Sometimes people say that water is removed from clothes in/+f tcq8qx8urob9n*f a spin dryer by centrifugal force throwing the water outward. What is wrong with t * /ffqc x+9buqnr8to8his statement?

Will the acceleration of a car be the same wvu blq,mw az)(4l1 wc+hen the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed?, c+()1lvl azb uwwmq4 Explain.

Suppose a car moves at constant speed alo ./7 0 n mth)byhj0r1puff3fwung 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, (c) on/y 0phu3f)w ut17mnj ff.0rh b a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horssboa0;zmi6jk7 )eqk x w185yze on a merry-go-round. Which of these 1;z5kok 0z7)6xsem aqb8yij wforces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle witpg)h4qpu mjd:)9uc, u : 0aevthout the water spilling out, even at the top of the circle when the buckgq4ha:m , vup9e))d0 pucu t:jet is upside down. Explain.

How many “acceleratob,)u3zztq*rp ytfbw p2 y1x 92rs” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? Whpuq)2 z3fpy xb ,y*t bt1r9w2zat accelerations do they produce?

A child on a sled comes flying ovb* b+o 8 5fdqh5i6qqmuer the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not ab*5qh8+5m df6qq oi ubchieve “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 ;qxwh ofx0xy --. lq:j pm*s4dwhen rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking any6t (h2ak cj8agle given it ty826aakj hc(s speed and radius of the turn?

A girl is whirling a ball on a string a9sd k:bk vm )kx7iw*ln(bl//u round her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When sh / lb9 lw:umskkbni/dxk7v) (*ould she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how laro*s3tgvsn09mw7gfz/m o) q+0fm7ll nge a force? Consider an applel loq gns097+*v0m f/gsowmmz3) t7 nf
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double w) jjhp0f9s( gzhat it is, in what ways would the Moon’s orbit be differentz) j jp(fshg09?

Which pulls harder gb(5.iqu1df rss*vaj *ravitationally, the Earth on the Moon, or the Moon on the Earth? Which .(u5dr1bas vq f s*j*iaccelerates more?

The Sun's gravitational pull on the Earth is much largeqoxg8 z n9j/pm)d 8 tw2cya *nz(5-muvr than the Moon's. Yet the Moon's inm q8 u-(9xj5z* pyvan2z gwmd8/c o)ts 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 polth5z oz:0-p o.gg 2edres? What two effects are at o:gg 2- o0z.htder5pzwork? Do they oppose each other?

The gravitational force on th+. fmk f*ww/p71mpuld/5yehqu c+ hq/ yywp..e Moon due to the Earth is only about half the force on the Moon due to the Su / mf5h/*cy.dw1hepm.wwlf 7pq/++. uk yyuq pn. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars i vciw 546em4bj j8kgh,n its orbit around the Sun larger or smaller thancw 54846igev jhk ,jmb the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) towu7kv6 var72 aik(l b 2skw*r0uard the east or (b) toward the west? Cow02a6(2 sl b7 ruuva* krki7kvnsider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured b zym00kbm :- 8+lmqhmcy a scale in a moving elevator: when the elevator (a) accelerates downward, (b)ybkz:0 mml8+c0 mhq-m accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer sp3/d mmk1qyu:jl 9i7 ozace could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical s1ym3il9uo /zjk dqm:7hell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessnes:gz- d, )e-amhfv5gzks” between azmzfe)h d -kvg g,-:5steps.

The Earth moves faster in its orbit around the Sun in January than in Jul,t 8isj(u0jolg.6wj gy. 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 ma ujgwgojl, 06.8s( itjin factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a mo6lhp)2p e4ahk ffflj-9 6t n3ton. Explain hoh296a h 43-nptp)lft kf6 lejfw this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is 2kxpza1n8 ;29b ,so brzzpe /imuch 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 other.]A child sitting 1.10 m from the center of a merry-go-b9,n z/espr bi82zza1 o;p2k xround 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 yr -9ehsl 4unp m4i1v-1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit arf m8vbso-)4 nkound the Sun, and the net force exerted on the Earth. What exerts this kmf o- v)sb4n8force 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- 5 n5; zyi*yc8m(kw t:zcphup;kg discus as it rotates uniformly in a h:5 nc;p5hcuz8 y;ywpz*k tmi(orizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 40;6 f 8k x;lqetk*q7sxe0 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of theq*lf e 6k7x ;8sxetkq; 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 edge tyi0 f i:1w.qqz: h8hww19hhbof a potter’s whey8w: qb1q1hhfi z0h iwth .9:wel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a s3 ouzzl ysywf11m9 v4e/p8 7iftring is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spue3lz 8ffim9 wzy/yo711v s 4peed 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 carl1irx r)x 1tjho8gfi 73)pdg 2q2bdx ; 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? Is this result independen7jldx281;gh r qb2 1gpxfird3x) toi)t of the mass of the car?   

