Sometimes people say that water is removed from clothes in a spin dryer by ceno u*5y.m+msy ntrifugal force throwing the water outward. What is wrong wnsm.ym5*u+o y ith this statement?

Will the acceleration of a car be the same when the car traviurha9bk0di ;yl 7,8zels around a sharp curve at a constant 60 km/h as when it travels around a geiayklb9i7 ,uz0hd ; r8ntle curve at the same speed? Explain.

Suppose a car moves at constant speed along a h9- tx 9w6xjzue)t8w-3s q vzcdilly 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, (c) on a level s3 uq dx6-jt )x w89cz9ewz-tsvtretch near the bottom of a hill?

Describe all the forces acting on a child riding a horbmsep/ :m6: ae7g;rw (brd:d s; qtq.gse on a merry-go-round. Which of these forces provides the centripetal acceleration of t de::qa;gm( sq7w b sp:mrt.;/6bdgr ehe child?

A bucket of water can be whirled in a vertical circle without the water;fu) w zy2/wdy spilling out, even at the top of the circle when the ;)ud2y/wy fwzbucket is upside down. Explain.

How many “accelerators” do you have in your car? There are ,x6k9w8 fo3 uxnaaj c/at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they prodc69wjx8x onau3 /k ,fauce?

A child on a sled comes flying over the crest of a small hill, as shown in Figi5my1zf8i zj11k v7i+ t9 xuho. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normakix5zovify1 ju+ tz h7i911 8ml 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 ru5gw-x ce5n f rgh5p.;px9wr/ounding a curve at high speed?

Why do airplanes banku s wn;1voxu /jq)q2 6l 4x0l2hx;gncu when they turn? How would you compute the banking angle given its speed and radius of the turllx ;snx041ujnwuv;x q qh26gcu o/)2n?

A girl is whirling a ball on a string around her head in a horizontal plane.6my dwhb1pq+.u ag5 i73lqrp0 She wants to let go at precisely the righ0 u5+1 . md hqbw7qi6alpy3gprt time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how larg3c -r;r qe4f0w/mp saq 2fi0yue a force? Cq4r3i;fqws00c-er/u f yap m2onsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon, 9 cniq2auy2 5:aqhop’s orbit 9u noc h,q :i2q5y2apabe different?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on fz iweu76p 89edv08fg the Earth? Which accele 7pv68fg0edw 9uzif8erates more?

The Sun's gravitationrnae 7wjstpea1a1 g * ;t:yyym .)m22 )lto,lnal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the otoyasee1g j:)w)ym p r ty2a m,l7n1tlan.; t2*her.]

Will an object weigh more at the equator or at the poles? What two effects af fnmg*e* 3.5lbd 6w 9k7elq.6f legwere at work? Do they oppose each ole73eeelg lf 56.9wf*qbkm*dn gf6.wther?

The gravitational force on the Moon due to the Earth is only aboul.5txtn( kda 8t half the force on the Moon duttnx(.la58d ke to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or 3:9r (l)g,tyezk hwae w,c0 fdsmaller than the )k03(gz lefrtecd, y9w, :hawcentripetal acceleration of the Earth?

Would it require less speed to laudmnfi0 )4yp19 g*dj wynch a satellite (a) toward the east or (b) toward the west? Consi9)0did y jg*y4fp1nmwder the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a m/rb+ i+u-ziz lfe-t 9aoving 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 whfia 9++u ztlrie-b-z /en you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be advert6hrub sv std v071,1pxk8di0sely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider vbhi dv 6u7s08 0xdt1p1s ,tkr(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 weig (uuhukjrygt7v9dz++ye v( 1*htlessness” between tyz (+e9r+uyu vj1(7hudgvk * steps.

The Earth moves faster in its orbit around the Sun in January than in July5wb6gm4g6is3 e urpf6. 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 s 6epu 5b63fm6rw4gigto the plane of its orbit.]

