Sometimes people say that water is removed frow)y qi,fpck44y/ nazd- n;-lg m clothes in a spin dryer by centrifugal force throwing the water outwag),-- 4kw ylnf znqy4icap;d /rd. What is wrong with this statement?

Will the acceleration of a car be the same when the0aa8e/ 1ou8lpn4w6 g c;yjnpu car travels around a sharp curve at a constant 60 km/hc18uj wn na8a6plpue04y/ ; go as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly roalj9c n9g2osji/q b r.8y,q 6nckj g8u3d. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hillji6jg9r 2scobg,n 8.j k y8cu9qn/ql3s, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a chi5v j,8dia jfkd;b z*x*ld riding a horse on a merry-go-round. Which of these forces provides the centripetal accel8*5 d i*kxfdjjzv; b,aeration of the child?

A bucket of water can be whirled in a vertfdp 7d+9/04 qzs g tqd4vp2csxical circle without the water spilling out, even at the top of the circle when the bu24zpqxfts q0c9 v d dd7+sg4p/cket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least thr8.gef.e.4-8 shckvsnh-vk xlnsl 9 m 1ee controls in the car which can be used thfe-vxl9s..4lk nnmchvs -88 g1es .ko cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as s,ail9) :1 cgulaa3dng hown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chestua3,n: i gga1cldla9 ) 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 roundin,wou3kx p9:cjpm p-z6g a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle gi*,o(a2oo h eqvven its sp(ovo* eoha ,q2eed and radius of the turn?

A girl is whirling a ball on a k tdjhua6ah 45rr*)kw yg7m37string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on h w k7r u3a*45kd)a hym6gtj7rthe 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, hooq;ter(r ao9- fh: :m8 gbyu-dw large a force? Consider an app:-fg-: bta h(e ;mr9oyqd8urole
(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 or8*o1;2 du h9 y6y* pghzfletdibit be diff 9*z1goe 2 ufpy 6;tilh*hy8dderent?

Which pulls harder gravio g9s/x:ve1bp4l/t sytationally, the Earth on the Moon, or the Moon on the Earth? W bg se//t 1xo94pvsl:yhich accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Ytb , amv9-ksg ,a4mx:oo7fh8t et the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the f7s 9ha -t, 8mt:xg4koov,bmadifference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the p .2s)el+z +mbs0tqia e+sfndu ax,63boles? What two effects are at work? Do they ofs +e2 )s+6zq+xbma uli,0es3nbd .ta ppose each other?

The gravitational force on the Min9p4;cy ync* oon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t thecin 4*n;ycyp 9 Moon pulled away from the Earth?

Is the centripetal a ubsrb62w8dkq*.5i7mp,g qfc cceleration of Mars in its orbit around the Sun larger or smaller than the centriugqi. w5*br, bkq8f2cmdps6 7petal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b*n :a pj0b w4r/c vpn*y2gry9w) toward the west? Consider y0w /pg **b4y rprnwa9v:cnj2the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a 9scttq - bb+5r84hk jf0-tgpiscale in a moving elevator: when the elevator (a) accelerates downward, (b) act --4i5hgb90rjpfs8b +ctkt qcelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in1b/z-sfj0.cx;dnblz 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 astrona f.-x1b0z zs j;/ndlcbuts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apunp-t m0(f mt3) s:)t+k lccawparent weightlessness” between steu sw0 -)(t3fktcmcatl+ : nm)pps.

The Earth moves faster in its orbit around the Sun in Januayv5s, 49 lua)zn rar/bry than in July. Is the Earth closer 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 Ear r)y/5 aznvurlb9 ,a4sth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was fi2rl6*fqt .;eurd)f discovered to have a moon. Explain how this discovery enabled an esttfqr2e6l) u; fr.*idfimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is muc.guo ;kd3jct+ a m;wv/h larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravita;cgt3/ j;dmkwv uo.a+ tional 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 td)g, r1wp h9e*j906 blykbrmyq+3c t 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 Earth in its orbit around the Suniqx * ;*by+u(ivv: el8 cb9,uawv w:ck, and the net force exerted on the Earth. What exerts this force on the Earth? A+ 9i*i:cw8uxvkecq ayvw;u*, vb: l b(ssume 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 discet/k48vch spixmm ci 1 *q-4+aus as it rotates uniformly in a 1 4ch+ac4t-vpmmsi qxi/ e*k8horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttleerf m-cm: k2 )jnidm)5 is in orbit 400 km from the Earth's surface, and circles the Earth abr mj:ik5n c 2m-m))edfout once every 90 minutes. Find 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 of u fb jz8j 12am-/(ksat8/ jxllclay on the edge of a potter’ mz / 8jt-k2 jjllsaa/b8x(u1fs wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform bk5co :l9wvx5 rate in a vertical circle of radius 72.0 cm , as9:55wv lkcxbo shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of radius 9q o-j9j60 xnq*tkx n xjsx-6e77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independentxx9 xjnekq -sto * j06nq-6jx9 of the mass of the car?   

