Sometimes people say that water is removed fromvq+gr7t20 : qxl bj1le clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statr :+vxebq17ll0j q2tg ement?

Will the acceleration of amj 2nxy:.(o2dzhd y ;c car 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 t h2. 2m:cndxy(odjyz ;he same speed? Explain.

Suppose a car moves at constant speed al;fzgw )zu+y s/u (axyb0d 2r(wong a hilly road. Where does the car exert the greatest and least 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 boy(rbua w) g(z/sw2 xf0y+u;z dttom of a hill?

Describe all the forces acting on a child riding a horse onqd3 q(bqcry1di yi15( a merry-go-round. Which of these forces provides the centripetal acq 51br 1(3cyidiyd qq(celeration of the child?

A bucket of water can uvwecuv 8h1 8(be whirled in a vertical circle without the water spilling out, even at the top of the circle when the be8u(w v81vhc uucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least th-zd,c6kx(q tk5yw8ow ree controls in the car which can be used to cause the car to accelerate. What are they? What (zw,t k cxwqk-o5dy68accelerations do they produce?

A child on a sled comes flying over the crest of a smlwcqe)-e4ql0c+((g2m npl haall 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 decrea2l l+l wgpq(h0c-q(ec)m4anese using Newton’s second law.

Why do bicycle riders lean inwaymyco n374vh hkg+wj5 1;s g,hrd when rounding a curve at high speed?

Why do airplanes bank when they turn? How wbcs/ea t-95qa ould you compute the banking angle given its b9aqse-5tc/a speed and radius of the turn?

A girl is whirling a ball on a string around her head in3 8 dj3/yhzpgrmy8dh8 a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go o8j/rh3y gp3mdy8 8d zhf the string?

Does an apple exert a gravi:g1p0 p,cjpc itational force on the Earth? If so, how large a force? C pp,c01jci :pgonsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were( ypb9l* 9.s)jquxxubii, l z* double what it is, in what ways would the Moon’s orbit xyi 9*jqls 9 )lz.xb (bp,u*iube different?

Which pulls harder gravibxx+x354 rcsp tationally, the Earth on the Moon, or the Moon on the Earth? Which r35xb px+cs4x accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet tha) xhp)5) zcsi ev/+ete Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull fs aix)h v/)zet)+5pcerom one side of the Earth to the other.]

Will an object weigh more at the equator or at tc bu2+ 0qnwirwk7p 64iih; *qqhe poles? What two effects are at ni+ 4 bpq7rhqw;wu06qi *ci2 kwork? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half theyxj+78wufv-6j2hm,in/4(l9jbs j ow f g .gjf force on the Moon on lgvfjgu2f.j94j ib myfx7/w-8w6h j,s(+j due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larg4 yu*jpg, 3 z ozlkka4m13ru*n/pmr 8fer or smaller4oz 4az pr83*gm/1kkn murj,u3*pyfl than the centripetal acceleration of the Earth?

Would it require less speed to launk9r7f+.0f0 mutwfyd sch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s r0smrf7fw.dt+9u y 0kfotation direction.

When will your apparent weight be the greatest, as measured by a scale in a movir9d6 +nojr13 xfusr8lng elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in freelu96x1r8drn o rj3s+f 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 ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in oute9z2 (xe hpb(lak(pq 2ar space could be adversely 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 o(9 hqbk xzepapa2((l2 bjects 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 “fhn(;w3nc y u.kree fall” or “apparent weightlessness” between steps. . 3y;wc(nhkun

The Earth moves faster in its orbit around the Sun in January than+y we*:s+f shninse 4yrph10 hivv3-8 in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]vsne8iyhe-104h r3s v+p:in* w +hsfy

The mass of Pluto was not known unti +9(irexc25 4rzwitddl it was discovered to have a moon. Explain how this discovery enabled an estima 5rid zx 9iw24dr(tce+te of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much lu llm //e,ku-m)tmnq,arger 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.]A child sitting 1.10 m from the center of a merry-go-round moves with a speedeqlt,uk-um/ n ,/ lmm) 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 1980qly6o nh mzxx2*fr1 9 zj 5d0hp7ytx36 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orbiyqh / 0 ..ngupy gwj/v*f)yqp9t around the Sun,q 0p/ .pfyvhwynqug /. )*9jyg and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates unifor)a 39t5by8qux+ xudkb mly in a horizontal circle (at arm’s lbq3 y)5 da+u t8xbu9kxength) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the r /,u1nvo rf:d(h 4zsgEarth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttl1/hnsfrguvr:d z4( o,e in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude ofcll 95 d-7pj8cirt(jg the acceleration of a speck of clay on the edge of a potter’s wheel turning at 4(l lt8 9cicjg-j7pdr55 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a unifmd2:lqb5fuu m hq0()a orm rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 lq)5d0 :qfbm uahm(2u $\mathrm{~m} / \mathrm{s}$ 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 c) e 37u/t;7votoos );gzitwj tso3ko) zl6(f 1050-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 this z)to t3go;)67jf (tk c7owv is 3;szteo/u)lo result independent of the mass of the car?   

