Sometimes people say that water is removerjv/oku/: o9nd from clothes in a spin dryer by centrifugalovr/:uo/ k9nj force throwing the water outward. What is wrong with this statement?

Will the acceleration of auie2o.ev8do;lvwph( 2 rb 6d wn8)na4 car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a ge r2e 4vdu)e( ob.ipn2 h av8onww6d8;lntle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whx,oby1,yq4 1j- bvs , g8udu8om ifq0aere does the car exert the greatest and leavomf-jaxq 0y 1,q8bb si,,u o14ug8yd st 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 child riding a horse on a merry-golu,s(hzjojw34)x x 2ze-4lh j -round. Which of these forces provides the centripetal acceleration xjhj,j - xu24 l3)olzh4(wzes of the child?

A bucket of water can be whirl)j(rra g q6g:g8 vd;mned in a vertical circle without the water spilling out, even at n dmq 6ggg)ra:8 (;rjvthe top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least gmcm 1o13z. afthree controls in t.1 zga3m1ocmfhe 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 cres(l oz*/jxs /htt of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hillolzx / /jh(s*t. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when round jc-hb76 raj2 dgqb4gg);-veumk53djlqm4, ting a curve at high speed?

Why do airplanes bank when they turn? How would you compute the baiekt+1ac/ bn4nking angle given its s1t4ni cba+/kepeed and radius of the turn?

A girl is whirling a ball on a string around her head iahtj:z h2 ;ste;+.2a- 6 1hxdauz3+eqwv fxcqn a horizontal plane. She wants to let go at precisely the right time so tqzt-j es ce 26f:hdqa 2+;utxah1w3+zx hva.;hat 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 sw2u(nm+( n mbforce? Consider(mb2 +nswmnu( an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in waxx hxp; 7jy0+v5m,,zxatu)jhat ways would the Moon’s orbit be differexxya ,ux+j5mj),a;v0 pz7h txnt?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Esk w **kmff5mpr 1;w;jarth? *5 pjwrm ksw1;mf;f*kWhich accelerates more?

The Sun's gravitational pull on the Earth is much l*v*8w1wj zqfv1t7dy uarger 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 Ew zdqywf* j1v1tu8*v 7arth to the other.]

Will an object weigh more at the equator or at thi2.d nm+,+w zf i.0y/ zzkdmole poles? What two effects are at work? Dowdf2z0z ymlki+im.,z/.o+dn they oppose each other?

The gravitational force on the Moon due to9q5d a2gng sz*)cmdw* the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon*cg 5d qgams*w2d)z 9n pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger 7v djn.f )6finor smaller than the centripetal acceleration of the Earf n) .6ndvji7fth?

Would it require less speed to launch a sate5r,9eja 1u shillite (a) toward the east or (b) toward the west? Con ,uhej5ir91s asider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a m38 idfiu e+l-hoving elevator: when the elevator (a) accelerates downward, dfuil+-h3i 8e(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 perio. an b fjkw86pk1)ie6z2vf v-saf *u*gds in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that e6. -n fv8i)fgvwfa1s*6*2zp uab jkk 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 fall” or “apparent weightlesm2k 3;lmpko5 bk +-ruza:d b2bsness” between sk25b;l u:kbabomz p-kdr3 2+mteps.

The Earth moves faster in its orbiz5iv-zq6uj.4a ya lpz75ktq ;t around the Sun in January 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 Earth’s axis relative to the plane of its orbit.]vj4q lz5a56 . tpyqik7uazz;-

The mass of Pluto was not known until it was discovered to have : vav nzk(-:jfa moon. Explain how this discovery enabled an estimate of Pluto’sva njkz-v f:(: mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. ; ail cjfgulpc wh4t+0d(:q6 -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 ga+t :w4ch0 (flidp6-l j;cq uof 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 1b:wiu 08ys x,esq qxqh +(2(xs980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelq4tlg8of-1ns ql. 4scon +zi+eration 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 Eartiotnl 4+ n1s-gflc+q. 84szqoh'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 2j7xisb5 met 9.10 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.xb9t 7s5ji.e m   

  Suppose the space shuttle is in orbit 400 k/n-s5pfv fbi* m from the Earth's surface, and circles the Earth abop-f5bf/*iv sn ut 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 accelerati kvk* f)p0vil8on of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minutekv vkp)l8 *i0f) if the wheel’s diameter is 32 cm?   

