Sometimes people say that water is removed from clothes in a spin dryer by cents;y ;h, bq fdjp(c(o9xrifugal force throwing the water ox j ;b(yfc(;qs9,pdh outward. What is wrong with this statement?

Will the acceleration of a car be the same when k05qnzt gt0 p)the car travels around a sharp curve at a constant 60 km/h as when it travzt5nk gq0p0t )els around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wheeoll :vx/-7 more 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 nearmo7-ll/oxev : the bottom of a hill?

Describe all the forces acting on a child riding a horse on 8bq mst* td(ts x.h:b/a merry-go-round. Which of these forces provides the centripet8ttst/. q *hm:sxb( bdal acceleration of the child?

A bucket of water can be whirled in a vertical circbo)b azs ).w5v+1yjk ple without the water spilling out, even at the top of the circle when the bucket is upsidzov 5))+bp1jbsky.a we down. Explain.

How many “accelerators” do you have in your car? There are atn g-m3t2 )et/efv:xs b least three controls in the car which can :-sfv3 tee)/ mtb2xgn be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flm.5u2yr 6 lcr7; mjpm6i+m5(yi/sqed cm e(mlying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the nl5(ceru6. mp57ymrm lci+ q 6m2jmmye/ s;d i(ormal 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 rounding a curve at hi t),w c nnryl8nfwi).(gh speed?

Why do airplanes bank when they turn? How would ylpo 9 9l5o8sm9b6/ss i)stushou compute the banking angle given its speed and radius of the sht p99l95ss/mo8iloub )6s sturn?

A girl is whirling a ball on a string around her head in a horid3u6kg m(7yqfk ew - kr(:)okwzontal plane. She wants to let go at precisely:y3kw ruk(6f(go kq-7ke w)dm the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how lh9:bcjoat r/ bp)x9- large a force? or )c -pb9tx9:jhbal/ Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would a8 bx*;pkto*x the Moon’s orbit be dk*b8xxpt* ao ;ifferent?

Which pulls harder gravitationa-ii0b 2brevqf3 /c; cmlly, the Earth on the Moon, or the Moon on the Earth? Which acceqi;r0 me2cbf /c-bvi3lerates more?

The Sun's gravitational pull ok1i)-r d9tjpfy95c ;rg5 bsqkn the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Considt 5jf p-g5r9i; k9cr)kydbs1qer 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 effects a9)v0a*cqmj-jh;vq8lu26dn dt. yukz re at work? Do they oppose each otherc.k8h6j z9*qd0 n)a-utd qlv;2y vmu j?

The gravitational force on the Moon due to the Earth is only about half the for)k9(s s 2cvzlqce lv)s2qk9zc s(on the Moon 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 larger or4,:vgi jyl9w-fs,gyx3xv0e l smaller than the ,we lsiy9xv,3g -:f 4l0ygjxvcentripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the eaf7gih4h- m )wast or (b) toward the west? Consig 4hafmh-)w 7ider the Earth’s rotation direction.

When will your apparent weight beezi3wq1ipqu2-f vnk9r2- ff 9 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 yourp2 n kqi-refquv91ffi-z392w 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 periow )um3che (wl*15 apm)lhg xj j3mo.i8b rs5l2ds in outer space could be adversely affected by weightlessness. One way to simulate gravity i5l w53.rij) 2 3choxlu(hwemlmb aj 1sgpm8)*s to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experienc2rofj* r+.wwe es “free fall” or “apparent weightlessness” between steps.w 2rwjf* re+o.

The Earth moves faster in its orbit around the Sun in Janq8+v1yi+nc.i 2b bnwquary 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 Eart ic1bnv8+qq.yn+w2bih’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovere:z6ols-xm5dr s3 xa (7v. sqzwd to have a moon. Explain how thi wx(ol:z.- d6x5qmzs ar s3v7ss discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much1i47nip+*hbw3e*mz tx hva b( larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting n+zbb*ah wx*4i3vpm1 (ehti7 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling i1c yg dy-t9d*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 i6 e il*3b(+zxii 2vlnfts orbit around the Sun, and the net for *izx3 ilf+bel vi(n26ce 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 rotatessepmny6rxa(mnba40 i - y 4ys1,2tzkrnik ,+4 uniformly in a horizon44rk6a s(i+,x z2 a-syn4b mnkper 0yit ,ym1ntal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Ear4q6o7d)7 d hie*lx2ah p0pmz wth'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 term2w7e*7ixph hqpdma )6 0lz4 ods of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of cl fmkgmv-0+6k b oz7g: lu,gxp.ay on the edge of a potter’s wheel turnin-x : zo.mbggp+ gkfku,0l7vm6g at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is jl32im+vk gaeo oy0skkeb8;i*i2 5t -revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.03v+o*;0 ylkebgs2 i 2-j ktiao5em ki80 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of radiu44+k5hln ykb ls 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result ink lbhkny4+5 l4dependent of the mass of the car?   

