Sometimes people say thaw)is*qgk6;5 u7r ojpt t water is removed from clothes in a spin dryer by centrifugal force throwg u)7ori ;wtk*5 sj6pqing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car toufaap(g*:z0yb4qxpe* m1o; ravels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same0 z** po4e:(uyag1qbao; fm xp speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car:4yftex lqx /id:;f 4p exert the greatest and least forces on the road: (a) atepxff;td 4:l/yi4x :q 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 h 1v+zx9xk0kyz orse on a merry-go-round. Whichzxykv kz+ 91x0 of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled i do d of(26n77fjqkdq8n a vertical circle without the water spilling out, even at 8qff2j6 no7(d qkdd7o the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your,n29a r, u v2ord74bgrh/xkp2xk j4in5t(evu car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acnd2u9r7h, t5(jrknu,/i4o vkexb2 rv2 g 4axpcelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as sh x* m1d rusd49d1dssm1mm;vc9 own 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 Newt vm1uss dxrm1d;9 1mds*49dcmon’s second law.

Why do bicycle riders lean inward when roundingqn+kph3.wuyr9* q t:es9g.td + 0rcxg a curve at high speed?

Why do airplanes bank when they turn? How would you 1rzy5, cmog )lunsc,:compute the banking angle given its speed and radius of the m)c , g,1ynruo5szl:cturn?

A girl is whirling a ball on a string around her head in a horizontal c0aphs )n1o4cip7h :z plane. She wants to let go at precisely the right time so that the ball will hit a tarh:1 p)chnpi4c 7 osaz0get 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 so, how lar-:n/(ppbnd(gh i e5c age a force? Considcgh(: -5ap db/ (iennper an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what i7c/t0.da p:;j vroab pt is, in what ways would the Moon’s orbit be daj.;/bvcd tpp a:o7 0rifferent?

Which pulls harder gravitationz cu0 pidrd;9)ally, the Earth on the Moon, or the Moon on the Earth? Which accelerates mdz0d 9);piurcore?

The Sun's gravitational pull on the Earth is much larger than the Moon't2e xl89ly6 .ulbb +nu4az 0qvs. 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 lx0b2e .u l9 vl8unyq bat46z+other.]

Will an object weigh more at the eq:6+ qk69lh tx1/tho bkiymyj;uator or at the poles? What two effects are at work? Do 6k/h1xk iqtj;h m bl+o6ty9:y they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the forhfubju)r2*) - rq5xxh ce on the Moon due to the Sun. Why isn’t the Moon pu jfux-hqxh))5b rr*u 2lled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger3i2(, ixc n2uq1wn a8oxfvgb- or smaller than the centripetal, -uaqbx32io xvw 1cfn( n2g8i acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward thew+ 85( jyb6 .51qimnky vjaauy east or (b) toward the west? Consider the Earth’syibya jqkmwua5 n.+6jy 8 1v(5 rotation direction.

When will your apparent weight be the greatest, as metb40k) w+d g)atvv(gnlsx /. sasured by a scale in a moving elevator: when the elevator (a) accxgsa0 s t.gw v bv)4(d)n/lt+kelerates 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 ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lovwjxrp gz 9i 5tat 9s-.4:ct+ong periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulcws.ai4t o5 vptxgj-tr9+9z :ates 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” 5 sfjm6k/ajpxz o8c1 *or “apparent weightlessness” between steps.kzj/c8x*6mja o1p5s f

