Sometimes people say that water is removed from clothes in a spin wf;br su( szul 8lo8m bm1)m55dryer by centrifugal force throwing the wate5 brmu81ul(os)wsm 5 ; b8zmlfr outward. What is wrong with this statement?

Will the acceleration of a car ;tddr.*8 k,wcyakyt,rpjf k)u:i 28g be the same when the car travels around a sharp curve at a constant 60 km/h as when if,u,.*ky;)kr k cg dptw2iyt8 dja :8rt travels around a gentle curve at the same speed? Explain.

Suppose a car moves abxycrj ja; 6yj4 ;8w .6tbdx)wt constant speed along a hilly road. Where does the car exerrx;jtxw6jyd6a;b yb )c 4j.8w t the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a mkrs3 yugg. :8terry-go-round. Which of these forces provides t .k ugr:gyt8s3he centripetal acceleration of the child?

A bucket of water can be whirled8z2q9 rfpoqf+ in a vertical circle without the water spilling out, even at the top of the circle when the buz qfoqp +rf892cket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least thsu1va ban1a 6;ree controls in the car which can beu1v6;1saan ab used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the c fgr0- jt7tnf./x efn+rest 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 hill. Explain this decrease using Netff+r 0nnjgt.xfe- /7 wton’s second law.

Why do bicycle riders lean inward when rounk8 v3i6.sbp u5qr3zp hh41mml ding a curve at high speed?

Why do airplanes bank when they turn? Houo3 ur+ggy w-ak6e0lfzg +3r4w would you compute the banking angle given its speed and radius ofo w euyfz6g34grg3lr++ -0uka the turn?

A girl is whirling a ball on a string around her head in a horizonpo w/q* s9vf7stal plane. She wants to let go at precisely the right t *9oqs7/vfpws ime so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? ldoc bic*+7+ gIf so, how large a force? Consider an ap+ *bdli+g7oc cple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublt;p,o b1- ygsue what it is, in what ways would the Moon’s orbit b uby-gpo,s;1t e different?

Which pulls harder gravitatiozdy8 cznc mqkc)..k.n,7a6jlnally, the Earth on the Moon, or the Moon on the Earth? Which acceleratdql)jkkc c6m7nc .n8 zyaz, ..es more?

The Sun's gravitational pull on the Earth is much la al 221xge4qodu4,ph1lsjt7r nc;/ zprger than 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 E ceplgn74aux24sdt,12 jo /lrh;q z1parth to the other.]

Will an object weigh more at the equator orfk9b:y:nr/cqqkgku- fig82 n v 0d+7lr, 6wsr at the poles? What two effects are at work? Do they oppose e, wks b- +r rq/fr6: gkyn7029gdlikvc:uq8fnach other?

The gravitational force on the Moon due to the Earth is only abvrn2hyn: *3rcy)xctw(e n1 (ak 3k7bmout half the force on the Moon due to the Sun. Why isn’t(:r tnbhnn 7ka*)exvwkmrc2 (3y1 c 3y the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit-y ybumu8fo: 1v78ln e around the Sun larger or smaller than the centripetal acceleration of1 bule:vyyum8fn-8 o7 the Earth?

Would it require less speed to,j/r nvt 4d rfcxsy wdc3;:/.m launch a satellite (a) toward the east or (b) toward the /c3.x/dvsr;,f 4mt d: w rjncywest? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scc3 .ah+u tboi;ale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground3;+.hatbu i oc?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lonl o9oq q;yka67g periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cyli6a;9 qolq 7ykondrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “a(8zijft47uvo,+n mc) j sdy dr)k+vn/ pparent weightlessness” between stepsjd ndokt8( ,v/cz4 m n++u7)syfijv) r.

The Earth moves faster in its orbit around the Sun in January than .u esb 3o z6 ,89yhxyiipwgj6-in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is eg6yb.px zuwh o9 3jy-i8,s6inot 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 discover e7 *9r*a lti w9*)fqvupov6zped to have a moon. Explain how this discovery enabled an estimate of Pluto’sz *9fw va7q* i6tvruppo* )l9e mass.

  The Sun's gravitationpw 8jlrq effq 6(+fht;t f6m;.al pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitationa.l tqm6( ;fjewf;rp f68+hqftl pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19h-o8 mz.khd2 / 6-qjsh njvl4u80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripetpl)fhlu04 hb 49ivkj* )i;qs mal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit il09; q)4bs*hif kv)jl hm up4is 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 21zm-(6qg k1u8ayo6mb2 2eswfcv fd,o pi9r:: a0 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 the speed of the discusfzse: 2bmg k-yq26au6:o8vw9p,ci (rm 1ad of.   