  How large must the coefficient of static friction be( y r0pkcq4ps2 between the tires and the road if a car is to round a level curve of radius 85yr 2pc(4kq0 sp m at a speed of 95km/h ?   

  A device for training astronauts and 1ic: tn8k /bf.oe*lyjjet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the t:lkj1 b.8/ofynie ct*rainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable b a1k/ pevz+ih)s) n,skjt 6z: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 b:ajsvie sn) p)h z tk61+z,/kstatic friction between the coin and the turntable?   

  At what minimum speed must a rollek/lxpq49,a6bxy -ust) u ) e2vh vt9jmr coaster be traveling when upside down at the top q, t6seyaj2xtvhl)k4 p- m9/xubuv9 )of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded q.;g: 4vswrzv top of awsq gv;v :4r.z hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diametq7/hv4 d:n35lioavy z er Ferris wheel need to make for the passnhq/:v57 i4zd3yv olaengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circlryfl mdb fxx/ z;o+jr k/ 06l26vwgb2-e of radius 1.10 m. At the lowest point of its motion the tension in tvbxd-// 2jx6f 6+frmo zb0kw;l2 lryghe 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 i1q)2;xhip p3k awo3 4t 5onrqcm from the axis of rotation is to experience tqow5aq rp pi 1o23 hi3x;k4n)an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricall *;ipwhhx,8mc7 :f+lzf( iwluy walled "room." (See Fig. 5-35.)8+wi if*,ll (cxzufwhm p;7: h
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 ;wv cm 7w2-b+ i9exbkkin a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord con xwbw2e -;kb9kmivc +7nected 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 ign 6 r vrg:le 4q;hze)*zog8p;qforing the weight of the ball which revolves on a string*)ol4v6hgzqq ;; e 8zr:erfpg 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling vpm26svx bjf9 r,(4y;p fav-m75 $\mathrm{~km} / \mathrm{h}$ , 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 6b + :(f8saow;fhzfnj$ 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 310 zz,v/ )b ubz3cp96ked $\mathrm{~m} / \mathrm{s}$ . 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 co uqem, dv )s2nhbvf./ci0q6z/mponents of the net force exerted on the car (by the ground) in Example 5-8 when i)6 , i 2vnqcvm/hqe0zs. /bfduts speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 ao1 .o vs8 6swkspc*js,6l8uv uccelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Desv 86uwjspcv8ous6s,l *o .k1termine 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 ifpk:to -xnd7+jrg5lig *9 *tw mnof6 .n a horizontal circle of radius 2.90 m . At a particular instant, its accelkt:*jo+ i d *ton- .p9gmglr6f7fwx5 neration 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 spae wt52ea5 xvv;cecraft 12,800 km (2 Earth radii) above the Earth’s 2wav e55xte;v surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleh 71gnliv5j- bration g has a magni1hi n5-7jlgb vtude 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 Mba2sv d 68dbv-oon's radius is 1.74 6d-vb2 das8 bv$\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 + z3stuhllx ejts96 a9)x:wlkl 7t n+/that of Earth, but has the same mass. What ij x/ls+ 93 xsuktt79 ah+:lt)nlzl6ews the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius.va9h07 duqrv; What is g near its surface a0h;7ud9 vqrv?   

