Sometimes people say that water is removed from cycxxt ;jnm,-z cs;. v9lothes in a spin dryer by centrifugal force thrs9nc j ,xvctz-m; .;yxowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the 7b4hz r+a* 8x.y petfssame when the car travels around a sharp curve at a constant 60 km/h as whf ypb87xshtz +r*a.4 een it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constw/,4m +eg61dbhjjhx/3yrnme ant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near/h+ bhnwjyx,1/rm gd 3 m4e6ej the bottom of a hill?

Describe all the forces acting on a child qmnx4k7)+d c :ye*gkq26a sejriding a horse on a merry-go-round. Which of these forces provides the ces:cndyk j mx +ea4q*6 k2eqg7)ntripetal acceleration of the child?

A bucket of water can beggifb+c m w.)+ whirled in a vertical circle without the water spilling out, evb fwc g.m+i+)gen at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your carm:ut da6, nkh:97vubva 7)p pd? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? Wh 7av9 :ubpnk7v tuhp ,)m:dda6at accelerations do they produce?

A child on a sled comes flying over the crest of a sjh9 85 o-y crilkoh2ltjgx, :-mall hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his,-lt 8-cjh kh25jx9 oy oglri: 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 9yp4mvbtu/x8bila 4i4cs 6j( rounding a curve at high speed?

Why do airplanes bank when they turn? How woupy6g3e3j/soz7 m +7fo)urbnhlh/td;s,h9 sw ld you compute the banking angle givenmw9;fp/ +h)g3hl7 s6hr7edz,bno t /3oysus j its speed and radius of the turn?

A girl is whirling a ball on a string around hwh)ns vu6)t w6er head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on th6tvsh)w n6w u)e other side of the yard. When should she let go of the string?

Does an apple exert a gravo nq/q7lig g3)qnh:m 3itational force on the Earth? If so, how large a force? Consider mgq :q)iog nn37qh3l/an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways vl(lgni/afh 9/zbe 7h2e +pw *would the Moon’s orbit vlwlahb(zpg*+i7/9/2ehen fbe different?

Which pulls harder gravitationally, the Earth on t,g0c1z,l3 ,wdqm u qlz1gr1ughe Moon, or the Moon on the Earth? Which rluu,q1gm z cw1 gdl0,z,g1q3 accelerates more?

The Sun's gravitational pull on the Earth is much large ix2vaio*bi7i73 h07 xisqz)dr than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one ii x*) h7o iv3i70bi72adzxsqside of the Earth to the other.]

Will an object weigh more at the equator or at the poles?)s 5bd9e ta5vy What two effects are at work? Do 9btv ys5)ade5 they oppose each other?

The gravitational force on the Moon due tog*u7mnwv+nf wrfsb5+fv3( 1w the Earth is only about half the force on th+ 3gffv+7m1w5vnb n fr*u wws(e Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit aro5xuxhu/ra h+; dwgah u/, z:/hund the Sun larger or smaller than the centri hud:,zh hh//aguax5/ wr+ x;upetal acceleration of the Earth?

Would it require less spe2(ck 7jbwd0v0 s jp1deed to launch a satellite (a) toward the east or (b) toward the west? Cocpe 27jd d0k1wsjv b0(nsider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measur*otnhfd 6*a5 zed by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the odfat*nh 6 z*5same 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 affect:hsf oo4qwx-: oz7.n k+tz;bo ed by weightlessness. One way to simulate gravity is to shape the q-on 4;sf+zw:otb k:z7x ooh.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 you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” bebqiqu :y4mlj- n2up/ s d88nb:tween steps.ln 4ibnm8j qs qd-:y/2b8u:up