The mass of Pluto was not known until it was discovered to zzgm84x b:yaqdl80ze-qv** g have a moon. Explain how this di-mb0 48 *zd zl8evg axyqqz*:gscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. odzfz6uj.eo3u - 0wpne1l;l -Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Considerwf;e0 -oz 1njel- .p36lu douz 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 19b 9c3mqbd 57zyg lt3*u80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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/vos ua k1(8yc acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts thisa/so(c18uv yk force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it ros44vez3 r/m+/ew bvc ktates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus. c4z/3s vrw/ ve4e +bmk  

  Suppose the space shuttle is in orbit 400 km from tdunt9/az j-.bdiv- -e g yw,-ohe Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration ow--.uoa-bg,de 9-i/nz jtd y vf 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 d *ea7l8 , ctw x09zd20aeauztspeck of clay on the edge of a potter’s wheel t2ea tec a*t897azwu 0dx,dzl0urning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertic010rc fm wazixc5*ao8al circle of radius 72.0 cm , as shown in Fig. 5-33. If its sp ioxwafza*m r501cc80eed 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-kg25en q-jp*3k ;7i)t p2ocafl eck9hwf car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? I2e n;f-) 5ofpqcp 7iwj2*k aheck39lts this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and x2c uky+4aa(b the road if a car is to roun4+b acx2( aykud a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fightenpv;j42oul)a o:t v.pr pilots is designed to rotate a trainee in v: pto2a;v)l. oupn4 ja horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotatix j e pb;3fhubjq4b5x3 .uj(1yng 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. What is the coefficiey41p hb.u(3qj xbx53e;jbuj f nt of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down atof76;1zlv6ypsw p9 kv the top of a circle917v66p lo;s kyvwzp f
(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 tbasbt4)h+urqw y4x wt: r3o5.op trw.whq) a54ou3syx rb:4b t +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 would a 15-mmcgftbr:9 xa*s-hh(b*by eltwct2*u5r 8) l+-diameter Ferris wheel need to make for the passengers to feel “weightless” at the tblle2rcgw*bf8ht* + 9y: rta )*u hsmt5bc-x(opmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vero5qu ..lo:*zzza4apb tical circle of radius 1.10 m. At the lowest point of its motion the tension in th*:oz .b zl4a5opquza.e 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 if a particle 9.00 cm from thaxemx6 xt 1wocu.t8(3e axis of rotation is to experience an acceleratiom8(1 cwt xoxxau63e.tn of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, fl6h wm0ma/9kpeople are rotated in a cylindrically walled "room." (See Fig. 5-35.9kfl /h0m6m wa)
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 rky4*9al vuj0 k1+xst6 mi/t thotated in a circle on a frictionless air-hockey tabletop, and is held in thi1mvt*h /y 0ljtk ax96k4+ itsus orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , tdlvpi:9j 2-zprecisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude tvz :dl9- 2jpiof $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 hm0ax0ffv: 8,/hnewwcy1k d 5 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;ke56 :tjoa tbq6 z,hms $ 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 vertit.wxeoi7+ u :00l etpically 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 componentsto*kf3 m2tc p3 of the net force exerted on the car (by theo*3km2fptc3t 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 Indianapolislngl 9j2 u8at. 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static frictiona ul.g2t l9jn8 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(r2 ajf6que3e of radius 2.90 m . At a particular instant, its acceleration is 1ejur 2fq(e6 3a.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 spacecry29kjy9aa u0x aft 12,800 km (2 Earth radii) above the Earth’s surface if its mass jyau x90ky2a9 is 1350 kg.   

  At the surface of a certain planet, the gravizwvx78 c:xhud ze2bui6; /i(kx ; i+zttational acceleration g has a magnitude of 12udh/xzv(7 ;2+e wc i6xb ikz tzix;8:u 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 acceleratewp0gl6-nbvd 6 g,u+fion due to gravity on the Moon. The Moon's radius is 1.74 g-pe66f lwg,n+b uvd0$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 mt0g6;3vbkhh rwn/2up sv1ch: y 9h(ytimes that of Earth, but has the same mass. What is the acceleration due to gravity near its surfac6hvcy;/mgtn (r 9 y3s:1b ph 0vhhwuk2e?   

  A hypothetical planet has a mass 1.66 times that of Earth, but t4w kcfhpk, 9s9l06bw dhe same radius. What is g near its surfacef96lkw b 0dc pkh4s9,w?   

