Sometimes people say that water is sp/ g9p.4w.uckojv*oremoved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statjk su9 v/poo4gw .c*.pement?

Will the acceleration of a car be the same when the cwf4 nu7ma,isdo r46k0 ar travels around a sharp curve at a constant 60 km/h as when0n ou a mk,w4f6i74sdr it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car hc vm9 n43t);m;.e82fhchqf* urgyfm exert the greatest and least forces on the road: (a) at the top of a h2t)4*vcu9mnfe;h8r 3h y;mqg.c fhmf ill, (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 un c55p)cf3uh child riding a horse on a merry-go-round. Which of theseuc5 c3un) 5fph forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle weqq9u)s, g6p xithout the water spilling out, even at the top of the circle when the bucket is upside down. xespu,9q)6q gExplain.

How many “acceleratorxmja2dm8f6 - cyhu k: go*1h+gs” do you have in your car? There are at least three controls in the car which can be used to +:8ah mxd6j -k2*h fmy1ogu gccause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hil5d f6g*, uzvjql, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve ,u6fvqd*j5 zg “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 p75h8.o x bzxxur 1/iorounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute t u a+w5.tzu9kthe banking angle given its speed a 5.tw+9kuuzat nd radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. She8qzf:2vc 4j*ta1i jh x wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of thtj*:41cxi vq28z ajfh e string?

Does an apple exert a gravitational force on the Earth? If2h +;za(md1r *ixoi/wjrcdt : so, how large a force? Consider an appl+i*1 o rr2ti whdza( :mdcjx;/e
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon0,x- rogpdj5p ’s orbit be gor-j0,p x p5ddifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Mn),n5bws0bx j oon on the Earth? Which acj0) xnbb sw,5ncelerates more?

The Sun's gravitational pull on the8bv lj80ga8 jh Earth is much larger than the Moon's. Yet the Moon's is mainly re8jl08vag 8b jhsponsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at thq9 ,37 rjoq31rj zwq(4yqio hse poles? What two effects are at work? Do they oppose eachq1y , wozq7hsoq q(94jjr33i r other?

The gravitational force on the Moon due to the Earth is onoa3hn)p1: ;t6cx22vhrf gxrxly about half the force on the Moon due to the Sun. W6 chf2p3gnoa)x;2tv:x hrx1 rhy isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun ,bou9d 09 db f-sgtkr3larger or smaller than the centrifkb r-0u3osdb g,d9 t9petal acceleration of the Earth?

Would it require less speed to launch a satellite (a) to;ek7 zaw)y (tdward the east or (b) toward the west? Consider the Earth’z( tk)dw7 aey;s rotation direction.

When will your apparent weight be the greatest, as measured by a hk e4.xjb;pn;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 b.kpxnh4; jbe ;e 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 sth34mppz). . cib:tbadversely 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 you can t:t cpm.h3z)ibbt. 4pshink of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betw myr3:7 rn/6zqqjgvjx,2ly +wgd g h/lrz-7.jeen step rlj., qjq3ym7gwjn-g:l/2xvrz + h7 6/g yzdrs.

The Earth moves faster in its orbit around the Sun in January than zd sz7b6:qnkt30m rb: in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative tn 7bzr60d:3 bmkz q:sto the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a ,8;2ksly to,z)opq t nmoon. Explain how this discovery enabled an estimate of Pluto’s ma,k)p so8qo,zt2; tyln ss.

  The Sun's gravitatio5hha6 uwt ,w2rnal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth ,6h2u5rwahtw 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 fkx9i:4nics99lovb- t(dhw( 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in is4tph2.i8edc s ab85 xts orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assumd cht8p8b2as. i5xse4e that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates uni1)sxhol8 (mra p.kk17, dtz ryformly in a hohz( tkrr7,o pmd a.1kx18y) lsrizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shut+6/n g ggpomcz3q9g3 ttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. mg+noq9t3g/6c gz3 gpFind 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 +oj6x pv-2dl ib1rys/the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32px6/ vrosi -1+y2jl db cm?   

