Sometimes people say that water is removed from clothes in a spin dryer by ce pn3 gjiuhdl6t*kv4 h9mq,n, j4cx0p8 ntrifu09p,t3jnnq v *6,hjl u4dp8mk hxg ci4gal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a c m4* l rev6ebdn ojdb:2:hpa,qa(61nkar be the same when the car travels around a sharp curve at a constant 60 km/h as when it1n: j,vhrep2keqnba6o6 :a d(bd4lm* travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant ,w tk zp)5ozn;2hi wr2speed along a hilly road. Where does the car exert the greatest and least forces on the roa5,2w i 2tzro)w kpnhz;d: (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 oe3*myjrqie ec4 .nua-) q ,x9an a merry-go-round. Which of these forces provides the centripetal acceleran3q,m x*iquj e4 ar.)ye- 9ecation of the child?

A bucket of water can be whirled in a vertical circle without the water iali4-iio yn 0k6j+-vspilling out, even at the top of the circle when the bucket is upside down. Explai-4oain l-ij+ik 60iyvn.

How many “acceleratorsu:na2lofdh k e3/e ul na8,9 42j3rygi” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What arelo 28,u:defj/ 3gakyrn29naul3 4h ei they? What accelerations do they produce?

A child on a sled comes flying over the crest jnc6 ;+ei9n)e8eylrh* xv ,dkof a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrea; +ex el8 vc6*nk)yen,jdrh9ise using Newton’s second law.

Why do bicycle riders lean inward ecj l25t4ll0z5; q9oej ,dqc, gjf3iiwhen rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compu::.rl p kstxl3te the banking angle given its speed and radiusr.ls :t3p:klx of the turn?

A girl is whirling a ball on a string around her head in a horizontal p/.:cv l )viekeg;n:ez lane. She wants to let go at precisely the right time)/igneelv:.v :ek;zc 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 gravitational force on thej 5r,+ ubn sf)b8wk5ez Earth? If so, how large a force? Considu,sjerzb5 k8nb+w5f ) er an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the 1r,rvfi m o++lMoon’s orbit be diror+lm1v,f i +fferent?

Which pulls harder gravitationally, 2tx6jwt4k f ,88tagiithe Earth on the Moon, or the Moon on the Earth? Which a8 4i6 wtjft,xkga2i8tccelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yetgfp z8d j 4s.x.oofa)ar6 *e3m the Moon's is main ef4* z. )3oxm8gfa6 pd.asrojly responsible 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 equator or at the poles? What two effects6u*4 j53f9lm 9 c9bf)vonbbqgr5b nyi are at work? Do they oppose each othemuf cvn959 6 bo5)4b9f3nib b*qgjy rlr?

The gravitational force on the Moon due to the Earth is only about half the forjnz(zh k5 d/b3ce on the Moon due to the Sun. Why isn’t the Moon pulled away from jbdk3zz/h5 n(the Earth?

Is the centripetal acceleration of Mars in its orbi9x97r 0sxyt uot around the Sun larger or smaller than thex yrs0x9to7 u9 centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) tocr 22g7j tdj7 eq96pmwward the east or (b) toward the west? Consider the Earth’s rotd7 6p29wg jjrec2m tq7ation direction.

When will your apparent weight be the greatest, as measured by)rwa25qs-t7cs ib* y5xazao + 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 2 7qaiasb5t sr z+-c*5o) wyaxyou are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space ckm zrkhb:p:*:ould be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the:mhb*zp:: rkk 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 “r6tst0gsjcg-i mw6 -we416phkl v,r+free fall” or “apparent weightlessness” between ste6+gp-r0tc1 ,mwkil shs-6 jt64 wevrgps.

The Earth moves faster in its orbit -ppezz0zufq3. .,q+yt i-bgc around 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 Earth’s axis relative to the plane of uypz.qpgzqc-f z3i0e +, -.btits orbit.]

The mass of Pluto was not known until it was disce8 a5ec ;g9zukovered to have a moon. Explain how this diseg58cu;z eka9covery enabled an estimate of Pluto’s mass.