The Earth moves faster in its orbit around plrxh- *ey 8(k0 unf:jthe Sun in January than in July. Is the Earth clj0k(lfuh:-n*r xepy8 oser 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. Exi -6 ok r n)8n+kb xm+fzqf2l0cy8jr-nplain how this discovery enabled an estimate of Plutoo08iz2n -n8)-jkfx 6+l mnfcrkr+ byq’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Mooxio 27x sjw9(un's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitatijowix( 7s u29xonal 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 travelinxg9rl*ptv*dw yk-y/n f9 8r+wg 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 Eart82 9;nvgp* iz3*xskd3 onjemih in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the skm;*3i3xonv9gzidnep8* j2 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 ia3vwtm qf;e2v-6e:vexerted on a 2.0-kg discus as it rotates uniformly in a horizon2i3tvwv:em ;aq6 v ef-tal 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 Ea r2p69 fxe-qpurth's surface, and circles thp epqr9fux-62 e Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of a79lqe t4qgj+: b(c yxg xoe10clay on the edge of a potter’s wheel turni1etb 9(y+4gq:lcagj0e 7qxx ong at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolvs2)okg (0nas .pwm) l8dey9nied at a uniform rate in a vertical circle of radius 72.0 cm , as show(s29ayd s nkgw).80 )nlpeoimn in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with *lj- 60ru -v3uxaroda ozq1e :pgcy85which 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 this result independent of the mass oa3u6o0 j :ep*8l vdrgaq-cxy 1zo-r 5uf the car?   

  How large must the coefficrq lfltq-+62rient of static friction be between the tires and the road if a car is to r+q2 -llr trqf6ound a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate a 74 hk7 5jkvccp.rk)ottrainee 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 wei kkp5 .c)kocrj77vth4ght, 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 variable sedve niv3uq734wjuat -a)b+j hm;4a6 peed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate ofitw-64 u7u eaqjhm) nad ;43b vjav3+e 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 co/igd e*1m 54oii v2dwfaster be traveling when upside down at the top of a wv5o1m edigfdii *4/2 circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses tbk6h3f wmk3 pq j 51jje5a5vvwxc2g+;he rounded top of ab 53mp;+5jvv c kw jqh2jg3e16wxf5k a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel 3e8r qi,xkd 9h17cqieneed to make for tiq8iece39, 1dh7r q kxhe passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg imelr3b ( w db8p;5;zs:ld/ qris whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rop/;rq3pmbw8d z slbrl :;d(5iee supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate i lptb bo,q*)r,f a particle 9.00 cm from the axis of rotation ,bqp)rl,b* to is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carni 3x acmv6m-jjh2+/-9hkum9jykql h s9val, people are rotated in a cylindrically walled "room." (See Fig. 5-35.) al m3xmucyvj qk9 j-+-m/sj h926k9hh
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 ) 3tuh9m lper 7jf,/;rf is rotated in a circle on a frictionless air-hockey tabletop, and i tfl j3f/9p,h u7rrem;s held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring thvlv 8r 4sfd,k)e weight of the ball which revolves on a string 0.600 m long. In particular, find the ma8v)ldvs4kr , fgnitude 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)firiz -,b)tptz y gs 6t,gf(6e7-p lu 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 masses u8yv fr ) b9b2bfpw;b9$ 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 3 d.t yxv4mr3l310 $\mathrm{~m} / \mathrm{s}$ . 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 tangentialwuutbr 97 t2*h and centripetal components of the net force exerted on the car (by the grr*uwhb29 u7ttound) 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 uniformqkzf c:sx :a.:pi*w.4iw*f ag ly 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 nog. wfiapa c:wk.xq::i z4fs** slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of 5e66hi 9olg pmradius 2.90 m . At a particular instaphei5om 96lg6 nt, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravit/7 igl s3yw0xh0j5a lfiit8;d y on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfa5;l3hxwajd00i y8i/ tli 7f sgce if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelero mm2h7)c,o gration g has a magnitudecrh,mo7mgo2) of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity ozm3 y9fjly u.abcrltp q- )s7ac)yi53i+ l 39tn the Moon. The Moon's radius is 1.7syyacyi7a ut-.tmlz)5fj3 lqi c9b r)3+39p l4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 t5d9o06 +0ybjnn cv p tiwsz9:vb8dwz /imes that of Earth, but has the same mass. What is the acceleration due to gravity neacnw9z0vj 8vip +w/:zdo6nysbbd 05t 9 r its surface?   

  A hypothetical planet has a mass 1. fpvx9n givvl5+q);,x66 times that of Earth, but the same radius. What is g near itv,p+x9g) x f vivl5qn;s surface?   

