Sometimes people say that wabq/tmz iry vu.qw)t82ai)u 5 y .+f)aster is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong wit8+w.vs)y ai5 tmf).2) ut aqqibr/zu yh this statement?

Will the acceleration of a car be thecg:5o0, fusodie+ wq+: 3qnis9 s rxu- same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same spe,wq ogi:du3c- su f rn:exsi 0s59o++qed? Explain.

Suppose a car moves at constant speed along a hilly road. 3d k nbc-r5v3gWhere does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip betwek r-3dgnb c3v5en two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on b o.g j-ni o(+t3dqkr e tlj63g.:-fpza child riding a horse on a merry-go-round. Which of these forces provides the centripetal accelerafl3e63 tjo dt k:j+(g q.noi.b gzr-p-tion of the child?

A bucket of water can be whirled in a vertical circle withowcs s7kot i+ 0rull407ut the water spilling out, even at the top of the circiroksl47 0ulstcw 07+le when the bucket is upside down. Explain.

How many “accelerators” do you have in your+vf; v. znui/k car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do theik/;v .+znfvuy produce?

A child on a sled comes flying over the crest of a small hilx a(xa1 0hm-gpl, as shown in Fig. 5–31. His sled does not leave the ground(xa hg- mxpa01 (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a cj)n7 z7y /xirvurve at high speed?

Why do airplanes bank when they turn? How would you compute thekflaq/bo+,g2ay afmo 0fr9m98s .s 6 k banking angle given its sf,.m+9b faaoa2ymsl ksk q9/gr0f6 o8 peed and radius of the turn?

A girl is whirling a ball on a string around her head in asbh9d0 : 8r bx c w-mz-/ox3jznw0qmv* horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side /b3 z0xxjvzn0rcwqow b*9:-d- h8smmof the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If ;ziak,y bz 0 a1t+dn*tso, how large a force? Consider ,a0 +ani;1td*zkt ybz an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double s bazg7yj*r5gkq1x) :z8caslc 7ng:iiq (0n/what it is, in what ways would the Moon’s orbit be diff*gq1ixjz0aqzg 8r g na57 /y)i(csls :n bkc:7erent?

Which pulls harder grav r3h(:cmw z6oh/iir) p ygw*8uitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerahi: w6 p3uw*ogmyhczri8(r/) tes more?

The Sun's gravitational l0s4y xr-e6cp.8til s pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for th6r80cpisl e.s-l 4txye tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects are a7/ 5*d rhb y c8;onpz5s*tjm6pmho ;qqyotq;npd655; * s *zcm rqjhb /oh7p8mt work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half the forc6ms (ud;/l-, zorobz be on the Moon due tor 6bbu(d,z/ moosl z-; the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun kcd)d(c *q4 pzlarger or smaller than the centripetal acceleration of theq (dkc*4pcdz) Earth?

Would it require less speed to launch a satellil2a:9k-v /bcbt 0 poqste (a) toward the east or (b) toward the west? Cons9oak:vt-cslb2qp/0 b ider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by wdx05y9k)jtp k:px*w a scale in a moving elevator: when the elevator (a) accelex0 9)t5yd pjwk:xwkp*rates 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 the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adverse .i/)sb)ubld a/njfyy s*a)0n +upk6nly 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 (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity 0 )nd6.fpsi jn)u/)ubsy/b+kn a ay*lyou can think of.

Explain how a runner experiences “free v,mr9(p cx8oz8ovoo/ 5tz ,wbfall” or “apparent weightlessness” betweer8o,9wvcto/ zb, z o5x(m8opvn steps.

The Earth moves faster in its orbit around the Sun in January than in July. Is t( (fg.4 hwi8qseo:o vihe Earth closer to the Su8ovgi4fsiq :.e (ohw(n in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not 0pe gi4 (p7yms07fqbxknown until it was discovered to have a moon. Explain how this discovery enabledxpymf4 ges 7bp i007q( an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Eart* suscm./nyu 3zj8fg -h 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 oth8nucg/ *-jsf3 usz y.mer.]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 -8/c;ii-d/l, 5e wkj vessnec 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 iaul*yq7jyf 4q l8; 1hon its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that thef;quq 4l*a oyh1l87 jy 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 m-ds 6hq ai48vN is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length84qmi-v s6had ) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and ciru y);hw9e85 gd54dku 4 yrwfqwcles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your 9yu)wd8y 4 d54hgr;k5 ewqwfu 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 e. wcb: 2zovb,8ln3lyo dge of a potter’s wheel tur lwb, vl8o2:oczbyn.3 ning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of 3 m)t zqiuq/,qa string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-3,/t )umizqq q33. 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 i 5 rs7r 2pes6oww, adhg6o 9d7/s2otdwith which a 1050-kg 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? Is i6tw2 drg ,ow5o h /edssrs7op6a927dthis result independent of the mass of the car?   

