Sometimes people say that water is removed ,c6erb3 qir/o from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this stateme 3o6r,/ebrcq int?

Will the acceleration of a car be the same whan 2qs6i j2 n4/4auvhu,mjhf,en the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve ata,s, nv 2u nf4aqu2j/h m64hij the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the h1k4qzo)9dh* rz e(af car exert the greatestd)4 z9r fqz 1hoake*(h 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 chcc+8 6u(hk-zymod3 iqi4 lc.nild riding a horse on a merry-go-round. Which of these forces provides the ceu3izli4c .y-d h6+m q8nk(cocntripetal acceleration of the child?

A bucket of water can be whirled in a vertical);::ewqvf90ffj vytvn l4lzz / o g*w1r0fz4m circle without the water spilling out, e mt 4zfyo00vfv 1 wve)*l:wzj:z;/g4f9nqlrf ven at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are 5tpg)41, xz c uzz6fghv76jegat least three controls in th)ejz1 pt75uhgzv66ggcx f,z 4e car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the cre(u x2 dx3h4y md0 ebll,axl,fs)71ljrst 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 normadu h)b,d mjx3y0l1la2l, x4l7e sx(f rl force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders le:nqv8o-v wn-d an inward when rounding a curve at high speed?

Why do airplanes bank when they tur z fr:+4viociz ,;ugi5n? How would you compute the banking angle given its speed and r :;c+zzi,4giu5orf ivadius of the turn?

A girl is whirling a ball on a string around her head in a horizontal p/brp cp k78gy)lane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. Whenbkpgp)y87r c/ should she let go of the string?

Does an apple exert a gravitational forceeem4vfyal/- jt / yg(: on the Earth? If so, how large a force? Consider e- /yla( vgt m4/jyfe:an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would thej tm*v6:0r hme Moon’s orbit mrmev0jh :t *6be different?

Which pulls harder gravi)y+ gd.xc)aj, ywe z1utationally, the Earth on the Moon, or the Moon on the Earth? W,g)ezy.+ycd )1 xwjauhich accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon'5+g0)mvgze*snllbj 5*g7 wsb s. Yet the Moon's is mainly responsible for the tides. Explain. [Hinwss 5j)ggb0e*l b7 5nm+z*l vgt: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at theh1/u:nq .rshp 8y/qda poles? What two effects are at work? Do thehqp uyda.h 8q/1 n:s/ry oppose each other?

The gravitational force on the Moon due,:2o 4rj qvkwx.h py,y to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away fryr4hx j. vy,kq2w:p,o om the Earth?

Is the centripetal acceleration of Marsxwu4x* fs- u: w1cq4qb in its orbit around the Sun larger or smaller than the centripetal accelewq*u1sw:4bq -u c4xxfration of the Earth?

Would it require less speed 0o*u q9hkkj16cb ucw4 to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotatio9kb0kw u1q*j4 o 6cchun direction.

When will your apparent weight be t1s)f3 e wz x6o4xjs.ftuf1hk1he greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall,o h s1f4txfu311.z6xs)kwejf (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 outer space could be adversely affected by4fv4-fez* jtew-za 6 guhm)h5 weightlessness. One way to simulate gravity is to shapez4jth6a5zfueh4)w -fvmg* - e the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “md ek,;wtizx-g.nh0 ( free fall” or “apparent weightlessness” between steps.xmn-tg (i k0de,z;h.w

The Earth moves faster in its orx 6hhmg2rin*8ifl7;oj*bp a 9ra* . ypbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: Thm2nba.pahxfrlj9*hr* ; go*i 7 8yi6p is 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 n-a8wqdh4*m (wxkjs-ut: vr: known until it was discovered to have a moon. Explain how tha-(wdq t*um :4rsn8wxkhj-:vis discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on theye8 i a:c.,mvy Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatio8 iy:c.mev ,aynal 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 10svl 4u)d(swy 980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around4p-p fuh ek3*s the Sun, and the net force exer*sehpk3 4 f-puted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discup. ng uy, 2 8nukhd44.ikipci9s as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate theng8dn p,24pk u.y9k ii.4ichu speed of the discus.   

