Sometimes people say th gk1guwxvo jq:*k-j*ve 6 z3b,at water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wron g,uvzeg*jb *6x 31kqvwk-j:og with this statement?

Will the acceleration of a ca)xwu,v3k0d+c 7a-odnlojfm4r be the same 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 speed7-acldfovuwd)m ,+ kn ox0j 43? Explain.

Suppose a car moves at constant speed along a hil6 sw:z ceb ; oq b1dgd25oe,+jcg40njfly road. Where does the car exert the greatest and leastedj61 ,nw4q se +20zoc;: obg5cgbdfj forces on the road: (a) at the top of a 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 horse on a mbcu5. fl, xtosb/ :6iferry-go-round. Which .istfuo,5xb6:b /lfcof these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withoutr ba.a; whe151yrmkfl,o9k8l the water spilling out, even at the top of the circle when the bucket is upside down. Ew,helr1r a ao5 f;1l9bm.k 8ykxplain.

How many “accelerators” do you have in your car? There are at lma7sb ltve6/qv0**m.7g3 j/dw+th tg - suqvaeast three controls in the car which can be used to cause the car to acsa73-.t/t0gve m mq*u6+vbq 7h *tvdgls/w jacelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest ofh y+hteb:z:k5ukqo3 * a small hill, as shown in Fig. 5–31. Hi3y+ t*khohz ek:bq5: us 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 second law.

Why do bicycle riders lean inward when r(c gh/(oa2 mfp*z/ xuzounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankq evs/)mo0 2myer3v k+ing angle given its speeeykso2+ mm r0v/vq3e) d and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal pcv6a/,d w2 oaea/ ,0 pqyt*xizlane. She wants to let go at precisely the right time so that the b6t0zdai2o/ /*y,wex,pav c qa all 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 odiy 0m/ gjs tatg0iirw88 1m06n the Earth? If so, how large a force? Consider an applew18y as0jmmid0i0 gr 6ti8 gt/
(a) attached to a tree, and (b) falling.

If the Earth’s mass were dl djq* pfsb+*e byuh:;w6:h0youble what it is, in what ways would the Moon’s orbit be difqh6dbjewl+;fb0us:* * py: hy ferent?

Which pulls harder gravitational prq /;o,g-8o:admjez ly, the Earth on the Moon, or the Moon on the Earez,mp:qooj- r/g 8 ;adth? Which accelerates more?

The Sun's gravitational pull only4l tlklhp.j62w z)r ,( bj+t the Earth is much larger than the Moon's. Yet the Moon's is mainly responsibl)( llkp+2,hl yjzrb . w6tlj4te for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equsvyh(/5nbjq /ator or at the poles? What two effects are at work/s5(j y/vhbqn? Do they oppose each other?

The gravitational force on the Moon due to thegee*d e.;,j sd Earth is only about half the force on the Moon dued*es ;.e g,jde to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acvpt,j,w y/y ek65s-jzceleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Ew-yje pzsvtyk 6,5/,j arth?

Would it require leslnm2m:32 iadh s speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Eara2 l 3n:idm2mhth’s rotation direction.

When will your apparent weight + jppm/ (f(k ml9satx*be the greatest, 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 les(kl+pjx9 tf*p / amm(ast? 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 couldeoz6 i3.9 w;nc1kpkru be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship k 9kne.31;pc uizow6rlike 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 weightlessnl tucyld 205ssj otv:04k( dw*0rhkj+ ess” betweent *doruh l(0y5wds cj0k kl+t: v0s2j4 steps.

The Earth moves faster in its orbit arom;95qe5 ezmjrgxi 5 k/und the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This r mgm5zkjq9ex/; 5ei5is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moonw6s yr7twe s,-. Explain how this discovery enabrswst-, y 6w7eled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much largeiq+ p;m*:a obfr than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one sbmq+: pfi*a o;ide 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 traveling5) n-xss nsy8h 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit aqww1qs cb1 j1:round the Sun, and the net forcej11s1qbw :wq c exerted 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 210 N is exerted on a 2.0-kg discus a()j/bq c 2eqwps it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate t q/ejb (2)cqpwhe speed of the discus.   

  Suppose the space shuttle is in orbi*x lehcdhjxltv84.p hq:(+v :t 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shxv jcv tl(h:p .+e 4xq8h*l:dhuttle 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 u3h wxb45ryrypu* o/)edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel4 bo)uph yx5*r3u/r wy’s diameter is 32 cm?   