  How large must the coefficient of static friction be between t xxl0q5k :k7fd evnwp2:q+ +rshe tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/h ? xx k:rnk+pd wq20lq:+ vfe 57s  

  A device for training astronauts and jet fijj7x blp4*: ,xo hhuz.ghter pilots is designed to rotate a trxzoh* p7xj.jub,4lh: ainee 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 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 rotating turntable of variab8xlh+ ygjd+ek f2m j(*le 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 coefficient of static frictijkjlfh8g (2++* dxmye on between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when,q l - .7;cdilknovmp )i4g7va upside down at the to .4viclmkg vq i7a;p no)-,l7dp of 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 qjf py d ,b6ghe6q ,+p)a+*3dyp xhbk6the driver) crosses the rounded top of ad*qx3)b+j,k d by6ppgeh,yph66aq f+ 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 Fer.9se w 7 +*c(ndupzkrrris wheel need to make for the paz7+ucp ( s*rk dw9n.erssengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is w hxi gc;6+znwm+6 eqgx98qms 82;n qlxhirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the w9ilxqc ;n++ ;q8h m 8genxgq6msx26zbucket 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 rotat6qvlu; og5y0 4 ch o.7ii7zxrre if a particle 9.00 cm from the axis of rotation is to experzh 760olxyrivi4uo5 rq7; c.gience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wal,u94dv uyq or7led "room." (See Fig. 5-35.)vr7u 9o4q,udy
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 r0a7gtq rpmiao q*x-vk5b 23o tg:j. 8hotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light coaqx3 pt.ha:o0jbt mk8g 2i5gv* o7rq-rd 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 , precisely this time, by not ignoring the weight of t+u7tf a+tzj *hhe ball which revolves on a string u 7jtfat*h z++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 perfectly banked for a car travel8usbwdqm;ytm i*i( d 35 /fbz+-j xyu6ing 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 masses1ylibyl b qp:jg2bx(xd86/6 w $ 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 manetunba w75q6;s uver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangentiali7t( v)gsgbl: fcfo/xs;6z q+ and centripetal components of the net force exerted on the car (by the ground) in Example 7lq f v gb:gcx if6z/t;(sso+)5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly fromnm-)nwrwnrb * tpp 0 b;a2*ne7 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 rnnmt*)0pr*w rbbpnwn a -;7e2oad to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of dl(quti x2y8 *radius 2.90 m . At a particular instant, its acceleration is *tuixd8 (ql2y 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on m8k(f6stn*wz.h3v : q8ytmav a spacecraft 12,800 km (2 Earth radii) above the Earsmt6t .zqfah:kv( 8vy3w*8n mth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a m 1tw+ irl9h7xrm7(eovagnitude of 1wext 9hr 7(r17vo+ilm2 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 Moon. The M wn):qa4,rawr oon's radius is 1.74 ,a)nwwqa4r :r $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has thy*+ 13ttkx ivwf0h+w je same mass. What is the ac1t+*i txw0y j3w vfh+kceleration due to gravity near its surface?   

  A hypothetical planet has aa n;z.*ut+5pcyi s+pl mass 1.66 times that of Earth, but the same radius. What i *l+ ;5yac+upzipt.n ss g near its surface?   