  Suppose the space shuttle * f :ryrvmn9m(is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in itsrf:rnmmy *v( 9 orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a spez cw ,l,fbf .;c.c:aycck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diametf.z y:.cb,ca,c;clwf er is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical ci,cw ef-9ip wht4 up-0hrcle of radius 72.0 cm , as shown in Fig. 5-33. If its-09p huhftw4ei cw ,p- 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 which a 1050-kg car can round a turn of radiu**gc li*g 9(ty967aqtk,mt dcb xyoi-./qia cs 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the cartgqa* byt ao*7 gc99i*c.(my/c x6 klii-,tdq?   

  How large must the coefficient of static friction be between the ld.0vzr:vn m u,hop/6 tires and the road iov:6l,nr. 0dmz phvu/ f a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighterht:a,q6w1 s mv pilots is designed to rotate a trainee in a16v,hsqm w a:t 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 fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis ofp ;):*g nj bkspm6,lyx 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 off. What is the coefficient of static friction between the co)p km,glny;x*p s:6 jbin and the turntable?   

  At what minimum speed must a roller coaster b2.b,-h,slj6 x ivp8vlq +skts:s v8ia e traveling when upside down at thej . - lvv8sx ,is8vh:si2a ,6s+pkltbq top 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 z 5o1vr( zo* i9b(25ftgcbpc jdriver) crosses the rounded top of a hill (rav5gt5c(2 bpj*f(ic1o zrzo 9bdius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need: ;5nqnvis:d,l fm/pw to make for the passengers to feel “weightless” at the topmost popiq;5::vd/ln,n s mfwint?    rpm

  A bucket of mass 2.00 kg isa3tvpn9 9c ym1pcuf(, whirled in a vertical circle of radius 1.10 m. At the lowest poc9a,vucpyf 9np1m (3tint 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 rotateh*l,ip)jek ,7 4wbpd v3ox;hrzhf b7) if a particle 9.00 cm from the axis of rotation isbe xfp 3lj) r7ph);d*h, hiwv4zo7,bk to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a q v2p+c:1alv da*3h9c7ycbcg. f ,rpfcarnival, people are rotated in a cylindrically walled "room." (See Fig. 5-35.c+ r9lf hb.a,f 1*yv 2acdvp73cgcq :p)
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 frictu/7-rx a7mkcgz ei) ;oionless air-hockey tabletop, and is held in this orbit by a light cord connected to a danglieuzcg;xr/ ok m)a7 i-7ng block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ign;0l +; j o.xlnaykkr:ioring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnit.ryalj:+oki n;xk0 l ;ude 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 l-wff c6if77:ss9hp+lj pcm3of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses )ys54*drh usw$ 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 maneuverwu1q+xuc tk 65 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 force eu9p9j f0jj9f jxerted on the car (by the ground) fj09p f9jjuj 9in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, pes6mc-h o:h0going 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 accele- 6hmcseh:op0ration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal cifhqniv(: r4q cz: m0x5rcle of radius 2.90 m . At a particular instant, its acce:5zcr( q:mvx 40hfniqleration 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 15;x w8vhli9 lwj xz97m2,800 km (2 Earth radii) above the Eart xh7w8l x;w9jli5m9zvh’s surface if its mass is 1350 kg.   

  At the surface of a ce,pbkm (wvu0 .sm cu 0:,fttu uc82/iwfrtain planet, the gravitational acceleration g has a magnitude of 12i0, k.c0c vt:mubs/w tuf( 8f u2uw,pm 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 on the Moonyc,9eeg jw 2-u. The Moon's radius is 1.7,- yucee2j9w g4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hascv x)n*pdrs0nr 40. fb a radius 1.5 times that of Earth, but has the same mass. Wpnbn4 ).fr0c0s vdrx*hat is the acceleration due to gravity near its surface?   

  A hypothetical planet 8+muqx 4(xjrv+dyo 4 thas a mass 1.66 times that of Earth, but the same radius. What is g near i+yxu xvm8rd+t4 q o4(jts surface?   