  How large must the coefficient of static friction be betweeng s(/z34 gcsrh the tires and the road if a car is to round a level curve of radius 85 m s/z3(gcsgr4h at a speed of 95km/h ?   

  A device for training astro)alv.g f m-g ghygjm0k1g 9h4n31 /lpmnauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weigv9 gnyhk 1mp/l lm a4g)fggj0g31hm.-ht, 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 o,mtn.:lb)ffh72 w xj lf a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a ranf b.f2mxh7)wtl: l j,te of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller ctu z ,hgilxp: c41h1-fe+ nv6poaster be traveling when upside down at the top of a c-1ncupeghlp 6+z, i:fh 4 1tvxircle
(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 the8c43la8;c kdcq: x fviuw s+x) driver) crosses the rounded top of a hill wfc: a3 ;c)dxuklixv8 +cq8s4(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 9)uzc,l qony 9would a 15-m-diameter Ferris wheel need to make for the passengers to feel “wz),9cnu 9yoq leightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1u:u9 ak)9 z-av2o;tmtt o wc(f.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0uzkt f ;w99o:v-ctat) m2u oa( 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 c b4i0urs+ 7ic)wm,dkfentrifuge rotate if a particle 9.00 cm from the axis of rotation is to experiebismi74,f d +ur0 )ckwnce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotatz i)2hncsin7(tmr2x : ed in a cylindrically walled "room." (See Fx2t ri)7izchn sn2m: (ig. 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 Mn g+/soxang;,op-5 ddoo zlvu6/ x d9( ) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (massv+5xlxs, ou-nd n /oogz6/ddag( p;o9 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 ignolsxk5e,,vfr,r1we z 1ring the weight of the ball which revolves on a string 0.fr,1w , r1slkee5v, zx600 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 perfectly bank83(f(pxfdsfsxca 4j 5.n 8fhwe4o 5 teiub)z8ed 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 masses5;6td 6i/a6jk*rd tzjim3a ks $ 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 (ve3;imrv r1k b 8rl-k 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 exdo96l6 hjis+d iyev/4 erted on the car (by the ground) in Exampidh69osj6li yed v/+4 le 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 uniformly7-s7p joo)qduc ,tg -p 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 between the tires and the road to provide this acceleration with no slipping or ) 7-jdpuo ,g-co qst7pskidding? $\approx$   

  A particle revolves in a horizon0 ,5z xm7l bp6/ej1/v5 ;skgfag hdwqutal circle of radius 2.90 m . At a particular instant, its acceleration is 1.05 v,zuxhpsg/ 7 m5flkqj; 6105b eagd w/$\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Eart+ ie/bwj td054j0m 0aca,5vx nuebz4 jh radii) above the Earth’s surface if its mass is 44zw 0ajxic5nv ab0+je 5b,0/ t jumde1350 kg.   

  At the surface of a certain pidb hhi-np*;yqw5-+yw 1 kdl0lanet, the gravitational acceleration g has a magnitude of 12 m/0 5*wykin1ly wdibq-h +hp- ;ds$^2$ 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 h os,/ okgc1kjib+ x8*2f d,xbMoon. The Moon's radius is 1.74ib*/x8d+jx, hc1 g ,2kfso kbo $\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 thaty +bwb 2g,b;dx3xc(zcry* y;x of Earth, but has the same mass. What is tr2gdz;y ; xcb*bxwc y(bx3y+,he acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sezgm5n,qfqk;um4 0c1ame radius. What z m54k01 q; cgqf,uemnis g near its surface?   