  A ball on the end of a dtal 0k+r6mvk97o:,rjm)m v i wd8pk1 string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spee6: k9 wdvo j,ld)1a0tp krvmmi87mkr+d 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 1lw23gk zsj *p+050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is thz g3p*2wlks +jis result independent of the mass of the car?   

  How large must the coefficient of static fricu+-h dc. xo(fation be between the tires and the road ifh d(fux-ac.+o a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate a 8xuj/dlm 6d(oe0/ dnkcc b0l) 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 weig )e/c60j m(d0kn8uld/ocx dbl ht, 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 a2cw*p6w ckxn6 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 coin slides off. What is the coefficient of 2cnp cxw*6kw6static friction between the coin and the turntable?   

  At what minimum speefd,.f.n0yt f*h. tud:.x psoe d must a roller coaster be traveling when upside down at the topf.ny :ht0pudx.d.f.t *e ,fos 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 of2y 4flhp 5kqz1e h d6x)d+rd ya1.lw9e mass 950 kg (including the driver) crosses the rounded top of a hill (radi.621zek y) xfd1rw qldhp45y+ hlead9us =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 nee35 hi1gktlc0),oo7 kcjj n6xtd to make for the passengers to feel “weightless” at 3,cjng tchjtlk5 07)ik61oox the topmost point?    rpm

  A bucket of mass 2.00ug/-mwxy;at3 kg is whirled in a vertical circle of radius 1.10 m. At thetxyg 3u;w-/a m lowest point of its 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) mubxbwh)9tbnv z:p41 (v st a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to 4pb) 1wvx vz(b n:th9bexperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rot6tri8a s aui5dl4 8o1gated in a cylindrically walled "room.a d1ra s6l8gi54to8iu " (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 circlae7k(0dyy 2 hxe on a frictionless air-hockey tabletop, and is held in this orbit 7eh20x ak(d yyby a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoringj :( pyph /s2cbfm) ecr)x1bs1 the weight of the ball which revolves on a string 0.600 m long. js 2(hp) yesx/:11)rbbpcc fm 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 perfec9,ey0ttreg-r.apl )( e+ j ypar6 lx8itly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses 3wt - nm.ho3hp$ 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 310kmkyu8 o9ge mn/g0;o 0 $\mathrm{~m} / \mathrm{s}$ . 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 centr6ka;eif hcj4)7ns:o tipetal components of the net force exerted on the car (by the ground) ;chfo6e:ikn4ajt7 s )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 uniformly from the pit area, going vy xsrw 7x k1ov9yh07e z z2-w:hp9/ilfrom rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial accel0ex zvih yp wz9/27 -srwko1lv x:9yh7eration 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 horizontajtoeetb5( c;aimby/3+ vx9 mlq:2 i 2dl circle of radius 2.90 m . At a particular instant, i;3j9e/it dq c:o5mtx2abl (ym2ve i+bts 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 spacecraft 12,800 km (2 Earth ratumx/4 msu qo,zimq 4.3k;;yjdii) above the Earth’s surface if its 4jmz3./,xm tuums qkioq;y; 4mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magnr-o2i9(k uzome m7 ze*kc k2d3itude of 12( 3eo2 kmmr7k ko2c9i*-udzze m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon'smqphf -a 034ty 2y-kxy-u tp7y radius is 1.74-2fy pkt0-xy h- 4qtumayp3y7 $\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, buul1;vk 6z.h dxt has the same mass. What is the acceleration due to gravity near its surfacxv16z;h. k lude?   

  A hypothetical planet has a mass 1.66 times that of d;6v d57 ckpyss* ;fjg78l wwdEarth, but the same radius. What is g near its surfac5pdsvl ;sd7jw f g ky7*8dcw;6e?   