  Two objects attract ea.w 7uqsr 5jbo2ch 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 acceleration of gravity, at (as*s-1aab( xkfz1mb)p jyp c9l1 2r/n w) 3200 m lbs c a1mr )1kw 9(xjp1fasbn/p2- *zy   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from e6 s5t.v3(3kmc9xt tsmx0nr (vh of8athe Earth’s center to a point outside the Earth where thegravitational accelerat hx 3o m((s3nc8r0txv tf65mkav.s e9tion 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 pab um8gze3:1znfh4,ke6a36zq4ub0jqy + gnpn cked into a sphere about 10 km i8 33q0yjkza4 6mu1qbnn +:b u,fzgep6 nz h4gen radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which oncf bg,sza+ i) 4ksa3e.le was an average star like our Sun but is now in the last sta.es si l,f3bz +aa)4gkge of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why -kk3zo+w i+r* ;stduiastronauts 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 yourself that it isn’t so by calculating the az iw+uroksk3 i*;d- +tcceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres ar+ziy8 k ,g:ko 9bn3,stekdy,(col)vse 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 by bkis ,,3koyn g 8(:tlevo,k +ycs)d z9the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yearsnv6h0 8z;v dxe most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, ;xv0nd86 vhe zassuming 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 surfac87b tzvvff /-bt/u qa px:mgrt3*,q)je of Mars is 0.38 of what it is onp r, ubf t -j*)/t:q873abtvmgzfxq/ v Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass o1bgr( 3h/xsc smfz+s8f the Sun using the known value for the period of the Earth src gs /sb3f+1xzh8 (mand its distance 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 a stable circular orbit ab4537 5lqoxktmtiamh*/ e 1qekout the Earth at a height of / q53xke1i*qmmk4lo5t 7etah3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km a1mr km.jl,n e2bove the Eamj,km. n 1lre2rth. How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshjw: - xsn wk;;fu04jjnip rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, an: njwu;j-4wj0ns xkf;d give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit th(8,d-in pzvl0c p 73g-vay mz-jxaxi:e 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. Does your result depejvd n7z l 3gxama0 (px-cy,i8vip-:-znd on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite havx2tc6w0 d6i: ar(ghdbe to be launched from the top of Mt. Everest to be placed in a circular orbit around t6wr ga:i( thcx602bddhe Earth?   

  During an Apollo lunar landing missehhfhr 2d ,3w4ion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to gofehw4,hd32 rh around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that or( xe((+orqciibit the planet. The inner radius of iq( (ciox(r+ ethe 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 rotat ud ynh oo()6e,;gntz;rh 792vs,mokves once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weid7v,s noh)h2 moke;,g;rz vu69o(tnyght (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km hcd 4vwm 2j 05e0(xdhefrom the center of the Earth'shd 0x(52mej hdwv40ce 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 binary-star system consists of two stars o ugonjp 5ml7zwk5)n.id; k 70ff 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 each? 5n d5p;07miowkk.jfg n)u 7lz   $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator t i) f4ld:jle/fhat / )f:4djelfilmoves
(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 c8z vzg,8lx;;cx9k :xbgx 9pv 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 cvk,x:; g; c88vgzb9l pxzx9x(magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with peric10nf632kb 1zdyc0dny; 6s (ege 3j:kkhdodj od T , the density (mah0;ysckn( 6d2zed1kygjd0 c1k 3f6jen:bd3o ss/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 pe8jhcil4 w v1k8riod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting vec i1lj4vh8wk8 ry near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundrel.ym1(a b1,m:a hknrvd meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distan aln:v hm11m, kr.b(ayce from the Sun?    $\times 10^{11}$

  Neptune is an average distancus-w v2orahc8)vs + m;e 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.qy s+j4ud39oi* 18kh dd l-rxu It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of ohrd1*d- d93qy 8ls+xkij u4uthe 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 -,(dj:e csn5n9ejso lGalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 meal 5b ;gh55j)xs 9qzvj al3 2y18nqgcgvn distance for the four largest moons of Jupiter (those lb5;an s3x5jjv2zlg g9vc15y)qq gh 8discovered 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 ana q+k 5;wbfkg/d distance of the Moon. ;+/ka gb kqfw5   $\times 10^{24}$