  Two objects attract ehu)g+w n,;qk*ty kugg.z : 6egach other 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 wykq6.djo 56o acceleration of gravity, at (a) 3200 mo6 6k 5qy.wdjo    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poi* :jvia *pvnxys di7j qs*9t),nt outside the Earth where thegravitati ndi xjy*is,p q7tavv 9:sj*)*onal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphe 8xd7j0hx5hrc re about 10 km in radius. Estimate the surfahx j7 x850hdrcce gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star v lf)1 ;qwbl7ffl7ds h/yb99llike our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity onfwyslbv f/ll9bfhd1 7 7q;9)l this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space sh64c xp 1pwoq ee;6;qjnuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earx4p; 1 ojw;n6q 6qeepcth’s surface in terms of g.   

  Four 9.5-kg spheres areu-k en7( x*/o4yh2 sxwe1v+dcr ne +ce located at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere /u2w4 v1ex chyer eo7c-(nnd x+e+*sk by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sunl, rbnv sqb7*,. Calculate the total force on the Earth due to Venus, Juplr n ,bsvb7q,*iter, 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 accelea8hnpg ix 803tration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the m8p8axth0 i ng3ass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using thaz6 ke+s 10yaoe known value for the period of the Earth and its e+ 610k osyazadistance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed ttqn 0b6c6xy4of a satellite moving in a stable circular orbit about the Earth at a heighbntqy4xt6 c6 0t of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbiu+ug(l 7ru yd3t 650 km above the Earth. udrlug(3 y7u+How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate iihu ),q+ ti5ewf 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 n)5hieuwi+, tqeeded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a 6wi2d* uszyq5circular “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. D 5zwdis6yq*2u oes your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a s/o rx4fva, d-lw(*s/ xbw2wm matellite have to be launched from the top of Mt. Everest to be placed in a circ2rxo -(m/*,/w4mw wsl adfxvbular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbif0t+u nduwa 3 yqx0+fly106v;-9j 1 eyiuqypnt the Moon at an altijyp -l 6x1f901 ;wuq +de3n0y y+qu0vatfnuiytude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that oy0la.2klsn9 3+iwq -x 6wvtp qrbit the planet. The inner aktlilwqyqsw9 pnv2. 06x +-3radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 5–9). Whqzbvx jxiw sn;bls n*5xm 6.8,ir.-:xat is the ratio of a person’s apparent weightisn5-*6 n vxb wqxis:; 8,x.bm.zlxjr to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cent:emfzrjs 6 8mnjt9t7 6er of the Earth's Moon in a space vehicle (a) moving at con:j89enmtz76j mrf6 t sstant 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 st)a e6jrs:4oi qars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of ea6o:qje 4siar )ch?    $\times 10^{29}$

  What will a spring scale read for the weight of8 mbh o--y9my,iyih aqx6nwc kt43r ;4 a 55-kg woman in an elevator that mch83;- n9h44,ix yw6m-qriykmoyt baoves
(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 froq q-k6h ,m)qyhm a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration 6h qh) km-q,qy(magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period l(n6z : p. 3 c4genpf-u zxn+q5/ttzpcT , t3 5xngelztp4c(p/:.pzu cq-zn +f6n 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 determin-j;zkc;-hb9 sg8h(gfdu 6 pice the period of an artificial satellite orbiting very near iz gc-;6h;dsb f8-9pu(g hkcj the Earth’s surface.    s

  The asteroid Icarus, though only l7vymx ,q m3,fa few hundred meters across, orbits the Sun lik,y7xqm3f,vl m e the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average - oeyd:cqm 6yxbq.s8 prw03t7distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76q u ys-7lswk;, years. It comes very close to the surface of the Sun o u7s ,yl-;qskwn 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 Gaxtr2pf2s42 wo laxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 thh8izfysuo0:aszkb hy; n w+. c4-j ;.re four largest moons of Jupiter (those discovered by Galileo in 1609). oh.k-ry;s b wz;4 u:ns chif.yz+j8 0a
(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 distae5 x( c2zlvltd1bk*+wnce of the Moon. (d zwb5*kl1+ev tx2cl    $\times 10^{24}$

