Sometimes people say thatl+n a vufcbf,099 d(5dnbmnl3 water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong wi5bm+3ln vc u9dafd(b0lfn,9 nth this statement?

Will the acceleration of a car be the sa9,bf b6r v3tuml8-oj*b 7a xckme when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same sc7 v*m-ob8r bu txj 39blf6ak,peed? Explain.

Suppose a car moves at constant speed along a hilly road. Where dldt6.*pj c0, yzn-ub eoes the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip bet-dl ce60nu, j*.tpb yzween 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-roun*uo7f l3jr/ aid. Which of these forlr ajufo7/3 i*ces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without t;vfk n0ytj)s5he water spilling out, even at the top of the circle 0f5)jtkns vy ;when the bucket is upside down. Explain.

How many “accelerators”yx1uq:65.q san-b 5d 1dzxahacx ,v6g do you have in your car? There are at least three controls in the car wcxhy6s:d aaungq .dv5a651,z1xx bq- hich can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the cxwf:g 2 e8dtiaae:o:4rest of a small 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 chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’sxe84a2aof:w: :iegd t second law.

Why do bicycle riders lean inward when ro/y3h v92yowp aj7co5bzb h,n 3unding a curve at high speed?

Why do airplanes bank when they turn? How would yqjf-+ppz y s))ou compute the banking angle giv-pf)+syzqp) j en its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal z8jx17,e k jnwplane. She wants to let go at precisely the right time so that the baj1jz8 knw7x,ell will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If sophm t q*0mggs7 n 7:3bj*zx83wcvkg*i, how large a force? Considegbpt:7 m*0 kshw x icz38q7 *mn3gjvg*r an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it pby:n/x oa11bgs 1/qp is, in what ways would the Moon’s orbit be dibo:ay1 p 1gx1q/b/pns fferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on th9f wh l.:x8(,kqtty ywe Earth? Which acceleratet y:89 wkw.tyxh l,(qfs more?

The Sun's gravitational pjayt p-ex4 4t6e;t5tqo ce 01hull 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 e;t54t1xj- a0 htcy e4tpqoe6 one side of the Earth to the other.]

Will an object weigh more at the equa5mr2bq /j.blz tor or at the poles? What two effects are at work? Do they oppose each other5/zlb.rq bjm 2?

The gravitational force on the Moon due to the Earth is only about hals4 dqx)8jgjo g6+ w0slf the force on the Moon due to the Sun. Whyw 840os6g+xlgjd )jsq isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of M;w,r ota-ima q 8.k31aju3rpqars in its orbit around the Sun larger or smaller than the centripetal acceleration of 8k1, -.jtqaa3ir;rq 3auomw pthe Earth?

Would it require less speed to launch a satellite (a) toward the 1d 8e:4dh zknmwmqn15east or (b) toward the weskw1 1dnze:4nqd hm5 m8t? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scalg5qa 7) vw3ub3r1qih, w to)xne in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at const 5gb3 3n, v)wt1row iqx)auqh7ant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periodsyhqxuo/:6it pax ;/0oaa27ki in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like ;yxih u:/2t0io 6ao xapk a7/qa 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 “ /qw6j*+vcmna+be )yv 8sz lw5zg( bp/free fall” or “apparent weightlessness” between labzev/)6(ps w/ qb m5wzgn yj+v*8+csteps.

The Earth moves faster in its orbit around the Sun in January than jzm 9ysp sv,*)pxe 89slkk:w w7s ,ex7in 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 seass:xp, 8 swl9sezj ymw7k,)e * 7pk9xvsons — 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 uncjrsd;t + 0,wwtil it was discovered to have a moon. Explain how this discovery enabled an estimate of Plut0t+w wsdj c;r,o’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yem 7y1w7m0iy 2pscbyz3t the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A 2ws i7 pyy7m3ycz1mb0 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 travelinhh .n775ht szjg 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 Eara(om9tj19mn 3;jfkb zth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radiusk z(nmom 1tb;jj 9a9f3 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 o4rwf9kw n*rjazf4 1(*ho 6ngz.w,ysk n a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s leng1awfz*w 9n4kzr4 gw.,o ( h*jsf6ryknth) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Ea-(.aweoeu8uj rth's surface, and circles the 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 surf ea8-uu(ojew.ace. $\approx$    g

  What is the magnitude of the acceleration oq zrye5w9aq(7 f a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per mi5rz9qaeyq (7w nute) if the wheel’s diameter is 32 cm?   