  A ball on the end of (;t).n fmco 9n-ncqmxjay85y a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in- x;m 5 )fc9yntn.j8(oay qcnm 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 wj vo:)f;dmj0 bhich 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 rjdo; 0)fjmb:voad is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the t/ 3qf hjnqk..fires and the road if a car is to round a level curve of radius 85 m at a speed of .hfjf3nk/ qq. 95km/h ?   

  A device for training astronauts and jeypd ljh ;ct3n6u(s/z;, v5ayh*p(b wnt fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 time bnjs apnz(p( *cvd,t y;/h3yu lh;w56s 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 cm8ubc (lo4h3t)psnx0 d from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coio8s (d3lx4u )bc phnt0n slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down a7gue2+ 6bqa 0ght;zept the top of 7bgpu hg0zeteq2 ;+a6 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 drivexy rjj a/jfvv gx8f,541 1h.uyr) crosses the rounded top of a hill (r/gjx8 v1 u xfhyrvy1j,afj45. adius =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 wheeo+mz nj .8c-dql need to make for the pn-ojmzcqd 8 +.assengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled inpltr* ytt27mx61i d )g a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope tg 7d *x1t6ptrymi2)l supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from theesvxihp u+ 3/- axis of rotation is to experience an acceleration of 115,00h/v-3 eus+i xp0 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peoply 34 jvs2fi8wge are rotated in a cylindrically walled "room." (See Fyg2vjw8 3is 4fig. 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 rotated in a circle on a friw mh9 w3;r /fjn8pj2pqctionless air-hockey tabletop, and is held in this orbit by a light cord connec9hnfw/q j3p;w2rpmj8ted 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 wev:nvgpr9eez.l9/; i q ight of the ball which revolves on a string 0.600 m long. In particular, find the 9;:nz lv.q9geive /rpmagnitude 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 perfj8 iua b,p5wqhn:8+ocectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masseseobi(x1x h8y0oki prhc u4vag /)8g35 $ 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 4atu s7rzy gb6ykc/+9ku 8h0q 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 component:u v)4fp.bcah x;wx:ts of the net force exerted on the car (by the ground) in Example 5-8 wh:p4x:a ;w vchxf.u bt)en its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis i.zs7,tcf pxb6 knm y7h:;y*t500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangent *7 hy:;xcybnpis mf7zk6t., tial and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particula .su .iczx )hy/ejh4+:cppb/jr instant, its ah:e+4ic c bz /ppjxus.h/y .j)cceleration 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 gravity on a spacecraft 1 x:2ucb0-lpn j2,800 km (2 Earth radii) ab0ujpnx2 l:-b cove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a cqyn .w*)sqmvi,db9 o nh/3mq,ertain planet, the gravitational acceleration g has a magnitude o3 ,dsn )9.qymh*/qbimvwq,no f 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 on the Moon. The h/;a mr ;lwle+7pz(imMoon's radius is 1.74 zlm;;wrhpla(i7m/e+ $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 time2p1tu4o b9(luds; kl /*yfvmvs that of Earth, but has the same mass. What is the acceleration due to gravityfs ty1*4pb;luuo2k/vdv 9l( m near its surface?   

  A hypothetical planet has a mass 1.66 times that p/d. xrg4g)pt of Earth, but the same radius. What is g near its ptr d/).gg4xpsurface?   

  Two objects attract each other gravitatir. v y;xhpr7 noxju:/p.t/.xm onally 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 acceleratiyfe1 /tmt-q0pon of gravity, at (a) 3200 myftq0e/p -t m1    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’mn r 8p .qy rr04c4c yzhu.zkv0hf405zs center to a point outside the Earth where thegravitational acceleration due to thez5nm 4uz4. 8y0y0r .h0r4cf rchv pqkz 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 packmxhfj s+x4ny7 bv*78yed into a sphere about 10 km in radius. Estimat* 48nx vyh7sy+ x7mfjbe the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is -a;t ; edkos8inow in the last stag-ia8 e;;tso dke 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 astronauts feel weightless whi3fvx 9 57rw/fr ;ontf9bcmzp6le orbiting in the space shuttle. Your frio9vnb r7fxwpf 3;59tz6mrf /cends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Cal. xbhlr9 oneq+6hq3c; s bs75tculate the magnitude and direction of the total gravitational force exeh7th+653n brql;9bs o s. qxcerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up ;.d7ctry xi ,hon the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-.d xhtc ri7,y;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 accel 5olfbt,o6x9o p5awj(p:d hyg38 k; tberation of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Marspw9tp:8o x55b lydbg; o k(,3ja6ofth.    $\times 10^{23}$