  The Sun's gravitational9wupm;9 u c95 ndswne+q,sd +l pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to tmpdw9escwq d+ul9 u;5n+n9, she 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 travelinrb,-f2 taqb(,bd;7f. octn b ng 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 orbkg49w1ag1cyoy5 -nv6 wj( nu oit around the Sun, and the net force ex 61aoy1o( 9uc4g- 5wnn wygkjverted 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 rcup.vvwh 5+t 1p3*iq rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calc cvp r.ui5pqt*3vh1+w ulate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Eajo:piz2r3b je hflw .d8t./p3 rth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Ep. rbphdwf: .2 tlz/ejj3oi 83arth's surface. $\approx$    g

  What is the magnitude of0l n dj39qpxy0pxi2 vpih.0tf0s -ul . the acceleration of a speck of clay on the edge of a potter’s wheel turninpy0fx0dlpjin9qp 0 h 2x t0-3is..u vlg at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string4zlw e4r5sw zl: u;qf/-be d/m is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If 4e4l rms5b:z qez;u-w/f/l dwits 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 uup/p 7a2 3: xn fya-9dsfgui)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 result independent of the mass of thay7dgf u92-:)i3 fau/ sxup npe car?   

  How large must the coefficient of styiuy(h9 11i5. ckydw(w dpc .tatic friction be between the tires and the road if a car is to round a level curve of radid yp. 59u cd1(1(kwiicwyhy.tus 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is df9ma7:-btbww esigned 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 mbb7 fa-:w9tw 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 sp0)wyw.; o at 3.zbxdu:xz1 f w9l*lb5uayb8xm eed. When the speed of the turntable is slowly increased, the coin rewab d 9x*b8.lo 0)5.zumb:u; 1zftxxyy3waw l mains 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 beex.. lg vrov/+/ d6qmc traveling when upside down at the top of a circlee. d m6v/ /lx.cgq+ovr
(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) es3eiiy n5o) (including the driver) crosses the rounded top of a h) e3e5 )oniiysill (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 neern.**65gr dqv *dg.j j)h wryfd to make for the passengers to feel “wegjg.hq 5 jn)*r.*r dfrwd6*y vightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 gia ox*n9xm;, m. At the lowest point of its motion the ;i*x nam,oxg9tension 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 bh( 53wwh32ktb wiohxo : h,m;from the axis of rotation is to experience an3hk3 thwwm(,ob2i hwo:x ;h5b acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylink a h74pr)kmg8eed( h6drically walled "room." (See Fig. 5-35.) ep)k ramegd84( hk76h
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 rotro64 :rmobr. vated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a centrar rbmr.v 46o:ol 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 nu3 qk jitwqm6e7+j0i: ot ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude ojtm7i0u6 3ik:qj q+wef $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 banke3/vio(/agz8wvp* djp7p7c fgd 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 lga jk28wx 2w/$ 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 a6:an8 o i0zerbf,w,rf t 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 centripetal components of the net force exertet;wo6q ovg)r. 0qugy6d on the car (by the rw )q.qvg;g6oo6t 0 uyground) 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 accelern w :6sjia.;qqmtt5xua 44yn-ates uniformly from the pit area, going from rest to 320km/h in a se;nmqnj4a .w4ty a :q6x-5iutsmicircular 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 cir3aoz5 dvc h4u g0s* u;9bjfqd;cle of radius 2.90 m . At a particular instant, its acceleration is 1.05 5 ugbo3hd9c0;vazqf; d*sj4u$\mathrm{~m} / \mathrm{s}^{2}$ , 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 spacecraftqfi reo,g*x 46zax j,0or-v w5 12,800 km (2 Earth radii) above the Earth’s surface ox05 j*q-6 ror ,wvze 4fgixa,if its mass is 1350 kg.   

  At the surface of a certain planet, then37el lj*;9z. g:t sl mbzc:su gravitational acceleration g has a magnitudnze 7s; l3zbumt l: :gclsj*.9e 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. The Moon's radius is17;rt;9g-o(easxwy 9p s dbek+ 3doza 1.7s3-k o9+;(wt ;ap dzs1gea xydo9eb7r 4 $\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 Earbe v(/*druo+u th, but has the same mass. Whaureoud( v/*b +t is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that ofuhyo0l6z+ y+d Earth, but the same radius. What is g near its surfayuoh d6y+ 0lz+ce?   