  How large must the coefficient ox0l ,uma (h3zb:ean/3o dd (wwf static friction be between the tires and the road if a car is to round a level curve of radiuluwaw(3 b,he/x( 3 z:dd noa0ms 85 m at a speed of 95km/h ?   

  A device for training astro; 6exahto;y-a/n6 glt nauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her eht/;6y 6nlgot ; a-axback 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 variable xv0 ofkwngk l*vi. v/m3 qw,,+speed. When the speed of the tuv k.f/w0wmn+ , q 3k,gl*ovivxrntable 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 static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster .hsiz3xj:v3 q q 1o +5aqy+wbabe traveling when upside down at the top of a s+zwa:+a5qqo yb. 31v3hx ij qcircle
(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 drive3h0a+vmce75j jbg: k jr) crosses the rounded top of a hill (radius =km 3 gcbje057v:+jhaj 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 to m*.gult a(md1gake for the passengers to feel “weightless” amtu *gl1(d.ag t the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At 8 3ovxwvf e e .yb3q-qnhq,z+3the lowest point of z h.83qx qe -ywn f+q3,vvbo3eits 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 centrifuge rotate if a particle 9.00 cm from the axis ou6 grla7 lo 9y6e sb2hs1-zuy/f rotation is to exhyz21ab6 ylou7ls-sg6e /u 9rperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, i/ouse m, b+gk9gr;w *bvfs.:people are rotated in a cylindrically walled "room." (See Fig. 5-35.r/:ug ie k*,b gov;.m9 s+fwbs)
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+0g -y. hdki mk)ksl5p in a circle on a frictionless air-hockey tabletop, and is k)d. 5lim+phkg-ys0k 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 , precisely this time, by not ignoring the weight of th 4ryag/u+fl)j2 xv6i9rja6i ye ball which revolves on a string 0.600 m long. In particular, find the ma 2ylu/ g4+jr aiarjf6xy6)9 ivgnitude 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 travelingr gsj5gm qh(37fi,b 5ftdv2l* 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 massesxufi k(50ofm in v6;5ka4dmi- $ 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 vsb)ern(vq 3 i:ertically 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 cenxli6x mmf, s +t13.jojtripetal components of the net force exerted on the car (by the ground) in Example 5-8 6 jmjf+3xlo,si.1txm 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 arom4crx52ksr , (9taa tea, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and t2t5aa r ocm,(rxks4 t9he 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 particularwu-- - z1;tokcmkjf yq9 o;ju- instan k;;zoj-9uw f ctk qmjy--o1u-t, its 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 graz7uo7o7wzo m.laf:c 9pqx + q4vity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s7:o7up xlq 7+z c .4zqfomw9oa surface if its mass is 1350 kg.   

  At the surface of a certain play o3le 0hs/7,jpz f .sx;kuqly;n,mj8net, the gravitational acceleration g has a magnitude 8sheqof n;p0.7xys/; ,ylmzu ,3 kljjof 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 td 4bb12c zjsy98lq*mnhe Moon. The Moon's radius is 1.74bms zq4yd nbj9*c812l $\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 Em4fi mbk8 :pa3z8*lrhu; sw b,arth, but has the same mass. What is the acceleratio3 8k;w 8sf pi a*l4u,zmhbr:mbn due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiusclki5*j9a znj ;) p)cr9pbfi( . What is g near its surfi j*bc 9( ip);zpac)ljrknf 59ace?   

