Sometimes people say that water is removed from hd a5. zmzg7n o,(uy,oclothes in a spin dryer by centrifugal force tuzhay ,.57z mond(, oghrowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels ( fxb)o7vq(wanue c2 3zhg+2uaround a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explgub ()+vnxea27uc( fwhzo3 q2ain.

Suppose a car moves at constant speed along a hilly roadjf vo6az.1 o/m-mfh-q . Where does the car exert the greatest and leh z6- o-1j /mv.ofqamfast forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forceoivliat vgobf5+xjr-v ,/7- +qwpx ;7kd)j9 vs acting on a child riding a horse on a merry-go-round. Which of these forces provides ib-+dj)/t gow-ilxv a+ vf95pxvkrq ; j7,vo7the centripetal acceleration of the child?

A bucket of water can t77 vb 37; wvgi 3jjr8x8fynmwbe whirled in a vertical circle without the water spilling out, even at the top of the circle when theg ixm7w y8;7 bjfnv vw33tj78r bucket is upside down. Explain.

How many “acceleratorsa r2u;n .*msc0 )oty hesn)3hrz7pod3” do you have in your car? There are at least three control n3msa7n dpuhoe z.0t sryro)2 h*);c3s in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small ngsqgp8e2 7zgm1 e7,u hill, as shown in Fig. 5–31. His sled ,qsgzgp2 eun 7e7g81m does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a cur0 fim-dty+e6kve at high speed?

Why do airplanes bank when they turn? How would you comp vfzgdp8i0s-/ znjx+ kr2q,(a ute the banking angle given i ,rgd-8/xvapnf i0z+jqz ( 2skts speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal pl/ugmk37 t(jy lane. She wants to let go at precisely the right time so that the ball will hit a target on the other side mk ugy/ jtl(73of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, eni *tyb-d4ztt tqhw8k57*8ehdk 1)yhow large a force? 8httb8et- w4)nzy*5 7dyi*h e1qk tdkConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways w-:s/ dpm rvi*eould the Moon’s orbit be dispr -dv/me:*i fferent?

Which pulls harder gravitationallvfrg-k ols-wjj 6uy-:v 7x0: oy, the Earth on the Moon, or the Moon on the Eart l0gs:wjvj:kr- x y6-fou-v7oh? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yriutt.k9)wuu; rnoa*x rhi- wy:- /2let the Moon's is mainly responsible .o29ryni/r;lk : tt-auu*h )r-ixwwufor 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 pd a+hpow2p (3xoles? What two effects are at work? Do they oppose each othp3dh wapx+2o (er?

The gravitational fortw idxvb m v*1(;h*w+xce on the Moon due to the Earth is only about half the force on the Mobx;t*( wi mvh+1wdvx* on 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 larax1z wzhjoo3- uo1,uve . *+sjger or smaller than the centripetal acceleration of the Eartoha usuvxo1o- j.z1z e+j3*w, h?

Would it require less speed to launch a satellite (a) toward the east or (b) tow aq:)xw ot k+y0op .-1ewcra(vard the 0p1ke)a.t(w vw a-+xqorc: yowest? Consider the Earth’s rotation direction.

When will your apparent weight be the greates oig)5hl :62whvkv m4kt, as measured by a scale in a moving elevator: when th)hmk2hk5o igw6lv:4v e elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could n j;y b 73rxie9d2db(qbe 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 objects fall, (b) the force we feel on our feet, and (c)9je3nbqbx2ry7 dd ; (i any other aspects of gravity you can think of.

Explain how a runner experien 6nb1q03gok*et otz; ices “free fall” or “apparent weightlessness” between sik0* totez;6 bo gn1q3teps.

The Earth moves faster in its orbit ar/ker rnqpw:, gukg,852xbl8 round 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 producip8b :rnr,k q,wg8l/ 5g kex2urng the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to higx , z;98uoi uy,cp5pave a moon. Explain how this ui,8ugip ; xzy5o,pc9discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Eart jgsxbvu)du*v3x 00 sewp:oja./w6 q*h 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 u3w/ax :.*jpdv0x)ewsbgo0 s6v jqu*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 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 travelin x/c ov)zqg1. k03sugeg 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 tht,m5tdo cf+h* e Earth in its orbit around the Sun, and the net forc om*t5td,+fch e 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)wf9 ci/zw9 kv 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of th)vwkf c9/i9wz e discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfa tw+s )-bp0bzfce, and circles the E)s 0p-bfwt+bz arth 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 Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a s .t prkzc.t o2 sw 811sww+(:(buhgwhpz10nhapeck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameg( a1nh1 h8hwspcz: wbrk z.top.uw 2(wts0 1+ter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vebd pbh33/euo9 rtical circle of radius 72.0 cm , as shown in Fig. 5-339/ub 3poh3ebd. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can r4cvviaz qcix- udw(1wlu k.1;nx, ):nound 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 icul(wq1 z-k; )c1 nxxaiu.vwv:,nd i4ndependent of the mass of the car?   

  How large must the coefficient of static friction be between the tires :5zx+ x l5m20kf.w abuwy(ci xand the road if.x u2a5ixw yc : +50flzx(mbwk a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate a118tm fpcp y t::hotv2 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, howfpc1t:1hvt2 oyp: 8tm 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 turnv -jvw3i3*bt ctable 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 static friction btw-*vv3 ji3cbetween the coin and the turntable?   