The Earth moves faster in its orbit around the Sun in January than in July. Is ,3,8rbl;bpzq;pj0mvfz 4:d z0 cnal kthe Earth closer to the Sun in, jpvf;d,;3c8z0z:lbk anplmqrz04 b 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 knanw1c4a5 0qtz own until it was discovered to have a moon. Explain how this zw0a51t4n c qadiscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is muc6i *kb2 lkt0g s91evzih larger than the Moon's. Yet the Moon's iselzi2g1 *0ki9s t6bk v mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 7tsvf1dezs,pj j0g+6 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 Earwkz 3q9.9mtixbq)9 :ay 5go nwth 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 cta5zym 3:ig)9.wxowkn99 qqbircle 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 rnmm12s +u+uwbqz m62w5vy m7i+ ec-hiotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Cami- mzw5n+ 2 6+ qbeyhviwm s7uc1m2u+lculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth'vn 69)sbjp* npw5w3jvs 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 ofsb 9nwvnpjw5*3)jvp 6 g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a/1rzzgomi2(m speck of clay on the edge of a potter’s wh(zm 2ozim/r 1geel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolvedo*w zcmf+2(o x at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spe( +*fom2xzocw ed 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 cv51bkb1oj p3z ar can round a turn of radius 77 m on a flat road if the coefficient ofbv51b pkzjo 13 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 static fcck 8sd:4l:06jsk tv qriction be between the tires and the road if a car is to round a level curve of radius 8 0: jk l8tkdc4vcs:6sq5 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilotq o 6o.r8:aaiks 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,oak o q:.ra8i6 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 froo+n( kzy* pb + :w/lv, kkbdjf uwf;1i))d(qbum the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remv,jziu+bqd)on +) kd* (b(1;pyfk:/wwbkufl ains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traaub5 bz;gpa/v2tvv(gq -iux 0r ;/v 3gveling when upside down at the t gu qva ;p 5zarx;vu ig3t-(2bb/vgv/0op of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses x7andaimc(3 7the rounded top of a hill (radius xmn77c aia(d 3 =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 mindd(c:ugff i 04ute would a 15-m-diameter Ferris wheel need to make for t4df (cgif0:du he passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radi,tpd0eur *vb /us 1.10 m. At the lo0,u t/pb*edrvwest 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 fromc 5 epgm2+ zboa-;81d,dfhofg the axis of r ;,p1geho dd+c2 z8a ofmbf-g5otation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rot)0r 3 yr4ktp2t9phn rsated in a cylindrically walled "room." (See 3rhk)y940s2n t pp rtrFig. 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 circld1+cxkdu86dtul7, ete on a frictionless air-hockey tabletop, and is held in thi ltu t1+ex,ckd6u7dd8 s 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 f:h g3 (yjiklkvsc; w:n g-2h*61h afgnot ignoring the weight of the ball which revolves on a string 0.60gs( :ik;g1a-*3fgch2yk6:vfnwjhl h 0 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 baeuhy y- mu/( cl9l 3ja:(1nnzrnked 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 a1no9i7jr0 2 anean+0v23odm b,np i;t4jkom $ 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 maneulw7b j ddt15h8ver 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 components of the net foro3kfp 9x:yb8 a-tjj,q ce exerted on the car (by the ground) in Example fjtp:a983 yqk-jbo,x 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 tjbh) ,y2whiu4u1bq.ly ,5 em6go6.t dzv-vpjhe pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires an-gym6 evpqvt21 lj yzi5who. b6j ,b uu4,d.)hd 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 i -wdrjs9 7n5c;*uv acmnss;n*w c9 daj75ucrvm- tant, 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 Earjbgl:b sgh-bi3*u sd,v3j , u2th’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfac3j- uv*b2us :,3lb,ggsdjih be if its mass is 1350 kg.   

  At the surface of a certain planet, the gr nc-)a*o02 bf 8xdccccavitational acceleration g has a magni0o2c-*c8dan c cfxc)btude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity onigr5+mny-c w ps135ej52hs v5g 9q5- gdkx oia the Moon. The Moon's radius is 1.713 25h5 ssqr-5yja -xgegwo9gmnpkvi i5 dc+54 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hawk,pc1r;:q9b5ewag a s a radius 1.5 times that of Earth, but has the same mass. What is the acceleration b wg :kqr59a ,wacep;1due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same wu7mkcqfg ovm)5 0; gd(rc-f2radius. What i-gm 2fgd7uq;v ocw)0(m cfr5ks g near its surface?   

