Sometimes people say that wateeg3o8x i m5 xsow x +3gmb0i:zb9t-0nfr is removed from clothes in a spin dryer by centrifugal force throwing the waterzxgt+ xoom b3b:0if8m 3n0 e -9sw5ixg outward. What is wrong with this statement?

Will the acceleration of a car be the same whenfz+u ++z-km1g *my dil the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle z1 zfy+u-d*k +mi+lmgcurve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whe l g/gvycvcv8yk+2 9v-re does the car exert +vc-l vvvy ykg/c g829the 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 child9 b( pt0e*f*bxwdk/g8zz iny, riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of epx9gf0 ,by zw*8/d znbk*(it the child?

A bucket of water can be whirled in a vertical circle withou*4 i+2fnt bstft the water spilling out, even at the top of the circl sf+*t2n f4itbe when the bucket is upside down. Explain.

How many “accelerators” do you have in your c0 r an)iv,eayzf :y5b0ar? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they prova5e:iny z,0 )ab0r yfduce?

A child on a sled comes flying overjh::zl,av qbn0r i8n4 xh0+hag-,z pn the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes overv0:n, xhz,0pqa8 rh+ jngi ba- hn4lz: the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean -v)xs.wcqu)tlgp 4ki:2eu) rcs m*c7 inward when rounding a curve at high speed?

Why do airplanes bank when they turn? 0 ;13 epm..+anfl0 un iwrkednd(*bjgHow would you compute the banking angle given its speedu3( gen1.0dfj*rn+el0 a ;.pnwbmidk and radius of the turn?

A girl is whirling a ball on a string arb k gzi+we )bf5o/) djf(;f,zuound her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a g/ ez)f+u) kjoi5f ;bzw(, bdftarget 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? If.2*b ix x ebg-a:4udnx so, how large a force? Consider axg-ua:be i* .xd2 4bnxn apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is ybwr .mv2q(;a, in what ways would the Moon’s orbit be.vmq;yw b(2ar different?

Which pulls harder gravitationally, the Earth on tll,;k,wr qfbw89 q) whhe Moon, or the Moon on the Eartlr8qkb w9qfw),,w lh;h? Which accelerates more?

The Sun's gravitatio q xn7ubf 5q:6gz3uif6nal 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 gravitational36bqz 7u5g:f xfnqu6i pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Wdexpjsd+c7a v v ;-:2xhat two effects are at work? Do they oppose e dd; cs:a xv7vx-p2ej+ach other?

The gravitational force on the Moon due to the Earth zo 8)22w8n/refc pr dtis only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the zo) r ne2dtr2cf/88wp Earth?

Is the centripetal acceleration of Mars in its orbidskp,iyc k /(w4+rbh 7t around the Sun larger or smaller than the centrkc b,d7kph 4siwy/ +(ripetal acceleration of the Earth?

Would it require less speed to launchgz0ga ,8x ,ifd gs:n3o a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotagn:gd ,xof0as8z3ig , tion direction.

When will your apparent weight be the greatest, as measured by a scale in a mo;i94zhx do8zrno61 qa.zk;kx ving elevator: when the elevator (a) accelerates downward, (b) accelerqrx4. o1i 9akzh;x okn;z8 d6zates 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 ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in ou5jle 1;8in mjpter space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship j1i enp 5;m8ljlike 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) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiencesamye -u 4g,m.o4je6l h “free fall” or “apparent weightlessness” between steps ,o4 ga4hme6m.elyu-j.

The Earth moves faster it:bh cu9,uqjv v4wjax+b m7if1 iq;:(n its orbit around the Sun in January than in July. Is the Earth closjh,mq+a ti947(:qf;c ubwib1 :juvx ver 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 tild /oui 8t)c0 :dla6po have a moon. Explain how this discovery enabled an estildti)alp 0d uc:o6 /i8mate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is muc+ihc-z9yo./ je:*n *mgj)ak w )vamet h larger 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 Earth to the * kvjijg * 9-ea eyw+ahc/)ozn)m :.tmother.]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 1980-tmb6 k(ih1w(eyj,nz a+5;l f3pjbre $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelerat,qn,t+hc,osy 4umvksk 1q75getty , + ion 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 is a tst47v,st,n uky,oehym, k5 +qqg+c1 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 it rotates uniformk89c6 u a-xn kyay52f kvv4sp.ly in a horizontal circle (at arm’s length) of radius 0.90 a4c-pun yy vf8k26xavs 5kk. 9m. Calculate the speed of the discus.   

