Sometimes people say that water is removed from clothes in a spin dryer by cet h ,b1topv3ol7ihw2 )ntrifugah2ottb1,3h) wvip lo7l force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same w* f *,qpf3zbtmmlw y lj(6;,tghen the car travels around a sharp curve at a 3t(mtwbpz,*gf*q; ,mf j y6llconstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whej1 4itrhc m+b6re does the car exert the greatest m16rhji+ 4tc band least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-roundc- oy m/ysx0fo 2e eldwb9j080. Which of these forces provides the centripetal acceleration owmb2-0 /xjc fed0lsoe0y9oy 8f the child?

A bucket of water can be whirled in a vertical circle without the water spillin),/cqq j)k* x hduvdrq9q+ 0iyg out, ev, jrq 0v9k+)yxdhu/q qq* icd)en at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three coghcl44ep l(w1ero 4x1 ntrols in the car which can be egxeor(44w 11p 4 lhclused to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flyin qti;,b bf71 7mtydr1ng over the crest of a small hill, as shown in Fig. 5–31. His sled does not 1n 1 m dt7biftb,rq;y7leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roundiuer.lrt61f y.ng a curve at high speed?

Why do airplanes bank w7yix5 ,bm+e )sfeao+ when they turn? How would you compute the banking angle given its speed and radius s7aof5+e) ye+mibx,w of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Sb(q 0l*:0t0 snswobbw he wants to let go at precisely the right time so that the ball will hiqn0* bww bsl:bt(so00t a target on the other side of the yard. When should she let go of the string?

Does an apple exert 401weo z/kky y)ffeo0a gravitational force on the Earth? If so, how large a force? Consider an app fyoeey4o00 )kz/f1wkle
(a) attached to a tree, and (b) falling.

If the Earth’s mass were d u /aw5r. +im6ye hadt;4rcbx8ouble what it is, in what ways would the Moon’s orbit be d. xw6 ;aahbitum+ r5d4r/e8ycifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the4ebzdq+ 9e93tsrp8f t Moon on the Earth? Which accelerates moredtq49t e sp+ 8bf9ez3r?

The Sun's gravitationa7y jm5i13jcd ll pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible fo15cy i 3jml7djr the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two evr 2bk8 4yecj6 ,upcf*ffects are at work? Do they oppose each otvjc82f*c ey6u,r4bkp her?

The gravitational force on the Moonc 2wvt 3 q1jnt.hsc,g; due to the Earth is only about half the force on the Moon due toqv2c1jsg., wnt h3ct; the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its o *2ka:;dndvhtrbit around the Sun larger or small h:; 2*tadvkdner than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the etm xmbio0 l:6-ast or (b) toward the west? Consider the Earth’s rotation:otx i0m-mb l6 direction.

When will your apparent weight be the greatest, as measured by a scale in uj 7xac8xc2k50kk q,n a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the sam2jxku,0a nckckx5 q78e 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 adversely affected by ult4ue7jf5 5t weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the ij74ef 5tt5ulu nside 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 wet q5;;/ i vxc3v-t6wqzgn 6scqightlessness” betweev 35qtz 6 -/s;t6cwnv;qixqg cn steps.

The Earth moves faster in its orbit around the Sun in January than inxj ne1kj,fvxav2*d.) July. Is the Earth clx n*v,2).jv xedafk1joser 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 to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. E,7 cape xq 62ea.sk)wbxplain how thisck2)aa.qsee 76,bwp x discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitationa6 s)tojx,o,oc l 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 jso6 )o,t,xo cin 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 198 v45z,uro4vxzdhfe .+hlvjc+qv3 f- 30 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orb i7;sqi vhus;*it around the Sun, and the net force exerted o uv is;;7*hsiqn the Earth. What exerts this 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 gj.kexc;)zvth* 1r+ g is exerted on a 2.0-kg discus as it rotates uniformly ie zv+cjkgr*;.t1h g)xn a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circt 6 *7i72..-vgsy wbkqc mtt.ksfi3n fles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answerit n s.yki2qw7. 7fc. 6b-m3vt gktsf* 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 of k;ijlrw,7jhq093 wnea potter’s wheel turning at 45 rpm (revol0e n,rhj;jl 7i3qw9w kutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved2bor( d,pusx6pf4:co3m+s ge at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. +46s 3r :2epo,fu( docbspxgmIf its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn7jlce9 y3u 4hs bykk35 of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass o 3esc k3lbu9y4yh7kj5 f the car?   