  A ball on the end ofx8knx2u+muz)9 k0f 2/x shs;i4xein w a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig.+2kx2)i ui/0h ;nnz8umw k9se 4fxxs x 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 which a 1050-kg car can round a turn o pb(+fdw)l5uv waou :*f 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 tpo+)abwvu(f*5 l du w:he mass of the car?   

  How large must the coefficient of static friction be between thputfz, z ,wu-hd j:cd5.8 jk-ke tires and the road if a car is to round a level curve of radius 85 m aj5,udc kzdtkwj .f8 :z-h- p,ut a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots ih 11v2.umh6 hmz7cwo ns designed to rotate a trainee in a mhw c6u17h1.2m hnvozhorizontal 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 dri9b d 0 wwis)zc1*7:pk,wgscm 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 cid1r iw*zk9bwg 7dwc,p:s0 )soin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coastek cip3mf;1s) er be traveling when upside down at the top of a circlkm1c3;fsi) ep e
(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 z62sq:*id0 qcp1c2 lxm da su)950 kg (including the driver) crosses the rounded top of a hill (radius s)u12q : 60azsqd pxccdi*ml 2 =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-dia x)sgfd bmh912) t0xhmt0z q.fmeter Ferris wheel need to make for the passengers to feel “weightless” at the topm9ffdbh m1z)th)0s.m0 gtx2 qxost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.1r:7xf1cka6tr0t o 8reuxul hb 41u2s00 m. At the lowest point of its motion the tension in the rope supporting thexlk2ctx0 1f1es hru 6uab408 rtu:ro7 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 kx40fyy vz1s+7e m,ehparticle 9.00 cm from the axis of rotation is tef1 ,ey kh4xy+ vmsz07o experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnio0vs qbztzdk2( z-e 7)val, people are rotated in a cylindrically walled "room." (Seede)(70 2zkqob -t zsvz 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 rotated in :+qfd* notbu6a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a centro6 du*nbf+tq:al 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 thi2nqm)a(t) u4/ j7cgij znk-bws time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude km()cij -uan/7n zb)wt g42jqof $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travp+hm *z1hvv tbvp.d2zrx6:)feling 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 massesrj j. de *zo/p1z0kg+y $ 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 mao2tosn7a8 -gtneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and bu7st3rk ;w2j/ 76oimd wdi+ecentripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed iswut o3ikd77j2i 6b/swd+e mr; 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapoli yyfutix8tj;wg/l;dr(6d *t; s 500 accelerates uniformly 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 acc;x; y y t(ltg;dtfwdui*r8/6jeleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particularyh8,ilret, vd*iu n ,2 instant, its acceleration is 1.nviy82,d ,lt ui hr,*e05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Ea01 / r a;2iyv*kh c.i3daowkw+pek rq/rth radii) above the Eqkh a2/vp.k *;w ik0cy+w/do3 1 arirearth’s surface if its mass is 1350 kg.   

  At the surface of a certai ;(b bc .bfa/lt(k,b8h+cskdf n planet, the gravitational acceleration g has a magnitude of 12 ( l8b kbksc.hdf;f, ctb(/+abm/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 acceleratiow* ;;mqz0j xi 7ruq*xhq1n0s u8*ekge n due to gravity on the Moon. The Moon's radius is 1.74 1w7** nx0zk;i0qje;xuq8 q*ehrmusg $\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, bupv;(n8-gz n gh6pukn6 t has the same mass. Whz6 (nnng 6ppuk-8v;ghat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a massboata85 zwt2w*z c7b;n*uww4( a boz7 1.66 times that of Earth, but the same radius. What is g near its surft8wt4 ; 7 (a zzb7oaw25co*wbz nbw*uaace?   