  Two objects attract each other gravitationally wi ot8;czc5ae+ ath 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 gravitylevqc5 p v*6k*, at (a) 3200 m 5c*qlk6ev*vp    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centfg c5fvw ixkf1 +t:4h7er to a point outside the Earth where thg xf f h7+:t14f5vicwkegravitational 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 into j 5alxindb:x5ji n l0 ;;:/pxja sphere about 10 km in radiu0n;i adpb/j 5x:j;lxlnx j:5is. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star likee73 8;qa bujloae2 nd+ our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this sta+d b2qaeeaunj7 3;o 8lr?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbidyo,h,4h ui)vm2:keg ting in the space shuttle. Your friends respond that they thought g g,ohvydk),m e 2uh4:iravity 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*/pd e+ qiny7phe corners of a square of side 0.60 m. Calculate the magnitude and direy7q ep/dn *+piction of the total gravitational 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 1fpjb* c o:jj4tv */n8vgdd2 qon 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. 52:v 4 j/*got jjf8p1dqdn v*bc-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 0v:tdzd.qa+hs 4p +xx,t0ant1a(rs fav//hgwhat it is on Earth, and that Mars’ radius is 3400 km, determine the mass (q:ag.0v1nxttf,a 4t/advs/d0 p rahsx+z +hof Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earth xyfrfaxhz 127 5w) -wmand its distance from the Sun. [Note: Compare your answer to r7 )axf2y1 wfxh- m5wzthat obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular o..+j els r f;zhhn;7vk.hnq: d94 bbwxrbit about the Earth at a height of 360hfnbld9v4j h:k7z.wn.re ; h.b+sqx;0 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular ;ga * ,b)widkgorbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurgb*gk id), aw;s?    $\times 10^3$

  At what rate must a cylindr4pxkg kj7.0n; 7 hmemmical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answpjx; h4 m7e7m0.kgmkn er as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular ; *x dd0*5ojtvr 6imbt“near-Earth” orbit. A “near *orbx0itv mdj*d 5;6t-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?    s ~    min

  At what horizontal velocity would a satellite hr)4j*hgu9jh2u w q5 zvave to be launched from the top of Mt. Everest to be placed in a circular orbit aro wu9zh)qj v*5jr 24hguund the Earth?   

  During an Apollo lunar landipup 9 r czq:.kkk:5h(mng mission, the command module continued to orbit the Moon at an altitude of about 100 km. Howc rpp(q5zm u::hkkk .9 long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. Ty,6 -uo8 b+vma0u eiyche inner radius of the rings is 73,000 e+oyu ai,u6 8mvby0c- $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). W jhp0z18 d/k g(og2gce3 o6lsvhat is the ratio of a person’s apparent weight to her real weight (a) at the top,dv/g jhzo 820c g6os(p13 eklg and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg f+wu6;vz y7rz astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocityrz7 ;uv6 fzw+y,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They are g(f qh:5a)k aciws;kd7sb;fy, )n d /bobserved to be separated by 360 million km and take 5.7 Earth ye ,asa)5yk f 7d bd)q(:i/w;sfn kbg;chars to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale w6 n6vbze :vw y:e(vn7pmo3)mread for the weight of a 55-kg woman in an elevator thatve76pmnv3e :w()bo zn:m6 v yw 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 ceiling of an elevator. Tw5). ickzdxn ,he cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevatorc)5ziwk ndx., ’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfar) o.dqmtzkjj2j2;-3 y,v cq xce of a planet with period T , the-xkydjorm qt. 2jq jzv c,23); density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determinxdi0+ qn ps;j;e the period of an artificial satellite orbiting 0p+x n; jdiq;svery near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbitfv .*iri ottf8ff 2lyzh;w63,s the Sun like the planets. Its period is 410 d. What is its mean distance fromz.f 8,ti32*6fh;v yflwf r tio the Sun?    $\times 10^{11}$

  Neptune is an average distance of v08 h6gmj8 * tr9ktszot po6v9 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very closea9b, 2yuev22f v/ralr to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greay/v 2f2,ua ar el92rvbtest 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 Galar sz3hv p)-x8qb cq09yxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distancx) 4 rhpw.m *3ll9nphle for the four largest moons of Jupiter43 np *xpm.hw)ll h9rl (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known periw*.lrq(x0+1vkqmo. k nhrm *d od and distance of the Moon. r .qm+1*ov* nh( rkx ql.0dmkw   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’sv6 tr1t1tiyc/:*vt7grxgq 63j c xca 7 moons, using Kepler’s t7q tt31c/xjci:v a1ttxr* r67y cg v6ghird law. Use the distance of Io and the periods 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 of many fragments dk :g q1leveak fuoz(199 p8h)vgg 6i.g/kpk 6(which some space scientists think 9kg1 vf: ga .(6k1ekp loekzvg)pq 9g8uhd6/icame 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 artificial "planet" in ts fnd12xs *+niqf d.bj v6jzf8ttz0:,he 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 temperate), and that the ring rotates quickly enough to produce an apparent gravity of g f2f6tdts* vzq18+: jizn b s,fjn.d0xas 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 xsqsv8 2a0s:dc 4*xec arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N o4a0cxq8xc sv *d:es2sn 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 what,qoq 8/uhvix5e6qo-cn l69b z it is on t8o qbovl ,nqz -i5exh/66c9quhe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutua,f,ex.gowse o 8yv5 ha34m,s0xt zx(a l circle once every 2, oxazo(evtx.,s85,3agmh 4x ywfe0s.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 pulling on one another?    $\times 10^2$

