Sometimes people say that water is removed from clothes in a spin dryer, lotj..phej.m1wl+x by centrifugal force throwing the water outj ep.+mw1xlljt,h o..ward. What is wrong with this statement?

Will the acceleration of a car be the same whcwdc*l41v w+ ben the car travels around a sharp curve at a constant 60 km/h as when it travels around wd+1wc v*4cbl a gentle curve at the same speed? Explain.

Suppose a car moves at consta)vq *hdzmrx -,nt speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a -hvqr z*dm),x hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a 7feib./k( vz y8do6 f2(qdqd hhorse on a merry-go-round. Which of these forces provides the centripetal acc d6o bzqi2(hyd8v7(ffe/dq .keleration of the child?

A bucket of water can be whirled in a vertical circle with++o;p b)npe*sd2xpg fout the water spilling out, even at the top of the circle when the bucket is *oeb f +spx+g2d)ppn;upside down. Explain.

How many “accelerators” do you have in your ca;6fi tch: tut+r? There are at least three controls in the car which can be us: tu6fchtt +;ied to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of dn9:e)g lxg +zsrv/pz*/n4oejr 0q;ya 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’s secondys9lg:nzxe/rez;*nq4+vr0j o) gd /p law.

Why do bicycle riders lean inward when rou-(i.n93dn 7x ij l hrsrkz)zn4nding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle g*fw ud-ubt3.9n qw 3zgiven its speed and radius of the tuu n9d-3 bz*gwf.3ut wqrn?

A girl is whirling a ball orjgs.r7s7akw p/ f57 sn a string around her head in a horizontal plane. She wants to let go at p s7kpg. jfrw/a77r5 ssrecisely the right time so that 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 gc l-bf 5 ut/g*r5q.kp t/u(magravitational force on the Earth? If so, how large a force? Consideqta up5g.- /mtfg(5b*r/u cklr an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is,t;3csw2eew ;0sbuf8n in what ways would the Moon’s orbit be diffe e t2ucsw 3wfn0e8;s;brent?

Which pulls harder gravitationally, the Earth:n6vt k;e lif8 on the Moon, or the Moon on the Ea; l8tnek if:6vrth? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. dq 1z.l0gvb) ;p*fzceYet the Moon's is mainly respons1 e.;l0gbd * zfzvcq)pible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh moregzn8xk/u *2z u at the equator or at the poles? What two effects are at work? Do thzu/k2n zg8*uxey oppose each other?

The gravitational force on the Moon due to the Earth is only about half the forc f:twy l+n1cd,m *g)i4dm v/pke on the Moon due t 4t y:dwnmfvl1d+ikc ,*mp/)go the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun lar0q4y 7;i34cy lh og1x5 nputkyger or smaller than the centripetal acceleration of the Ear4lc;y q3 t goyhx5ki14u7p n0yth?

Would it require less speed to:; *xewk+9a b 3;u gfrdlqrv,e launch a satellite (a) toward the east or (b) toward the a:e,+r kgb fxdwul*9rv;;qe 3west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatkpp 9z1 rcv81k..nrk xest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the x1pc8.9r zkkn1r.pk vground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be advtlk- 6jp+w f+zlm7e)qersely 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, anep+mfl6t7w)ql -+kj zd (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessn. 7:mqser +(oav7tw s*knbaq (ess” between stepq.*bro+:(swan7s(tqk7 mvea s.

The Earth moves faster in its orbit arol;3s6olrbax:e a7d1 f o2jmf5ryk n6:und the Sun in January 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 the seasons — the main factor is the tilt of the or1 ::lndjfb s276;a r 5lfaxekyo63mEarth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was 6k p-xjma3;p j- t(.uyeiwuv.discovered to have a moon. Explain how this disc3-(pu;yp.j .vu k6a-m tewjxiovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's.o 4aq 2mtsa2w2+qwk obz 947vq Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one mo4wqs w9o7a2bktq+ vz 22qa4 side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 198v 2g04 msejpt40 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 0gkplc p4cw/:2asl -k.;mb pv**+ qhi4pdnk bin 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 p0.pib *- cmwd+nk4:hkpa bc/* g;lpklq s 2v4of 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 rot cxx be4wx4,bozryx )*0m/u6uates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of theu0eu zb4c4,xm xx *oy6w/b)xr discus.   

