Sometimes people say that water is removed from clothes in a spin dryer by cent pcjvxw3tdu b;e6tt y)uw 42:y(0 czb0rifugal force throwing the water outwarv0b 0wz:u ty;jud2 xw 3(6ep4)tytcbcd. What is wrong with this statement?

Will the acceleration of a car be the same when 9f6awe4am(zuvy- 4;bz-fwld the car travels around a sharp curve at a constant 60 km/h as when it travezmu d4a-lf- v 4b;efzw9wya(6ls around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly roayxv yrin1ta3q,/5 u h3cdp*.1,cnqrxd. 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 , x5*qrqd/1a x hcnycnyr. 3uvti ,3p1two 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-go-rz-:k jn6mw7nrzmje h 0y3 25ehound. Which of these forces proviwz7:ny mm2e3 k-j 0rezh5hj6ndes the centripetal acceleration of the child?

A bucket of water can bex- / *a;uqfcl dxaqh+* whirled in a vertical circle without the water spilling ofcq *u* -;+ xahaldx/qut, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have inn1w0 mzaeyz8z( j9kik00s3zrjil k skq; p+38 your car? There are at least three controls in the car which can b8z 1;9a (m08zi rlk+ek zkyj3i30kqzswn0jps e used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest ofsbhr)31-- adl im j9ir a small hill, as shown in Fig. 5–31. His sled does not leave the grou)ls-3di1b i ahrr9m- jnd (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curej19ym q80cblk g7 ; y7f:rnczs wbv*:ve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angljy:0, itor 1hee given its speed and radius of the turn?jyhtr:oe01 i,

A girl is whirling a ball on a string around her head in a horizontal plane. Sigjwgq.90 4k dfcfv 9;he wants to let go at precisely the right time so that the ball will hit a target on the .f;0fj wvgd9k 4ic9g qother side of the yard. When should she let go of the string?

Does an apple exert a gravitatk3p w0++xb hykional force on the Earth? If so, how large a force? Consider an ap0 ykb+3w hxk+pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were /kan+1 vtb i-zdouble what it is, in what ways would the Moon’s orbit be divak1z itnb-/+fferent?

Which pulls harder gravitationaldp:lgng *d +q,7mr ,he)vx.slly, the Earth on the Moon, or the Moon on the Earth? d,ml*. )xr gehn +gv,:q 7sdlpWhich accelerates more?

The Sun's gravitational pull on the Earth is much larger than5s 5.jg45aiebnq(tt- s cwmi:g* c(qv the Moon's. Yet the Moon's isvt(i:c5*(j.qbaswgscmtq g4in e -5 5 mainly 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 effec :7y: eusux,yru /gx .gc9zh4 nm9hf2hts are a4y/ ru,.y: zcxmfh u7:99suheg2 nxhg t work? Do they oppose each other?

The gravitational force on 5iu5ibp6 gw/;;sd p 9z0 ws)d ws-czhbthe Moon due to the Earth is only about half the force on the Moon due t/0b6;dgdi s sw)w-cpus5ip;z 9zw b5ho the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Marez.as -v525k3o .zav 5a+ guk.wtqiw ss in its orbit around the Sun larger or smaller than th-5.k5.sozuka+e 5via3a 2 .zs wtgqwve centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east o-.7rg 9bak4cvqb *k c ;u)qqxar (b) towa;a*qq q)kc-x bu ra9k g.vcb47rd the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in aes :slxy+:wt e.w) t1a moving elevator: when the 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:1aye :l+twswes.x)t you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space coul 9 )y9oohuzi,wqt)9ey d be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts w9z9eoy) tyhiu, o9)q 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 “s f s6x54cqv6cgb8 a2mfree fall” or “apparent weightlessness” betwee 6 aq4cbs 5gs6v8x2mcfn steps.

The Earth moves faster in its orbit arou3h4k +kpq xtj6nd 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 t qjkk+t4x63 philt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was disco , zllrl 5g9wjm9:vu.yvered to have a moon. Explain how this discovery enabled an estimate of Pluto’l rwy5 9l,jmvg luz9:.s mass.