  Two objects attract each other gravitationally with a force of 2.xsu cndx ;(yu0rsk5/; 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 5m vz,uu;xnflp 8l5d,l5nq9uvalue of g , the acceleration of gravity, at (a) 3200 mml d5vnzl,x fpn8uquu;,l 559    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centyfm + wzbmm+f:23ks/x 3nu8cyer to a point outside the Earth where thegravitationaly/ ckf m:w+ m2bsmxy+z 3nf38u 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 iyode(3oz7du(ey k0 /bnto a sphere about 10 km in radius. Estimate the surface g( dyy0 o3ukode( 7ze/bravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average sta 0sywguqv sc7d: ff860r like our Sun but is now in the last stage of its evolution, is the size of ou7 s68: qcd0 0vygfsfwur 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 whisdy6u7k t8d n,q;z) cfle orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Cofdq zk)y;7u6ns,d8c tnvince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a e- k1z 2qysfnk0z -vl9square of side 0.60 m. Calculate the magnitude and dez2vs z-k0kn9yl 1fq -irection of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yeaepo6 4r(gy nw6rs most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-p(g6 enr64 owy38). 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 ofm kgzu:ym :3/s2p(v zf Mars is 0.38 of what it is on Earth, and thg 3zkf:(up 2/:mysv mzat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value fl4.f k. 1fg)mj sf,dsuor the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example4fs)l m us,kf1gf j..d 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellitdv za)j bi5(qs f5x.)je moving in a stable circular orbit about the Earth at a height of 36xbq)zfj i( )d5ja.5vs00 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above )ml (r n: e:p5o(nfnnuys3q.x the Earth. How fast mm rly3.nnuof:s( npne :)q(5 xust the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occu ptn d3;d 2v;*3bthpxgpants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.) ndp;v3d;t* 2hg 3btxp  

  Determine the time it takes for a satellite to orbit the Ear us-zs k3ae h56uj(p1g;ccu q:/yvx t8th 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 of the satellite? k 6eu(c/sax5 y;-t1 pv u8uq:hzcsg3j   s ~    min

  At what horizontal velocity w eg/ bh.mg f:o5y 5bt9z/aj3uu0hg7 umould a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbifuemg5u 5o 0/ag:g thh7b3uzjb.9 y/mt around the Earth?   

  During an Apollo lun (w52z t5ejwsy a)/phvar landing mission, the command module continued to orbit the Moon at an altitude ofht 2sa5/e5y p wvz)(wj about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunksrzvy;li6 q q) yw;af)pd(u4:9u eff7u of ice that orbit the planet. The inner radius9q q u:r;ua6i()zyvfye7;wu f) pdl4f of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in dr+dl6v l0iht - o4ggs;b)z 5iliameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’sd)s li4llthvzi-b r5 g0+o;6g apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weighe hh6mi5 en)q;t of a 75-kg astronaut 4200 km from the center of the 5mnhiqe;6eh ) Earth'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 cons lvhmrn53:kkx/volh7 eb inzo60e2q4ip, t5*ists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to 6 vzi:53lnh5ro,/0 4nio em2*vpbt7h kkeqlx orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator thm7o4t *:f qcmeat movecmmeft q7:o4*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 from2a/l4;bsag2/hikho qt2u t2k lh t+*m the ceiling 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 (magnitude 2 al2i2 /as qb/4oh2klt gt;+htm*hukand direction)? a =   

Show that if a satellite orbits very near the surface of a pyzui6 d6d. s g)xzw4p,ut mnm- 79dqm,lanet with period T , the density (6tis-y)d. g,m 6 qd,dmp97zmzuwxnu4mass/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 the3hr (afys9u0xojo/a ; period of the Moon (27.4 d) to determine the period of an art(uh93 xy0oraf;a o/jsificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though onlw-5bbfe; e4v jtzw kyp1 1z7;iy a few hundred meters across, orbits the Sun like the planets. Its period is 410 vz;jfp7iy1ew -1 5b;z4kwebt d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanc.s,qqum m*4u7 hbv03ae6qihx e of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sf-px1afoy f.c hv 5e7+un roughly once every 76 years. It comes very close to the surface of the Sun on its closest-fe1 oc+fh5v.ayf 7xp approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy xow, +w 1n+jcw $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, perx+w3 kxmbwaaf61+* bsiod, and mean distance for the four largest moons of Jupiter (thosb3abm61xf*w +aw+kx s e discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and dista.,r d2ksz mb0vpj ho-3nce of the Moon. h k3.s,pzrd- 2bmvj0o    $\times 10^{24}$

  Determine the mean distance from Jupiter ftp yhgk*ry-w -nb 1t6 o/ds5bss(;+faor each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods1(bwrg--* ky 6 tbs oy/ fsahtnd+5ps; given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists oj/md7pfx( f6 pkc :-wkuybq(3 f many fragments (which some space scientisqk-3k ppxb dwy6( fu7cj(/:mfts think came 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 tag9d b: el0z h7l-wd*xmle describes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate tempe: *xbdm0z-g97hd llwerate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an axrmz,kd +:du6 g(aso+y0 ja)brc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of ) dsxagm,z+k0(ojau b+r6d :y1400 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 )b4xr8r iwu6q the acceleration of gravity be half what it is on the surface?xr )b4u rqwi86    $\times 10^6$