  Determine the mass of the Sun usings4t+-wiil+rp i6l)i r the known value for the period of the Earth and its distance from the Sun. [Note: Comr+lii+ri l4wts- p) i6pare 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 about)p012tzxsve q o5 p5hb the Earthpsb02 qoexhzv) 55t p1 at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite int6 0 ddzxzvnu4b74p .mko a circular orbit 650 km above the Earth. How fast must the v44d.nb7x60zk mduzpshuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to e(s;tn)h sxsj. xperience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one r; t (sshs.j)nxevolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbiu owriv/ pic /v77z:uu7g4xw( t 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 rad74ozugxv/c r7u7puiw :/vw( iius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity woul(9ph p b)yrtfm4qo6*dd a satellite have to be launched from the top of Mt. Ever )(oh9bp46mrpdq*tyfest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module coc./dxvtou3s 7( aeao) r0p z4intinued to orbit the Moon atzus(p0ar3 .i )exoadotv74c/ an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet;6v*g1:nbqjw qp0xk k. The inner radius of the rings is 0x* :g6 nk1wbj qqk;vp 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s e7 fm4l b*pll3gr14zk;9pv ukp: ;a,k4zs ufa(see Fig. 5–9). What is the ratio4k4s4pu1f plv ul9 zzemrkb3;p,a;lfg *k 7: a of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75i he/f.b27z,*p x3kprqc+6e;t x ulan-kg astronaut 4200 km from the center of the Earth's Moon in a space lh6preu +,fax723;. cztx /k *nqepbivehicle (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-stat 6l ki7v2k5r1dpds n7r 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 point midway between ttsk lnd6pd7 v i2r1k75hem. What is the mass of each?    $\times 10^{29}$

  What will a spring scaldz ts*9fr+jvh d 2m*v/e read for the weight of a 55-kg woman in an elevator that moves dvthjfs /z* 2+m* vd9r
(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 ceilindek)3 j02 1vzqlh8bg hclchdu p.w340g 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 (magnitude and direction)? a = 0hp zd3l)hqd0hgek384blj1cwcu2 v.   

Show that if a satellite orbits very near the surface of a 952jb c(,m/ siryjv qiplanet with period T , the d ( j9cq5b,mv yi/2jisrensity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period o:ythl;gu/zo yb :px:gwv 21 y/f the Moon (27.4 d) to determine the period of an artifi/ly w:vxuzo2/yt: p1gbgy: h ;cial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a.b e:v r -(;vynw/x66lns yvhq few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is iter. :6hy(xn v-lqnb;vvwy s/ 6s mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average ;lrjt4ear lyc+y1ks,lilf 1 8 z6yw:6 distance 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 clh/u b 6kpje5v5ose 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 is nearest when it is out there? [H/5hjbve p 5uk6int: 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 Galzbewjd d )ta5q;;l 8wfc* .uy-axy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 moo .sp+ )k rfq.;tr:e))av ihtcrns of Jupiter (those discovered by Galileo in ).s ;r c h+tei qr)ap:ftr.kv)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 period0 kid/c* (d).;gbvqb vp m7ebn and distance of the Moon. n(d i. b;p/evb *d7gbk 0mqcv)   $\times 10^{24}$

