;j t6*l-+ qd44omasak4ruc oy2m y ns 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 k0b87gbv(s j ma spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg. k0b j 7gb(8msv  

  At the surface of a certain planet8qlvh y.z; a5t, the gravitational acceleration g has a magnitude ozv.lh y5; at8qf 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 accelerat,f2i+jixj,6 r -z9 wnd0jcyhaion due to gravity on the Moon. The Moon's radius is 1.74 r0+ihaz-nj,fx wj2 iydjc6,9$\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 Ear x bwtm9p9(h,yth, but has the same mass. What is the acceleration due to gravity near itsbtm9 wp9hxy( , surface?   

  A hypothetical planet has a mass 1.66 times that :,65bbaca.* tkxsgs(w eq+qzof Earth, but the same radius. What is g nearz ba5.gw+t,(6*kscs qq:e xab its surface?   

  Two objects attract each ot jsc044 lz) i+wyt*hkxi: s/pqher 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 effectivem e4qu t0+x8emy,rgfs e3-y)n value of g , the acceleration of gravity, at (a) 3200 m -tm4qr) 8 ufmeyyx 3ge0,sne +   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the E qcblne2i/a,gl:j)0mi 8if7 qarth where thegravit)7lc 8/i jlmfaiqgeqbi2 0n ,:ational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed isz-tup7 d3g/ onto a sphere about 10 km in radius. du-opts73 g/z Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once 9n l9w;kozm* ,gxz ;diwas an average star like our Sun but is now in the last stage of its evolution, is the x;m nw;*l9k9zo,dzgi size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space- uaxz+:6x k zmslckn9a*b2;h shuttle. Your friends respond that they thought gravity was just a lot weaker xzxcuzs*h -a6b+:nka m;9 kl2up 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 ,n0d:2hg ihuw dbp, r0 (blfl.corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphehu,wlbd:. r,0ghfbd 2ln(i 0p re by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on th-h (yhg:wm3ffy nsrq-),m* sc e same side of the Sun. Calculate the total3fqcfm,(s m y:-hgnhw sy*)r - force on the 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 the surface of Marsqqc:h7iwzs/n:q g 3 b8 is 0.38 of what it is on Earth, 3:/7b :qsz qqn8 gwchiand that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun nt yj*i zb/-f0o3cy )yusing the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that )f/-t 0job n y*3iyyczobtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orb,v +;ewlb/(qjvv1qcaz7y3 z zit about the Earth at a heig ,/yjw;qvv(qb3lc1 ze+ zv z7aht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a cira:fj 3+q pxey7i lurx5 u:yl,2cular orbit 650 km above the Earth. How fast must the shuttle be moving (relaqy5: uuli2al3 f:+e y7x ,pjrxtive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship l*gc ishd2 nj: 3s*;garotate if occupants are to experience simulated gravit;djg :3gh2*si cs*lany 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 satellikcsw lp3ix; 4xp5u-k4te 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 o k4kwc4l s ixpp35-xu;f the satellite?    s ~    min

  At what horizontal velocity would a satellite ha o6fse7o vnelk:t)ddq31j vb1edb.6gm ni/5)ve to be launched from the top of Mt. f)3ne) 5:1bqjn.6s 67mob1ke vitdgd delvo /Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module con5) ymbp3dspct,-d;en tinued to orbit the Moon at an altitude of about 100 km. How long did it take tp, 3c;ddp mbs5)yne-to go around the Moon once?    s

  The rings of Saturn are composed of chunk7n*/7qws.b p1/gxe8gx( wxk ifr.sfc s of ice that orbit the planet. The inner radius of the rings is 73,sr17(.*cns epg7bfx kwg fw 8qxx.i/ /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 oa6s,rf8 9w 0rdahj(yw , e ey/u1y8wmpnce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottpya9ur8j 1w6waysmfdre , we8, yh/0 (om?
(a)    (b)   

  What is the apparent weight of a 75-kg astronautgu0lui j+*fp b 1c-+qj 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at coip0 +quf 1j*c-ujg bl+nstant 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 em2k c2pcqba.. dwmm.:qual mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of wm2q dp:.2 cm..ackmbeach?    $\times 10^{29}$

  What will a spring scale r0 /2j rwh)filpead for the weight of a 55-kg woman in an elevator that move/wj02f h lipr)s
(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 elevator. +t gd 0k7mjpt,The cord can withstand a tension of 220 Ntkt0dmjp,7g+ 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 surfacef15 k9hkhjktej42. qa of a planet with period T , the density (mass/volume) of the plan 9hakje2 4jt .fhqk5k1et 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 (270xot32jhoh-xv o7z 4n .4 d) to determine the period of an artjtnho2 7 - oox04v3hxzificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a zctt7v o n aq*.yzey c9d/(+;u6+uzcb few hundred meters across, orbits the Sun like the p 7zc + *t.;bd6o +ea/(qyczycvnzut9ulanets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagi+byq :2r22l+ u*jga5djxn +/lekg aqe distance 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 theshucbo s ,zv/t* 4h,)o(x0eyz Sun roughly once every 76 years. It 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 vxo o, / zb,)eyzhuh4*s t0(csthe sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy +wapq a217 nhl$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, perior1mt ,ifdm 7hsk,)1b(jnwd 6od, and mean distance for the four largest moons of Jupiter (,t7 ijn1m6dom,(hk sdrb1 fw) 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 Earth f:ywrcz cswsa. (i ,/xxn- sa58 7e)llboj7u8 mrom the known period and distance of the Moon. oc7n/aj5lr7-. sawz:b8m x(8 seysuiw,x)l c   $\times 10^{24}$