  Suppose the space shuttle is in orbit 400 km from the Ear,fw9omc. h9 d53p2a z blj/jmfth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express youo,.l92b /p awjfhmz9fm 5d c3jr answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelek) .x* fxeod1gration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s dia*okdxfexg .1)meter is 32 cm?   

  A ball on the end of a string is revolved at aun/6t lskmq5( uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speedu /(kml6sq5n t 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 turf;x . -wnt5cwvn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independntw.vfx;wc- 5 ent of the mass of the car?   

  How large must the coefficient of static fricccwpvk5tf60 3is.o*a+v -uob tion be between the tires and the road if a car is to round a level c3 ovc uik+6pba-.*tc5ovf0sw urve of radius 85 m at a speed of 95km/h ?   

  A device for traininyfez*lv+zq zr7c. +p6zn x1f :g astronauts 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 fastyzzl. *1fr7z nxzpv6e+:q fc+ 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 vz,vn:x7f qvrn iz 60+tlg:l4zariable 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 thex:0l 6vzf nl4n:q7tz+zv,ig r coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travel a;si.1hdd dzunt8j1: ing when upside down at the top of a circle ujn8 dd;ti:dhz1as 1.
(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 drivm9x,8r 8e kdt*tzaw9w er) crosses the rounded top of a hill (rtw zeraxd9 ,t m9k8*8wadius =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 wobzr1fkm + 2bng;)lfe ,uld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless2r,+kblf1e )z ;fbnmg” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of r2bvi,n12qnqs/ xui d) adius 1.10 m. At the ln2un sd1/i , )xiqvqb2owest point of its 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 centrifuge rotate if a particle 9.00 cm from thqjoud pm)s;4yo)e +y ,pw)+j le axis of rotation is to experience an acceleration of )slpo joj4wuyyp,d)q e+;)+m 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a fhyb)qu/;p9fqpg+ )uajrg2 ( cylindrically walled "room." (See (gfh/ gypu2u;9bfqjrp q) a)+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 abr g(/;xsgns* frictionless air-hockey tablexgg;s(rs */nb top, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the *4vss2mw,syu ball which revolves on a string 0.600 m long. In particular, find the magss42u mswvy*,nitude 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*g0l o+x 0 a8(pfkieeo(q)xbr 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 masses h8igbnz72seq)d ek5q y/+jb x+40aw b$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by+zr nsl,sn4v: qq1py9sip 2x9 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 agl a05xmufm7 .nd centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 1x.5gm 0fua7l m5$ \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,u vmb: i/0b:fd k*,tl9/ wrmrm 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 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 sk: um/9r0mm* :t,v/wf ib rdlbkidding? $\approx$   

  A particle revolves in a horizontal circle of radius xhs6g,p eeu vyhfe3m. lj 9/d3we; :o92.90 m . At a particular inde ym g.6s3;j wl9/voh: e xue3h,fep9stant, 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 o5,b 8s+:rt e4 x nz ,rwoyxbs6+lyoo2gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg.8ts,xbo:4n ,w sooz+2 ybyor 65+r lex   

  At the surface of a certain plal 1wgnmftyc63*:z n8lnet, the gravitational acceleration g has a magnitude of 12 m1gmyl t38nl:wn*cz6f /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 4,q6ngs ( zxs06kdk xfh:hi+q the Moon. The Moon's radius is 1.74zd kg 6:hs6q4xf,qi+xshk n(0 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 time 2e69e+hccuzej+ i9s jt2qg1ks that of Earth, but has the same mas2+ s9hit2ez+ e ujqkc69cj1ges. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but *;wohkmy kh 8/ ;q8p+gykl 56mgsd :mtthe same radius. What is g near its surfac;wm6gmo8+y yhql;p/kh ks5m*gd tk8: e?   