  Two objects attract each otv hq474,4rvdxg1 yic zher gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3200 m25l u9hd xbme0u5sap3 hb92a3msl u05 ud 5xpe   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside th ob6n8qf(p/c8tcrf*l e Earth where thegraqctf*cbor / pl(8f68nvitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has f*:t*shg6tum0 3s 7m)u mxwx kyive times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on thikxu*um73ymgt ) *6s0xwh:tsms monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is af8ds( n-01n/ 5:ns jyfgdysunow in the last stage of its evolution, is the size of ougnnfs5 ju8s0(d- yf:/sn a1dyr 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 th-i 7w u:iy8)c+psvs zme space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that mi sci- uzysp8)7vw+: 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 louog z4:c:jlu 1cated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravit :g 1ljzc:uo4uational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets lj + p3tqga /2/sgqzc7kine up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all fou/c /2gtajzgqkpq s+ 37r planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of 9fk8qau597j4szrz d wgravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determi ds7ufa8495zrzqj 9w kne the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Eav01jdgq2 o-hfqgfm, s/6t6qg rth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example -6qv/16qg0sfm dgj, g t2qh fo5–16.]    $\times 10^{30}$

  Calculate the speed of8lzi;w )j 4p)jn(-obj qk)fdr a satellite moving in a stable circular orbit about the Earth at a height of 3600 km.bd kz) ji wp8jr 4l-jfqno));(    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit ldhzt; b ll.y.l*;ubp) 9f ;e-ovp9do650 km above the Earth. How fast must the shuttle be moving (relative to Earth) -yf d9u9. btl* l;lvbh z.;eoopd);plwhen the release occurs?    $\times 10^3$

  At what rate must a cylu/f7b3r5pl 8 lfcb(caindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spacesh8f3p7 l/f(5c c rulabbip’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite +32oj89* qwuchey6qf */n ngnptrc,gto 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 ver jrg+23/f c nqn 8ngt ,hpw6q*eyu*o9cy small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity wouln37o;vmnc+,5z nr :i4ij ufowd a satellite have to be launched from the top of Mt. Eve n+ziv43 u:o7i,j; ofrmnnw5 crest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued twf+/ q+dq+ riko orbit the Moon at an altitude of about 100 km. How long did it take++k qr i/wf+dq to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plcj* 4wpq4d f*wanet. The inner radius of the rings is 7 4j*fc *wqdwp43,000 $\mathrm{~km}$ , 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 everda-dg6rx-qb0x pfn /) 3p9txay 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent wei 3n0a)q d9db pf/tg--xrxaxp 6ght to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent wei o/e)j/pddgd v1 4swz3r,- gzlght of a 75-kg astronaut 4200 km from the center of the Earth's s vdop ,3rjdg4z- e)lg/dz/w1Moon in a space vehicle (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. Theko14pmi kx,i) +o ne4:la2abh y are observed to be separated by 360 million km and take 5.7 Eart:o ) lk4 p+i2 4xokihe1maab,nh 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 dcx6p* yv tk+y w;5mdjtl4(+e the weight of a 55-kg woman in an elevator that +v pdxekjm;twc4l d5 t(6* yy+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 the ceif7 4ry h 0yuj6 (fpgzo46 hk0ad2kf*oeling of an elevator. The cord can withstand a tension of 220 N and brefy4fy 07 o4fz2p *r6 a(koukdejhh 6g0aks 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 period2p:5e7yzb jd9- jlw fxr 5kk.k T , the lfkb2rkx.9y5-p j:7dk w5zje 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 determine the pee5dv5 gf2i4kf riod of an artificial satellite orbiting very near the Ear25ff 5d4iv kegth’s surface.    s

  The asteroid Icarus, though only a j8rdgsrv0j*me; t 4* tfew hundred meters across, orbits the Sun like the planets. Its period is 41 *dg rt;0s*4vetr j8mj0 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5*n6+4iel )rxrwsqfd3j w;( uj $\times 10^{9} \mathrm{~km}$ 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 ):hgd-w qsd9, s ftqo-(l p4wuroughly 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 or, g -fh4sd-wu)lopqdq:tw9( s bit 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 Galax b 457t33gd-dco+jpxe3: *revp i vyryy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 fo6xxind3 l8vo1) nx0cz r the four largest moons of Jupiter (those discovered by Gd618i03) nzxclx ovxnalileo 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 distanc4 yog 5sc8/mkqe of the Moon. o5ckm8/4sg qy   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupitf /z1e) dalws4er’s moons, using Kepler’s third law.fzwda /)4le s1 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 and Jupiter co,/r oxwlnubg5 f :,5qgnsists of many fragments (which some space scientists think came from a planet that once ol5 rqgn :w,gb5u/xo,frbited 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 w+tbygbf j*+j b*- 1qian artificial "planet" in 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 distg+ b*+w1-y bb jfj*iqtance (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-s rsk 8 5dn.7fpjhh+g59xmz z by swinging in an arc from a hanging vine (Fig. 5–41). If his armmshshrz+j8d k g9-. fnzp5x57 s are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s suq+363m:yuq:s.x.ijq iwrgez rface will the acceleration of gravity be half what it is on the surface? qy r6.::i+j 3ug.qism ex3wz q   $\times 10^6$