  Two objects attract each other gravitationally wc98 2 tpsqn(pyith 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 acceleratioc.lyfmf /. ,rin of gravity, at (a) 3200 mryf.f clm./ i,    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ou +kvnsgfdq/ * ,3iubd(tside the Earth where thegravitational acceleration due to the g ki, +qd dfus(vb3/*nEarth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five ti2du0pl0ub 5snlv 6-sw nvi*.f mes the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this s lb0iluufnvp -w5*vs60 2nd. monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star lisp*fbp61ed c qk++9o *x6k6k/dvfx gzke our Sun but is now in the last / +c fekqx*okf6p6vgz9 s* 1d+d6 xkpbstage 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 wh )tww55 qjxgm/7 j8wwry astronauts feel weightless while orbiting in the space shuttleww jww/5gq5 r mj78tx). 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 gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the cornerfdsv)l8me fc u01fe9b ic5,f (v0 rvd.s of a square of side 0.60 m. Calculate the magnitude and direction of the total grav 1ev0s8(, vcr l)fi9fef 0bf mduv5d.citational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred year - 2m,bpbz;9pn-k: 3l mykeiecs most of the planets line up on the same side of the Sun. Calculate t ,lpp;-k:e 9inkm3bb e2m-cyz he 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 at the surface ofbz kq (l3.wpi1 Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determzlqpi.kw3b 1 (ine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of raih l*7h/;pi6h9xr r the Earth and itr 6x/hri7*l9hp hair;s distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abou g0zcxwd+h 8rett/;16kgyk z5oj2g;jt the Earth at a height of czxz tgrd8t;w1+k5ge j 60 /hok;gy2j3600 km.    $\times 10^3$

  The space shuttle release,x1fcsrfs qwj29j ;v 3s a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle bev 1j3fqwsj xs9c;r2f, moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylin5 -9/imaod39n o1ov4x it ruoodrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship n -a9/ 4it 1u3div59oooroomx’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 it takes for a satellite to orbit the Earth in a circular “nwm, nc1j ju/*eu9s9u,q qn um,ear-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth whichmsm,j,uc , jq9 u*un euqw1n/9 is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to bew)uhxc)k1v2e afd-2sn+vj+ i launched from the top of Mt. Everest to be plj+nwu21)ias)- vx v 2 cehf+dkaced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, s yd(pp a,2dmeg4w 1zg1xs6-01 n6 vknna;fzothe command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go2 1(gnp azed1m;zs,66ak4 wnpo0 1v-dxg yfns around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that (v bu**yg7b m2cuoxc*orbit the planet. The inner radius of the ring o* xcu2( *bugmcy*v7bs 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– ll nxj.pq6w51ep4g:w 9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom? lw .pxgqejw5:6 l1 n4p
(a)    (b)   

  What is the apparent weiuf(eqzx 6mzwl9/( b .sght of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space ((./s eufq9bmzlw zx6vehicle (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 two stars of equal massc c+g)y)3t1no5* wtp a c8zylj. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit abtzc*c))c3w +y lyopga15n 8jtout 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 el *y5id ( ogcz3vzr+1 lle/edc1:ne( fmevator that movdeneg :c5 1r+mil/dfclyz ve(13z*( oes
(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 awno4qdxuug6ot38y6q1q x 6 n-(ri7 vrn elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was 6d6(ruo rq3nu- i 8x46o y1nxtw7 gqvqthe elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits ycmr ptqs9 a/ 4q6,.pyvery near the surface of a planet with period T , the d/qt r9m yq, ya4.cpsp6ensity (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) tobpg mv,092bmbepw9n- as)pj 8 determine the period of an artificial satellite orbiting ve bgwaspp0)92p 9v j8bmmn,b-ery near the Earth’s surface.    s

  The asteroid Icarus, though only a fe vx2-oz2gp+o mw hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Szgm2v-x2 opo +un?    $\times 10^{11}$

  Neptune is an average distant8rmv cj4,sxlw2z qg+ f e1d58ce 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 o/y 8/3z ssncr.bgo wb uup)/)wnce 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 nearesyou8s3)z//up. bwcrsn w)b /g t and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy go14.lxv v8ak$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 dism4elh ;ocy, 9v:jq ,kotance for the four largest moons of Jlj, chm9,kv :q eoy;4oupiter (those discovered 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 Earth from the known z; ac,d*t- zgx3vw0jk period and distance of the Moon. cdz a-wtk 3,v;*jxz0g    $\times 10^{24}$