  How large must the coefficient of static friction be between the tires and thei;*/(m xh* bdmyu8wba road if a car is to round a level cu ;bmxh duw(b*y* ia8m/rve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighigws t4,s7-)8xums h kter pilots is designed to rotate a tra) 7m ,kx4shgu 8ts-swiinee 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 variable8fs/jom 0)474 w ct-dkooe qt+hass 0x speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is resek /- 4doxc0to+f m07a8tjss4ho )wqached 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 coaster b1 j :t+jccw btt6cxl:;e traveling when upside down at the top ot 1wcl+c 6jt:c btjx:;f a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the drive)lp0 xzd57yy+ 0 dfjwar) crosses the rounded top of a )dljfdw0 yzpx+07 ya5hill (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-di0 )k4kqsdjvnkx1,e3n ameter Ferris wheel need to make for the passk nx)q1nkvj30s , k4deengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is 2vrkgxb3s i6y 65s1 zjwx q9v/whirled in a vertical circle of radius 1.10 m. At the lowest point of its9 63/zk vrgq5 xb jwx6i1vsy2s motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge roh h 8k4k fj:ridf*91ymtate if a particle 9.00 cm from the axis of * 9mkfdhr hj48:1ifykrotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a car(:,xqc te/2ff k qq-qonival, people are rotated in a cylindrically walled "room." (Sqf q(,te/-2 q:ofqxck ee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rota y-k6yob +vgy2ted in a circle on a frictionless air-hockey tabletop, and is held in this orbit by -+b2y yov6kg ya 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 , precisely this timev-ndadv ricpkkh 6g o,x) k+oqbie, 1-f 5k08;, by not ignoring the weight of the ball which revolves on a 1-oo 0,,xkdv-vikr6bk ) ped8h +q;c i5g kafnstring 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 cac3l mub wks4ps3/ln+avj8 u .1r 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 massesm.l-6n +ceqagq 2-k 34 oevgga $ 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 verticallyj oqq brwh2svx5+y* i*i5ny:so u* 0*n at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the netwitx91( lpb l1 force exerted on the car (by theiwxl1(t 1b9lp ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from t 3j 6ddf8z6ndxs-.uzthe 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 acceleran8fd z6dtj3.z- sxdu6tion. 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 skidding? $\approx$   

  A particle revolves in a hg 4,apr4d aq *m /eouzs2j0,oborizontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.,0/ardgs2e oq4pm b ozau4 *j,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 s2 +i qj9fviacf5p4 qub2y+jpr.;0eg of Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s jiujiqb+;4 2 eyp5c srfvg90pq.f+a 2surface if its mass is 1350 kg.   

  At the surface of a cw9f*xa7qs 0hh ertain planet, the gravitational acceleration g has a magnitude of*9 7 xhashf0qw 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity xm-qm *d+w7 rgon the Moon. The Moon's radius is 1.74 w7gxmrq-dm* +$\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 , qr4c0o 0x3bdm jwq8b5 yb/vdzexf.4the same mass. What is tz db/0dobbqxr cv.je, 04q85mf4xw y3he acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the s .t0 ao04td 3uva;s(4zzcpnjoame radius. What is g near its surface? oadus0(; 0 zp avctno3jz4t.4  