  Because the Earth rotates oncb nvz7sc.mybgf3ym5f, hdbew ly +*cr -/p( 00e per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnit dp /0 synfmyrbbc3efm(y w+gzv705c-l. hb*,ude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling dire- +aj8oi6nt g:rznup5ctly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opgr8oinp+5n:j z- au6 tposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale inw0bzq*5e- yoy( lk 8uf an elevator, it says your mass is 82 kg. What is the acceleratiyl-(8*5zb qyw ke ouf0on of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stationls07snm mp (+v consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formedl sv7mn+ pm(s0 by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in 72x2u xvog12,sf 5jq qagtr -g,rsei4 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 planet in terms of its radius r, the ar44v371 n qp;)2 /g1 np8xyascqi j cpugbpi:vcceleration durqpp; 8c4/p7 p3:c4s ib2uv)11a jivxq ngngye to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a il u 41,0wukxfm k+io:string) is deflected from the vertical by an angle ,k1fx +uko0im 4i w:ul $\theta$ 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 db c9jip5* n1ppf.ni h7esign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle th i*.79 ipcphb jp1nnf5e curve?

  How long would a day be if the v9z(z)f ., aupg wx5cqEarth were rotating so fast that objects at the equator were apparently wc.(qx5 gfz,u9v pa)z weightless?    $\times 10^3$s

  Two equal-mass stars maintain a consta3nf n h/e*6de:7 xnqt yu9kd)jnt 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 cxo/njst (0dr6qa9;u.4cf gdradius 235 m. A lamp suspended from the ceiling swings out to an ac6 rg/ d .u(jn4xdf 0;c9qstaongle 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 9nsavk;o*+c8 g;cn om2* kq)va cgje/, it has been claimed that a person would be crushed by the force ofma8g)k;vsq/no2+g n* j;cc v oe9ka c* 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 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 deduced the presence 1xc, i7u0wafil e1ck5t ,t7wjof 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 meas,u175f,a 1ilt7tjki c0 xewwcuring 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 valley showq3;x53.)hd p5qknxkyowhr9k n in Fig. 5–45. Both the hill and vqyh3 .o;5khnx3rdqp 9kw k)x5alley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Sanw*+ y:f5gjt ystem (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 approxi 5 :jgtfn+ywa*mately 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 travelinoly:*j3a ik4i;sui 2ng 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 io:*uy2n i4 l;kajs3i$\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 satel ggo0t dj mz2+o8t/vg0lite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind gjvg+og 02o8ttz0/m d 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 -tp.: qmr-t 138dyoo7rbyj bzv42 l heof 3000 years. (a) What is its mean distance from the Sun?r7-ytt-d4 ebbj 2zvy8p m rq.lo o:h13   
(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 iq30y wpkb2l/m 4f-(z mi*n- tkz.twbkf you could actually "feel" yourself gravitationally attracted to sokkmq-btw -2pbfzt/wli 43y.nm 0k(* z meone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centztqo6lwtv f0 7*y/2 rxg d8cd2er of the Milky Way Galaxy (Fig. 5-46) at a distance of ab7ycr82tfd6 d t/zvlq2 oxg0*w out 30,000 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 are locat9us9r pjlxm z3bj*u t ;7hne27ed at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of thu7b2hzl;r n9t *j us3mej7px9 e square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits )cqfo n+x 06.jmh3n(f9f f mzo7ou3vc 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-cq 8r an(,rypq2m-long sweep second hand on you rn aq2pqy,r8(r wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sink ticx35v -cp60pvyoa0er weight around in a circle below you on a 0vo6 00pxtav c-5p 3yic.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car tj+tegt90dkqm 6ipxyo; qr jg86e. i3 *raveli ;6m3*xger6qjyt9pe 8 joik0d .gq+ti ng at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when niqm)i tk*r 3z-egotiating 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 )i)ztrmk3 i*q- . (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.$\approx$    $\times 10^2$