Sometimes people say that water is removed from clothes in a spin drhq5u st-f 7xgxpl my;pzro 5gk1x )*;3yer by centrifugal force y3l5p7u)kr*m xxo;sg -q5xhf;z1gtpthrowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the sa ys8 w-6qj62cz4/w tgenm osg.me when the car travels around a sharp curve at a constant 60 km/h as when iwtqyzo-g8 c.g 4ms2 s6wj/6ent travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wyzb mx5x v 8(s6:xs 0 ;ur3mbtzr2nw8jhere does the car exert the greatest and least forces on the road: (a) at t(3mnbru5y :w;z s6xj 2xbt88srxvzm0 he top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a men doc;-q +tuz0sf3 ya4rry-go-round. Which of these forces prsf340tcyzd; n- o +aquovides the centripetal acceleration of the child?

A bucket of water can be whirle9 47qe (wwnti.fosr2qd in a vertical circle without the water spilling out, even at the top of the cirwe( oni 92wr q7stq.4fcle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are atnvq: efw3f64cr* pi*9bs(dl l least three control4ieqf rv3 wl*cnf d:ps*(6bl9 s in the 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 cresnn t67 ;w;rhxit of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but ;ntw x6nrih; 7he feels the normal 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 lean inward when roc1xq1x* fk,ut *scywcp ni k2;s(. p-lunding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle gieg lvx4bu*dv:t7 ( v(bven its speed and radius of thev* tgeuv7x( (v4dbl: b turn?

A girl is whirling a ball on a string around4.4lbm gx5zgm*ruxaf vf-.y: m7 7qc y her head in a horizontal plane. She wants to letz5bf cxm4 4gyv7.q*7y :.-fgalmumxr go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a fo )iax;)z6zcpju)+hk srce? Consider an )uzicpxj s;azk +)6h) apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbit 7e a/dkzn2 8rs7jju8sbe differsjzrd8us7n 278jke a/ent?

Which pulls harder gravitationally, the(wm9, ikac1n96w1r/vv iq hef2b*d ks Earth on the Moon, or the Moon on the Earth? Which /2d1*9wifeachwv(siq k ,rk m1n9vb6 accelerates more?

The Sun's gravitational pull on the Earth is mu97:axkwzrdxj1;9nm7t(*v wqh5n hp b3q / m mfch larger than the Moon's. Yet the Moon's is mainlytx 1 rwhj(:nfwbv /7p7aq93q ;z* hmmm5n 9kxd responsible for the tides. Explain. [Hint: 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 the poles? What two effectv. i ylfof00a.s are at work? Do they oppf0ao0li.fy. vose each other?

The gravitational force on the Moon due to the Earth is only aq40:1o juy) qh/dylj gbout half the force on the Moon due to0ug4qy o:qdh j)lj1y/ the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal awbjm 4(k:6 sp*9 bnicapk (dcc1nf32zcceleration of Mars in its orbit around the Sun larger or smaller than the centripe bzn9( kkfa w:db c6n3s124p cci(mp*jtal acceleration of the Earth?

Would it require lessfrz1;9q3 h yfq speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Ezhf9 q13f rqy;arth’s rotation direction.

When will your apparent weight be the greatest, as mes18k9yn.rbu m asured by a scale in a moving elevator: when mk1rn9 sbuy.8the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long( 0kgexd l: hq2dt6sm* periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the 06l:s2dm gt(qxk*deh 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 “free fallx.k,y; ydls/v” or “apparent weightlessness” between stepsldv sy.;/y ,xk.

The Earth moves faster in its orbit around the Sun in January than in July. Isw6chj)9h jrx* the Earth closeh)rc6j*jx9 wh r to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to haveu m) 7*jyt0nzwv t;l b uvla78m)k8+vv a moon. Explain how this discovery enabled an estimate of Pw8lkv7+uv*tbt7 8a)uy ljz m0)mv;nvluto’s mass.