  Two objects attract each other grav8pkxdt sfu5s),2;wre itationally 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 a4bd( 2hu6wu3ipys u1 icceleration of gravity, at (a) 3200 m yh 3 dpwuisiu u2b641(   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Ey: dz8 ui8nqhz-0zox +arth where thegravitational acczox8zdyzhq+-n0 u i:8 eleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron stabjzabid9y)k.kx. :rag,* d) u r has five times the mass of our Sun packed into a sphere about 10 km in radrak)j,.y9k )a xg. :d dbuzb*iius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was anks m7cm*4zik3,f ysmys1)4 bsdl+z ;k 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 Sun. What is the s,yszikm c sk;44fks1*mdz sb+7m3y)l urface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel xp+.r9:t oknlnbg1 euran+ ,-weightless while orbiting in the space shuttle. Your friends respond that they ae+ :.k g1n+9pu,-nolxrnbrtthought 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 locate eemmk61)v b2ed at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted kv6 21b)eeem mon one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of oy*hrt.4t kedlkxw 5z )3,7rvthe Sun. Calculate the total force on thd3zt5yrxt4r.*v ) 7l, hkwkeo e Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface u6gin5 cwpme9v 40s/f of Mars is 0.38 of what it is on Earth, and that Mars’4vg5uesmp 6n09f /wci radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period b,3hi t7vgx3g of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s law3htbgg7vi x, 3s, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in ahkn ,uui ;cb9, stable circular orbit about the Earth at n9 ;uubhc,ik, a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abo5s 6 3mff(tkvsve the Eart(ff 65 t3msksvh. How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience i zhnx g7n)b/9ag2v2itir )wu 5/mcs2 simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as tirznsg2m9 it/ hcu 5)vx2i) /b7n w2gahe time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the/+0jvxgxy g-m 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 revg-0xg/+ym j xsult depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched7jol(z2v6gnf.tb f su*) cr2k (g(uqi from the top of Mt. Everest to be placed in a circular orbit around the Eart*q22.)ggu 6v7cbt(zkiu fnrol (js (f h?   

  During an Apollo luna2w j:7 meumn5u wz9i)6z 6hxvuq4ezq9r landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go a 2j7niw4m9qqxzezw96v umhe)uz: 5u 6round the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plt ku0c iwgp l,/vhm34cn )e)/ cj*ver6anet. The inner radius of the ri34 /kc vc/ pwut,6n lvgc0*emjrhei)) ngs 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 diamew;y. +x klok0ya fr;iy(k :/mlter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at thef o(iy k.+;m;l w0y r:klkyx/a top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 kmtyno9 qnz9 ..cyc a8y. from the center of the Earth's Moon in a space vehicle (a) moving at conct9nyacq n9 y.ozy..8stant 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 of ob,k d*h k,a *tib,kowh9:8lxequal mass. They are observed to be separated by 360 million km and tak* i ,k:oa,x k t9wb8db*h,holke 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 tha+qq7 w o7z-or :ue+frbt movesqrq +o:rzfe-uwbo77+
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of a-r7o/335o;ibvncxsp2bkvn p n elevator. The cord can withstand a tension of 220 N ak53ovibp-3xc;v r/s2b nopn7 nd 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 surface of a planet with periox oru ;h**jjzq-)rh-sd T , the density (mass/volumej*)hr x-juh -rs;*zqo ) 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 deterxrc onrkl b)lu o5r rwd6 o7;;-,*0geimine the period of an artificial satellite orbiting very near the Earth’s surface o5rdoi0l rxge ;ur,ko)b7rnc; wl *6-.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun l0 w/*etjdhcyj7u6 4w bike the pl4 jcb ud*6et7wwj 0yh/anets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 sgu4n10krkvz(z3e,icxyk zmw324r : ;v u9q q$\times 10^{9} \mathrm{~km}$ 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 op,a2 u749-sfy vixz,f8c o ddmnce every 76 years. It comes 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 is nearest when it is out there? [Hint: The mean dia -8ov2479 fmsyc fzdd,i,ux pstance 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 Galaxv2+rw/c*j uspoig1c/j 5r4vjy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 distb3 gasajmpz3 ,d(3,fzance for the four largest moons of Jupiter (those discovered by Galileo in 1609 f d, 3(3aj,zpmasbzg3).
(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 of t ust(h)2h.y lae 8kq0i x(xs5q.hzh :khe Moon. .q.s h8khyh:sqtzh) kix2((5 xla0ue    $\times 10^{24}$