  Two objects attract each other gravitationally with a fot9m* /te y05-6utxgflx gnlg8rce 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 , df- a8a7y m9idofv 5r/ 0ii;rnthe acceleration of gravity, at (a) 3200 m inydfr; a/-aomi i d0v578 f9r   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wher1 y+u. fk yz-:sna+tjse thegssu -y f+:.yjnt+z1akravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star hasetxyd /6 d)ne9 five times the mass of our Sun packed into a sphere about dx e)6td nye/910 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average gv gc,tyj.m 6kd:x 5 ft2k(nz6star like our Sun but is now in the last stage of its evk:vcgx 2 z6t(tj5, f mndyk6.golution, 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 astronaiwc4.gbx-8 hw uts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them an -g hcw8xi.bw4d 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 o2qt3miix1 +6 -i)caqdjff d7corners of a square of side 0.60 m. Calculate the magnitude and direction of the toa1qic 72-d)3xtj+6id omqffi tal gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yearsl mcuv..fq-m d i;p;1c most of the planets line up on the same side of the Sun. Calculate the total force on th.i ;.mcu1pfv l-cd m;qe 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 khe+508dve+.gb-mj7yme) mm v z1ihp of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, detem 8-pjmev mvee5.70bz+h ym hg1 k)i+drmine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the kno4f0;cpxmdep , wn value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.] c4;efxm,dp 0p   $\times 10^{30}$

  Calculate the speed of a ic2f0/,f6pc se 2p fdmsatellite moving in a stable circular orbit about the Earpf psf/c06 def22, cmith at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite int2czezwem6q o h,2/i*eo a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) whc2ezez6 q i*w,o2/m ehen the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate4xoofmc4/6x vl 7cvq yzn17)q if occupants are to experience simulated gravity of 0.60 g? Assum77)1qocf 4 x/nq ovlzymv46xc e 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 it takes for a satellg jp/*ib3lc0 pif l08:jkbs2kite 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 smal:i*l ifk k3 /sj bg20p8cl0bpjl compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal veloc kq n1mbmy4*y ev;q*a :sdh 99dsp7m4zity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth?s9 ;dm 9mqmpd:*hqes kyn1*4 bzv4y7a   

  During an Apollo lunar landing mission, the command7wrfk-4lr z ek 1p5qdup w3)2a module continued to orbit the Moon at an altitude of abou-z4pw5)1e72k dqap3kfw lru rt 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of 9/ ggkg k1 qvll7j glff99;jl7ice that orbit the planet. The inner radius of tlvg/fkl7g;f 9g9lqgk 17 jj9lhe 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. 5–9). Wa;-, w3mw rkaihat is the ratio of a person’s a- 3wraw, iam;kpparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from ti 1gdbped9(.mf*gu mye v a.5 ,a9dm0fhe center of the Ea imea5a, (gu.g*9d0d1emf bmv9fdp.yrth'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-+ o90+ wtrk)tzequ- )ppqud +ustar system consists of two stars of equal mass. They are obser-pqet0p ur+uw9+q +ot)du) zkved to be separated 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 a4dzyv:(n6 -mbakj5cd-pa r5 j n elevator that movesd(pjzj4nr -acv: y bdm- a65k5
(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 ceilingv t 1hch,rwg.9,b)e/+jrbm gu of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimu9utbw r.jeh+r,b)/,mcv 1ggh m acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very ne5 t+md5*scait3yd6 jwa;*usr ar the surface of a planet with period T , the density (mass/volume) of the plana*5ru dyi5 +dtt* j;csaw6 ms3et 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 ioxeg( m* 5oi;7qx )psmy:d6f.4 d) to determine the period of an artificial satellite orbiting very nei qxmdoos5 m gy)iex (6p7*;:far the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, q1rv*9,c;axfjxk v g)orbits the Sun like the planets. Its period is 410 d. What is its mean distance from tar;vk*xfq1)gv x,cj 9he Sun?    $\times 10^{11}$