  The Sun's gravitational pull on the Earth is much larger than the s1c n**lu*)wq4a p-*srq qo axMoon's. Yet the Moon's is mainlcp*qu 1a4 lw aso*xrqq*) s-n*y responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling ao7ft ddfuxm2es04 5sys/wmo* un 66; 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 centripet1r/buflgq0by2k; xyco1/*go al 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 / * bkufo/gyyb crq lo1g2x;10orbit 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 exerte 1n7t/icy ox7v wsgb2q*rsw .tv,i 5t0d on a 2.0-kg discus as it rotates uniformly in a horizonta*. r wq1v/5 ctoiti b7w2 y70sx,tgsvnl circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth0ixy2ta (lzn /ygcrusb(3d 4 2) 0cans's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orb y4b gzc saal3(in d2xs/0)2ycur0(ntit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleraa1geibonvb;mg9 v 5 st2rr63+tion of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s di itb5gmsro2+1 bvrea;6 9gn3vameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verlc)2xmv1-ox /pva;gotical circle of radius 72.0 cm , as shown in Fig. 5-33. o;x 2/p a-vlgo)cxm1v 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 10q:db; p ril1e950-kg car can round a turn of radius 77 m on a flat road if the drebp 1;9:qilcoefficient 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 beh01+(kzyvg a j8,nnez between the tires and the road ,a1e8+(zv k nnyhjgz0 if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is l9pvz0b)pbd2 w)6ld,bof :8 k*vhdt s designed to rotate a trainee in a horizontal circle of radius 12o*,vtpld hd8 b20db:vsfkb)96 )plw z.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 rotati9ra1uco) rft/ ng turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the co)u9 f/o carrt1in slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum spee9 ka/k3rqx/1 u1gxi zgd must a roller coaster be traveling when upside down at the top of a circle az//r9giqk1kxg 31 ux
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded top s9kkbt(/cb *a of a/sb9*ktc ( abk 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 -y 9cdy f;8pg, tbcc8swheel need to make for the passengers to fef8y;98b c -yct p,csdgel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 mrw2vm exm(ju5g h0l8 y( +qw4u. At the lowest point of its motig2r5h j+uywuevmx8l 4w (mq( 0on the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate r -l: s+bgr-)m/ynuvm;gvos ( if a particle 9.00 cm from the axis of rotation is to experience an acceleration/or+- m ;v)gsrlvyg:- b u(smn of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindriqn vy*(f --+c oype;gqm-kcn( cally walled "room." (See Fig. 5- (eg ypfykq;vm +-n-q-oc(c*n35.)
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 rotatedr8m5lrun. 7+la4dwp e in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connectedw7nue+.rap mdll8 r45 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 lg-wgz)1, phht*tr6 h2;xsuk the weight of the ball which revolves on a string 0.600 m long. In pu1r h)k;sg, -2*lwx6 ghttpzh articular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a o m ji/zi9++fscar 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.fo x191t eo4jaisl m3b amo3- $ 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 vertical2/: ij vcglwvp5;zg1zk.n f7zly at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net forc igq,lq+/jit:e;) ;2xrqxh4dtqy /dv9ey* q ee exerted on the car (by thtlyd/;txxr qqq2:hiyq , *i;e/4q+ vd9 e)ej ge 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 acceonyv 3ub ;.w8bkf m2:olerates 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 bet ;u:k8yov2bbn wmf.o3ween 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 . At a par cy1t. m (f6a s2bmvkg2q;qt/aticular instant, its acccqym(;1 fg.tmsvk /2ab6 aq 2teleration 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 sp ooc1:dg x,o6v1xcq(p7gn2ce acecraft 12,800 km (2 Earth radii) above theocdcq2 p1 g 671g:cnoxevo,x( Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational a 9b: cvtq:;f/pr4kdu acceleration g has a magnitude of 12 md4;9 rf: tbcukv/ qa:p/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 60 .p vw+*te19t-* oejo gwh )jmqdtq2vpir:sMoon's radius is 1.74 r21+ovq-jtit6s p*t )e.9vwd gqw0p eo:j*h m$\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, butqrnrmoyii :6 .,5,v *dau4 vdqd*m1kk has the same massurd4,idi5a.*dq: q,vkyv 6r1 *nk om m. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same rae od2hxu z2:ok-p-2jy dius. What is g:uk22poe dxj-o 2- yhz near its surface?   