  Two objects attract each othe4hhd jj2uge9 7)vtk4 oun*ol, r gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceq yw1 uj6r 66lg(xa4bm9u xnq1leration of gravity, at (a) 3200 mq1 u9j(x 6u1 q ywlaxr6n4b6mg    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center tozy we9olm ,1xo igvq.9g ::x1z a point outside the Earth where thegravitational acceleration due to the Earth isgzm wx :vg,:1 o99z1oyxi. eql $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphere aoa :v p8hqia/nalt8://-are ubout 10 km in radius. Estimate the surface gravi 8n:oa hu/ilq/p t-ava/: a8rety on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our S 0ke+za /l14s:y*rycrxc kuw; n f*.xoun 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 surra+ z: on;k .x 1wlcsef *ykrx4/cuy0*face gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while ot t1sf *kv hv8wu yjt8n36soim658ywg*p 7zj3rbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calcum ts6y8zug7w53th 8fw 1sv68jkjntp3* o*iyvlating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are lghg1r*bqjcv 2 -u .uu7(ee+llocated at the corners of a square of side 0.60 m. Calcujr-lgb7l+uq (ueucg.21* hvelate the 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 dqaq5o-2 v2sa0mvo y3 the planets line up on the same side of the Sun. Calculate tyqamq-v o 503vs2ad o2he total force on the 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 avvs ps3ukq es/gy-q40 5fw5:kt the surface of Mars is 0.38 of what it is on Earth, and that Mars’ rapq: fkksy3v 0veqw5s5-gsu/ 4dius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the iiu5;l8p5ibb /, v1 nsn/qcls known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Exampllp/vi5 nc isb5si/l ; ,nuqb18e 5–16.]    $\times 10^{30}$

  Calculate the speed of a sa6ox9 lf8i jwf9*4zwvy 9x( jfhtellite moving in a stable circular orbit about the Earth at a heigh 9ij(l9h fv6fx8f w9yw*xzjo4t of 3600 km.    $\times 10^3$

  The space shuttle releases a satellitlx o.g dfak/*kl11z h*e into a circular orbit 650 km above the Earth. How fast * x1kl*o1h dfz.glk a/must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical /b 1 e9adrnxqs5ya2- fspaceship rotate if occupants are to experience syb1/f na5-easdx q92r imulated 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 5–32.)   

  Determine the time itkl38a7aroj- p takes for 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 depend on the mass of the sa- kj3 raalo8p7tellite?    s ~    min

  At what horizontal velocity would a satyie3-i ob t bt,5n,vbf m,p3f+a1or;jellite have to be launched from the top of Mt. Everest to be placed in a circular orbit aro,bf pt+3rmoyii n 5ea;1vf3-tjob,b,und the Earth?   

  During an Apollo lunar landing mission, the com bujm g(e.2iccgl2 v;pg*q73tmand module continued to orbit the Moon at an altitude of about 100 km. How long dg( g2u7*23.ibjeqp mt l vg;ccid it take to go around the Moon once?    s

  The rings of Saturn a74* uk-7vrbcl.jignoja4 h*ere composed of chunks of ice that orbit the planet. The inneoc 7jr7 *.u4*hl- gkjai4nvber radius 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. 5–ip2- jqbr 2m:i9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) atb2-m q rj2:pii the bottom?
(a)    (b)   

  What is the apparent weight of a 75-k6-kn v.ugt9su g astronaut 4200 km from the center of the Eartuu9k6g -.nstvh'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 q+dk+d8 q8)trrly 0lzo:wbr4sn63edconsists of two stars of equal mass. They are observed to be sepae0dyd:4 k +olq3n)ltq sr6r 8r+z8wdbrated by 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 the weight of a 55-kg woman in an elevator q) udw,6w+b0yldx uc1that moves u+ lxd wu)0c,b1 6wyqd
(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 elevator.g+jc5 +h tau9/fw. n.pczhkx91feyf 0 The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleratiojpf0w +xh/g 5u9ycnaf 1 fzke9t..c+hn (magnitude and direction)? a =   

Show that if a satellite orbits very near th qnqi-tnzqc4. -8 ia7ze surface of a planet with period T , the densityiicz7.q -4ntq qz8- an (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 (e17lx0 s/rzzoi, cl5xu )2qrz; ct/bg 27.4 d) to determine the period of an artificial satellite orbitsz/)/7e 5b2xzlgur, z;xrcotilq c01ing very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters a+at.l ks2twn7cross, orbits the Sun lik kt+w2a.t7slne the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ofj2 2llpaq. 8et 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 orbit ; m5mi2qvtix0s the Sun roughly once 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 m mxqvt25i;0imean 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 Ga zg0 t6cc)-thmlaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 ll39v*g9-x)mv58,rjidddjc lpno 3t largest moons of Jupiter (those discovered g8vl)dld ,3d vp-ict n jm5939xlr*joby Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known d.x1z+ndiw6)o4f+b r wkg0puperiod and distance of the Moon. fw b dk+u)r46od.n0g+pixw z 1   $\times 10^{24}$

