Sometimes people say thc( 7hb7 4blcxeat water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wronbb (7ech7xl c4g with this statement?

Will the acceleration of a car be thep9uam 1ei(uj.w y.3 piyif6 *c same when the car travels around a sharp curve at a constant 60 kmeuicm.9u 1yppaiyi.w6(3 * jf/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does thdtuaise75b.j;/y9 z r e car exert the greatest and least forces on the road: (a) at the top of a hill, (b) adiz;jy.9utrb/s 75 aet a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child ridinbs6, n ifc8s+(ud,noqg a horse on a merry-go-round. Which of theses (fq,,u8 6n+ ibnocds forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withw y8aw+ah4imgt2 o4lv0o;(thout the water spilling out, even at the top of the circle when 4la4h8w+hy0gw2m a; vo( ttoithe bucket is upside down. Explain.

How many “acceleratorwt ku pl7mr:nw8:l0 l8s” do you have in your car? There are at least three controls in th8utllwr0 8nm7l:kp w:e car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying oveqy, +*:-n xt xgybf ix1mc19pjr the crest 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 asxycf9m,ybxit -p:x+11j*g q n he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a cutvi8 mdgf+p82z +f bbn/ep/s+ rve at high speed?

Why do airplanes bank when they turn? How would you co:de 0)jpd)v*mcuw4p 5.(hd ,pz zgjfompute the banking angle givenp m0.jgpzd v(* uodz ,d)pew)4:cfj5h its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Shqy//ry t-y2iu)btsgvmn5- /e e wants to let go at precisely the right time so that ttm-/)gy/5nbu-se vryi2y/q the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gr1a(y c4m hs ;ml)sfwo7avitational force on the Earth? If so, how large a forcefocs(ys7l mm)1wh;4 a? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s oe6kq5p n x vx42e.rq7mrbit be di2enrx p.meqk65v 4qx7 fferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Enbzv jcf;e2o*ei b0 +,7sppt9arth? Which accelerates moreb0+sp*zj97 btv;pn cf e2eoi ,?

The Sun's gravitational pull on the Earth is much larger than tl vfq0-8yygfb 3 :0exehe 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 t:q83f 0vy b0y-gxfeleo the other.]

Will an object weigh more at the equator or at the poles? What two xjg bfy* - yn9/xzj.-oeffects are at work? Do they oppose each other?9b y f-* gjy/on-xjxz.

The gravitational force on the Moon due to the Earth is o bzb.).u onojur(o )9d6uq o-rnly about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from r r.9dnubuq zo)6.ou ) boj(o-the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun 5*1nawybz ,csbhm,67jl a o 6xlarger or smaller than them76c6zbhb oxsw5,* n1aj,y la centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) tot;.) ih0q emhgward the west? Consider he0 )imt qg;.hthe Earth’s rotation direction.

When will your apparent weight be the greateso l zu24e jz6fp1qf4p05*uufut, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, 5 4uzf 0q2ep*zpfoju6lu f4 1u(d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be ad2, ), ugmwfh :dh6pb73wd;u/ dcpwsg5defp,mversely affected by weightlessness. One way to simulate gravity is to shape the spaceship 3p c;7dd,mbpg,s,)u6hudd 5 fh2wfgw/m wp:elike 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 weigh aouwq*ux4tpob 2; 9x/tlessness” betweeoo4w 9x *p2u/tbxa ;qun steps.

The Earth moves faster in its orbit around the Sun in c ox;a;h92q irJanuary than 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 o2iqcra ;;x9h 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 untilqlolilu0k1 x f(;k9l39 8d xspxf::nj it was discovered to have a moon. Explain how this discoverpl d lfk1;qxfi0s l:uo9 9xlnk:3j( x8y enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth i rh e. w+lkf4h5wq8en: dvft/(s much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]Aq+:h5.e he wndf8/r tvl( kfw4 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 19uopm+o*:5, lspnn z;p80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 8wfr5,x. ih*uyb(sosxtqq 6/ the Earth in its orbit around the Sun, and the net force exe5fq /rs,.sx*tq8b uoi6y hw(x rted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 21wszvr, ..u 2dxw e/hr,0 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of tuhswrzv rx/,. ew.d2, he discus.   