  Determine the mean distance from Jupiter for each obd53tqvo ocqz .6h3 :zf Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods giveno.z d6o3zb :5qh3tqc v 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 ,vdirlo0;+ 1pxfo v9kMars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbiteo; k9f vir+x1pdo0v l,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" in tha8 wr: ):abt4c3ud-+c4jef3b t(esvlol8 bsue 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 (t u8rdsb3c a:vl48jbwe (lc:oa )sb-+u 4t3et fo 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 irg8o3 :31* mzbkble xfrom a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? Hx3z:br3bie ogm*k 81l is mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gra+aw 8deu40l4ky, . qawxz z,rivity be half what it is on the surfaawadwkru+8ie4z.ql, ,z xy4 0ce?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual ciria:n 6rge5u(s cle oni5rg u es(6a:nce every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparentz sae5m.3hni v-dm-a1 acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnit--h e.3 md5n ami1zvasude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will agtbw +wgg3 1l9h(mk+ tj,4ce n spacecraft traveling directly from the Earth to the M3t4thgl( gb9jenw+w,k +gm1c oon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kgo) c kfo6*dw+w gjd7ch; 1ik3f, but when you stand on a bathroom scale in an elevatow1g 6kfoi)d7 df ow*3jch+;kcr, it says 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 c( evwrt.m e+x5ircular tube that will rotate about its cen(mw5. rvxe +etter (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 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 liu +/ xmx o2yk1bl*:kroop (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 radiumv wf5 wxt97.v-n3 t7xwhy 6mps r, the acceleration due to gravity at its surface a6fx.yh3mtv p 7w5n-mtxvww 97nd the gravitational constant G.

A plumb bob (a mass m hanging on a string) )2y nwlical pdun64 16is deflected from the vertical by an anglen y2)a l61uw6i4dnpl c $\theta$ 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 det b9i,qa3l z 5s2huwr4) g+npnsign speed of If the coefficient of static friction is 0.30 (wet pavement)42 t,5 a3slqn)w9r+u hibpz ng, at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotat :7jzp3m*tl- .pl phh.qm, 4 mwqtda(jing so fast that objects at the equator were appa:ph lj(t.mq7d.3m q-pzw,ltaj4 mp* hrently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dihccx(/2( x-v-a gw dibpjs el r,vp0.;stance 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 ouqy;l/6u;w 7o;9wgj(zay 7ruh 4c fxn f radius 235 m. A lamp suspended from the ceiling swings out to an angqjzu 6u( ;xory7uwca4y/l7f hn;w9 g;le 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 5e atigzwq7:9f /w8i.(wc k e uc7my9pbeen claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a8m u g9w: cqzww/i57et9p.yaik7 fe(c 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 presfiq8 dhclk3d z6lxp) - 296lboence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no lig)l26x l9lbdchzqd kfp-o836 iht 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 sn o.*7vz-cxiy+kiam0;9 ypm9bj 0vw s peed 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 nmwj*- .yoi a 99svz+cb0k7xn vym0pi ;ormal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 5qqhs,,j9 eb y24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit s5q,9 jbqhye, 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 trav;moq z x *o2ich+nw9b(eling 2.1 billion km, is meant to orbit the asteroid Eros at a heigh+mn qz2b(;i9o*ox chw t of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a sateezkk)+ b ;luw,llite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it. b,)z kwe+uk;l
(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. (ajrasjiya 7yz+ -/r-4a) What is its mean distance from the Sunj r7ri4as+jyz/ya --a?   
(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 nz7 ru1onb1 u;teed to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptio unu;o7 rb11ztns, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (soux/tf: q 4if2z)gd :Fig. 5-46) at a distance of about 30,0/o)f4::fuigd2 txsz q 00 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 on each ljh sw6c7.6sm side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kj 7.6lscs h6mwg 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 ; h:ukq ;kdxi1*d/s sw ;mjor(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 acceleratm3o 0xvudi.buk-+ vz5 ion experienced by the tip of the 1.5-cm-long sweep second hand on your wmu-z3ov5. ku0i+b xvdrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinkeri)ajcm.4 /mh o weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete ohma cj)/i.m4circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a b ,1 .pcmvjhm wc qreav 471s-;msljz 4nr1w0;car travelq svv- 7jaen441j;bmwzw0pmr1.r h ;clm,c s 1ing 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 Ace qo7t3)zxu3c xla, 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 toz)x3x u3cq 7speed 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.$\approx$    $\times 10^2$