  Suppose the space shuttle is in8xrw2/g7 n/roo ;oao g 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 ter;2 w /ggr7or ano8oo/xms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the mie5n l1c fax5g++k o6acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 325 m5i fnl +gec1k+6xao cm?   

  A ball on the end of a string is revolved at a uniform rate in a vrjqkbjxy rgmw(3pl6ry: 90p. ;n k+3s q.ohi/ertical circle of radius 72.0 cm , as s6;k0sxipqq9 ygrlr .hywmjopb+:j3/.k(rn3 hown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with wh)h1he+g/icov aj7 * wqich a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of staticq*hiehag1 +vcj7)w o / friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static frictyq vp,*-, 3i qxj 0cr 9j1ke.xc9iquskion be between the tires and the road if a car is to round a level curve ofc, qr9jpkxx0 i1v-c k9 e*q,.jqyu i3s radius 85 m at a speed of 95km/h ?   

  A device for training astronauts a.h0;.gs4,z r gbpweus+itage5bd8q2nd jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.u s4 bzwt. +aeqr,ggdse .8;h2pgib5 00 m . If the 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 ff3+7vua p- qm1o2 eoktrom the axis of a 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 of7op +vmfu-ko eq 1a32tf. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travel) (djsxn eptd62vb e3i7t1 b4zept.-cing when upside down at the top of azsxejv 4( 3t e17)dp .t6 tndb2epicb- 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 4*zob qxo( oj :nn:xc0mass 950 kg (including the driver) crosses the rounded top of a hill (radius =9jooxcn0bz4o: x: qn*( 5$ \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 Fer ex*rv9g ta:4rris wheel need to make for the passengers to feel “weightl ar4xrge*t:9 vess” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At 7sro ia3exusi5(c 54mthe lowest point oe oauc5ms4r(i5s3 i7x f 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 aqdf )fyji0 6/s particle 9.00 cm from the axis of rotation is fj0sf / 6d)yqito experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rota l4wo4 d it8h kj+g-/+d,e.fprjnrv-dted in a cylindrically walled "room." (Seo+, dt4ewp.-rd+n ji vl 8-kgdj/h4r fe 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 ta :/qbt4v*p exafs kw.1bletop, and is held in this orbit by a light cord connected to a dangling block (mass m xsw41ekpa/bq t.: *vf ) 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 weighmnhi* 3rsoc) a0l,bz9t of the ball ws,*390lon hbc )mazirhich revolves on a string 0.600 m long. 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 of 88 m is perfectly banked for a car trcqyd )ydp 988yaveling 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 massesj2( feo; 2zssm $ 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 bmv 6vfq.tc 6-k2oim -ly 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 96-93hr hsfxw;ottzcxcs9vy+/dyw 4m .xr 1v and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when it39/sc4vhyt v coz+r.1w9xtsr f6;d w9yxhx m-s 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 uniformbcjz) t*8xb) ,aj.,ips y(1 vchzvf 6uly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 2)tsfiv)j,6(zc u *jz.81v,x c bhypba20 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 r4tuiew7.0 uam adius 2.90 m . At a particular instant, its accatwi.4e u70u meleration 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 12,8001jdnp 0 m6 pyfusw(b51s:n :su km (2 Earth radii) above the Earth’s surface if its mass is 1350 0n:fu nuwp:d51jms s(pb1s 6ykg.   

  At the surface of a certain planet, the gravitational acceleration g hashi6o4) 3w+nb7i vtdlc a magnitude of 12 m/)l t6ochiw+4ni73dv b 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 gravbv.qpn,weoc( w07xf/7gttf+voj l/c *zv- o 2ity on the Moon. The Moon's radius is 1.74 o ,p0*t+e7.l2xzvoq/wc-7vv / (owtg fnjcf b$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has ac(3 gidutqh s gq pj)w,8n-a5nz.:4ba radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to grac,g )i- qhw3puszq.g (4 an 5jdb:t8anvity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but tiyg6o;u: g6e halsa+z )cb+ wr16x6uche same radius. What is g near its surfac 6u:cwy+a 6gusz)xb;1hla6cg6o+ir ee?   