  How large must the coefficient of static ,,f1bmx)4rp3su nt aw friction be between the tires and the road if a car is to rounsp r)baw nfm4,x t13,ud a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is kcr2hv 5zy/bqb98q;fdesigned to rotate a trainee in a horizontal ci; z/qkv h95yfrb2cbq8rcle 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 of a rotating turcb)m ou4. (b8(f ctf g+-xfbcx q0jcr4ntable of variable speed. When the qcjc u8xmr -(b4 bg.)ofc 0b4f+ftxc (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 coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside domnjpniwf;, o47-gnq3wn at the top of a circli j oq4n;fm,np7w n-3ge
(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 drij65f 8d -eddk kbqkq1(tnwj1)ver) crosses the rounded top of a hill (radius (k 6d jkbj1qt1nd5 w8ekd f)q-=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 tov(uhv- *fe0cih y dy:c* +us3o make for f: v+ iuu3h* chdoysv*-(0cyethe passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verthlq3bzn7 +pbr ws036vj8 )nzc ical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 Njrq336)nw sp7 zvzc0 + hbbln8.
(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 frv83+9jxdm+l ruzz2). xaecy nic8y;9frcfi1om the axis of rotation is to experience i+r+fdz )jzv3;yux r9fc2c c9 a1 8.l8xmyniean acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, pr/g)v4y54ss gc2uw4z eug ze;eople are rotated in a cylindrically walled "room." (See gr) s s;c /uew2yz4zeug45 4vgFig. 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 ) is2t- pfan 75i0n7ed2bup atn4t6 ixc:m rotated in a circle on a frictionless air-hockey tabletop, and d faep2:u0m 4-n7 nti7tibnca 2pt56xis held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of thbg6mg5j u g44ae ball which revolves on a string 0.600 m long. In particu 45aggjgbmu6 4lar, 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 perfmuhou- 5u*ea(x.k. ,x+hv jir5 ,wrziectly 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 ue+h2 gsc. ft:$ 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 manu ss j/6b9dav4)f3wia euver 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 thebipi wm4r 489jnp.v3k net force exerted on the car (by the ir3mjkwn4 pv i8 bp.94ground) in 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 accv)lp3 4ozwh8y elerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determlh3z8yp)4w o vine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m .9;k-za a;nb59c( p:iaiwklqa / acc 0f At a particular instant, itsln-za f9q; i ;5waac i apkbc9/0a(k:c 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 gravity on a spacecraft 12,8(amok7-/9 i6x jvp5bm9tlf ya00 km (2 Earth radii) aboveokfp/a tmy5 7-ix jb(a9v69 ml the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acs9wt83 swn8wdy 4*tl xceleration g has a magnitude of 12 m/s xn88wt 3syl9t*w4sdw $^2$ 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 Moonrp27b5rr .ezw. The Moon's radius is 1.72 rr7ewp. zb5r4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times thamcp0f n f9,do3gs)oz9t of Earth, but has the same mass. What is the acceleration due to gr9 f3gfmcoz0,)dso p 9navity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, 19cev*v0kx95ytdx wwbut the same radius. What is g nyev0vkwc *xw5x9d 1t9 ear its surface?   

  Two objects attract each other gravitationally with a force of1i b2g kf-8nk o-rs+yy 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 effectrwld 0/x 6tcd* c /)du1b qw.qfji znf0)e(nm-ive value of g , the acceleration of gravity, at (a) 3200 mmjcx-ef. )fnl 0r/i)c/d0u1 *dbn w6qz(d twq    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth ,f xmu62 )iblyk2 :mxcwhere thegravitational acceleration due to the Earlxi6:cy2b,mf ) uk 2mxth 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 pnw/qboepz+/bzt(ovr5 7 1ww45g)sekbw/ we0 acked into a sphere about 10 km in radius. Estimate bgesez (kbb1/+rwwewz7p0v/ o t54 no wqw/5)the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avert/c:u1pan;x sn ++ra s t;u+haage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our stuua r /;h1nxtnc++:;psa a +Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting intc9/se 6w9nlah5nwxu 3vk*b:l dfo8- the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. sx6 b:t 3ac5evnh8 lw-o9kdfu/ n 9l*wConvince 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 square of side 0.60c1 t e54sivg8d m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the idvte1 s845cgother three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mostv ej38ufx + napga+:;a of the planets line up on the same side of the Sun. Calcg:; f +evaxjuana 38+pulate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at(p* c:lmrlvvp eq9,8t the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass oftpl p ,qvv9rlm*(c 8:e Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the p*khbhc 9ug pgz (6r0+seriod of the Earth and hg(kupr*hz 0cbs9 6+g its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the Ev t6t(,*s6dlu kxj :3mlq4p cearth at a height of 3600 km.u:v,(6se63lq*k lpt4m dxjct    $\times 10^3$