  Neptune is an average distance of m ;k ga5o7y1dc4.5 $\times 10^{9} \mathrm{~km}$ 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 yea6o*jc fv5- i 9hxsqkt-.3lix rrs. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from thk-j- .iis3v*5 96lf qohrcx xte Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galajo ln*.0hwbjc8q7vx77but; v/u ca o)xy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 foupfj8 e;la3krsz(*j 2 hr largest moons of Jupiter (those discovered by Galileo in 1a8l( zf23 ;k rpj*shej609).
(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 ozt+e +-e trhajx0,c-sf the Earth from the known period and distance of the Moon. s+c et xat0rj-- +,hez   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, uv--bdri,-h0n;q ze.wia+ t pzsing Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to thzp-- tv h,ndi-bw0raze;. iq+e 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 Jogjab7s0s8 3 aupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was d bs7s3go0aj8a estroyed).
(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 desm:t5 xln8 o)zwlg1/vq cribes an artificial "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-Sun distance (to make the climate temperate), and that the ring rotates quickly enqv owt)g 8n/lx z:l15mough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging v+ sr8eak,u ne9ine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on theseak u8 en9+,r vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gr ehm* gjzd.yn+5f4hh ;e4es3pavity be half what iez 35jhs;yehd.g4fm* +e 4nhpt is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutua rxa.:sn).hj d hf*ls+l circle once every 2.5 s. If we assume their arms are each 0.80 +.lsd n)xf:.*as r hjhm long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per dalvm/)egh5a c +y, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of th5ghv lec/) m+ais effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth wbi(a 755j hvjuill a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon puluvi b5j7( ha5jl with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom ),cg/vd lx n z2wkon06 psdad qp62i-xm )l4j8scale in an elevator, it says your mass is 82 kg. What is t d2n x6)6izpsk p q8j v2dw,l/macg)dlnx-o40he acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circul-+ zz )0cl::zxqr aws lxwb)h.ar tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The cirx z-blzc) )rs0:xwzhaq.l:+ w cle 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–*222uxknnq ;gaxcz3a43).
(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 ra0ppd o*yq jn 8/l(qtz26m:ff idius r, the acceleration due to gravity at fqln iz d( 0m82ppqj6of */:tyits surface and the gravitational constant G.

A plumb bob (a mass m hz9*w )is .ad 0tee5(;qobcsfe0ja(bv anging on a string) is deflected from the vertical by an az s;jt d5a. cv ebb0q(a)*0(oi fews9engle $\theta$ 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 coefficie4j,x fxcnxl /(*n+p ;i;-sx ouhpvy-ynt of static fripxnin4cjh* v/+(xy -f;oy x,spxl; u-ction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotatingkyn ,c-mepxo9* 6 i2v:abch 8v so fast that objects at the equator were appayb ovx 86*9c2kanipv -ehc m,:rently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a vp7t ir ,ra;/q.vcydgskk*)+t4o/ b m f,j p.gconstant 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 constdwrpo j4n+3 ;ipj *;igant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of+; 4pwni*o d ;rgjpi3j 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massik c b j,bt2oal3m,,dw6/9 ezowve as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since p,9z,md,bwwa e2 ocltk 3/6j obeople 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 -fnzr 3khg2::h98:za dqk*p ry5 iubq Telescope deduced the presence of an extremely massive czka8:i:b-f hhqzn u d59yq:gk2r*p3r ore 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 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 vawvj+ks/;u i1hq pg0p4lley 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 cv4hsj;piwq0 gp 1 +/kuan the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 sal1q5 5 ldhmv.dtellites 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 ap 1.d5qvllm5hd proximately 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 Rendezv8jn (nz cxy .6vufiaj5w86; szous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 ki8(6xz y nn.a;s5zjj6f c8uvwm . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing ast- ar0 jf:u(x1xdt;r satellite in need of repair. You are in a circular orbit offat 0t (;r ujr:x-xd1s the same radius as the 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 4sr*fqfzv h1c8qw6 0i period of 3000 years. (a) What is its mean distance from tqhf60s1c z*f w8rvq4i he Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actuwo( h +rcxs37jally "feel" yoursecxojs37r+hw ( lf gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Mx8 m c)vs-5v5emcv5.j9 d uut4vsq6bcilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years frm55vs j-qc49cx) vmu8d .vbst56 ucveom 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 squew0g0tcje t0d eh *10lare 0.50 m on each side. Find the ma*ehg 00j 0td1w0etl cegnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eartm0+c3 qj8exoad-j*a )x.v yqhh $ \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 th.crey ipw k6 fxx3aq35yc-c).e tip of the 1.5-cm-long sweep second hand on your wrist watch? kwfccyxp. 5cia - 3ry.3)ex6q   $\times 10^{-4}$

  While fishing, you get bored and start to s(oh:egrc*j ca 1+mmb8a zdh5.wing a sinker weight around in a circle below you on a 0.25-m piece of fishing lin cr8: m(jad.bch h+om5e1 gz*ae. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is de c tnc)odv;z)j26mfe,0 av;r osigned so that a car travelingv)aevtcjo )z0 d m2;,o;cfnr6 at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, uk jl 8ko(c.mdl0 9h47* m nnxlz(qve( si,f9lmtilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the pass4n7x98l.n(svilmhoz(f( ke qdm ,0 9lkjml*cengers, 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.$\approx$    $\times 10^2$