  Determine the mean distance from Ju v :fp070l*p+yfhqkvipiter for each of Jupiter’s moons, using Kepler’s third law.y qhk+p0f0fvip:l v7* 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 between Mars and Jupiter consists of man5xf/p;fx5zcp yk2y ;dy fragments (which some space sc c;dk;fypxx 5zf52 /pyientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in t: iye8 qnq;z5vhe 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 thi;z vy :eni5qq8s 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 revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorgez+;ae).m03 ff z(uh8go ayg wr xxi3w- by swinging in an arc from 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 lowes)3.(g u+rag8w30fmfy zixo wex- ;hzat point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration ofl94r4lot9f x/w l6pbv gravity be half what it is on the surface?4l9tl9ofvl w/x6 p4br    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands e(te d4s s2rd5;0xxloand spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their in2rsdxe5s0 x;eo 4t( dldividual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acc6 y ye: twx264idao5eqh px(p+eleration 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 this :ea ehop+d q6typ54 2ixwyx6(?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from tz3t0kn6nx 3xgd* *xqshe Earth tondz nqgts*3x*xxk36 0 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 sl tvh(oft91:jh(n k +ztand on a bathroom scale in an elevat(okv9 +lfzjtt:h (n h1or, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station z3ohqj1x9un mwx l5i2f6sa 16consists of a 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 equal to gravity at the surface am iqnf2 6zx1wsh3ju5l 91ox6of 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 yspleag7i2m0 7hx.0r).
(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 i )aiu9iir4apf0h *bsfd g40 6cts radius r, the acceleration due to gravity at its srp*bh04 ii6fias acd9 u)0fg4urface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical b1 t6yer;pd+b by an anredyb;pt+ 6 1bgle $\theta$ 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 des4w3.p , sttxnk3.x r ff9vxh8aign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range offxa3spr3hxf.t ,tv8 x9. 4nwk speeds can a car safely handle the curve?

  How long would a day be if t/ )o )*u3-mh bxpycladhe Earth were rotating so fast that objects at the equator werx3y l)/ubah)-o m* pcde apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apq ;nr p:vy;jhgq26: mhart 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 spexut9u:mqshez+vog:u q5t.u ) ;f9du 4ed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an )zmt:vuu; 4huox9f+teug 9sd. 5:quq angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus,82bj(fj/ nss s 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 surviveb/8(ssfj 2 nsj more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an ewz(n- nj/ij(p xtremely massive core in the distant galaxy M87, so dense that it could be a black hole (from wiwjj/pz -n ((nhich 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 the hill and vallne0.1jrvfp3.zc*:g t3a;t zq6f gza iey 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 heaviesi3ctvr*fj ggn:z;6 ptfa. 1ae.0zz3 qt? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positiortz9j/ + gfhqi st jfin.f.4:p2sw5/aning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals trp2i5h fr fa. j+ntst/.4qjfi / zsw:g9ansmitted 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 Asteroid Rendezvous (NEAR), after trksx3 l hh0r.2 uzepmgsrd8d +0c;2by:aveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eroh2+lp8gu3k m.dh2dc0ze sxr :ysr b0;s 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 fsy z)za,fpa28,0uceiyl ;h4 space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the sa szc20ha 4eufyiylz f8,;ap ),tellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mea,+*1:if vbyerqfbymp fzz dp3/82ws9n distance from thef3 p8 wrp,zb/v+beiqd2*zym 1:ff9ys 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 couh)e;ye x)j i-yatobc,sg w* 7/ld actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assum w-jxgy7itbo/se, h;) yace) *ptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Wafdt 4c,dhkra 9b.x8.*sz7rp sl)t ic 4)joey.y Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cent,)dtesldrtfzc .4h84jpa)x o y79.* kb.rcis er $ \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 a+ww7rgdjve n1- 4sif-t the corners of a square 0.50 m on each side. Find tiw4-r7j g wn-+d e1fvshe magnitude and direction of the gravitational force on a 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 kgpu 3ly+ xq1;fmr3iu7xg9l1vx orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experiencep7tx4 0,cw /rat.k z0r pzh.mrd by the tip of the 1.5-cm-long sweep second hand otmrc0pp/ .zkh0at 7,.rr4xzw n your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight ars y:-s,hs- nzjound in a circle below you on a 0.25-m piece of fishing line. The weight ma h-szysjn -s:,kes a complete circle 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 car travelk5; lh9mff5zging at spe5k5z 9g;hflmf ed $ 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 trazgny+ f22. ulfin, the Acela, 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 bank+z2lnuf2 gf.y ed 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.$\approx$    $\times 10^2$