  The space shuttle releases a satellite into a circular odx,z6-lnl+ uhj42 qyix8,z emglv s (59wfme.rbit 650 km above the Earth. How fast m,8(e+x qizh e.46ml5lg ym9n vl,sfujxdzw2- ust the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to8z clsoq7k p0/ experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for o0kqs7l/pcz 8one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellnjjxodw /1imu g+a( wy(w6x8vh1 /nd 7ite to orbit the Earth 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 ofxwd/18 (1j6uoh(yjx in+mdvwn w7/ ag the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be x6)1l4)a ma pkpxdr9klaunched from the top of Mt. Everest to be placed in a cir 4pkamd9xl))px1 k6a rcular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module cjzr-( xytbk5j6 ud; 3gontinued to orbit the Moon at an altitude of about 100 km. How long did it tzd b(j -5r yu;6gxjk3take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planegbrnuhg /q::k4m41be5n 7ai f0t r9xqt. The inner radius of the rings is4r :4a/bmgfq1k 7extb ungiq:h5rn0 9 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fgag/ srw71 j1qig. 5–9). What is the ratio of a person’s s1/ rw1agg j7qapparent weight 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 the d7ixk+es/ sn: sv)vvdx-u;a4) yh* dccenter of the Earth's Moon in a space vehicle (a) moving at constant veloc+xdcssau hin)sk:d *4 vx;)/d v-v7ey ity,     ----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 binary0 zoc8fvy )v)2i/crzu+ljrax d/92ek -star system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point mi))j vlkoz02 zryucc /ae/9fdxr8 v+ 2idway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55- ob l7nx(9 .qo3o:xxoxkg woman in an elevator that movesbxoq(x. x:noloxo 73 9
(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 cecv.t iezujd*ola2+ku-w62mnj 1i v+-iling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator acceleratesv2ndvl wo uimiu1kct2e +6+ -j*.z-ja. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the sur*bwgw.ws t4q z30i/0p.swxcn face of a planet with period T , the w.i w. p 3*w 4sqtb0/ncgzw0xsdensity (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 Mooe af)z+4j cs wxn.n66in (27.4 d) to determine the period of+)n.niz c6ex jf64aws an artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hund 8zzhkoqq+ f1sl +/k6vred meters across, orbits the Sun like the planets. Its period is 410 d. What is its 1h8q q +ozf6/kkz +lsvmean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dismx8q 8 )z/wh6n5xz(5- kb5t b8ny2qmqur rbdatance 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 Sun rouh,1f n+zmiku mc69 6 c5aelzc6ghly once every 76 years. It comes very close to the surface of the Sun on its closest approach (F+ fa6zhc,mzcu5 696 1ecnlm kiig. 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 cent wwsvw ih2m:0)jl8 l ,ac xh10f9ult.aer 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, and mean distance for the four largest yxh 4*( :3*b/ c5fjhuyfduqry moons of Jupiter (b:(hh5x* rq*yc34df j y/ uufythose 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 did2k atxnt 4,3yzbn(xet 3q): zwbd5.tstance of the Moon. 25ybxn4tn3 wtz)xtaz(3d q.e:tk bd,    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, w+ 2e7ak4 cr1hr 0h vwgs+h+mtusing Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare vrkwhw1g7m c4 s++ t+hae2hr0 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 manz00i: 8i)q:y1nk bo ujau+ui 8nxf em9y fragments (which some space scientists think came from a planet that once orbited the Sun b 1euyizu:u8bkajq9nfni: x o0mi 8)+0ut 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 thej,lxv (h3 rr1g 5a,kc(zihes/ 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, (la/ j5 hkz,v3 s(hxe1,gircrthat 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 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 from a hanging vcui3rifo)n : ki(y6h0 ine (Fig. 5–413o 6fkyhu 0ii )ic:nr(). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of graviyo)/1l hk un+fty be half what it is o ouflh+y )1n/kn the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual o fe9z/, a*:jzlwaqp9(b y(vacircle onbwl9z*(a( yzj9eq vaf,/ap:o ce 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 one another?    $\times 10^2$

