Sometimes people say thap1q(o*.puijg 30 nzr( w/crmafv0+jat water is removed from clothes in a spin dryer by centrifugal force thr 0/(fzp prw 03n+armuo1c j.(vjigq*aowing the water outward. What is wrong with this statement?

Will the acceleration of .v/ad g0v( )wav7t ue-llko/ka car be the same when the car travels around a sharp curve vk old7vka)u 0t/-gw(lea /v.at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at conb rv 16lp8th0tstant speed along a hilly road. 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 hills, (v0ht8lb p1 t6rc) on a level stretch near the bottom of a hill?

Describe all the forces acting0d +tv.k bercl()zj v7 on a child riding a horse on a merry-go-round. Which of zvd)celkbtr0j (.+v7 these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle wit2coouj + k)gd*hout the water spilling out, even at the tou)j+g ok*2cdo p of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your 5toq pq90g1-b xsa odn7h7f m4car? There are at least three controls in the car which can be used to cause the car to acces10 q gb9 7-adh4 xmfopon5tq7lerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small f kz;bid2a/lbpn c6w ),:24ad cbibg6hill, as shown in Fig. 5–31. His sled doefk2b2cg p wb4b;: 6ia,ndb6zd al ic)/s 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 hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when ro -3psroyuyxajgn9d *6ha;7(9m vj pb*unding a curve at high speed?

Why do airplanes bank when they turn? How would yoa+b(,s)grghd u compute the banking angle given its speer,sh()gab +dg d and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane.h 5(:qfkv96j e , vbwqr3dnp+y She wants to let go at precisely the right time so that the ball will hit a target on the other side of thek njhf6qep9 ,rwb5vqv (d3+:y yard. When should she let go of the string?

Does an apple exert o r;cay.rc )vedwt2. *a gravitational force on the Earth? If so, how large a force? Conwer; c2.*ra dyovct.) sider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, i+hyo- 1 58.wbg.;dun m rjmufq9 sb)gvn what ways would the Moon’s orbit be differe d1yv;9u) nsu-fo5.j .qrwg8 mmhbg +bnt?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon onfm l0 -hkwn2t7 the Earth? Which accelerates more?wltn7fm0 -2k h

The Sun's gravitational pull on the Earth is much larger than ph5. zuec*+fu,w.oqp the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the d,q*.pupoufc. eh+5 zw ifference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at thef8x7;xwb 5jv j equator or at the poles? What two effects are at work? Do they oppose each othvjb wx7;xf8 5jer?

The gravitational force on the Moon due to the Earth is onld1lj*gb:+ lecy about half the forcel*gc+1 j b:lde on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in i(bgyy-jxm+ f (ts orbit around the Sun larger or sm x+f-ygmj (b(yaller than the centripetal acceleration of the Earth?

Would it require less specf -.ya1+bdw yed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotationd+y fy1wa- .cb direction.

When will your apparent weight mz;abv8si- 2wa/8 r sfbe the greatest, as measured by a scale in a 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 you are on t-v2fa/ zb rs8sim 8a;whe ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space cd: fk*b4a.kuuould be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with 4.fakk:b u *udthe 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 expery4s-f( v-mzuy iences “free fall” or “apparent weightlessness” between f u--zyvy(sm4steps.