  The Sun's gravitational pul0m1y m5ohj4.pnc7f 6*re hjggl 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 gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-1fmr j4gy7hej m0n5p.oc gh6 *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 l( m3ehbx)rf-9ui* rs 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 centripe z es( ie+5hxd)svo8u1tal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radiz8dhs1o u5 e) svx+ie(us 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 discu83:yfnc-el yd s as it rotates uniformly innfe:3y-y ldc 8 a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 91 +nhi/xmb wdcq .m/q400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Fwhx/qn c. m1b9iq+/m dind the centripetal acceleration of the space shuttle in its 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 speck ofxyqnjm : w*x(p c1h::ko08vfh clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) ijyqp* o0:cxfhhk:x8wn1m :v( f the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate ir.gneh .omh;pzg k.o..wx /qxh;)1 ckn a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed iswx gor...kxhk;m. .phe o/q)c;n1 zhg 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 y5k)sq fm:z6-8je c mrprv3y;radius 77 m on a flat road i mjrpy) ec;v-fy6z58:msk q3rf the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of statim ob38 nf7.9uz4z* nm+z :vwmdq3lvnkc friction be between the tires and the road if aq8kwbnzz4*vfm +3: zu9nm7mdln .3 ov car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pu* lk dcy/ j)a(hq4*vmilots is designed to rotate a tr4 dm/lck *vjay qu)*h(ainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how 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 wq*snfszus rm0*; 4: a2zfj+tthe 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 **un f4jm:2fza+0rzss wtq;sis 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 travelv+a f 6mey2ghewr2m45 ing when upside down at the top of am42w+5ehm2gfry ev6a 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) cr7a s)cwl7 gmu;osses the rounded top of ag) ;7ma7sul cw hill (radius =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 neej lc 5+x t*ehmw.c:f*q46wzlbd to make for the passengers to feel “wtx+: qlfcbww5l c* 6jh4m .e*zeightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circuthl+jae 7ox +7gu.9x le of radius 1.10 m. At the lowest point of its motion the tension in the rope supportj77auo+ h+e ltxgxu.9ing 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 s ; ywcb-jof;9jw:jd .cm from the axis of rotation is to e yj.wc9jw ob:j;sfd;- xperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wax0- yeq6 ol1s(xkefz.lled "rooes6ez x(yfq -0lxo.1km." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hocken4)o l o-tqke** e3mw e37rtaoy tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole o3*)lqw7 kerenot a3oe- 4m* tas 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 thc2l:q4f cwx 1cis time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, fccc:w 214xlqfind 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 rag ;z rqa9( /v0 nqfg)pqnn.;vodius of 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:lttdq opkn d()*r)+r df1z,v $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 31g:-5dyhfl* s q0 $\mathrm{~m} / \mathrm{s}$ . 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 th,4xazq zm /(1qkd)ts je net force exerted on the car (by the ground) in Example 5-8 ,tx(z4m/saq zdj)qk1when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis ;xb 1jwx7gecp dm5i7xc87 1to500 accelerates uniformly from the 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 and the road to provcc1 b8twj77;1xmgx7i5 pedx oide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particula u/n8.o45 bw(fhinnbfr instant, itub (f.oif 4/nhnw85 bns acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravitybs ..k(s7vx:a/qrxs t on a spacecraft 12,800 km (2 Earth radii) above the Earthkta/q xr. sb(:.x7v ss’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravit)* epxf 6rex9uational acceleration g has a magnitude of e)fxu6*xr p 9e12 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 Moon. The Moon2o0smb/.u jm;r3l qotj r dz4;'s radius is 1.74 m2.r4rjo lsbjq;o/m3 ;0z dtu $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planei;y3 py/mz/ lyt has a radius 1.5 times that of Earth, but has the same mass. What is the accelerati3yl y/ /yzpmi;on due to gravity near its surface?   

  A hypothetical planet has a mxe ep 7;rj6x:scoy*; jass 1.66 times that of Earth, but the same radius. What is g near its surfaces;x r7p :ejx*;6ycjoe?   

  Two objects attract each othz8 a 8bgyj9ho3er 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 5e gwh k1yf7(x g , the acceleration of gravity, at (a) 3200 m(hf7gwe1k y5x    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’idr3i r;)l g5cs center to a point outside the Earth where thegravitational acceleration due to the Eart gcrdir 3l;)5ih 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 a sphere6ed5s jul xy) tc31ted+qd1y4 about 10 km in radius. Estimate the surface gravity on this monster. je35 16deltt y4qyx)+ ddcu 1s   $\times10^12$