  Two objects attract each othjlcm n-7 -ybqq1ix;gao/ 2(el er 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 1qknsq bhi f ng-a ;k*2uj09t59q1y znh lu+m;g , the acceleration of gravity, at (a) 3200 mfm* u 1nby +n;1qzlktksjn2 ghiaqh5u 0;99q-    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cegh /3m bl+3xctnter to a point outside the Earth where thegravitational acceleration due to t3 ctb3g /mx+lhhe 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 sphzx5jxw; :s2)wwk 3mowawwd-z1o/h1 were aboutwz:wx/1 o 5sk wz2w wjo)w- wmx3d1h;a 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once wa;w5. )zkp ,pyf)ww z yg6t;jcgs an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sunf),ptw;. zc5gykwzjgw yp;)6 . What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space 03q7v 3 hgam 2xomush*shuttle. Your friends respond that they thought gravity was just a lot weaker3xaqv3g2m0h smh7 * ou up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.6 /eex;ng*jm fk0.vj q1my0yjvh)5 r7 k0 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other th f57jj .y x)*km0v;v/r1h0 jmgkeqe nyree.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sun.cc d re;jx(92w Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all(ce2 rjxdc 9w; 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 of what itiuq3uzs b0+5+q e fc7u is on Earth, and that Mars’ radius is f iqq053c+use+7uubz 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the kz)*hul6*hv y qnown value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’sh )**hz uv6ylq laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite w ist2yfx64wag;/bq/moving in a stable circular orbit about the Earth at a height of 3600wy/4f 6 qbgtsw;/2x ai km.    $\times 10^3$

  The space shuttle releases a satellite intt+ 3 yt69gx5ltnjg -er:kv-h1oz - bdmo a circular orbit 650 km above the Earth. How fast must the shuttle b-th6k or-:-9vdm 5y1t bzgx3 nlej+tg e moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical8xkb8q2f 4t ,(m wtd ;a5 62qdw ;fripfpzzpj: spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one rev ,: fidp4j;pwrad5z;xf8m p2kt26q8 ( fqw bztolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Ea- n2 p3 l8mocu9h/uidmrth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at 32 o8 cn-pudihm9lmu/ a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have k88s(6yqf ouywxx/d3f 6 ;i jhto be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth8xsyxw(k/uyd;fh866 jiof q3?   

  During an Apollo lunar landing mission, the command module contu9u603 jek dpw)fw, kminued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the f u kd3)pkujwe 0m,6w9Moon once?    s

  The rings of Saturn are composed of chunktb7vz uz t4gy2947x ie :da0bms of ice that orbit the planet. The inner rad9t4: umd 2it7 z4zvg beax0yb7ius 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 6wo)-bb *h e o*wt-dwuonce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparenb-*bdo6u whw w-te* o)t weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75;b7ah l8izzb2d: ;rla-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) movingi;d8hl 7:ra;2bbzl za 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 consqd1j55)m9-)n*qgfo.g (jci g tp esvwists of two stars of equal mass. They are observed toj p(sgwnv5gif))o .e5q d9tgc j* 1m-q 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 each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator tbpv:9yidnq7x+ h 82d1 vkrg6that m8d: k9p+26tbhx d1 rq7iyv vngoves
(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 anipja95 rbto-m.87 k: ofe/bf z elevator. The cord can withstand a tension of 220e-oft /k5pfa jbbiz9or 7m.: 8 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the x2upq, yy l+u8surface of a planet with period T , the density (mass/vp8ux2 uq+y,l yolume) 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 period 15sigt27;tr dfxho5ngn 6g5 aof an artific5 7;sg6tt2 gari5onhd 5gfnx1 ial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sunbirex;rnb(z a 1z 01y/ like tr1x(aezb 1 zyn0/i;r bhe planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance od7aiy+e g-d7s3fb q tmh -9/zgf 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 ckfyo ,v97p r/z-)iquwomes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit irz u,9fiw/q 7 p-)ovkys 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 ce wv:e*6s yya6cnter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four lar3vu/lb8gt4cu jmj- g a+6h:cigest moons of g:hu a cuvb- lj/6c8gt4ji +m3Jupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance jutc +**dq1xjof the Moon. xtjq 1u**c +jd   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, u1t4rivu a6su 8m k5c9dsing Kepler’s third law. Use the distance of Io and the periods given in61ut c8k4d u9 svri5ma 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 consists of many fragmentohi llxgj8m; 7d -(.ovs (which some space scientists .o l go- 8ji7(vdx;hmlthink 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 describesonc-z 4k: .y colbsip- ;0+ iu1qy:vus an 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 Eartk--q+u .il: c4ys;:svcby 1 oun0z opih. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swizlw: *vzjk g0y1z5q*lidm)d ,nging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exertin*zz zdki5m v1*qll,j0g:w)dyg 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 sov 6.o8m3srni urface will the acceleration of gravity be half what it o86vsro in.3 mis on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal /fav8g5 pco8m mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, 8f8gcvmo5/ pa how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once peb .os90(rdfdm b 3q2ssr day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is (q9fb2.sbrs 3m ds0do this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraftg 6(ba /vu3mec traveling directly from the Earth to the Moon expe (6mgb3eca u/vrience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 652uf. ;.f fpd wyived8/ kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the 2wfdd.uyep f8f i;. /vacceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a c9/t.yir ifp,j9a) qt circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equar9yqctj f9,.)i/iap tl to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his azt.)g/ 5i uz6 :7xnwbi0h mjagoy5 )luircraft 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 k l2x0v ,(fk,h7r,movqgoq: f/v rp p:terms of its radius r, the acceleration due to gravity at itspqvrp/g0 x:,hl(rm2o:k kofq,vv7f , surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the ver5-a e7jpw ds-pf5 jrq0tical by ansp je 7aq5d 0rwj-pf5- angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed mwp hddv l1va-77vany5t.p );of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a ct pa)v1 pda75mvdnh; .v-yw7 lar safely handle the curve?