The Earth moves faster in its orbit around the Sun in January than in July. Is/f;hbc 55pkff the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the sebf5;kffc5/hp asons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not knogq p *8gzp2g/ kyldq;+omn:i,wn until it was discovered to have a moon. Explain how this +od 2pmqgglz8pyi,q:k ;g/n*discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Y(q ,x vs.zh8tvxhdsudqs 43 m*m1.+qjet 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 th.v m sj3qst z+hqx814* qudvh,(ms. dxe 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 travelin .ws2lqo71,hmmfr xt2g 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 centripetal2 acnf:cj0+pr5c .* m1r tjgzm acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radicrn102r:gmm j*c .p 5fjzca+tus 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of vzid 4o0w,k3d 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circ0d3i, wkd4vzole (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 Ear(sf4daeb a c e ;nr5v)5g8 xxj1o4w/zuth's surface, and circles the Earth about once every 90 minutes. Find the centripetal w545gc;fndoas8/a xbzu 4xree1j () vacceleration 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 clay on the edg ,fg-x rg4bo,he of a potter’s wheel turning at 45 rpm (revolutions per minute) iffrgg4x,-ho,b the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical c*(e7 wl*.l baxnmo 4kbircle of radius 72.0 cm n* le(mwo.x7l*kab4 b , as 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 7z qyj*6dgty*f+/ f5ypaysc0 1 7 m on a flat road if the j/d* yyyytcgfs0*6+ pzf1qa5coefficient 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 ,qeigw ml v *b:0vxv-2static friction be between the tires and the road if a car is to round a level curve of radmi, e:-vq2v*x lgbwv0 ius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rota:,g0lpjz8a 1t x uosi-te a trainee in a horizontal circle of radius 12.0 m . If the force felt by the traini, tuaog 0 -l8jpxzs1:ee 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 rotating8h;f vf +3nwk2 *yp; jtm+qab9 vwoaq) turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. Wh 8*;j qffkhow+9vy3q)vabt pn; ma2 w+at is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travel cx8 t,44bq8j tfh5xdling when upside down at the top t d, x4hbtf5xq88jc4lof a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crossek * 5ct2/rgl0tdb4 )ejudq;c2cri hlxy.:a8z s the rounded top ofdgci52ckr:).l*u4 8xtj 0dc/z ael;ytb hrq2 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 would a 15-m-diameter Ferris wheel nee0w-gwt dh,r ln hjuz8u4;t0r7 d to make for the passengers to feel “weightless” at the topmost point? uudr ,g7 0l0znj-4 whwr8;htt    rpm

  A bucket of mass 2.00 kg is whirlen1b vot 4w2f*ud in a vertical circle of radius 1.10 m. At the lowestot24 *fw vu1nb point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rom4hgx5hja er 187* yz sbsz;/htate if a particle 9.00 cm from the axis of rotation is to e hj5yaze/z4g71 b srs;mxhh* 8xperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival1e; hyamhi3z mm0yy9u/ 9i2hd, people are rotated in a cylindrically walled "room." (/dy3ia2;ehmm1z 0y 9iumhy 9hSee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionlessmy l7na (4excaq)+fz8r uw5y1 air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a centra1feraw+c(xqa 7 4u ln)8zymy5l 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 n f0wpybr ;z9f)ot ignoring the weight of the ball which revolves on a stri fp) r0ybf;9zwng 0.600 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 per31d9 .l(d5)leh lful 8iyy mtj-rbhd4fectly 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 masse m h(vbxx-nd .*wwp.w(e7:g sms $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at gn 5pnm2n 7*vw,v ht5c 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted o.u3f id9j n8lnd1lzk 2n the car (by the ground) in Exam9.1nkdn 8fi d2lz3jluple 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 unsyq ,zawdh cd)5 if80+iformly 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 codwy8 5is0hf) a,zd +qcefficient 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 jpik9 zoe t5(p 04b1ce2.90 m . At a particular instant, its accelerati01b tpi9jz kco5e 4(epon 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 onfq6x2n3i 2v5cv -vzpj a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfac2j v-f3 5v6x qvncizp2e if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitationa3 nfej d 1l/hld74rgn9l acceleration g has a magnitdg7efn 49lh1/n djl3rude 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 the M)gj3ehj v/)p moon. The Moon's radius is 1.73jhjmg)/ p)v e4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has *:: roe0xt xrya radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near it:r* xo:x ey0rts surface?   

  A hypothetical planet has a mass 1.66 times thaaen :* qd- 40dw1qqadmt of Earth, but the same radius. What is g nea1n ed4a d :daq0-qqm*wr its surface?   