  Two objects attract eacs *jeh; w7i8 gbidlr63wjb;p,h other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of g la 4s0y9giu/aravity, at (a) 3200 mlsgy4/ 90aau i    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centw n-)q qzqi/6wer to a point outside the Earth where thegravitational acceleratiowq- qwq6i)/ nzn 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 m9dve /+kp anx9ass of our Sun packed into a sphere about 10 km in radius. Estimd+pkna/ex 9v 9ate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our i0ill0ci0hv(;9g s qu Sun but is now in the last stage of its evolution, is the size of our Moluci li0q gshi(v00;9 on 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 innn92b nn+r qf:;kitho6 0xq n*f,gc) l the space shuttle. Your friends respond * xfh n bq96l+tn,gnn:q;in20)rk focthat 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 above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at t /40j gkea;2j5bnz4 q wc refj2/ux8ckhe corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by thke4r 0uzcb e2/52fcx4wang8j/jq;j ke other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets l/alg,+e:0(jsld, )8z jw+fctvatlkf ine up on the same side of the Sun. Calculate the total force on the Earth due to Ven()set+ ,aw+f 8lgt jl:jv ,lf0zdk/caus, 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 Mars is 0.38 of whatb2/9 ryiddt*o it is on Earr92 b/t* dydioth, and that 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 peri89d er1srtci1 pf08 gqod of the Earth and its distance from thesrq1etg8018p r9cid f Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stabu2 di++zh0cxvtl3 k-lle circular orbit about the Earth at -zl3 d+k0htvi l2xuc+a height of 3600 km.    $\times 10^3$

  The space shuttle releases a sabgc7wx(a( j0 nm6rw, choy/5wtellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release oacmn( rwg,jcw5w0ox (h 7y 6/bccurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience-3)h0 w(7b6h /m s9swi rn3nxpelem 8fgq1tz l simulated gravity of 0.60 g? Assume the spaces0br8wle s)wt7lmgnx39/mn f( sp h-6qh3ze1 ihip’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbi ,nrs)f xg2ml1t the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is ongm,1) 2 rsxlnfe 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 fr d6g1fc/ zscw0om the top of Mt. Evz6sd0fc1cw/ gerest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued tclzhd ) znv/-0dqc ;m*o orbit the Moon at an altitude of about 100 km. Hondlch)d /v *0-cmqzz;w long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the :9cp4o ln4gl5 7simot bub5)kplanet. The inner radius of the ri)l cb 7s4kmiu4bg9lp :n5 oot5ngs 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 (6ssax. u s5-juu;x ;4 szianmwf3*cs*see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) ux jza* m *f a;s3wsn.;icx6uss su4-5at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaups ,bkl*df:31 vp v-xwt 4200 km from the center of the Earth's Moon in a space vehicle (a) mobv x,-v3p*sw :pkl d1fving 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 equalcocvasrfh8e)lwe9r a (4+,r0 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. caoe lsvr(8), rcfa09 hw+e4rWhat is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the we ymnzq ::cuhno 3/gyn-er)n31ight of a 55-kg woman in an elevator that moves q):1ne:o nhny/g3r m3yncuz-
(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 suspendeopry/m ef+.pv59oobr:8eu + kd from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the eley upoov5fkp+eo rrm8+: e./b9vator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface 0gj41fkf j1es)n1q (uwd5wxlof a planet with period T , the density (mass/volume) of thn0 eduq5jk x1f )w (j1swlgf14e 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 q1xxv 0wi/bes k07m6l period of the Moon (27.4 d) to determine the period of an artificial satellite orbi16qx0exswi7 bmk 0vl/ting very near the Earth’s surface.    s

  The asteroid Icarus, though onl8u dpaq( i y7yjuc(ft *ftt6h,py7ye-,*1f vey a few hundred meters across, orbits the Sun like t*( hc(qyj1pyuf , tf76- ay8t7eyfpvtie*d,u he planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance dx2w-v 2pcv+m1 ji72oly)v;l b. rfj lof 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 orbitvvo 59i6yw vjm i61zw+s the 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 neaivzj +wyv 6m9o16wi 5vrest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gal4:64ubg szbfbda , /mvcdnwr +x;o 3b3axy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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,mnsmmq gv ho-hgkdy9 ov38(/)o 3 7y7a period, and mean distance for the four largest moons of Jupiter (those discover7goh 8q3 maoomdv)ykv(3s-mh yg 7/n9 ed by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and 2u:vw+yl z8qq distance of the Moon. 2uq:lzv+ y 8qw   $\times 10^{24}$