  Because the Earth rotat*a-zcvbw-bpqlit7b 6op9 g.jvi 92 9ues once 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 magnitude of this effe7b9upj9viio6*l.c-2t z ba 9wvqpg b- ct. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from th 2 4lesnmhi(l mq+ug-*e Earth to the Moon experience zero net force because the Earth sl(m - mh2qeign+ul*4and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when youlbf,p(a8h waxfrp)1 e4/ 1p k-tci9hj stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is thef1( apl fa-9i,/xpc)hhe jk4wpt18rb acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consistsai.o c)io: ;eg 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 ;ic). oga ei:oabout 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 jj1 .qu, 9:7gz hb rvda3kp7tl(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 of84f med71eqqd*lo.rpzn6 v( x a planet in terms of its radius r, the acceleration due to gravity at its * oxfd4v6qzdn1lm r 8eqp.e(7surface and the gravitational constant G.

A plumb bob (a mass m hanging on a svyyxtd6a9pp vtssl 2 6,/x 7der/)i05 buura)tring) is deflected from the vertical by an apu d/sa,x)pltdesr095v yx ayub/ t2i7)v6 6rngle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of; 4hq26jg yqsu.qx9;n )ai h8.cevcg h If the coefficient of static friction is 0.30 (wet h u8 qq.9c ng.yh hqecgvi24) ;;sj6axpavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if th:wvhk 9ac; (2pqm(qrjngbd+ 4e Earth were rotating so fast that objects at the equator were apparently weighmrc a+ 2bvk(:p;9w(4qjdqngh tless?    $\times 10^3$s

  Two equal-mass stars maintain a conatkkrv iq:pwo5-n2e46m (7l /nvhe;d stant 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 constanil tcmb 4dr:d0)dl dz 7-o(xpr6,dto+t speed rounds a curve of radius 235 m. A lamp suspended from the ced-z,p rod70cdor m i tt:d6)dl4(lxb +iling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, ,7gl-amjwuc.l40f gegj;1sfit has been claimed that a person would be crushed by the force of gravity on a planet the size of Juwcj4 f-g,f0esj 1m;g al7lg.upiter 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 Hubblt z:05)wa7u8 ;bar+suzcypyee Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbitiuczrb+etyuz5y 8;s )wpa:7 0 ang 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 hilwko+ +dr jd+ -mxc/txj0g1qc-/nh rj)l and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the 0tdxrcjmdj/c+o-qj h/r+x1n ) +gkw-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 System (GPS) utilizes a group of 24 satellit w6n bdzvb2q62es 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 cbb2 26vw6zd nqentimeters. 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 2.1 billion km, is mef,o/i,4 j . )9njlvrgceg0zruant to orbit the asteroid Eros at a height of 0/jj fg)re.i,c 4ruolvnz, g9about 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 astronautlv-hv sqm./+ p in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same - +vqlvm .p/hsradius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 yeag-wuz-oaan53j l6hz ,a 5ivb6rs. (a) What is its mean distance from the Suzoa-,vl5 bu5i63whag z j-6 ann?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "fm2e ,)a,lry v, li 7mfln8m:xdeel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like ,xlre a,lmmlf2:)vnid,8 my7 F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gab .*j/4qr2udzmks ; ,y 6j,yvfrld0j xlaxy (Fig. 5-46) at a distance of about 30,000 light-years from t.qzyyu,sv2,mbd*dr kj frx4 l6/j 0j;he 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 ar5zw0:iemflon fjk y,(i-(,smuo3 +cs or w/ d2e located 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 oo-+ m/sjs0 cri,ed,mikf5:(w nl3zuy (wo2f at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eaqto uvxklai ) 4px k+i9h93,7arth $ \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, 4:l8s a itjirou2p1vkefzkgv:w6( 9 of the 1.5-cm-long sweep second hand on your wrist wazwl:4i(kep:g,1ks6aj ov2fu8 9 triv tch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing aaq90w05 h wgv8kzyxq 9 sinker weight around in a circle below you on a wh 9 v0gk58 wyaq9xzq00.25-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 travelw /hr t3),wozhing at spe 3w,wh/zth)o red $ 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 g0bj) w9ktgka xbzb) pmtg7a;6(x :m :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 of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on amp 0azkg b)x ;t9):j:g7wt6b bxam (gk 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.$\approx$    $\times 10^2$