  Determine the mean distance from Jupiter for 0puva o +g)h0, y+spyuqm yj/9l -shm8each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and yp yugs h)u,myqv+8a/90l0psm -oj h+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 an,udpyki-i63 /cg1x 4 rmbiji 7d Jupiter consists of many fragments (which some space scientists think came from4r3ixj-bud,kg6m y1i p7i /ic 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 artifihs0d2fjj39 tf+j 4ot yr+ ;wqzcial "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 dista jwt2s; ot0h+dr 4j3ffj9zqy+nce 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 gorge by swinging in an arc fiep8n8k5b 9x)7av. ;jqvid6 k ol frk3rom a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing?r ;q5a9.87l 8xp)b fdkjvk3oii6en vk His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity b8wqofn 0f) ho6e half what it is on thff8 )w6 0onohqe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circ xj:dmr.se8xji .e.ead, 0g g4le once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hajm.e4sd.e:a0dri 8x .egj,xgrd are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, thd7 pf3/(yvzfve apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate./fz vpf3y( 7vd Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the ;5qa)uflp;-h j ri 4h +dhir7aEarth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the E i;a ha)phi-l dujq4hf;75r+ rarth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale i g-h2u 5fc-) t)eaohnyn an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which u--))ync e fh ah2og5tdirection?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate abo gl1nnz+uj2 ;,unm4wo ut its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the 1wgo z+jm,n;u n2nlu4tube 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 in8aij, aar :hek40dmd6 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 t,s: ymy,y/wcin terms of its radius r, the acceleration due to gravity at its surface and the gravitatios,mcy:t w/, yynal constant G.

A plumb bob (a mass m hanging on a string) is deflecte3rxwd j/x +z.bd from the vertical by an angl j.dr x/w3zb+xe $\theta$ 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 bad 8p9vxp 7w7oynked for a design speed of If the coefficient of static friction is 0.30 (weyopw 978 vxp7dt pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Eart0q 6bf /c (w6u.mqmheth were rotating so fast that objects at the equator were apptm6 6 q0./eh fqu(mbwcarently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8, hj)l.nbd 8id.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 avev+e2fr- 5 ab3fur(q curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.5e2a(be- furrvf+35v q$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claik3 94p 0muj7z l0f80bxb 6lymo lf6azimed that a person would be crushed byjp 078fb flxm09kmza63bl0i 6z4y ulo the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. 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 Telescopegaq79dtx 3gttt64, t s deduced the presence of an 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 by measuring the speed of gas clouds orbiting the core qst 3tg6xd,tgtt74a9 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 valley showbj*+yl ,m .:yph-x,w bnuw nm:n 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. wm*n.,b,l:p:hyxy -+nu wbj m(b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a .39xf ow;syspen gg77group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, 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 satellitpx . 9fs77ew; syggon3e.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendez -2v:/nugwofp)d 4nvxvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros uo)4 v :n/vgx2f pnd-wis 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 saten yq6tqd/7m g2llite in need of repair. You are in a circular orbit of the same radius as the satellite (400 k qq2 my7/6tngdm 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) Whmmoto0s 8j,boh xv50,c*7 dvl at is its mean distance from the Sun?j5lb7s 80vm,xmo*0 ocd, hv to   
(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 nee 2tn qruvcu6qn6o v7+(d to be if you could actually "feel" yourself gravitationally attracted tc6o 2+rvvuq7nq( tn6uo someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way7 dzvzy rlp:s 2.a :l8/luk+yt Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the centeryrp:z.2 ltv :+ ulzy/sdk8 al7 $ \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 l h/ t *)v2evz33bqmanqvp1 0ptocated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force qt1avm )v02*/3nbh p tqpv3ezon 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 o8) k,txa3ftvx+w hs ;grbits 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 thn3/+9rmdflw(b/f ydp e tip of the 1.5-cm-long sweep second hand ol fy//n rbd+wm(d3f p9n your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sink/ffc(4jmy8 fbs hsp7)er weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circles sf7/f4)mpyhbf(j8c 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 -o;at l6pi 0 ,9vzx u o)iot6/zw/fuwois designed so that a car traveling at spe w;ouzoui i)/x9oattwo,0 6p6fz lv-/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 train, the Acela, uoobo(d - eor+ s1led8h2fx 9c av4u2d1tilizes 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 d2 ocs4oavblo(1e 9ue8od d -h 2+rx1fwith 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.$\approx$    $\times 10^2$