  How long would a day be if the Earth were rotatiny(zqp1d(,cu t q x)*yvg so fast that objects at the equator were apparently weightless? uctyd,x(q z 1q) y(vp*   $\times 10^3$s

  Two equal-mass stars maintain a constant distance apyook7 1zawa6ob1v-9 cart 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:zh8nvh8 sze1 curve of radius 235 m. A lamp suspended from te1zs8 n h8hzv:he ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as t,j dsuz cy(6 :8awkl1bhe Earth. Thus, 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. Calculbc y awsuk(l j8d1,:z6ate 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 g 9 hn no35wit-wel(s4presence of an extremely massive core in the distant(w4wl -tgei5nnho 9s 3 galaxy 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 4mj rb4bpzdc u5.z(kbix :0 rlk.v7-uas 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? Lightest? Explain. (c) How fast can the car god:4c0 5z u xk( -bb vurz7b.4jrmikpl. without losing contact with the road at A?

  The Navstar Global Positionzit8v-hwu( k) ing System (GPS) utilizes 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 distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the sui8-kw(vz t )hpeed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous pne8bqcd(,omybo 0e52kel344w gb *e(NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughlyco wpee qgmb4(by bldke*0o, 2e n8354 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-c 0im xsxh:mop*d,o( pursuing a satellite in need of repair. You are in a circular x:mp *di(xm,h- 0oocsorbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) Whatb +vhs0 b h*kj1uj+m,i8 *nzha is its mean distance from the+0jbjsi 1h*z *h+8 hvkba,unm 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 actually "feel" yo8nzjd(wd r 0 o2jq)rt571aec wurself gravitationally attracted to someone near you. (qz0ac1 n)e5 dr72jjrdwowt8 Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Wayy::h8x/jt qwa5;7n5m dowoi a Galaxy (Fig. 5-46) at a distance of wia/n5 h7 :xjw ydo;ot5ma8:q about 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 ar5ewl3r lzhd-:cwc,a. e located at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on -elwc5r .3c:l,h zadwa fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitso) t9ymvr(nrfy-fo26 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 the 1.h -cjxni /.lw+5-cm-long sweep second hand on your wrish/c- .j+ixn lwt watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight t- t6axd *x.ao 6r)qd r7.qqysaround in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circ-aqx rr6od7dqs) y.txt*qa6.le 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 carsoo-(lti+ 3/;lmjafh1:wegr traveling at sh3w:ro ( giets/lom-ajl+1f ;peed $ 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, utili79e ff,nk:o4w k vkhk1zes 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 roundv1w:khk9f7 4ekk,on fs 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.$\approx$    $\times 10^2$