  Suppose the space shuttle is inxk gb zl gm8-x)aj681i5hc(eh orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in itsm ggaxjib51zh)6(-8ec l8 k hx orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitudew p74,e do-xog-ybi si .5oh.z of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions po-4 .g -xi.dohzyibe57 p ,oswer minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform ratej;u(7cl)tb6nyqrl y (02hw2ot t2 agr in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed i;t 6y( ty)t7wjqcnb 0o2rr 2 (lguh2las 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 rouo mu32:g1j7cgtbtb*y v7+u fknd 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 kt vubj2o+t c17f g m7uy:*3bgresult independent of the mass of the car?   

  How large must the coeff (k10juj)x5sk7q u l6sva zh-licient of static friction be between the tires and the road if a car is to 0xlq7z ( u lu 5)vjhsja1ks-6kround a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts aa ,bnwr,e2)z;,im n1z9j u niznd jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by t n,znujm)wni91,br;a e2i,z zhe trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of var(kz mzwc rn( 4p+d oj99v:zor,iable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coeffic(nzzk+ mr rw,9(jp9cozov4:d ient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling whenhgh 6ed. b34 q(qt,ghn upside down at the 4qged bg(h t,qnhh63.top of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounjqsc0 ( a1jsaont9 lr1 x3jn2+ded top of a hqt10+jol sr sj9 ann3x ja2c(1ill (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 )sfp5apl8b m:)pn(yvwould a 15-m-diameter Ferris wheel need to make for the pap:pvnp)m ) ybas8l(5fssengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of -dw;v(lno 4ol,4 gvssradius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.;,w -oo g(44lvlvsdns0 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 centn (tty,5 2zszwrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleratio5zsynt 2,w(tzn of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricallc4 weu6uv,af7 0m er7py walled "room.4 ec,pf6eu ruvma07w7 " (See 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 a circle on a frictionless air-hoc egsco+vl (qfu(3g f5byww(p/ lw*ftw 6 .e-6rkey tabletop, and i+g66c fw s5-wrlew (t /.(pgfueqw o(vf y*3lbs 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 , precispb1 qhwp,ey6y *g 8xh:ely this time, by not ignoring the weight of the ball which revolvqp8:61w g yeph*by, hxes on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car iv fv 84 gcvu,kc6./ob2huvz0traveling 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 fvq-vi , 7ggj3dmzdk2 u6+3tr$ 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 3h4u6c; f3mdt q10 $\mathrm{~m} / \mathrm{s}$ . 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 tangen5tm q5m0. w)u: 5vy)o wbw-s*nrwmuxotial and centripetal components of the net force exerted on thowm 0*wwxqm5-m:n tby u.)sv5w)r5 uoe car (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates unind 1n5 l+;uovg/cpwfzy: m: 4bformly 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 wer4gzl5v w :1m/:p co;y ufnd+bne 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 mu)u4o y4 7vv v1ghgsw99mmhn9 . At a particular instant, 1nv gyu 97g)9osv hhuwm4m 94vits 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 gravity on a sp *ignjzs6 hv/(acecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is /sij(6z *nvhg 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g hasm*rwn9 n)ia45m 4 gmpa a magnitude of 12 m/s p4mmrim ) *g5n4wa9na$^2$ 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 M8:gicqj 3d5m uoon. The Moon's radius is 1.74 uqdm3g i5jc :8$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the same *4bxm7e o8qq; (rpwolmass. What is the acceleration due to gravi ;4rqo8( pl wq7obex*mty near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same rbhr) aw s,+o 1o hpyq+hr(,ne5adius. What is g near o5 yhpb r heaq++,rwosn(1 ,)hits surface?   