  Suppose the space shuttle is in orbit 400 km fro3 d1dv4zu b;,csgsueyy5 8o k5m the Earth's surface, and circles the Earth about on1kuosu cb;8 ,e3z sgy5ddv45yce every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of a p8lxhq4 w .ba1iotter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is bhx4. la1 q8iw32 cm?   

  A ball on the end of a string is revolved at a uniform .p(+7rzzrcg 1 op0 vvbr4df-drate in a vertical circle of radius 72.0 cm , as shown g1v (rz0b.rfdpdvor p 7z4 +c-in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of radius 7 4rlen)prmy *:7 m on a flat road if the coefficient of static friction between tires an*rnl:)erp ym4 d road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires an)fu 6/fbcn*gb(f llxna 2vc, *d the road if a car is to round a level curve of n*)* 6xnc uv2g/lafb( lfcbf,radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilo2b pwni 1(.gk3 0+gy;usmb6oy yzp0nd ts 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 times her own weight, how fn m.y zgn(bpyu 020ki wb3o6y+g;s 1pdast 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 rotat*7gzlmyvb-l+5klo( h g:ce q 8ing turntable of variable speed. When the speed of the turntable is slowly increased, the coi5beo:kc+ mglq*ly hvg8z- 7(ln remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at theci4 -mx t5rdc+ top of a ci4dxt5r ccm+-i rcle
(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 thj+xezd:+h o;eh jp; h1e driver) crosses the rounded top eh :z1jdjh+ hp;+;x oeof a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need toj wl(-z;ombb2 make for the passengers jo-l (b;z2bwmto feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cia4 xixuj dh6ls45a.5urcle of radius 1.10 m. At the lowest point of i 5a.hx 4i4x5ja6 dsuluts motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a cen5wf .r g 5ylcdw:x;js:trifuge rotate if a particle 9.00 cm from the axis of rotation d: srwj.;fgx5l5 wc:yis to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, pio 4zk0o;9iqdi 5-op:m 6kccj eople are rotated in a cylindrically walled "room." (See Fig. 5-35.)6i5o-okidk4 ; :moi 9jzpcc0q
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;wl((b 0 hgwjs:cfek o;tm:6g5h2ips air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m )lwi2o skp hg;j6:( sf5:(cm0e gb;wth 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 txhvbp09v. 4uv his time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find thev uv 9xhpb.4v0 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 6o5rc wh2 ebbfa3*ub 5traveling 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 n0ctk+ c f-ps;i8g 1l2th2vwt $ 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 maneuve:agg ogz8(tg2nfr/d :d *hev88 ztps*ru* w 1ir 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 centl3+hbngwj.5 pfx6 r8s ripetal components of the net force exerted on the car (by the ground) in E83g+fjx6w5 .npsh blrxample 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pitrt :pes;*1hu o area, going from rest to 320km/h in a semiero *h: usp1t;circular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular i 9n3lnrpt5 jly1-n6gznstant, its accet1 g6r9l nplj5 z-ny3nleration 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 spaceo rx6y5t uu p3,ls6u6j)j9kuc craft 12,800 km (2 Earth radii) above the Earth’s surfax tu3 6ljk5r,ouy 66s p9)jcuuce if its mass is 1350 kg.   

  At the surface of a certain planet, the gra80 /bqlyvcv :jvitational acceleration g has a magnit0:cv/ vlbqj8yude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. 8d-tr ioez 1-(wj.yfbu de2y: The Moon's radius is 1.74 y-.y e :b(f-1eo2zwi8uddt r j$\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 o:yqk 1m. (g iq0j/ ;ti)v/ ngb9orcoyjf Earth, but has the same mass. What is the acceleration due to gravity nea )g 1 qn/.jgc mtk; bo(:vqij90yry/ior its surface?   

  A hypothetical planet has a q5mduplh/fm,fd9(.y:( ulfi)w * az hmass 1.66 times that of Earth, but the same radius. What is g near m ayd (f(,uzhhm9lpu5: dfiw*. q/fl)its surface?   