  Two objects attract each other gravitationally with a 0m2bv0zwakn *ia1 n9jforce of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accelerat4mb* 5 mj6/hp3vrfmalion of gravity, at (a) 3200 m /5 j3f6hm mv4b*r lmap   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to /c4a rf-l; ,xlbf0d( ad.xqeaa point outside the Earth where thegravitater lx.dqx4 al -cd0af,fba( ;/ional acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star vv*r/s)-htrvo b22 ug5 dl2 fzm(qry ,has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the sur2fhd5z2 s-2v(l r,/qgmuv)rrv y*b toface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whic*a (pm4 .qwiv- 1xi6 uij;b .topsf0z9yed zj.h once was 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 ofzixs zudwio. p* f;q m(46b1yj0ji. pe-9va.t our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightles;ffee3) ll.mzs while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km aboel.;ze)3 ffml ve the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at thx+lna sv/ 6 t3o idwx8:bcv1d5e corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravi/xxl 5s8 3w1di:6d cbtnoa+v vtational 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 th5ss8*x67we)aojrwf vq2w6a c e Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all fou s6wcwo75e)s f2*jaqxw8v 6r ar 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 acceleratioc o 3zhnm36te3d6apk8 n of gravity at the surface of Mars is 0.38 of what it is on Earth, and th66 kt3amdeo n8h c3p3zat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period k9,q69+ym a onvrs *oh:yul :oof the Earth and its distance 6,oayuq 9:o:mn9rk l hoyvs*+ from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satelliterex;5bd2zv(e *3m z gb moving in a stable circular orbit about the Eart e*2(bxber d z5vzm;g3h at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite intogfhya6k,1;ox 9thhp ar+p9 ;m a circular orbit 650 km above the Eartah9hry1k ;xth 9,g + 6;fopapmh. How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience 9etfk/f x 5lr (r7nz6csimulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answ69et (fr 5k7nfl /rcxzer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the 1prf pbh-d*(dEarth in a circular “near-Earth” orbit. A “near-Earth” orbit is oneb1ppd*f h(r-d at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the tycy-9,f d3h lhop of Mt. Everest to y fhcyh,d -l39be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command modwm:8tr35yt3b h. xdl kule continued to orbit the Moon at an altitude of about 100 km. How long did it take to g kbt35r.d t3l:mx8 hywo around the Moon once?    s

  The rings of Saturn are composed of chuum6rfhl;1,1x 7 (bno4*ii zyed7n lwrnks of ice that orbit the planet. The inner radius of the ribe1l mndzo yr7 1rxi wli;*76,n(4 fuhngs 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 evfh m7xlf g1u*5ery 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, axff *5 1ugmhl7nd (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fewt8k,:ey4wr rom the center of the Earth,:kywert4w e8 '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 consists of two stars of cztmeph6 *1yf7 2cd:b 7kmhh: equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit * cm7te:z6pfhhh21cbd m7 k:y about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight o (9 zp8qmeu.9do*oql lf a 55-kg woman in an elevator thatoz 9 *9luodme l(8.qpq moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceilf(dggv hm0:+* o0n1/l wluj qaing of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitg01d lfvj mqlo wh*+n:/0 u(agude and direction)? a =   

Show that if a satellite o sh9:tycnz) -u-rrgy8rbits very near the surface of a planet with period T , the hzr- n)crg-y tuy:8s9density (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 periodh*/z3i.yg* jpiz tkv9 of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near thyiv9h3p*.jg*i k tz/ze Earth’s surface.    s