  Two objects attract each other gravitationally with a force of 2.5stf) 25ova1qfreu .;w$ \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 gravmhs w g2p c-ac r:p7uq,)n,vw8q(.lb3rung+ gity, at (a) 3200 m -lp:gr q) .,bahm7, +qugnsp ( vc8gru n3wc2w   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s 8 c)i gvc2fln)center to a point outside the Earth where thegravitational accelerl)8cnv gf ic)2ation due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron staru;ub r:gvw00 t has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimatet;v0bgu :ru0 w the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Suqtsyt9eo p/0ei 4rn/ti,4k 6jn 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 surface graviqii0 tnky/ se, ptoer96jt4/4ty on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spacelu ew;lfxh7nhj f q(*b-zh460 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 acceleration of gravqnu;xhjfhfh( -l6bz 7w4*l 0eity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at thwgtea)oq p ,:93ry*k rdi,g ,fe corners of a square of side 0.60 m. Calculate the,*,i9, )ryd ogwpqte r:3kfag magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planetsu9+baa9hmkr li3q 61q:yln l/ line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupq mnh3a1 bluyqa9/:kr+ li9l6iter, 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 sdjqsxkxa9u7 /ysd:c ,l/ec6o1 g */cfurface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine thc g sac79,x/jfdsdl*o /kx1 quey6 /:ce mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using91rxfp ima:4 7u*xvptz2e6s*yb j)jo the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s jra91*24)emt x 67jo : izfp *uvxspbylaws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite movingf 0q) gpz8ozt 5l:.6tmtdyjd- in a stable circular orbit about the Earth at a heiq5 ztd08-g6t tdo:ymfjz) pl.ght of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orby4 0nrfu +o5m1pf 8dg2.1wm zcrv0evfit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the rey d0m 1 p45c mwgf f81novz+0evu.rf2rlease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience (k1;ytae xb1 rsimulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time neede1xaerk(y ; 1tbd for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth i l;bb*of/-i k bd*7wyon 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 radibo ;-l* 7dik/ f*wbobyus of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would.1x7cg t srgr* a satellite have to be launched from the top of Mt. Everest to be placed in a gr1.7cts rx* gcircular orbit around the Earth?   

  During an Apollo lunar l8cfm 5 z8eaez fk(62k7mju,imv *,dpt anding mission, the command module continued to orbit the Moon at an altitude of about , e6*tjzkv m2mzap8fkmu7 e, ci df85(100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn 75wdv4n)acq x are composed of chunks of ice that orbit the planet. The inner radiu)qcd v7 5wnx4as of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. 562v o xyvzq+6e–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and + xz 6yv2q6voe(b) at the bottom?
(a)    (b)   

  What is the apparent weight 0u* 3tya: st ef+jfcy)moah7 su,p,f:of a 75-kg astronaut 4200 km from the center of the Ea,p 0 astf su)3ac:*e:+ujyty, fho7fmrth's 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;q :ex3lk;;f*t1m-vwvnfqm rajk-8 b two stars of equal mass. They are observed to be separated byrfa-:1m;tbqvf vj3 8mlw q;xkk-;e * n 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for hu6l xkwn;q /,5z tl8pthe weight of a 55-kg woman in an elevator that mo5q h l/ulx8nkwzpt ,;6ves
(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 an elepm9nr5c v*;/t 9m wuasvator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s m9 w;mc/tvrapsu9*n 5 minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period + ;. tg* xqa9pbafpmv: T , the densx:pf m*p9;+t .avgaqb ity (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 of the Moon (27.4 d) to dbht(n)m,eaqs hb+ ,u ;u01dzyetermine the period of an artificial satellitemub uhaqz)sn,;ey+tdbh(0 ,1 orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lik d.dw1)n4c;qcr hwa(1xy8 hzbe the pdb ch8a).d (;xwc4 1 hryn1qwzlanets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance osw;i*nzh6.s4k yn9 dxf 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 oieux-m 4go 9hnet:c8)i.ian4nce 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 distance s in Kepler’s third law is half the sum of the nearest and farthest distance from t-ixmngueae:4 i8th4 no.) 9 iche Sun.]    $\times 10^6$

  Our Sun rotates about the cc(zf7y g0klzd,m,5g fb3o( bcjf (pw8enter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest atxe7;rorr 1f/h q;23o; qnr z*nd +cumoons of Jupiter (those discovered by Galileo in 1609).nr7/hrr; oc*+qx fd 23qz e1t;rauo;n
(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 disv5*bse x v/f9btance of the Moon. vsv 5/*9 fxbeb   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using K mnytz )/r 2vnbk:lfdonzwh4 m *62g6pc/8j2a epler’s third : ljd 46)/8 z*p2w6t2yn kmgf2nn ch/zbrvoamlaw. 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 many fb b.3ize6r7e bragments (which some space scientists think came from a planet that once orbitebei.e7b b3rz6d 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 the foh.qyk*y 4og:i bti- *2cr .grdrm 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 h4r: ggir..qb2- *ykotc iy*dthe 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 from a hanging vinesm* ys87 bct v5tuvk,- (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine,8bs-tt*ky ,vs5vc u7m what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface wvxve +):r) 83w zhcsys3 cyhe2ill the acceleration of gravity be half what it is on thecz se:+e)8wxy3syh 2) vrhcv 3 surface?    $\times 10^6$