  A ball on the end of a snhdnqqun4n q7/nx9wg b y*)k n5+/j(d tring is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown dxj7n dyg+nnuqnq/9 n4 n5q hk(/ w*)bin 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 77abgwe+/ -z j:m m on a flat road if the wmbgea: / z-j+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 static friction be between the tires and ge/01jr3q dj fm (hev/6m4wqu 4h0qhq the road if a car is to round a level curve of radifqhg6m(e hw0h vquje1r4q4q0dm/ 3j/us 85 m at a speed of 95km/h ?   

  A device for training ast2- w vfg)m,dhmah ba3naa4 .c2ronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If thea,.h h4d3c)gma- a2bav wn2mf 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 thee* krn;a;)a:h 6 3(xwmfskxsg m-h 4cx axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on thx) r k43 - m6skahg sx(cnxwam*;:e;fhe 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 tra5d3 efo5. dqb2yq -qimveling when upside down at the top odo iy5 .3qmebf-dq25q f 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 (inhheu8odi0pf;.o x 7m 0m/ wwxn fx3i+;cluding the driver) crosses the rounded top dhw;nw ou/x7x0. ;f3mix m8peifo h0 +of a 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 wouosxqxmt 1)-t1bxrt+ )ld a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the tosrq)) x t+xtmtxo1b-1pmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of rad+ yr85 / 3qzdxejmi(zs wn6jr)ius 1.10 m. At the lowest p(5rz)8s/xzq yre3 6+mijjnwdoint 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 centiz b+l; 9.rzhgrifuge rotate if a particle 9.00 cm from the axis of rotatioi9. r+ghz;l zbn is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival.-khxacaqxqz ;e1a) 6 xpjce58e9ye: , people are rotated in a cylindrically walled "room." (See aqxe8j-c15xhqe;z.y xc:ap9ak e)e6Fig. 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 friy.4xax //- xo8qfd vqqctionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole asq dv.4-fyxx q /qoax8/ 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 not3 .8v.lvdv d:;ow)wg.: 4zo7yzndqr )q ng qrj ignoring the weight of the ball which revolves on a string 3q)4gd zw.wrjo dg;n v.)q.vd:7l8zvony r: q0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfebx*w dic,fyf6 v*j ,i:h: t)zxctly 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 ton7:s(rzepn t3 /du8s+ 3rgl $ 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 maneuve gxfcc ,m9kf d(8j4mnc fl:1v/r 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 b h:ewdu5cb2kzie:vs+6m ; g ,5k)qxz the net force exerted on the cbg:zv i xmd)qec6 suw5; 2+kzkbhe5:,ar (by the ground) 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 accelerates uniformly from the pit area, go+5 ja0cwx o46ix ryfe8ing 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. 8xcj+ x 4wafyr50eio6If 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 :;zxj jod/ d4z(5bvca8tl e8kcircle of radius 2.90 m . At a particular instant, its acceleration is 1.05 /8j8 b;ojta5dx( e 4z cv:zldk$\mathrm{~m} / \mathrm{s}^{2}$ , 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 12,800 km (2 Earth rr1dcm;x )uovz3 +iua .x td8h3adii) above the Earth’s surface if its mass is 1350 kg. uvdx xc;1.oz)8t3 3 ru+imahd  

  At the surface of a certain planet, the gravitationas-ld45 w 4wain p9byt6l acceleration g has a magnitt5wn6liw4 yd s4pab -9ude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on yi)hdtfp) 14u the Moon. The Moon's radius is 1.74 d 14h)up y)tfi$\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 that of Earth, but has thekjgt m3s6ud,x/,04 i.f kqjd h same mass. What is the acceleuq6g/jk f,ik dsh. m3 xt,0dj4ration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but4p*w h hf75apq,1ltk ow fs8a7 the same radius. What is g near its surface?pwospqft7kh al5 haw 1*f 4,87   