  The asteroid Icarus, though only a few hun0c0ga ;y 4qxinv i z5at0j)5yudred meters across, orbits the Sun like the planets. Its period is 410 d. What is its ma 4;z juy t5c5x ng00y)0aqiivean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of u6 r8 c g3l0x 9ysuii myb-qf*;fa97gd4.5 $\times 10^{9} \mathrm{~km}$ 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 every4udn x0+:o(7+mzwyiy6 pwlvb 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the gnup +ymd6(7 0yli:4o+b wwx zvreatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cenwvfyh4 2:jxc+ ter 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, periohj- ok4 aoro5egsbs; 3h f835id, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 1609i5 8bkh35h-oa ;gj oe3fso4 sr).
(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 ovk :ao+0 t-fwff the Earth from the known period and distance of the Moon. a0:+fv k f-two   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’sgrfim-;q ,8r,s mlx) c48 mbpv moons, using Kepler’s third law. Use the distance of Io and the periods given in Tablegrxc q8s,mf i8 vl),mbr4p-;m 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 cok:q,ngz5uu4: m 43.uc on yecvnsists of many fragments (which some space scientists think c:z:4nm3k5u,u ug o.v qcecn4yame from a planet that once 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 describes an arti,:a-svsnc lyru12ol* ficial "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 b lyvrlsncsu1a2 ,:*o-and 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 e:e95xjsv6bonxsoh4 uh- ,(d in an arc from a hanging vine (Fig. 5–41). If his arms avo9u4nd : e6sxhsjx-(o ,b5he re 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 surface will the acceleration of gravity be half s.f+3hxr pz. jwhat ih+zs. 3rjf .pxt is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equ1h8pj g, ni0re:vki0eal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they p 10n ie8p0eijhk,gvr: ulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration yb-l2q* ch,a/ duq q.6r- zsrq)ccrx/ of gravity at the equator is slightly less than it would be if the * qb hx/u s-.zlaqq2yr c-cqrcr6d),/ Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft tr0h6z fka(0q)*gma fei:d2 bq yaveling directly from the Earth db 2kqag) e(yzaf0: qihfm*06to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but wh0zg 8d.uu 218sbf ykqyen you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and y u8z u1s.yfg0d82qkb in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circulafi/ 2qsanfb8 )r-1ys,:cjfsy r 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 yy)sf8j-,s:qn/fa1fs i2cb r(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 q6 7ve lyem:qphsm yweib(+:( 4(g+wlvertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of i31kn+,u: 6br 4w q9xnwbeegovts radius r, the acceleration due to gravity at its surface and the graviqvw nk14+: wu,6grbn9oeeb3x tational constant G.

A plumb bob (a mass mk: cadi9 bd(mk,apd d* k9j7z4 hanging on a string) is deflected from the vertical by an angle bd7 m*4 k:dazjk 9dd( p,ai9kc$\theta$ 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 If the coeff-18(te 8d-ffnvdu69+c bjzmbh nc02ch;umz ficient of static friction is 0.30 (wet pavement), at what range of sped 1v869eutumfmd-cbz0cb(n + fhz2j -8; cfhneds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that obg7viqz*() um2jv hygx(:l/rxjects at the equator were apparently wei7(*/mh qx:( vluv )jyirxz gg2ghtless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distalft7r 67i07u,1qy c4xyj xwpdnce apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 237:aoy4g 2kyk mqw5ct zh4mj*/ 5 m. A lamp suspended from the ceiling swm*/w2ztk 5o47jacyhyk4 m :gqings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been 34zs5 ads5dtq:9zk ficlaimed 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 of g 's a person would et4s395iz kfszdq: a d5xperience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telesc6 oii 0l-fhq 7*8kheprope 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 0 oq-hp k7* lrf68heiiescapes). 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 as it traverses the hill and vallecpdz / fx/(a-ny shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel hea d -npazfxc(//viest? 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 0c:2v o jpzus :n4*djxn3 a0jrsatellites 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 ofd0n2po:avjjz nc0j3u4x: s* r 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 Rendezvouuz iy1gdy og/*1l7e2ks (NEAR), after traveling 2.1 billion km, is meant i12u k1gd*7elyyz/og to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need omu2v2fzz-b-/ a leb zy(w /q9xf repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.e w yzz/v22a9qb/(-z fxm-l ub
(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 distance fro j sf0thfq2 *e-3qxx (rp7d5kom thd xfo5qk3f7*0- t2 qe(pxsr jhe 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 of G would need to bex/j 0z6e tc)ps if you could actually "feel" yourself gravitationally a)j/ctx z6pes0 ttracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the gg:juejrgi22c20v8 :dc- d zqMilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 ci:rjj8:ggdduz-0 qg2v2e2 c light-years 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 aro,ds*l8 nidt1e located at the corners of a square 0.50 m on each side. Find the magnitude and direction of the grdt,ldno18i* s avitational 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 550ga8k9yg6.+ lg -si0fw d ms)hj0 kg 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 experienced by the tip of the 1.5-cmf2dy;4vu q8 zs-long sweep second hand on your ;uz4sqfy 28v dwrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around3qjn. vo nzpbn j:*c-j 7: ,3x0ewvsll in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hins*zpw3nbjc l:n30qxo,-jj v7:nve.lt: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car tmzol 5 a+6r,4fzv0hjudy4 0mv raveling a6a vm4z0r+0lzfuy,jdhov m4 5t speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiatingpda415dt e7 ,hv cass( curves. The angle of tilt is adjusted so that the main force exerted on the passp174sch e5asav t(,dd engers, 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 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.$\approx$    $\times 10^2$