  A typical white-dwarf star, which once was an average star like our Su 9ki25g f0 7m 6dnnvag0wgdd2mn but is now in the last stage of i a9mgg20d if6gkn7 02wddm5nvts evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orb1yk07u bg+jsmiting in the space shuttle. Your friends respond kb mjgy701u+s that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corner8 eeikrvk4 j yyn0s ff;7n;y2.s of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the otsk.;niy;y er 2n7ef4 vyf0jk8her three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mos2v;5ew9hnjcilh: /t u t 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. 5-38). The mass;eju29ic w tn v/hh5l:es 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 accelerationjvmz -09i+qzc0a/pu,o t5a j g of gravity at the surface of Mars is 0.38 of what it is on Earth, anu5gj+jtia0z0v, 9ma /-z o pcqd 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 thwoo6f;q y 3egui(e 4,re period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained usin(irue463gfq owy eo, ;g Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sa kmxvv +kq1lw,v),-tdzntof, ec(1o-oe f:+atellite moving in a stable circular orbit about the Earth at a height of 36d1, +woecm)vxkv nzo,afq+v (, -t:l1to k-fe 00 km.    $\times 10^3$

  The space shuttle releases)l+k4t qfxssz)*jy/ykd*vht) t- -vl a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when ths) -*tyx* d-4vv+/y)zt sfk)lqtlhjke release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants arjx ny(nb-nzkoby6ve9 8 )5jz:e to experience simulated gravity of 0.60 g? As6zk89j(:eb-j vxnyo ) y5zbnnsume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit th8.vucnz ;6 ffpzze6 b1e Earth in a circular “near-Earth” orbit. A “near-Earth” or;c1pzn8fbzfuvz .e66 bit 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 suuf2yz8 e)79- ud b1jacutf)would a satellite have to be launched from the top of Mt. Everest to z 7t 1ybjdeau-usu8 f)9)f2cu be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to 2gkvu;kwjn0 4 ez5i-u 3f up; ecp)1m2yr3pgr orbit the Moon at an altitude of about 100 km. How long did 4kj)3u2yupm p f12wger ;gnze0urv5c;ik3 p- it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbsanmsvq)23/b;(-pj dyfx a , nit the planet. The inner3va)-ym2 qap nsd,fb n( /xj;s radius 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 diameter rotx8 onvxn-b;p5v* r4 )oxo7gdeates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent wei-7nx4) 5dopob*e rgn8vo ;xvxght to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from tg6yq4y7ux,ct b9*e0uga - g avhe center of the Earth's Moon in a space vehicle (a) moving at g6eayu v9qc-gg0xyb*atu7 4, 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 c:1z ck+k)ipv nonsists of two stars of equal mass. They are cvp1i+):zknk observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of ugfg t /oc-*am 7cvy+)a 55-kg woman in an elevator that move */mfc+ 7oyguatcvg)- 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 co- 5hqmejvtdg9s3 ;v *5ztg6 jird suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N- dq jjsvggtizv;5 3et*6m h95 and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a pkps-u(fwdne k,p-7f s1r1i -n lanet with period T , the density (mass/volume) of the planet rdkn sep(,7-i-s1f- ukpw 1f nis $\rho=m / V=3 \pi / G T^{2}$ .
(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 determin(jh kyy 5.vq3ue the period of an artificial satellite orbiting very near the E.3yy(5u q kjvharth’s surface.    s

  The asteroid Icarus, though onlq3us*6kj*h k) u8 twcry a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean di*r*j3 uthcq) u6w8skkstance from the Sun?    $\times 10^{11}$

  Neptune is an average distance x34q4b-t* sw9tlxuzen y 0l l0of 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 everyk c4oq4gl f 620)jnltk 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the 4cfk0nqkt)64g lj lo2 nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the centek*wtggj fki+fk .j*:; r of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period ffa7npb3s d7zlk+ .;l, and mean distance for the four largest moons of Jupiter (those difn +b d7zp7. lsfk3al;scovered 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 k/v1zjmd )kf 3the Earth from the known period and distance of the Moon. )jm v1/3zkfk d   $\times 10^{24}$