  Two objects attract each other gravitationally with a force of uxe8e66ig *hz 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (1tfgy -ty6co8a) 3200 m tgy618 c o-yft   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wh(5n 2g *ctec9sprwn)were th2)w rwp *ge c5snt9c(negravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fg8av(ls4z2w o ive times the mass of our Sun packed into a sphere about 1slazv o2w8 4g(0 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was a-aoy7m/vrq+nri.cugi pzk2 rf.9(73 2s u ston average star like our Sun but is now in the la3tuu .9fz.rriic(m2+qp 77ko-2gs v syona r/st stage of its 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 orbiting in the space sh 8++ikkk.axt 5en)9 ajg 5skpfuttle. 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 k++itn55ekf8a jsxk 9p)gka .the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located aujvm6nukk 9qnubfq 844)+( py1wj k.ht the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exert9u kubqm4nky4.+wpqj6( )kh18n jf uved on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on thwd* -62afq9y py5r hfe7o y)ude 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 l-dyq fuf p9y2d7 w)6hoa*5eyrine (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 rjrxygz; 2gour m ,1(2at the surface of Mars is 0.38 of what it is on Emr g2;u1goz(j2,y rr xarth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun us9b 27mdsth4kf (qb-kving the known value for the period of the Earth and its distance from the Sunqf9sv7m(dt b 4bk k2h-. [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 orbis+sse353 xb8b6edkqr t about the Eartsed8x 6sqb e3k+b35 rsh at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into q9*berubaow s*:n9 5n a circular orbit 650 km above the Earth. How fast mb ae99wun:os *rn5b* qust 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 to experk;gvdqj8vcq01/ (2rpqguq.y ci uz* 6ience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer dj02*p1.;i cvqvy6kqcu g8qug q/ rz (as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a 0rvhzg9w/1tzcldvcw0ru 7(4satellite 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 of the Earth. Does your result depend on the mass of thw9 (/zlvcr40hrv w uz dg70tc1e satellite?    s ~    min

  At what horizontal velocity would a satelliteb cl8c,8 zj( z fzhxug+4,dk,g have to be launched from the top of Mt. Everest to be placed in a circular orbit around gxb z+ cfh, cjd8ku4,,g8l(zzthe Earth?   

  During an Apollo lunar landing misd c cfi/ga37rl4 xa85eacimb./uz8 g;sion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once 8u/ica 5 g43gci zb.carefa7xml8/d;?    s

  The rings of Saturn are composed of chunks of ice that orbit the plaqzzgaen)l8u0 0;j;x snet. The inner radius0);exuj0 nqgs; a8 zzl 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 evemgf-l/:0io z /4zsy pxkh.ol; ry 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the tos-fl 4lizhoy.gxom0;zkp: //p, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the centerenm((0bduixe,* m vw 6 of the Earth's Moon in a space vehicle (a) 0e(*nummwd, b( x6ive 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. Theys560i dape,t o are observed to be separated by 360 million km an,at ip 5ds0o6ed 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 a 55-kg woman in an elevator gp w):fvib,8wr d7rl+1e hv,ythat,dl ):erpw87f1+ hwb, irvyvg moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from tyr+.5ktjbf g4cd75yx he ceiling of an elevator. The cord can withstand a tension of 220 N and break5yy 57jd4c.g+tkfrxb s 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 planet with period +o6b.p(-ns nb tsyodtku k.6qv 34dm ubp(8 7uT , the density (mass/volume) of thn6n kkus 3sq+dy4 tdp bt6vb(b87( m ouu.op-.e planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to dpa3hm7-1z rdg etermine the period of an artificial satellite orbiting very near the Earthdm1rhg pz-a 37’s surface.    s

  The asteroid Icarus, though oo-nw7 nl/: /f.r hdjhknly a few hundred meters across, orbits the Sun like the planets. Its njo/r /.7lh:k nwdhf- period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance oi xn/x:o //teq 2a ts)ymwin./f 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 *g hc28 bt. mypd8:flqele1z+once every 76 years. It comes very close to the surface of the 1 fg8b:*hym2.lqplc + edzte8 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 nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the,x/d 9*t/vm (z3qn.u i4eysxbe s o t+,nae5rp 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,nfv, w +vj(dv0 and mean distance for the four largest moons of Jupiter (those discov,+vj w(n0vdfv ered 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 tb8sozd71u v (omgr48w he Earth from the known period and distance of the Moon. 48 oow1 dsv7 (rbgmu8z   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jtkyjqt;o( u+ mdo-s/,upiter’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 t-j+/yot d ;k qsutm,o(he Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (which soyda r;ix: 0i o4c+rp/gam: jb5me space scientists think came from a planet that once orbited the Sun but waj0 r4i+ i5 adorc:xm;b /:gpyas 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 bdfodu r4mca*20p6g* the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate te42 r*0d u6cgpbado m*fmperate), 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 ar6 9.+78i al gf/u8gtl1wmmirfn5 yglhc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine hawl76/.lnitf 8f lu1ymgm9+ 8grg 5i, 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 q/bpsjin07q( what it is on t(n0qsp b ij/q7he surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circlw 5jz/drs+y q9e once every 2.5 s. If we assume their arms are each 0.80 +w9q5sd /zy rjm 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 of gr:ip+x0 uyfb-savity 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 g is this-p0:yf+x ibs u?    $\times 10^{-1}$