  Two objects attract each other v:nsju833fragxv 2x9 / oux s6,rem+ngravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, a+2kwsw87 e. ijo ds0mqt (a) 3200 m sk .wowd m i7e28jqs0+   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Epv -nkdz(:fm5arth’s center to a point outside the Earth where thegravitk5- mnfzpd( v:ational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the (ck uvy/-m 9jms8*ritmass of our Sun packed into a sphere about 10 km in radius. Estimate the surfa*/tiyk9r(uc -v8mmj sce gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whic)v1ore32n + ajtqasajx s1 +9gh once was an average star like our Sun but is now ij 1eaajt n s 3)++ox1srq29vagn the last stage 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 fe8)5qyc1cztm0 phh8ps,s *xobqw b*; a el weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker 1 *bm)syq z5 h8qpbxs0*8;ct hoc ,pawup 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 ajc ;y,7,z1 qtsb 02zn8px hiwuqn- .nht the corners of a square of side 0.60 m. Calculate the magnitude and directionb72i8us0xnpwjt .- znhq;hcn1 q,, zy 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 planets line a) s,i 1. ewz*9rhmc:j bwtel7up on the same side of the Sun. Calculate the total force on thji m1ae)lst w rwh7z. ,9*ecb: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 surfa52bpwow++ bm pzp2-3y tk+ual ce of Mars is 0.38 of what it is on Earth, anp++ywzbp3w25m b2okt au-p+ld that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using th1de)c im7b 9dpe known value for the period of the Earth and its distance from the Sun. [Note: Compare your a1ip cd 7md)9benswer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellitwrkkb rq7b p6pf53 sxaq::84oe moving in a stable circular orbit about the Earth qopra8fbx:qsw kk:r7p b5463 at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular1 *1a vpg3gehd orbit 650 km above the Earth. How fast must the shuttle be moving (relative gevd1*hg3 p1ato Earth) when the release occurs?    $\times 10^3$

  At what rate must a xx)*.k7kyilp cylindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–3y.i lx*x7k pk)2.)   

  Determine the time it takes flyb8v1h7/tw f or a satellite to orbit 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 radius of the Earth. Does your result ftw v8bh/l1 7ydepend on the mass of the satellite?    s ~    min

  At what horizontal velocity w4 hr 1,8*y22 vu8znwoydfooi lould a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around4y1*h y2o 2,fo 8zw 8luirdnov the Earth?   

  During an Apollo lunar landing mi4fi t/*usjgppt *x05s ssion, the command module continued to orbit the Moopj*xt0puss/ i*g5ft 4n at 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 tlkk-r;;w8c;sj) *7rv d pplhvjb3kk .hat orbit the planet. The inner radius of the rings is 73 vv; ;kb-cldkwhsrpj.rj7p8k )*k;l 3,000 $\mathrm{~km}$ , 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 eversts oh* c/-jzj. ,vl8ey 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a z*eo s ,/jjvct8hs.-l) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg ast6, bi42kxqe 0u9wbsmbronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant veloc bq2b6esw ,x94k umib0ity,     ----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 equal mass. They are 8)ish(8+b r ovomxy13he)e8nx,ym md*nwev4observed to be separated by 360 milliononmemn)4e b(dysvy x1o8* 8r,+83hhi)we xmv km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator th cnr:ecfbk*/4at movr be/4nfc: kc*es
(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 ce;z3 -k sowm*ksqyqz;)iling of an elevator. The cord caq wmq skz oy3z*s;-;)kn withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near theao zk-zk:b ,t xum+0b7 surface of a planet with period T , t ztb +:k mbz7auk0-o,xhe density (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 Moowjw fbg/z (r(-wm l2h.n (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surfaceww/b2 hgr f-mwjzl.(( .    s

  The asteroid Icarus, though only a few hundred meters across, orbits um*(iq. ) da(1aqkhao the Sun like the planets. Its period is 410 d. What is it)a uimd1q(oqhka* .(a s mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagzktrq :9h-(73r hcir8w j8lk7vgo:o fe 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 cljv*k hqsb l-ldy rs97g ru f52*65i2px ,z6zlyose 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? *ki69bvxl6uy s5lz2d7 fryg2*-, rq5zhp jlsWhat planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gadjqp-pef m17,8zp .cklaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, pe h)mj .osfcs,, mdkk4 ;tx8j (*rcm/aoriod, and mean distance for the four largest moons of Jupiter (those dixrsaho*m,4/)k k. jo,ct8mdm j ( f;csscovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the 23 jhwge-nth -Earth from the known period and distance of the Moon. 2wtng eh-3j- h   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moooo y c1).jye js/m-hxloq t1*0;qz4ms ns, using Kepler’s third law. Use the distance of Io and the periods given in Table 5/y.-;o0m4 e xh ssmqc l1*jqzo1j)yot–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 3q,s1 n;.ktlzxdv k6aconsists of many fragments (which some space scientists thin3;d xq 6l,k svt1nzk.ak 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 seeg0s(xt ;(n "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Su e(sns (0texg;n 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 gorge by swinging in an a.doz4ul iaz50rc 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 maz i 05u4lzd.oaximum 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 suoacr)vz*u,wr(t d k;+y u7+z irface will the acceleration of gravity be half what it is o;ykoar)zwz(+7c u* ,uitr+ dv n the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and*85pb ):crlapd2 ul it+kpvh; spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual m* :rd52p 8kvlahip ;+ct lpbu)asses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration 1)gvrlc e 0uo6 z/sa8/reihr729 urbtof 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 r 9sre t/obu8 i /ez)gar7vurh2l 6c01of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travp/ hi+aneghjtt3s9o 1m q1f0cov;/ x5eling directly from the Earth to the Moon experience zero net force because the Earth and Moon p tegc9mfo;o njqat 1v 0/ +1hxshpi/53ull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an uoqzb)g+t p19nj nj*6elevator, it says your mass is 826 b1pzjq*9)n+ togunj kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube t jp; *tf:og:izhat will rotate about its center (like a tubuit:goz*jf :; plar 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 of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–1halirx+ 1qars) 6r 7pcork4/43).
(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 radius r, 32gr7 x4r cyxe 97amucthe acceleration due to gravity at its surface and the 23 cxugm7rc47re ay9xgravitational constant G.