  Two objects attract each otherkk+/4qwhmwqynd wj+1 ,( gus 1l aq*p6 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 acceleration of gravit va7ski b-2eguz( t cw/03zw6by, at (a) 3200 m vw- sikzg(327b0te6 czaw/b u   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eg/mpgs8i1gu h :, ;djoarth where thegravitational acceleration due to td/u:g1jhm8go isp;g, he Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron stazi25p8 :bxfu cr has five times the mass of our Sun packed into a sphere about 10 km in radius. 2:8x z ubc5pfiEstimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like x4u,*j(.se-zabf iy; 2n ghggour Sun 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 tg-j i4nh xs.aef b,;*y2(gguzhe surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightles : izl+lqi*m7znnhx8*s while orbiting in the space shuttle. Your friends respond that they thix *l*l7zm:+izh8qnnought 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 loca5eowme7 w535xi + gvdb:djd 9cted at the corners of a square of side 0.60 m. Calculate the magnitude and direction of th5b7e5 dvjxdcie3 :mw5w g +do9e total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the 98wq98 y4*yx gej gc8p jc y0ybhd9i1cSun. Calculate the total force on thghc81w j4q8 epxcycydjy 8 90yi*9b9ge 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 gra)4zcqh6bf(yx j 76w9 vxtgrq ken/ /x;vity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars)f ej; hqtx vx79/kx(q6zwc bn4r/gy6.    $\times 10^{23}$

  Determine the mass o vq0 m3euc0+9 nb sbc)y67:da3p mlqtcf the Sun using the known value for the period of the Earth and its distance from the Sun. [0me a3pd cl3)mctcu q6 yqsn09:+7bvbNote: 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 stabfk.bt xrg-( z4le circular orbit about the Earth at a height of 36 bt.xg-4k(frz00 km.    $\times 10^3$

  The space shuttle releases a satellite into,y89q;l ttxgy/.h u* rx2ep*y hl gx+m a circular orbit 650 km above the Earth. How fast must the ue,;t+ hh.2lyr89y/lmx*ggp x * yt qxshuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a j5uaw9 0bnn( pcylindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Que5u nn0 (j9bpwastion 21, Fig 5–32.)   

  Determine the time it takes for 6l /bal8v-wlk a satellite to orbit the Earth in a circular “near-la/8l k6vblw -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 satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top o(a qpn z .efh6ki9+qo)f Mt. Everest to be placed in a circular orbit around the Earth?zih(9qka eo pf +nq6).   

  During an Apollo lunar landing mission, the command module continued to oypm:., uzx1vc b 5c6.j9jtcyarbit the Moon at an altitude of about 100 km. How long did it take to go around thj9y cc. a6j pvyuzb x15m:ct,.e Moon once?    s

  The rings of Saturn are composed of chunks .lllzra*m ,c 2of ice that orbit the planet. The inner radius of the ringz.2l,l al*mcr s 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 rojpi36uv y7mt0x gu0k *z0a tg0tates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top,p00 juggyt k*7muzvx3 a t0i60 and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200bju* 9ifp 3q/h km from the center of the Earth's Moon in a space vehicle (a) moving at co3h q9 puif/bj*nstant 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 equa y0fi3 d9r;itel mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them.yte ir3i f90d; 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 eln3iwq w2jm5, wevator that m,wnm5j i32w qwoves
(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.5 mub *y1n;vaj The cord can withstand a te vja*bum;1y5n nsion of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the s4o ok/m r0zo2au+vc 9zurface of a planet with period T , the denz or/9oam4kov z02 cu+sity (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 per+(gl z en uspw71*8ftoiod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near t*f( 18gszl7eon tp+u whe Earth’s surface.    s

  The asteroid Icarus, though kz7t)f8g c dc,only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fcfgd) c,zkt8 7rom the Sun?    $\times 10^{11}$

  Neptune is an average distancedys 8l/kj*-mw of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once 8nykx.fo.( fp every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimatefo(nk x 8p.yf. 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 the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the G+(xbr7 bwm2p)q lv0 kwalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 dis f d,ku,lfi),g vfb/9ntance for the four largest moons of Jupiter (those discovered k, v)g,u /i9,dfbfflnby 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 6p ;xfr whcj:5Earth from the known period and distance of the Moon. pf 56rjcwh;x :   $\times 10^{24}$