  On an ice rink, two skaters of equal masnxi 6a * en+n3ub8zlq -0a8.m .dofnhgs grab hands and spin in a mutual circle once every 2.5 s. If we assume a.36nu 8e8 dznbli+0ganh.mn-qox*ftheir arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acce.01tu+ njhm vkleration of gravity at the equator is slightly less than it would be if the Earth didn’t rothn 0vm.tu j+1kate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a igk0o (ed2j w+spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Mo w2jd(eig+ko 0on pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you srr/e 58gz9mhjgi 11x7mmti z4tand on a bathroom scale in an elevator, it says your mass is 1/m rx5m9g gi 1ih84tzrz e7mj82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station con,5i-lqja q* ivj0lvw1sists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42) jvjqqa0vl*iw -5,i1l . The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircrafhx7 y07 -lcgrlt in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in hms5mshp1)kmg9da5+h)+kvc terms of its radius r, the acceleration due to gravity at its surf9d ks5)gksmv1)+5hm c mh +pahace and the gravitational constant G.

A plumb bob (a mass m hang 1yqtyh tf-.o9ing on a string) is deflected from the vertical by an angle -f.y1t yht 9oq$\theta$ 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 desiiv i7rjv9 +5 kqm+ytvoo w2i ynh- 17143inzewgn speed of If the coefficient of static friction is 0.30 (wet pavement), viin 1957+v-z7kye2vi qy+miw tjrohn43ow1 at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so f 3rs5s5iq+mmi ast that objects at the equatorrms 5 5misqi3+ were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance gn 7)s,k0qcukapart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp suuuq wwv 3h:0 .-cg/jenspendegnhq w c.3-wjve :uu0/d from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimek0l4kz-v9p: ni7zhh )e-nz ubd 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 a0-kp hhkeizvbn:u4l z-z9) n7 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 aya; -knkqyb 6r/-te; sq;c:c,cie yu *n extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this-,qy na:itu y6ec ;;scy*b kk -;creq/ 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 uf,g o9ucqodx v-8u :5valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can:odfquvog9- ,5uu8cx the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satdm++8w+nk6ay+gla12 ubaul vellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver ou+ +awn+ 8 + 1alaudgl6byk2mvn 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 Rendez 5xdj3s5uilyssr2 (g(vous (NEAR), after traveling 2.1 billion km, is meant sjyu2(s d5ls (i 35xrgto 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 space shuttle pursuing a satellite in need byc-oay18 7)ihvi2x2luv/uzb - ku5a of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km lb 8v7bvco5yhx k -yzia2u2i/ )1a-uubehind 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 peri apso 6pkdyyr2b+4vil m8,.+iod of 3000 years. (a) What is its mean distance from the Suni,s8 d+2a kym.io4p plby6+rv?   
(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 yojbmpy(g3nc .0w4gc: zu could actually "feel" yourself gravitationally attracted to someone nearz4yg: mg wj.0pbccn3( you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around thp:-jx)gphy d( q5r cq6e center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from tcq(qdjgx6 hpr y-:p5 )he center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses ar (9qmep, zzsv9e located at the 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 9zqpzs (ev ,9mof the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5edrz. vh f75wollm+o+k+x- 2p500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long swe wssk27:mx8orc-ze. qep second hand on your wrist watwcxerm kzs-2.:8s oq7 ch?    $\times 10^{-4}$

  While fishing, you g7 g 0sfl.jc1xqet bored and start 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 circl1 j7lsxfq0c .ge 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 h6j * h,d/ectghighway is designed so that a car traveling 6 h/ghd t*cej,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 emj j2l2rv p)r(tk3:bof 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 r2v:tk (2mj jr)eblp3 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.$\approx$    $\times 10^2$