  Determine the mean distance from Jupiter for eahco4; fs9is 6dch of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to th d6css4iof; 9he 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 jwc0e rxs(n7uf4 m3o+Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destrm3w0( n74sxc oue r+jfoyed).
(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 "plan;/j(ipf8bs3 ao:gofh h5vu*x et" 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 thah8/ ob5*(pxhua i;v:of f3jgst the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc f y7lg00ye u e3oi:olc7rom a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point ofe0eyu l :igo o70cly37 his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accelerod fes)sqzi ev-+. 8b/ation of gravity be half what it )b+/ osf.eiv-e z8dqsis on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hap(vokgy 2nd 5l3v5td -nds 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, howodp5nv-g (k3yv2 t ld5 hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the appyxy.p2j4 tr k6arent acceleration of gravity at the equator is slightly less than ij.k6x2 4yyptr t would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the E1e)av7jub el,d0cz 6yarth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forb6zee7a0ju d,)cvy 1lces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand 4d,jjd5 xl-ww )0uf hqon a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and f,0 -jhlxd j4wwq)u5din which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about itst2va9xsh; khj1)nd* s 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 effecsav;sn29xhjh)t k1 * dt 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 vertt1j zn gd:4a2 1po n55qyv;wpgical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its(fdh9qrj)-crnn0p j / :sn;do radius r, the acceleration due t9 jrnnjc)dn /:;0- p sqrh(fdoo gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected fromkv6chj8sf)6.ch m4he the vertical by an angle 4jk6)v.hc f m6hc8 seh $\theta$ 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 deso)dnci u1j4 pc*d yp8*t6b6tgign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a c8tc4 o16py**d6ndg u) ibct jpar safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at y0e. q*lhcm;pthe equator .phmyc;q0*le were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart lc)qk-u2y3/ h b, xefzof 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 akm22(5 xksuy b constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swin2 u2ys 5k(mxkbgs out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mass ,f5ccx0r.yx five as the 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 a person would experience at the equator of such a planet. rcx,50fy.xcf 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 Sphv3y7y bu z50s7co1ji jd7n +vace Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it71v jind7b+j0vy y7uso3 zhc5 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 u 6a-a+u)ghcn the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of caa+g6cuuh-n ) urvature 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 without losing contact with the road at A?

  The Navstar Global Positioning Sy he+iv+7(xelhstem (GPS) utilizes a group of 24 satellites orbiting thi +(lee +xhv7he 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 speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asterlfmjez3*o hr 5f +4c1soid Rendezvous (NEAR), after traveling 2.1 billion km, is meantlj3hs 1 rcom4+5ef z*f to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the :y k3e ,uj:(div5r0zgqk i 3gbspace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the bgy,0:3 : ukj ikqz rgi3ev(5dsatellite (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 y7 wtjkfm51pd/ears. (a) What is its mean distance from dwtpk5f /71mjthe 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 f lz( g /x6cmelfl+jn d-0o86bto be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptiond6(+m - ogzl/ j8bl6f lnecxf0s, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxkn8. )g7ffta q it;i.qy (Fig. 5-46) at a distance of about 30,000 light-years from the cente g kati n.qfifq7t);.8r $ \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 mevsm-4e+;irh7. 8ra c1ymfvl on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass pl178+ yserlfa 4rm.mec v iv-h;aced at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the ; umhf,yrr2oeu,*lu5t4kj w8Earth $ \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 1.5-cm-lon.3kzv9af(3 u2rjbkce/mb -m i1.s ssqg sweep second hand on your wesju/..rvm 2ak9f3c b-k bmsq13 z i(srist watch?    $\times 10^{-4}$

  While fishing, you get bored and starj; ve ao8p7jbv8,hqf 96qlh2pbk59 rrt 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 cqe2k9,p ;9rpj f8q h8b bavvjo 5rh67lircle 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 deq r(t;en ys4;p +iu1zvsigned so that a car travelit4y+q rnv;;i e(pu1zs ng 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 Acela, utilizes tilt of theqo*gac5n6 b .(a,wxyp :mso9e 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 (*:s6qeay59g.on,wmx p cb aoseat, 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.$\approx$    $\times 10^2$