  Determine the mean distance from Jupit;h:(lvay9j 4m 7 c 6kp1kffqcder for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in k:y f f kchavcl9m 6d(j4p1q7;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 ber6hjeq 8q12mq*yv pf5 i j,is4tween Mars and Jupiter consists of many fragments (which some space scientists think came from a planee mqi1864 r*pjyj h2s,iqv f5qt that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of +) xh .(/txb0yabzk 2zu xt1yna band comp()uyn2k xh zt.b1xtb/ay+ 0 zxletely 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 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 by66.u 9eyd mefpr ,fb;o swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and e6romp ;69d.u,ye b ffthe vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be hwdu5j64gp j dngu;9x8alf what it is on wjg pn4uu5jdd96x8 g;the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spb-d d 2qkujuqb7f39/t ve3 o:iin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hdk-bufij:q2beo v7t 33q/d9 uard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the appare9sryq a8g; 8pnzi+aw3nt acceleration of gravity at the equator is slightly less than it wo+8zi gw83ypq;a9rn sauld be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelint6zesv .)*v9j, yt*9jffip 9r3awh (k 2 jmrtrg directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equale sft r iph)j v2r*.,fy*k trzv9w3m 99(atjj6 and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom sc+ q:i/abeu; ck3r;zr3yync 8 zale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directi8r/y;+ b uqryze ;3ckc i3:nazon?     ----待选择----upwartddown 

  A projected space station consists of a circular rr6uopa 7e-qtji :x8 j-jg3;gz-j,hl tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutionq rjh87j ;gja j6g ,puie--o-zl rx3:ts 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 aircb3:6te/d5uiv/qr zl oraft 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*:q vgbibgwdcgu n2ac5l n,9 ;ue gui 6;*53bp mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and gpn,;dgq bl*5*5 bgciu bu;:2eua63n9 g vicwthe gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verti6d*udq,1/jdh8if ; z v aad(orcal by an angle 8zvaddi,jf1dd;h oq r6*ua(/ $\theta$ 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 ass2)k0 ntwzm8up :s) design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range )2mws: 08zsutk ps) anof speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating sdib,/xtp ztl, 6aaw:1 o fast that objects at the equator were apparently we id1 ab xa/lz,tt,:6pwightless?    $\times 10^3$s

  Two equal-mass stars maintain a cons636 i*cnfnysic8tg c )tant 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 0g+,qbn e /soq/ic9vq5: mdft 235 m. A lamp suspended from the ceiling swings out fqvq:o0+/5e9 qc,/gitm nbsd to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times ax-*(w+ 8-4o/l degyb(j egufpwzpkr6s massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a plag-w4(jepbog (w6ekl+xzr du y/-8 f* pnet 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 Telescope deducedumaa-w9nyu r6r: q9 j) the presence of an extremely massive core in the distant galaxy M87, so dense that it could ban- a9uyq)u 6mrj:9wre a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it travox 0 f(;ob jyxr/-(nwqo5/ppwerses the hill and valley 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 ca;o (box/ rf y-j(/wppnqx50won the car go without losing contact with the road at A?

  The Navstar Global Positioninf nk2b:6b / ct sm+7clqwn(2kxg System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by thesetx/k+l62sb f7bm:w(n2 ncc kq satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.12g*jwa/mg8u g a1u lerk 3sq+9 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros e g3jg kawmau91ql +r28s /u*gis 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 of repairdf( dkopksqi3*(v 7s /. You are in a circular orbit of the same radius as thi 3d* d pksf7v/((okqse satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000fr, t . 1on7 (7s0nsfegzi sypw-c0q.wh6pn)y years. (a) What is its mean distance frop1.z ( qscsw.n 7,fygt p)fw7 0rnno06y- heism 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 would need to be ;9q:h,kz cp64 o haonn oquw+7if you could actually "feel" yourself gravitationally attracted to someone near you.c,oh n 9zqqha;kwpo6o :+ n7u4 Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the g -n 0apwnnl l f.,4chkv,b.h;Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from th0l ,a. h;p.wncgn4 bv-fkl,n 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 are located at the corners oflj1fr 73 rc 2chot9b2e a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass 9 ce3r2 blt2 jhrc7fo1placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits 30o z+,/i gtqjzbmn+ othe 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 accelerax zzdfgv:*3jbc qr.;h2 /sq +f/vv-lotion experienced by the tip of the 1.5-cm-long sweep second hand on your wris:l32dj-vfh zbxso/.;cv fqv q/g +r*z t watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a gl;ssbf/pox,7 i2 kvu5n 3( edcircle 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 fishing line makes with the lvksg sf(;5 p7 ni,b23o/udxe vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so t8mi((dbtwr . that a car traveling at speed d(tm w( .8rbti$ 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, th ylg9,z2ggw/w1cws1+b xje i4 e Acela, utilizes tilt of the cars when negotiating curves. The lyzwbw1,ws12jg +ggi x/4e9c angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not 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.$\approx$    $\times 10^2$