  At what distance from the Earth will 3br7 )n+skfnwwni.*kufaoxk5 a5 e6. a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moonukienn.f r7 xfn+)ww b56as* k5k. 3ao pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kgz iw29l-lxznmdey *c h:6l57g, but when you stand on a bathroom scale in an elevator, it says your mass ihz eim*dyc:zl5l 9g-2n xlw6 7s 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stati ahv ii2,ml931(idtmz on consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be thvi2dla9t mh m31 i,zi(e 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 (Fx40g5:auoph n ig. 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 planetydt9so84batz7a 1rm- in terms of its radius r, the acceleration due to gravity at its surface and az-m y dt4ts 1r79oba8the gravitational constant G.

A plumb bob (a mass m hanging on a stringz./g g+gt1e v bd4je1d) is deflected from the vertical by azeb/.ggv1t+ ded g41jn angle $\theta$ 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 yh upa:z+;6 k-9cf0 tgwe6hv6aln mn 9of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely hande;tcmy w696 :k l0n+u9afpn z-h6h vgale the curve?

  How long would a day be if the Earth were rotating so fast that objects-( iy0 1yjn 9l) .u spesqkywd5c*vvi. at the equator were apparentlkuldcns*i9i - vy.5qsy(py1.w e)0jv y weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.rr w0404 bwsbu0 $\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 c 921z1 /pleor bkyxhy)m y.:qfonstant speed rounds a curve of radius 235 m. A lamp suspended from the ceio q1.mey9p:kxzyl1 2 f hby/)rling 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 t;t(0pj9aaa z/n auum3he Earth. Thus, it has been claimed that a person would be crushed by the force of upu(a/amnaz 0 j3;t9agravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extremelm65cuk :l2rwd y massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light esd2k6c 5uwl:rm capes). 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 tr02a ysuit mj;5averses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the drive250tu amy;i jsr 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 gr ui0dyxi/- gg,oup of 24 satellites orbiting the Earth. Using “trii gxg /i0u,d-yangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 bil .p2cx rokww 0)hkb;)nlion km, is meant to orbit the asteroid Eros at a height of abor p)w.hnokbk);0wx c2ut 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 purs*z0 bwc4,pslo7wnir+ k; o he: *st,hluing a satellite in need of repair. s7:;lzehth4n 0*,*ickprwsb wl oo,+You are 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 h28m kr948k.3oneh9u kciwkm uas a period of 3000 years. (a) What is its mean distance from the Sun? krm 9uw4ik.82kuen k8ho9m c3   
(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 wfd8b( 25g jn;k8h;kk4zu mp xwould need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonableu;b;mphkfk5jk2wdz8 gn 48(x assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milknq5oh5s 8q me82ffc 9yy Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center5cqefys o829f8 n5hqm $ \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 squaw +xv)(yp6c qhre 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 midpoinqc x)w(6+hyv pt of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth 6twdqr70yjk aqg 3 n/-p r-vsa2 +ze;c$ \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 swee md(gkc-xds * y/*he/9 6ksc0xdwu6trp second hand on you ex*dxy0dssm cdwuc/6thk k/* g-6r(9r wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swinb2jsf 2,qhq )lg a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle ehbjq2fq,)2 lsvery 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 tha -nkd9)m 5.yh+.yztke:x0wfl oiai q,t a car travelind: fyektx 9 q.mak0lih 5w-+ y,)i.zong at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the vyz55 1vzgmwrb, z 5)oAcela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate tzvzymgbzr, 15 w)5o5vhe 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.$\approx$    $\times 10^2$