  On an ice rink, two skaters ofdp 9r2xgiy/ l,7tow 6v equal 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 arwd6t7i2lvx9 p/y,g ore they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day8b s.:ls(salx , the apparent acceleration of gravity at the equator is slisl8al.sx(sb : ghtly less than 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 Earth will a spk ;ww73v .i b5dizqzy+ps,f2 gacecraft traveling directly from the Earth to the Moon experience zero;vib2pg3,z5+ dkz ifw7qy sw. net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand o*qu(pye2( wdq ,* vfot *y-b- jdxdm.hn a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of uoyd, j**wf(d-2bp*x .m-hteqqdv (ythe elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stationoqm9rh u/:rv- bk.b2 ui)x qv4 consists 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 12/)b.vhq9 ourkq: -bu 4xirmv.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aisjl5uzekd4n56mu.mw1 j* o6lrcraft 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 a plan*y0 tu*c*;l s yyty*jget in terms of its radius r, the acceleration due to gryty0*u*jtgc*s;y y* l avity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from tb42jtz a01jy,tdww -e he vertical by an angle2w,4bt1-yade0z j tjw $\theta$ 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 hrx3dc +(uah /speed of If the coefficient of static friction is 0.30 (wet pavement), a+a3( crdu hh/xt what range of speeds can a car safely handle the curve?

  How long would a day be 5 nxsdq4vc4u 09uawhpdmrtq;,4 0f 4hif the Earth were rotating so fast that objects at the equator were aph,c qsua4044 r;hd fd4pt 5mx09 nwvquparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constantskb)zn p7m8rbit,e(+ distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp bjzuu4mf42o 0qd :7 tmsuspended from the ceiling swings ouumbf: 7 40 tmjd2uoq4zt 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 f-n5bylw04qz ,y6jr -yl ss:s claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people ca 6rysyn,y-z:sw 0lf blqj4-5 sn't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduce3ci+ agcx(:;p+2m2l pcvbm b fd the presence of an extremely massive core in the distant galaxy M87, so dense that it3cg ;:+2(pmabimvcp +b f cl2x 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 as it traverselqnqi 1zb 2ly uw/rg+x/06 od0 1axo*es 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 forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Whereao/1qb/ g i2lqwry*1odl x0 nz uex+60 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 Posi1 r06(+ ub-qwosb7 l uiho9ckctioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of eacho 7r+kow csbi bu(q016ul9c-h satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 22/j: +ci sfyc xjegg17.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly jixcc g sf/j2ge+y:1740 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 put6v c6+fcxhm s8kx7itt39 wh 8rsuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km7x tk9 v6+c8i3th cx s8h6tfwm above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean njcas4zq+) z6distance from thz)cjsaz n46+ qe 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 tuc;/ ye48 3ggzxns,n -7m3w s8wfi cnqo be if you could actually "feel" yourself g8f,u7q-3c 3w8z/sie4cgmn ; snn xygwravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at(6yx kpenaxm 6(y(wr , a distance of about 30,000 light-years from the cenm, pnwyy6xr k(x(e(6 ater $ \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 lz b)ux-m72ux qocated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint b xqm-u2xzu)7of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eartf5hwcl g5yi*m w ovb/)yv u469h $ \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 0-sqx6k 2qpzz /;wja eby the tip of the 1.5-cm-long sweep second hand on your wrist2z6z-keqq/px;0w asj watch?    $\times 10^{-4}$

  While fishing, you get bored j3.lo 23b fgj16yafowand start to swing a sinker weight 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 theb jfl6 3 ogao.1jw23yf fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radiu 4h5g. vg7*oslbc*b /ctbs hlb/la89is R in a new highway is designed so that a car travel ct*g*ial95oslb47c bbl.s8ghb/h/v 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 trai ;opw37d z 9 yjlrxp+f84 zt+ecua7m3wn, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of7alxjt;97 w+ 84pyre3 +zuw3of p zmdc 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.$\approx$    $\times 10^2$