  Determine the mean distaj w8+ *umquq)ince from Jupiter for each of Jupiter’s moons, using Kepler’u)jqq +uw*8i ms third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt be4 nr /tf6 ez:ofy hg9nq500hfdtween Mars and Jupiter consists of many fragments (which some space scientists think cah 0q 9nrghzfyn6f:e5 t/fod40me 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 an artificial "plan3+pefj- h5c/h/.az .ue z ymbace.e6det" 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 of revolut j.+z 5 /b- /fhed3u hezpy.mc6aaeec.ion, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging yu)kp 0*ddwc;r 4beqj:2ao;f 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 hy;bdu*4:2kqca)woepf0 ;jd ris swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity b/lwbkixfi(;*7ic +q v e half what it is on the surface?bk7x fii( cqw; li/*v+    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands a *a/c9 qyj5gpsnd 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, how hard are they pulling on one another?*s9ycgp/ 5 aqj    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleradr 7 df :kr hhal ;*z;yq.)5u26htmajktion of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude ofht 6 7rhf *ja2;h)ruy:qa.d;d z5k mlk this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly fro 8n xfs+ltft;5qit80jm the Earth to qttsfflxi n;+ t85j08 the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a 13ba )rkwt5 kjbathroom scale in an elevator, it says your mass is 82 kg. What is the acj k5 1ratbkw3)celeration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will ro:e k48sc zgjj9l5 savg,(( svltate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1slegvv9 s8ca:5zl((4 gk jj,s.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 loop (Fig. 5–43 kx7a95.fqssd3 vskh.).
(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 /q ma1wcf2w gmh q)s3:planet in terms of its radius r, the acceleration due :3 1wf/ 2 mmgqwahc)qsto gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is de p()e d4xjwhh7qw4 r-kflected from the vertical by ax4hh)w(7j predq-w 4kn 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 d/y 4:h imdx-y dn)5xsxesign speed of If the coefficient of static frict-4 dn x/m)six5h:dxyyion is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects aas9*9 +q5q vkav wr.egt the equatoq gsv.qa9ve*a5w 9+kr r were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a cqyx(kr4h1 hn4 onstant distance 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 rou/nf(( imfbe.q +jly+bac9 y+r nds a curve of radius 235 m. A lamp suspended from the ceiliyif+y(9f /+ eqbjb r.la(cnm +ng 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 thecy a:gla. r+x1b u*l)f 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. Calculate the number of g 's a1:l)cub.ga*x y flra+ 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 Hvo.v.lc5lb 5 zubble Space Telescope deduced the presence of an extremely massive core in thelc zv 5lb.v5.o distant 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 *l r (:elyu.zr as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces actin .(zlr:lyeru*g 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 Systcusr 8 idf;jwh;7oj62 7who8wem (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, wuo ;f8cdoj6h2wiwjh7 s87r; with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroiclw jp 4 eo2ue;)zt/9dd Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height wejot ulc2 4pz)d9;/eof 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 as(jl3 f:wec)xsmb h/xk*+y)miu3v e 3 satellite in need of repair. You are in sfe w lv3ujmbx h3)+ cky3i se)/(xm:*a circular orbit 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) What is itcryh 5 g+)r .i**-l 71hvcoej1ltbibn s mean distance from the Sun.5iyc vhclr1h)r- 1b n*g oi7j+*tbel?   
(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 val p re 2sxas32+nhd1)lkue of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near yoss ak1n2) 2d3lh+xe pru. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a dy+c,iln o z5i,istance of about 30,000 light-years from the cent iy,+,icno lz5er $ \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 tfnjl7u1(gy) sc g l)2jhe corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the squarcn72(flgj)1u s) g ylje.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orrdtn (q8nlr np bp26:1pf1d v8up5bx5bits 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 tik pei).*llc) dt7.k.ufp3v d oo+k9ykp of the 1.5-cm-long sweep second hand on yf k)vd .idl c+.*ypo7ke o).uk pk3l9tour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and a ;/fytt 6z 4to.gaf-xstart to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle thata/tg zo ;f4a.tx6f -yt the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is desigv zyxsp.wz6izxhu., j1kd:/ 1ned so that a car travelinghks.jiz wz.v1u/d y:x 6xzp1 , 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 01mgj:zkt oj0yuu701 r v jh0)1goap zAcela, 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 speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not bankemth 1uj0:jpz1yugo7jg0zr k0 1 oa0 v)d 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.$\approx$    $\times 10^2$