  Determine the mean dista*,t fo7hui :svnce 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 ti,hf :o*u7vs 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 fragmentnkv7ud om :y78s (which some space scientists think came from a planetn78k7yu:dm ov 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 artificial "planet" in the forms6/ ynrg8rn2rg i 4j(i of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity o(8i2/s4r ijgrnrn6g yf g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gon xg2b/ra n55rrge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable gb/n5x a25rrnof 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 bh f,z0vo42x sbe half what it is on the su 24fo,vb0 zxshrface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and4hfs d ul+frx)f8. 0cs 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 .cr) l8f04+fxsf dhuskg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration n9 z:snh3s md9of gravity at the equator is slightly less thann9:zhsnd9 sm3 it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Ex r6dn ou7x7y;arth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earthy xxd;ro6 un77 and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand o2 rm x8)e2riidn a bathroom scale in an elevator, it says your mass is 82 kg. W2rix2)mid8er hat is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circug(-+ q *ye qo0fsrhfc:lar 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 s:f( sqfc0 grhy-*+eoq peed (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 airng t;in)2chqy ywsy()+9 qtm 6craft 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 the mass of+df6vlh-m t t( a planet in terms of its radius r, the acceleration due to gravity at its surfacfh6d+ vm-lt( te and the gravitational constant G.

A plumb bob (a mass .ld6go ak uxb.2pih7o8z (z fs.gr, 5rm hanging on a string) is deflected from the vertical by an adz 7,5 arbig2xuf.rz 6ol( ..so8khgpngle $\theta$ 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 banuvwo7j+0/ y9n6py zkh ked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car sw jph0uy+k/976 o nzyvafely handle the curve?

  How long would a dayyhu foz,)2m(igg4. h y be if the Earth were rotating so fast that objects at the equator were apparentg2i f oymh)g.,y(z u4hly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apar;rj fb;vz6hbj15 irrtn 9+ g8ut 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 co4knoe/ /k; hdlnstant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to k/eh dolk4;n /an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 q;dkl(( q.dfs times 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 of g 's a person would exper(ld.kd(f;qq s ience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope vlucd)8b d*r2deduced 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 gasvlb dr 8)dcu2* 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 hiez+(:isvd)4-w;t dyiayw a;u ll and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forcdd+y (w; izi)vu:w-4aatsy;ees acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satelliy-ziv: ) oe28 rcexce 6ap5g4utes 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 altcg-:cie6)u4 y8 oxpvzera 25eitude 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 (NEAR), after traveling 2.1 billion km, is /s*pmne yl.g-j8j mz)meant to orbit the asteroid Eros at a height of about 15 km . . *j8lpmjez)m-/g sny 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 of rbqsxt a-. (:qzepair. You are in a circular orbit of the same radius as tha.:t(x sqqzb-e 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 3r7gb nfm1e66ujs / q*q000 years. (a) What is its mean distance from thebg7q s/fj6*6n1e umqr 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 be if you could actually "kf;pjg* y+d (jfeel" yourself gravitationally attracted to someone near you. Make reasonable assumptjgdy j;*kp(f+ ions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) ga 1.gjv,gdll27qsg +at a distance of about 30,000 light-years from gv,s17l2ggd ljq .+g athe 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 cor 1q+r7d qme)euz t zkg-p,e29oners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-ke2q9-k q)e,rdo17utpzeg+m z g mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth z3jj/w14f pey$ \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-longk23*y)2ts m z8 qztyhf sweep second hand on your wrist wat ykyt2 hm*t)q3 sfz2z8ch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in .gr;h-mclnf/ vp5b cw+kua:l) 2r a1fa circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle eve-1wmn ; c ka+:l)ufhcbr/fr .l5avp g2ry 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 radli kvb8+m:xls w zt7lv 4s3qkuo;bv ,;fj 3s,5ius R in a new highway is designed so that a car traveling afl:83i jvl5 wo ;3usl7sx+4v,qms, b btz;vk kt 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 carsm9a7nb6zwd zw 7u me5oa+msn 2 d,2da3 when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the tracdm7m3d+ 5 n2,uzswm7ean 9 ad2awboz6k 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.$\approx$    $\times 10^2$