  Determine the mean distance from Jupiter nnx)fn /5wcf3for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. n fcf w3)nx5n/Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many frag)wl:mywiq m u)w;g;cvl2q4*n ments (which some space scientists think came from a planet that once orbited the Sl*q)yw) cmw2l4n:w ;;mvuq g iun 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 artifiloec2uvzi98 llw-+9g , ch(mncial "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 omewl n9c+ (ch-9lvg28iz,oulur own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in cu*ez006so zgytt8ow:4p6 28 qgw j uwan arc from a hanging vine (Fig. 5–41). If his arms are ca0w gou26 48 pz*u oc8gtezq6s:0twjwypable 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 acceleration of gravity be half wya9(1ao2;b399 kq oct k rrq oazuo/i2hat it is on qa;o3 koat2kb1 o29czrqrio(ay9 u9/the surface?    $\times 10^6$

  On an ice rink, two :v; yg r(o8wjca fzwrps3jyq/i /p9;)skaters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume t3pz/s;:f(p9rjywqraoj wg)y vc; 8/iheir arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotat5lkgeju ;eji13xycr + o509rhes once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimat orj5gix5jluy1e9;rech +3 k 0e the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance fro(b smn+pk ;0xq ez09jb9xuj9am the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces? unm + 9;pkq90jbe xz9x( jbsa0   $\times 10^8$

  You know your mass is 65 kg, buklt pq6: uk -2c /sy4lez.4ysmt when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the - /:yzy sl4.mpu2l4 kt eqks6cacceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station d(hf f/mwh4j 0ju);4kz2n gsfconsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity atf4(;k /m2)jwdhjf0 g s4zhufn the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes hiser pz0v aq4w-u4q;a;jn e7b. s 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 theoyp+ve 8wen q : +xig0kb euiqa8t;3r v30i+0w mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and the grap e xoyn b00euqw:0 8 +r;iitawgve3i8qk3++ vvitational constant G.

A plumb bob (a mass m hanging on a string) is deflected fcxf0( 2mqythoe6 9 (mmg5x h9vrom the vertical by an angle gmqcy(m9o0x ht62h 95vmx ef ( $\theta$ 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 b9;.7hszhjkj xanked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curv9hjsk x7;.h jze?

  How long would a day be if the Earth were rotating so fast that objects at the n5 .c(sx-zqwe*fp8lh yqbk(, equator were apparently weightlessf.nz e yw5s-(bp ,qqcx(kl8h *?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance asix/bo p x86ty,cj, (4 fvhej9zpx a9:part of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of pfumyy2:4l z53 i ibb9z4u+s nradius 235 m. A lamp suspended from the 9zb:ypu3b5z u4s 4lnfm+iy2iceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timeyhl4e1+ nbn lj ddf(6/s as massive 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 Jupiter since people can't survive more than a few g 's. Calculate the number ol+e f6jb4d( /ny n1ldhf 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 Sxzl49t8oluh )eq/lg , pace Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dgxzhel8)9 , ltlo/u q4ense 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 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 gz 5)9n;rmyyg as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal fog;5z9rn) m ygyrces 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 (G7qd,epqb0p + i) dbxu2PS) 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 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 approximateldqip0udb)+27pbx e ,qy 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 Rende,-ljca 2 e2hii0 kyu 6k3j+xe;tk/gpszvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 iu0k k3/h aspcx e-;kgl,ij+tey j2 62$\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 rtp ,8,tei58mjief1e shuttle pursuing a satellite in need of repair. Yej epe5ftii m1rt, 88,ou are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years.1jqye9b )9r*ll0k-tsyfe h + e (a) What is its mean distance from the Sun? kbsj09 e* q)yrel1f+e- t 9hyl  
(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 azx aux8h( fk 4(*johm0ctually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumpa0fz h4h(* k(umxx 8ojtions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the:(9tgzzf uzt7 center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the:uzf(tz t 97zg center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the cornerj41apjgj6fl3 s of a square 0.50 m on each side. Find the magnitude and direction of the gravif g136j4jpla jtational force 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 orbkgmb2zs5 9 +uttk a,9jits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long hy7ms a4wig7/ sweep second hand on your wr/7w g74msh iayist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight(ogsu9jn y kbu9w s105 around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line9uk0njgwbo yus(1s9 5 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 gsy.(rixwm ;7s *sf)ku +l6 nzoq+1jstravelw+u s r ;(*m.jlozss+ q7g)xf6k1ynis ing at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cax .8lie 8ij: rczb :0e16nn0gpoh1o zars 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 o:izpxe06 n:r0zjh.l8e1 a gn1icb 8o 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.$\approx$    $\times 10^2$