  On an ice rink, two skatersd- r7g lc4pa2nk(y7ec ifd6w, of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume-i2l7cgkepcd( n47,6 fdra wy 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 apparenzta 3)qx( 7j6.omwlkj6d2bjst acceleration of gravity at the equator is slightly less th2d6 j6jj)x.( bwo lksaq7ztm3 an it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from :bpiu4k8y) ud(zvz2 s the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pk2:sd zib4y (u8 p)uvzull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathrooll,5itnf /: hlm scale in an elevator, it say 5 /llfi:lhnt,s your mass 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 circular tube that will rj:2jfpc c(2/x n fv+u ekgw* 6bh5fk.uotate about its center (lik5bf+ f2 :2h ewxkfj kj(pn6gcc u*/v.ue a tubular bicycle 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 hisr czup:q3q,1riz y52d aircraft in a vertical 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 its radius r, the acceleort,wf rvm g(5.vw,j(+ )/md;z cgi vmrac ,/r.5m+o vviw g(,mwftzrvd)j(; gmtion due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass ,9 ds 7ytr:lqv lb:f7fm hanging on a string) is deflected from the vertical by an angle y7:t9sd bfrl v7qf:,l$\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked /bgue hv5 ))pxdevz 0wdr4( ;4ta9tjtfor a design speed of If the coefficient of static friction is 0.30 (wet j9e;44 vh)5a ge t0vud/ttrzb(w)px dpavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth ypil61 qir0 c/were rotating so fast that objects at the equator were apparently weigh l1ii qcr/y0p6tless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distancei;8ff8 t2rqo2 zs0yi *c u)eqcgur- q/ 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 rka yf5u8e 7k a845/zn4nefmtoounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an aay4z t8kf85aoe5 7m ekfn/ un4ngle 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 claim;6sks oni9a/2yvq qi gj(c6 s8ed that a person would (; s6voyak i6c i/8q 2nqjss9gbe 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 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 et*dd3z:segfxa/ 5c e:xtremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escedgd3/zfcx:t*s : e5a apes). 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 9n7c7 dn54sm2lia wm(guy0 upspeed as it traverses 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 driver feel heaviest? Li0 (a9 4u25 7yguilmcdnsmnp w7ghtest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utili9rq c ;y(tlr v xscpue9q/*c-q n08vt i2kp:z)zes 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 disvv9 ulqryx ;9 *k)qpis :zenc(2ct/ p8qr0 c-ttributed 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* cae q(x)sg3tbc 6g8s (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a hei8qc et 3x bs(sagg6c)*ght 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 ,a7 ukb7sx-xfpursuing a satellite in need of repair. You are in a circular orbit of the ssxa-f k7ux b,7ame 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 periodc7rvt q, :6jl2g/zcwa*; g jqe of 3000 years. (a) What is its mean distance froq tje ,gc/g:z*qac7lwr6;v j2m the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could 4e5 q tcycun/vkt2*u )actually "feel" yourself gravitationally a)yce u/v*nquk t2t 45cttracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy qcq/w u wch/21(Fig. 5-46) at a distance of a/q1 cu/qw2 hwcbout 30,000 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 corners of a square 0.50 m 6ckskqwp9nu n/kl ls80m/f.; on each side. Find the magnitude and direction of the gravitati0 sk;fk9 ps6k8nll.//w qc munonal 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 fcb)61g i v:s(g s*ihcy+s0av 5500 kg orbits 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 thgo9 vogdcd,+-e 1.5-cm-long sweep second hand on your wri g+, o9vgod-dcst watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a c;lb+b1 1eagpn ircl+1n ;l1ebgpa be 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: See Fig. 5–10.]    $^{\circ}$

A circular curve of radig7z:8/pbaj lz us R in a new highway is designed so that a car traveling at speed 8gb zal:p7/jz$ 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 wh8 /8ulrgkbz9 jen negotiating curves. The angle of tilt is adjusted so that the main force exertl9kjzbgr /8u8ed 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 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.$\approx$    $\times 10^2$