  Two objects attract each other gravitationally with a force ofp6b3ba4lfnr xw-1t/t7tf0dcaq w9 e6 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 b n;bm)2c:c ;kwds s979kgahqvalue of g , the acceleration of gravity, at (a) 3200 mw bng s9ahqd;2cmkk: )bcs79;    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Eartj9l j1cy.x gkqr7b :/mh’s center to a point outside the Earth where thegravitational amk bjlq xr.1/c 97j:gycceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times thur:abf*.4ruh -kxwflu 7* lh,e mass of our Sun packed into a sphere about 10 km in radius. Estimate the surfacll:uf u7h, f*kbx -w.uar *h4re gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an a7faaxwky, rg -5)zrx3 verage 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 Sun. What is tx5,akyg z3-x a7w fr)rhe surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while ok 1.k8m- *wcbfvy dq ).r2rhvarbiting in the space shu8bk mh)f2 d.vkyv*rar-c1w .qttle. Your friends respond 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 ca.jpao() iht )j-yww1orners of a square of side 0.60 m. Calculat1aywo- ). tijpwjh ()ae the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yeairov+(jrwokl8 w(v 3* ui/kpp anf)0-rs most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four plavrra i u8p*lkf/kin ) jwvo03+(p( ow-nets 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 k*h3 v8h7f tmvat the surface of Mars is 0.38 of what it is on Earth, and thatvm 8hk3* tvhf7 Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the *ujgl (8fj iqz oofg4o vdgk;z0*07f6Sun using the known value for the period of the Earth and its distance from th 78*(zdo0 0j *j6if4f z og;vgquolkfge 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 4ta ki a(s*z6bthe Earth at a heightb6zta kas (i4* of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abo ; jr*ku *kq*:7 :d1(dpxp mbfrt;qqrwve the Earth. How fast must the shuttle be movipx*rmr* 7dqktu:*fbpqj:q ;r( kw;d 1ng (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindc 2sljn/:ix3b .dxm -nrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21 ix3snb-c/mj2.xn :dl, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “wwsfyubzzzb04 mfb 7h+*bp9z /- w;7v near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earfsz z-7 zwbmbzb+/;0ubv97fp w*w4yh th. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from thexm)ox 04,w xxhuk;.l *z9 nqwv top of Mt. Everest to be placed in a circular okx* u;xw v9lzx q 4m.0noh,xw)rbit around the Earth?   

  During an Apollo lunar landing mission, 3qq dq6mmjl/1p) zo k*the command module continued to orbit the Moon at ald*jz3/o m6)q p q1mkqn altitude of about 100 km. How 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. The d*ph ,dxow5u( inner (dxhuw5,od *pradius 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 rotates once every 15.5 s (seot9y 9 w0xx 6kho*ep +hd8cl0oe Fig. 5–9). What is the ratio of a person’s apparepe60th 8y9*x cod0l+okx 9hwont weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 7og q-6p si90l1cf,x ug5-kg astronaut 4200 km from the center of the Earth's Moon in a space vehipf9,ig- lcx0 uo6 s1qgcle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They ak ln(q;i. l7ilre observed to be separated by 36 lli(7i ;qnl.k0 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 8v(b:ql2o ezxs4c b;jweight of a 55-kg woman in an elevator that mov4(sz 8l2e jov:;qc bxbes
(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-:+8 o*wte5wwc- l 9cish yexz elevator. The cord can withstand a tension of 220 ewyohtisle5:9 xcww-z+*c8 -N 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 ara35z7- 4z wlngx,gysurface of a planet with period T , the density (mass/volume) of the planetax5yang7l-z z3r4 g,w 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 6dt w5dn, y+1u9sltos 7j/nk3pp2 rnw of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surfacedd73 6y2pkjstonwn9 luwt sr5 1n,+p/ .    s

  The asteroid Icarus, though only a few hundred meters across, orf bss x(-rmp7.bits the Sun like the planets. Its period is 410 d. What is its mean distance from sx.-mfbr s7p(the Sun?    $\times 10^{11}$

  Neptune is an averagejf:0skck.b 4lg ;/r u5qy8*s4ux i btns9rls2 distance 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 roughly once ,t8hb3ax(ita5;m olwevery 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 Kom 8t,;awh ti35a(lb xepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cen -g 5h*wqn1nucter 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, p2x;lr 9 bapv3veriod, and mean distance for the four largest moons of Jupiter (those discoveredpb 3 alxv9v;r2 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 distance of the Moon. 5p) n:do8 ggus cza+0wh dv4w: pd:zh c4gnwu 0+s8adv5og):w    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupitmz- d3 i0t 0zk2jzntj0er’s moons, using Kepler’s third law. Use the distance of 2id0jz 0z-3t n0jt zkmIo 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 consi8xt/-; firllv2lr,; 2kv avm nw8i:l osts of many fragments (which some space scientists think came from a planet that ol8r: kfvan8, w; xmvr2;tolil/-i2 vlnce 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 f um3avzh,8eo9 :a d7al +jnb:sorm 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 likea8sz:n9vaae d7:uo+m hl,3 bj 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 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 j7;n c9i:eedje)lu o6 a hanging vine (Fig. 5–41). 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 li)coj9e;ne67 u ldej: ong.   