  Two objects attract each other gravitationally witl, x:jn2cztwh p 0:6zjh a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the 3 +mljv +r +giv:cmqk*acceleration of gravity, at (a) 3200 m+i*mjvm+: 3q cr+kvl g    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wher8wy.a;e, 9l zltfe;jbe thegravitational acceleration due to the Eat ell.;98way,f;b ejzrth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star h uf,k,)lrkgn e/f y9 l6jvsws9(h. ty2as five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surfacy9(f s9s .,kj6unywfkr v glhl2,et)/ e gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun b jg9 w.qq*pkp0nm)xb 4m1q-rhut is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. Whatx-m90 qj .h *np4k)1 qrgwmqbp is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronafrx mc )0 rzn1k9du96muts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince t1u9k6mfrcm0 r) 9nzx dhem 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 ofq0vo3l/(d pp x side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted o3(0polqvxd p /n one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets li64qmg *ezr d4ine up on the same side of the Sun. Calculate the total force on t6iq 4 4z*dregmhe 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 accelera wgm/ h6w.0fpxtion of gravity at the surface of Mars is 0.38 of what it is on Ea/x gmww.0fp6hrth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usin cf(kun:i8zz cdp )sgld dh2v/g:1i.,g the known value for the period of the Earth and its distance from the Sun. [Not zci: g)zdp82nvdl .(,d1k sfhi:c/ug e: 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 stax8 (h6f.j ozdqble circular orbit about the Earth at a heo.6 8f( zqhdjxight of 3600 km.    $\times 10^3$

  The space shuttle rele eey/i2pm-d8r k/yty6ases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttlekde ypme//8i2- tyr6y be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cea*pr ,(vgutf or51atfo tq: v -;vp98ylindrical 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 revolutio(of8qrp u t9;-av:av,vrg t1pf*t 5oen. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to ory a7n 4vzw(n+ebit the Earth in a circular “ne nza4+vwn y(e7ar-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 the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be b9 lk+1zca,p blaunched from the top of Mt. Everest to be placed in a p9,bcb1zlka +circular orbit around the Earth?   

  During an Apollo lunar landing mission, td cq6mg yvuf 471+qh;lhe command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to g64c+7mlfd qy;vgqu 1ho around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit 3qtv s 17xtnog;8 l*qrthe planet. The inne8xs; t nvg71*or3tq qlr radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once e m yad362 -rehc;*nonk.k 7hyjarg l3t ,2:cbqvery 15.5 s (see Fig. 5–9). What im-jq ,ta76rca2.*cog3 :eylb ydr h;nnk 3h2ks the ratio of a person’s apparent 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 asth. ks mdoc+zf: i-z3r:kap)l32wwuq7ronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at con :o 7mw sa qch zup.w-2+fd3izrkl)k:3stant 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)bi8.o 50rae hh8snwa of two stars of equal mass. They are observed to ben.5a hir ow0hebs8 a8) separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale )vbr jcl3p6uh- h8, vgx.nz *jread for the weight of a 55-kg woman in an elevator that moves pcz*8, b nrxv)-h.j gju h63vl
(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 cordjf ifxgb7.y4d;ue7 v* suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N*47i;y .jeufgb7 xdfv 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 su*c zed wdfy y-7d8x,z/oi6 qf6rface of a planet with period Td* df866zxzoq ycf d-wyi,7/e , the density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to dev+l 9nj .lhxatvw 1;+qtermine the period of an artificx v9t.vn+a l+q;jl1 hwial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only w9bfdy 4pw g px0h;bg34p s 3:r5rze6ma few hundred meters across, orbits the Sun lik xpr5g4bp f0db6 rs94ez g;:wy3hmwp 3e the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average di;npc 9af :8)edvx :ovtstance 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 rough/3 wh9vx ht7zrly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum oxrwht/hv3 z7 9f the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of thqbq: fvu/ zqb5uz4: gu*ij4.ojq t 6/ne 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 ibf30vq2 kcf 49v7jejfour largest moons of Jupitjbik 3q497e2vfjc f0v er (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance ofo(5if*-mt o mw the Moon. t-f5(mm*oo wi   $\times 10^{24}$

  Determine the mean distance fr:vaj(tqhir 2z1m,bt 4jnl n3blj te:z. 030 jsom Jupiter for each of Jupiter’s moons, using Kepler’s tn:a iz h00 j3vb4q.1(3tenj: lmlsb t2tz, jjrhird law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars anf.6bh zpi pwk;4 1zqe3(/wqwdd Jupiter consists of many fragments (which some space scientists think came from a planet that once orbite ;fw1wb4hpki3e6/(zqp zd w q.d 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" imgm6 )4l 1q c)e 4vy(g*wjpmkfn the form of a band completelwgvcm4y m(pmq4kf1 l*)eg)j 6y encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g 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 vew,c 2d2b,m*p7 wbnr fine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed bfbw2e*pn7 rdmc,,2 whe 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 acceleray;.oy,uu q9 wation of gravity be half what it is on the su ya;9 uuw.,oyqrface?    $\times 10^6$