  Two objects attract each 3 ctm+q(pj)n 8y,:ubqno yc,q 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 acceje6rgfu9,x* i gc am7+leration of gravity, at (a) 3200 mr,6+cum9jgif g 7aex*    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where;s4rrbq8oq, j (y 9zhd thegravitational acceleration due to the Earth 4 s ( 98hrrj,q;dyobzqis $\frac{1}{10}$ 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 gmc6l f0snvnu23):hpy0(j zwre about 10 km in radius. Estimate the surface gravity on thilw) v3fzp(06c gnm 0u h:jsny2s monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun b;dz1w 3wl j8dfut 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 grav8d lz; 1fwjwd3ity on this star?    $\times 10^7$

  You are explaining why astri +bq *xvbg83l gi1ii/31yapjx6:uy vonauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourse i/ +v i xxyb*38q1a:i1pjlgvuyg3i6blf 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(b h+kht,h2 yq at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational bq h+hky(,h2tforce exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years)jcjnfyu3 z4.)os j5veu-:9u xf aa+ d most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Vf5zo ) ayx4)f- 9+veujc3ju s:jnadu. enus, 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 acceleration of gravity at the surface of Mars is 0.38 fifjuz4 cgd2 1rr0p/, of what it is on Earth, and that Mars’ radius is p if,1gzrdcf2/u40rj 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of t f1 e0g3 e6,wwu.hqrjqhe Sun using the known value for the period of the Earth and its di rq6 u3gweq1w ,ehjf.0stance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in 1zv**y h q r/lgd ;):marhoq*ea stable circular orbit about the Earth at a height ofza* r: hr;m)g/qeo vh**1qyld 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abovemo am- 2,sv,pjnb9l9v the Earth. How fast must the shmn,9vo s-pav,9 mbjl 2uttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylin0cg yr ob*8b6tdrical spaceship rotate if occupants are to experience simulatrg8* y6 bc0otbed gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it tas1 us-+ a :f6:ffkaefukes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. esfaa u ku-+:s:f1ff6Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite hau wnzmt*wi78eh4c ,/ive to be launched from the top of Mt. Everest to be placed in a circular ormi/,u n h8wt4c 7*zeiwbit around the Earth?   

  During an Apollo lunar lanej2vwrs;tzq97. qu5jding mission, the command module continued to orbit the Moon at an altitude of about 1z;sqqej2w .5ur7v jt900 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of c8-wwj4 d v/t 4i/wc6 a1q1vw1efe rvsshunks of ice that orbit the planet. The inner radius of t- jr4/wqv4wsawv81s1i w6v dcee 1t/fhe 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 diamnlli;h-prj(2ytlz ; 2a 48csoeter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the boo a;( l pjyzh-2; 4inl82cstlrttom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fromvpmq5bsl*2u - the center of the Earth'sbq5vp- *u2lms Moon 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 binarvz5no4mb4z6r. v f4cd(a7 btqy-star system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a p(bvztvr5 6q4fo dzc4n4.b7amoint midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for thec4b9:qh (l5zhimxmho- 5 b9 aw weight of a 55-kg woman in an elevator that mov w9ihz b:9c5mb(a m4-o5hh xqles
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of a(iitvz -eq -dq 3u1nh3n elevator. The cord can withstand a tension of 220 h- q- 1(3niizt3edvqu N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbi(ivw1j5u;nzqx s8hl ) ts very near the surface of a planet with period T , the density (mashwx n8jv u5szl;1i)q(s/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 g/ i3y;e rm3s0vxglb +Moon (27.4 d) to determine the period of an artificial satellite orbiting very vimbxlgyr ;30 + 3/esgnear the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meter:ieu+2 azlp-k s72p prs across, orbits the Sun like the planets. :2zlau 2 iepk7ps-rp+ Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distan24)nw h3x uvfpce 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 76 years. It comes very clof5x 0d /.xkiryv0;egg se 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 pv0 g; 0gxxe5/kd. iyfrlanet’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 Galaxy gui: 68as)ym y$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 four largest moons y,m;eb+u s-gmof Jupiter (those discovereum- +gseymb; ,d 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 as gub upaqhl1s,;gh70q6 -7jEarth from the known period and distance of the Moon. la sj 6;uhsqg0p7, ub1q 7gh-a   $\times 10^{24}$