  How far above the Earth’s y.839 dgz6 pvenjt/vlo,)xst surface will the acceleration of gravity be half what it is on the surface? 9)ot.8dp,/6z 3 lvsetgv jxny   $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands a .t+p03zmcdiv v9trj-4w di .znd spin in a mutual circle once every 2.5i 3dm4pwzz9vdv 0.c i. trtj+- 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 once per day, the apparent acceleration omf6 ;q(e5g z j)seuir0sns-5u f gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of (; - 5ig6ue nsmzrj0sse)qf5ug is this?    $\times 10^{-1}$

  At what distance from the Earth willof8 35iynifo , a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forcf,5y38ofn ioies?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a uow7:-es5osd1jfl m ;bathroom scale in an elevator, it says your mas7j d elm-uof ws:;15oss is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consistac)poi1 h.a 17vxpae +s of a circular tube that will rotate about its center (like a tubular bicycleax oa)cavp11pe i7 .h+ tire) (Fig. 5–42). The circle formed 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 a vertical lo re .k40e 5;gufg-auniop (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 9kej vv0u3i x5w4x1wp mass of a planet in terms of its radius r, the acceleration due to gravit p1x04wuxk39 5wvj eivy at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on uuk;a-px/pr 7m udp.,a string) is deflected from the vertical by an p7,pxa;uu/um d- .k rpangle $\theta$ 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:n2lp u9b g/8ctx* te5b-vu et speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can2gt-/ uu9ebe l5p*nc btt8:vx a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects aj7rb i ool*na9 b7v*f1t the equator were apparently weightless? * lno9i f1ob vajb*r77   $\times 10^3$s

  Two equal-mass stars maintaig gszbck),qo q*f1 92un a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A la ahtzf;8g 7.j rc4c,nxmp suspended from the ceil f, tjc4nc. hx78rag;zing swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times 3.cskch47 gis0gjvv 4as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the follow3.c sv40ghs4ck ji7 vging 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)rjjku* m b e;o21i4gtc 6ajx6 presence of an extremely massive core in the distant galaxy M87, so dense that it could be a blau)*1jkc o 6eab2tjrm4g ;x ij6ck 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 vallemcghj9k+; 0 hr/; w3 vbc*a wr1hm(wfwy shown in Fig. 5–/r w+v1mbhhf hmw(9c c*aj gkrw3w0;;45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) 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 Posiure2;4q 8;fepj:p)aa mvrli -tioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit a p:mf;ie vj-rrq4l8)up ;2e aat 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 Rendua2 cvt23q9u m(oycj 7ezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Erosyc7q2au2vuc9j tm( o3 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 space shuttle pursuing a satellite in nen3i rxh u k(sg9yc+,w)ed of repair. You sxch,w (+ ki ynru39)gare in a circular orbit of the same radius 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 years. (a) What is p s(-uek gd0dz*h-a5iits mean distance from theezid dhg 0-k*-a(5psu Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" y9q2;q fs9m,v c jibh re(h92urourself gravitationally attracted to someone nermq 2r b92hfj 99hc(vi q,e;usar you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arounh7.v/c, )wuyyokrxb/d the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30, u.bv/oxy7yw),rhck /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 located at the kwc/44ti(t0(xlb n y acorners 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 the squa/0a(t 4n bcw4kltxy (ire.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg ot+;77je u-ppr: ldu.p o .bcfsrbits 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-cm-long sw 5yw(te:8m wrbd*rjv f8 0:usieep second hand on your wrist watcdvwr8j e:w us*m 5f0: tbi8yr(h?    $\times 10^{-4}$

  While fishing, you g5 d:;zn4 2ylfq xzui.bet bored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hq z iuz2n5fdb. 4;l:xyint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a cad 7k if9gl86ykr traveling ady i8fglk 9k76t 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 negotiatingv s1gp-8bo c1oz9;m nka a0-jb curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if thesk jc1-vgo1 nm8;a-bb9p0oaz 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.$\approx$    $\times 10^2$