A plumb bob (a mass m hanging on rwx*kl7u- 9m1saey f ,a string) is deflected from the vertical by an angl17wf*-sxa9,e r ukm lye $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coeffic) ryukt+8z ojmpp7r 22ient of static friction is 0.30 (wet pavement), at what range of speeds can a car safelyt7po2zryumpk2r j )8+ handle the curve?

  How long would a day be if the Earth were rotating so fast thas6jjc2diiwa::z 1u 5+,ywj h0l e ;rlxt objects at the equator were apparently weightless?du:+ h1xcwyj2 z,0 l ;wl:6jsiejai r5    $\times 10^3$s

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

  A train traveling at a constant speed rounds a curve of radius 235 z5o;+b ka jzs+tp)of kck8(o1m. A lamp suspended f(tsz 5o1o +b)o8 azpkk+;k jcfrom 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 cz*.zv+ m qjzs9laimed 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. Calcu*z +s.z zqv9jmlate 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 ex-;dyx3m z3scj 6znjt+ tremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no+cdn tjx3mj 36yz;s -z 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 d s9v;x6lmi ibp(vd6m: ).r anvalley 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 heaviess;xd9r 6im) (lip dm. av:6vnbt? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 o,2 f4m l(ncl2 aq 8wwnkdl7-xsatellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiv(ow q 2d7-lkncwm , 4a8lnf2xler 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 traveling 2.1 billion km, 8u4 -lq 93nazx4tlf. t ee)ec6iq9xzt is meant to orbit the asteroid Eros at a hei t8)9ct 4ez.6aleqxixet-9 l uqzfn34ght 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 thpnq zn,lej; xb4:p)j2wfo u y/0 .xq6ve space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km . opb xln2 :xqp/0 jvueqwz,jf);y 64nbehind 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 ye5c. nj.gw1nl tars. (a) What is its mean distance fromncnj.. 51gt lw the 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 wouldynz*0 fnxnhbx t b3b/(,ub1nc u/p.,m need to be if you could actually "feel" yourself gravitationally at(*tnun ,p hc 0fnbxbmb/uz.,by3 /1nxtracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milkbttxf5ij o*a 2godda/p4 2:c9y Way Galaxy (Fig. 5-46) at a distan4 aog 2 t2xbj:fcd5*d/9 aoptice of about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a s 2f/a1f7;- k+akzcfv z1kp2vrwzkhy 9 quare 0.50 m on each side. Find the magnitude and direction of the gz+2z1a/hkr 9 f vk2fwfpay;7z1kvc -kravitational 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 kg orbits the Earthobhn /-kym*e: $ \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-lobzhr2rum)hg/w w * z97ng sweep second hand on your wrist watc/ m2)zrwur *7zw hgh9bh?    $\times 10^{-4}$

  While fishing, you get bored and .)uh+ gtv lkn7start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishinlvn)k7+. tugh g 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 :yxrd f .6qpg4a car traveling at speed 4 6frdygq:p.x $ 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 the.btgqi-j n ).vhh1kt n05o +b 7etpg4e 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 ab tj1+vnnhot4g5g 7 .tqh ik 0)-epbe.gainst 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 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.$\approx$    $\times 10^2$