  Determine the mean dh 0hllel1h*a 2 z(8c 8ry +ugg+k5jrcgistance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5– 1ku ghlch(0lr8y+g*+5 zcg2l hja r8e3. 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 consists of many fraum a,4fk5oq u.gments (which some space scientist,k4m u5oa fuq.s think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes ajh3fz3mb .6rm,8 be ehn 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 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 h3jf eb86, emzr bh3.mof revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an9bgg6 tu0n7 pg35+ .lpp*f1cdyi hmja arc from a hanging vine (Fig. 5–41). If his a dp3c ygga 5t+l pf 9b16*.gni7m0hjuprms 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 surface will the ao*)4yvm .zx5fx + yycucceleration of gravity be half what it is on theo + )*u.myy5 cyzxfxv4 surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circlv mv3 :rp1ym:eiyyw3 cuk:t21e once every 2.5 s.1 :mm: 1tyv3ye2vyi3 ukcrw:p If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratf 3sto-m17 agqb 56ll fssu5os;2 fwz2ion of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of thwbo7ut s23;56 a z1sqlogsm- f2ff5slis effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveliqjh k r,x4v3c3ng directly from the Earth to the Moon experience zero netqj3vc ,43r kxh force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when yorrcv x36/8pnz jkie8(u stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and jxkprnz88 /( v3r e6icin which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about (k1nuxajh1fn9 g1tp 6fk m8kwf)0 6ro its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the0frgkkfwnh ku ft )81xa( 1om9 6jp16n Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his ai7v 3 qc0brn4:klp7knrz1bt ,fsii:(arcraft 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 th. oum7u.gd+fn-x 4kk me mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational constanumm-fo4.nu .kd xkg+7t G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by art9b.g+ahbedukm+ d t0h0j63n angl9 u3d06 jkht+bt0d.eahgbr+ me $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coeffily +d* q c ;va5r5z99oqm/ntpycient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely ha9; *yqc5az5/ovryn dtql9+ pmndle the curve?

  How long would a day be if the Earth were rotating so fast that objects at thol+hfao --liox5f8ya6r a ,e :e equatoe 6ol+:axy hfl -f8,aai5o-or r were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant d7: ffnlo+key0istance 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 sk-wrc7 ulz3heg i (d59peed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an79- 5gdurickhz( wl3e 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. Thuslcl44rv+.dbghb6y t xf 4xue4q3c wg2,fi 00e , it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the nufx4ei+2 glqcy4 4ctbghvbw6 ,r0.el 3xu 04f dmber 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 extref q00fqs8k1gy mely massive core in the distant ksq 1f 00g8yqfgalaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses th ge;pgy2*cz6 xfs/ pl*ae /dn-e 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? Lightest? Explain. (c) How fast can the car go withoufnz *e-xs/c2 peyg da*/6 g;plt losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satelliteyb 77r).xal8w aje spo m-.6cjs 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 altie7 yjao-sj wlmb. )rpxc86a7.tude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 b; tmvxl-2uc8 aillion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roug c-tm;vua8 2lxhly 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 saty da .0h5akvtk7ms.z/- qdb,h ellite in need of repair. You are in a circular orbit of the h0.,tyb k7s 5az.kdhmva- q/ dsame radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its me8pnpp grbh(g osj-r qn:/i8 3ln1)odfl5v) a2an distance fronf3nbn8g/8vll 5pi- g)rjr q 2sp(:ho)a pod 1m 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 :2j2kmjted(ij 02c -hiuqi3cneed to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasona2d (2:2jm uchet0jcik3q iji- ble assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arou61) 2no jkg9gwrd3 jm5agat (qnd the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 ligg wgat6njj23oam5 (1k9gd)rqht-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 side.fv0yh2w 1 khvq:rn sprp(v 078 Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of therv:0wvv n kph(1sf7p802h yqr bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass cd k cjcz+m rgy8-cq1:7hlp.55500 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 tizn 41 7yz bhz6yo7:ruup of the 1.5-cm-long sweep second hand on your ynrz:u674b ho17 zuzywrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arpy-eh 7w ,*e7big/azjound in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.5b-7 ,7ga/w z pei*hyej0 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 highwsshmnp(rg/ 9 j5s); gfn+ .gi i-ow5oyay is designed so that a car traveling at speed y+jn o-m( so i5gg5gws fsinh)9 ;/rp.$ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotialuv cb*o7c46bj 6knna8cu /r+ting curves. The angle of tilt is adjusted so that the main force exerted ov/c8ln74+cb uajrn6*6 ko ucbn 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.$\approx$    $\times 10^2$