  On an ice rink, two sadaw- qj+ex(71gecroa3 /- cvkaters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If weja3-wa exdr g/qc1(o- ev +7ca 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 accelerams,rk t 8k:c)9xq9,h tzp9ftstion of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Er q: f 9 ths,s98xc9kt,mkt)zpstimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelinwv*h2u: *x+hnrq.dg*u)wd iu4a -rl wg directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with *w.d q*nu2ah+)- w:riru4* d gvxhlwu equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on i a qa.j/t;dm1ni3-xg a bathroom scale in an elevator, it says your mti;qi3 a1-jamxn. /g dass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a ci y farr6-(wcb( n9iel5rcular tube that will rotate about its center (like a tubular bicycle tire) (Fy6fc(9bwr a(l eri-n 5ig. 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 r-2-uh h41sol xw 8zwq w,mpn-loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of it0kmdin 0cmxfx*ja3 1/s radius r, the acceleration due to gravity at its surface and the mxafc*0 dj13/k0nxm igravitational constant G.

A plumb bob (a mass m hanging on a str7jgmkv5b 23r 5ici hn-ing) is deflected from the vertical by an 7b c-m5ihnkg3irj 2v5angle $\theta$ 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 for2bjtlo wy;o p-vy rwg/wqil, a55j70)1va 4 ca a design speed of If the coefficient of static friction isl,1 p07 5)vy2vwr- tcajqb5ga4/ioy w a;olwj 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the 0:qiv,,dp3 suc.si bf Earth were rotating so fast that objects at the equator were apparently weightlessbd ,.qv ,fis3:usipc0?    $\times 10^3$s

  Two equal-mass stars maintain a constant di5 drm)5oq3 : ges +bmn/,tqgaistance 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 lamp gw0sylspl4-/sp 65 zwsuspended from the cei-sp lsl w6sp5w0/4g yzling 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, it has been claimed6xq sdngai/ 886sygcoigl* (kh 7 jx53 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 following data for Jupiteijasng8g 8xy d656(ogqi hs37*/klcxr: 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 Te9m:iluy77 gwv lescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which 9muyl7gwv i7: 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 azx4u qx+50 6jepwxoe, nd 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 x,j4e6oqzu xp5w0 x+e 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 sdhiun ng (d ygh+m:b ).n;6x5l :.hpsbatellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellit (d:x; binup 6hdgh. n+syhnl gm5).b:e.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after 4iezd2u1wcrr5 9aq5:u v2 /r7obwd h ctraveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is/vc9ouwd rrw2h5 b7 cd i5a2uz1eq :r4 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 sa -; yedlqu61fj10yg wmg8fpz e;c-0sxtellite in need of repair. You are in a circular orbit of the same radius sef80f guxz;;dmpl1yq 1gw -j60 yc-eas 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 its mean distanc-2(cvz z(ok7k+lp rfh e fro 2(pvck(zr7lokh+ -zfm the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would needkc5d k4vt fqqo:i)tmi m07,:l to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable a0),m fq45mcdk oiq: 7l:vtkitssumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centepeivjx (pt80 y wd*9b:r of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 ligy(d8i vx*09e tb:pjwp ht-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 aj,u/4 r tua8.uur1+z akk/w uqa t3j0wre located at the corners of a square 0.50 m on each side. Find thea1jkjuqw4u0t zuu8/ au+t rk .3w/r,a magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed 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 Earz-,3t lhslf0b1 bdxxa k+(e h(th $ \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-,l50 lvunorpwuk uq-+9i l27tcm-long sweep second hand on your pur5 i 2,k wnu7q9+v lltoul0-wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing,4 , c4,kqichoz(s6de ago aj( 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? [Hint: Sea ci oae(hd, (4s6z,ocq4k,gje Fig. 5–10.]    $^{\circ}$

A circular curve of radius R v-dup(;l(z dhgya1u8zk l /9 lin a new highway is designed so that a car traveling atz -1(zllld/ ;duhga (uk8py9v 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, t 6 8 hkezu0jz+h+sy a:geewuu/4s+r+khe Acela, 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 fee:e6ky +uk4zuhuwz8+ j s 0g+/sea rh+eling 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 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.$\approx$    $\times 10^2$