  Determine the mean distance from Jupiter f) bezy)s.t2+gmxm6;f 1e qn isor each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.2eb6))1 x+;mqzft ges. snmyi
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupkx )/2o:de j q h2(:unmpzv/j1xack-lj r8e 2siter consists of many fragments (which some space scient(/ /rlo vdjseja2:kn 8mux h1xck-e :z2)qpj2ists 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 tale describes an artificial "planet" in the form of 6ibwp g..68 f6qpzpn , 8biac5l klzmo.d+g0t 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 8gp i+ta5l .pkbwfz,nc. p bo86ilzg6.6dm q0 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 arc frot,9 , rue7cahlfwl 9sg.1 vlf2m a hanging vine (Fig. 5–41). If his arms are capable of exerting a forrll 9h9f1a,ctl7s fwg,2 e .uvce of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half whatyak s4 jg6av(0 it is jgya6 4(sk0 vaon the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin insbj:2. - q/. 5fitkwnovibhx0 a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on onx jto .k/svb.q0ib2n:h -fw5i e another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent 9 o2t2(zx zrigacceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fr2oxz2i9 (gztraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spa0j0ndw .kt cv2cecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces0wcdt k2.0jvn ?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a icjq(i wi3/yza7 x p7 kvy:q*b25 i/fdbathroom scale in an elevator, it says your mass is 82 kg.*2//pi(bjqc i:3 yzx77vf5dyqwiia k What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotj +dthwz::l ox/c-w.cate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube h-xl djwc th /+z.o::cwas 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 a vertical loop (Fig. cc.kw): vf 74o.e9xemwr9vgr jj y :a/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 ;p.jwe a 1uja0 (wk1kpits radius r, the acceleration due to gravity at its surface and the gravitational constkuawj . ;pwe0(j1ap 1kant G.

A plumb bob (a mass m hanging on a 5:wjf l(a61qj,ychj f string) is deflected from the vertical by an angle f:j j5hq6f j,wc1ay(l$\theta$ 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 b;ag wpw/kgs;7(yf 9xhdm83am is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavea3s(gdgybw /p9fw mx; h;78akment), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fa0tzmlgw9i 5ln/-9vthqtrf:l;7g k a,st that objects at the equator were apparently weightlessmlv/z rw l0l; hq99t5na:,t 7igtk f-g?    $\times 10^3$s

  Two equal-mass stars maintain a constant dist o gpyhak79 (xy69u:r r,u ai-ywj82ujance 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 rw9py:5)b qd*p o,g rzsounds a curve of radius 235 m. A lamp suspended from the ceiling swings o5gpdws:q,y b p9z r*)out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Eaf.nb8wp :c;n xm chw:8j kj172zh5j xprth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter8jkfc nm 5p. xhjz;7hwjcx: nb2 :18wp 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 2 n-t2e-(n0mh,m4kwt x :rr mor mw-hwTelescope deduced the presence of an extremely massive corrxtm0rt- (-2mwm4hoe wmnr k:w2,-nhe 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 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 vall))8:w*0olgo0oy sjjm /gm ngo ey 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 colso8mgw/o) 0g0*jog jm: ) onympare? (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 satelli i,p3kc, tltmxsmw i,b9)x, -ites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a r39-titciksx, p, )mxlbw mi,,eceiver 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 each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2n v.g 6a;m*tut.1 billion km, is meant to orbit the uvt *.m6tgan;asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the x rhf:g;9 y 0efz5wj8f5fmu8yspace shuttle pursuing a satellite 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 bey:0f xweg uz 9f5h8ff;yj58mr hind 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 perio(no)ajwglu qby x(1ykm35sql:; g,o .d of 3000 years. (a) What is its mean distance froymy:3l nw(j;(sx1o.) boguq5a gkq,lm the 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 kn926 s.0p 6iw1y wpyg xv2e2m e4mcdnbe if you could actually "feel" yourself gravitationally 90y 6yvm ew1 .6 d4wsn222meckn pxpgiattracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centea 8iudcb5mtq.vy,n*wzp)ov +08 jtj 3r of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years fr pjn53vvu)m, i tyoj q8wzc.da*t8b+0om 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 located at the corners of a square 0.50 m on e ,.say ;j+-2a ggy cls41zacnhach 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 the squ gjayzs-g.s,4ac1+;2a y n hclare.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth h y* 5ludvtgqfzco 5*g)4h(q2 $ \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 b1wn,v akc6shb* l,ayyv -8u .by the tip of the 1.5-cm-long sweep second hand on your wrist watb.,b vy v wa1c*6nsah,y8luk-ch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aroh*dyuv p:; co9und in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.5ou9 y*;d:p cvh0 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radimre6rln ; qn1tr/9zm )us R in a new highway is designed so that a car traveling at speed; )lr emn1trmz6r/q9n $ 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 th-ol) (xbh;sat5vfh*f e 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 comfortb5 x h -s*tolhfv);f(aable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$