  Determine the mean distance from Jupi0wlizp :ls8;ya gp*(oter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given ia(is*ygl: ppz;lo08 wn Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragmenthdd*i*+1 al vfs;jfi/rhni *-)aw-un s (which some space scientists think came from a planet that once orbited the Sun but was des-;/d rui) hia *n +iwsajd f*hv1*f-lntroyed).
(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" 1f ,pyb6 zcc8zin the form of a band completely encircling a sun (Fig. 5-40). The inhabitants lycfp 1z,68zbcive 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 5qnlstk(lq4qvoo5l ,8( t -kxby swinging in an arc from a hanging vine (Fig. 5–41). If his arms aqtlx4oll st5n- (5qq(, v k8okre 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 the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration o dywp0- k,ldpq86)fwkf gravity be half what it is on the f08y dlq)p6, kwp-kdw surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in 64p4n 3v9e bz4 xfkozqa 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 hard 94o kz fevz36pqxn44bare they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of graviqkx g4y/x evlx;+dx h l2;1;rbty at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effh+xy2rb; dqg/ 4exvkx; x l;1lect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the 9 s/2aylex7xr Earth to the Moonaye7 2/ xsxl9r experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bat/(8b4r0 z( y*sgoqpeo3+yv*bed k p wvhroom scale in an elevator, it says your mass is 82 kg. What is the acceleratiozo3(yb(v gkqvder0po *p*w48e /by +sn of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circuyx5 8qp;8y+ ztac: + vrmwf)aclar 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 mus; c+paxmtvw y y rfa)58+8zcq:t 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 aircr8 eb,u nla3vs.aft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of giu2(a 0lk ) 9xhqzmid pvo:-4its radius r, the acceleration due to gravity at its surface and the gravitationl9h:i0ma koui-qdgxv) z4 (p2al constant G.

A plumb bob (a mass j3 csq4jf9t( bccvv kjmf/(y0 (o):ci m hanging on a string) is deflected from the vertical by an anoyf(cs ccjk()b/f v(9 0 c4 iq3jvt:jmgle $\theta$ 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 of2p(w8vn7y vw g If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely wv v8wn7g(2p yhandle the curve?

  How long would a day be if the Earth were rotating so fast th hwo9 rw;mzuz0a 4/(,wev 90tdy xgu;uat objects at the equator (;o0wa/4zr9tv x;dh,geu z9 0wwm uyu were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart,p jtv ydz9h* /,6lbysn1yu/o 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 radtqbw62d6ns gu5fe yu(1r m*+mius 235 m. A lamp suspended from the ceiling swings out t *5 +n2gqbrw6(mtue1fdys u6 mo an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive iq 1x)gb-:(d rumy7bras the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the s m y-gqb7rbudi r1):x(ize 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 deduced the presence of a4hzqpx,ijv2q f+2mf4n extremely massive core in t 4i42x,qfz+jqvhfp m2 he 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 valley shown pro 5b36s.q4t 5h.7v;q mq e:dxknayg in Fig. 5–45. Both the hill and valley 5te..: rkhydn67s oqq3bg4mp;vqx5ahave a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Posbaunjdz ), m kgk0/y8:itioning System (GPS) utilizes a group 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 syu0nm,)jdakz8gk / :bpeed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2 fosyh*68xt b1.1 billion km, is meant to orbit the as8obt 61hy*s xfteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a s)pr89(3nc (jkwrp + 6hksubpyatellite in need of repair. Yo)9pnw8 63 y (+rurpbj(kc pkshu are in a circular orbit of 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 period of 3000 years. (a) Whxw; (diq2uszl4)6vhu *vco *gat is its mean distance from the gvdci2u*uv6; xz* s)4hq(l owSun?   
(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 ox3bs,i,z bp9 w+.ev o6)esjyb f G would need to be if you could actually "feel" yourselfsbpyiz+ojee6, w sbb) v,9.x3 gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centerco )uil xv,ko,o*e .3g of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years fro3xu,e *) oco.log,vi km 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 zeyenw)0 g894nuq 4tnlocated at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midp0uwngz8 ne)q9et 4n4y oint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass dq+azg:va, rhv5y b( 55500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-los0vt:uafab*64 t) jxj: l(q tlng sweep second hand on your wqtlflx j:tut:(a 4vj s06ab*) rist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arounyr0a--zodij fqm1 1vr 2jq: 8mo5axk3d in a circle below you on a 0.25-m piece ofoj: y v2d z35jxqi8mo-a amqrrk1-10f fishing line. 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 designed so th3u hd/zoq.nhi5v :nf v)sk)o12ix- znat a car traveling i2n5/z 3 vozvsxkud-)in)qo: fh .nh1at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiatingr5h 1p(fp0li ia2rkt/ curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the i /r5rhp0atil(2p1kf 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.$\approx$    $\times 10^2$