  At what minimum speed must a roller coastq,a4*e5p2y)tlaywf5 zcejot ts 4/3ver be traveling when upside down at the top of afyo4j/l 35), 5t4qp*2 atcetsv wy eza 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(xvcm1 if 39 izv+8p;ac7 vxs 7ink7sj (including the driver) crosses the rounded top of a hill (radius 7mx(+nv i7afzvssk97 x1jc ic;ip3v8=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-diameteredbz8 (hb gqs 9u7n .rw/.u)2xpx8vqf Ferris wheel need to make for the passengers to feel “weightless” at b8.8) ufxzv w/ 97rdxqe q.bh(npg2 usthe topmost point?    rpm

  A bucket of mass 2.00 kg is whirled4oc 9i7ck7kepc9d8p ke5 c e6y in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the roekko69 ccpc78e74kdi 59ycep pe 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.j1tz9oa ce e-ae:9.yq00 cm from the axis ofq-.zje9:eco9 1ae yta rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cy m7m0bw1 2huzolindrically walled "room." (See7 0ou2w1hmbzm Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockm *d 7 obe s/q*v7o5cgg8pjq1qey tabletop, and is held in this /opgq787 * qej5cogsm bv *1dqorbit 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 76ss8mq9m 7eay+l z-p1vb p ibuu0 y+aignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude o b9s0 vlym6paabui -um7pz+yq178s e+f $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 aq-)8ae azm ncg2yv e/k6(fq+of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masseso dui 8++9cqnm $ 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 p(cy,o5 p.swv310 $\mathrm{~m} / \mathrm{s}$ . 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 f6:,ls qy 17my pjwzsn,orce exerted on the car (by the ground) in Example 5-8 when n,qws yp7 6zl:y,1j msits 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 t(,iwl *iu,mr xmi+a7 mhe pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determinem m im ,x7*iurwl(+ia, the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a przwh yczg3 pd4p686pghg+ 69tpd7la/articular ins9a+ d ppp h r76lw6zcdtg6ygp84 /3ghztant, 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 gravity on a spacec/txhuxbow/;7, tco 9mraft 12,800 km (2 Earth radii) above the Earth’s su ,/x om thbt9xcw;o/u7rface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a --iecyxm-gc- +mxq c4magnitudc 4-xmx- egq-+ cymci-e 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 d mu f0yumo edr+:3wgi ,,ogs44)z bm8due to gravity on the Moon. The Moon's radius is 1.74 z,,me mu:3w 4df i0dg4)yb+8oo mu rsg$\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-g p1 fimp)+uy Earth, but has the same mass. What is the accelera-f 1myu+g)ipp tion due to gravity near its surface?   

  A hypothetical planet has a mass 1.66ipssi*+iq q64bv08 eu times that of Earth, but the same radius. Whatq *sqiiu8+s vip0eb46 is g near its surface?   

  Two objects attract each o t0(qbg 9m,vlsnlih);ther 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 accelerationc rm-2;gyj/ar;s7qcz of gravity, at (a) 3200 m ja-/qys;;m2c 7 zrc gr   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center tok6(umv rz oxxd7 .1w,n a point outside the Earth where thegravitational kumz o7dr.x,6wn(v 1xacceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star ha (,ww- tucg jg.tf;t7vs five times the mass of our Sun packed into a sphere about 10 km in radius. Est;wj-,t(twu7 t ggc .fvimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our S82z;rs xfx y9ha:0dliun but is now in the last stag;9 rd02x yh l:afzis8xe of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weii,rd aem*gkza8b00cd+pzjta n 6h91.ghtless while orbiting in the space shuttle. Your friends respond that th a+zatpa c r1,d0ejihbndk 96.8*gm0zey 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 corners of a square of side 0.5,l 3fink ;np1oa; mgpa3tn(e60 m. Calculate the magnitude and direction of the total gravitational force exerted on one s5p3a;m( o int31,ngkpl ane;fphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line uiz2fkhtx 98r/zm5-lup on the same side of the Sun. Calculate the total force on the Earth due to Vumhz f2 zil 98tk5x-/renus, 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* hg gtdtbq,34vity at the surface of Mars is 0.38 of what it is on Earth, and h,gtb d g3tq4*that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of ula2fy ah,81 :d lodz2the Earth and its distance from the Sun. [Note: Compare your answer to,dyldazu : h81lof 2a2 that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a d7e 4cu4i)q yldf(+:nk8hi ux satellite moving in a stable circular orbit about the Eard :qc di(hyx8 u+n )u4l7feki4th at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the qm-gt3vy 3w-j Earth. How fast must the shuttle be moving (relatjm-- wy qg3t3vive to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occ98ti8cc gt j2tknh6 g5sc/sh1 upants are to experience simulated gravity of 0.6/5 nc 1t 8h2h8c6gttkj scig9s0 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to :5xzk oy)o jk/ ve9t vq:ypeq*-xb8ac*o5u1 r orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the su1955qjex :z* ye/bx vkoy o:k-)ctruoa8v pq*rface 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 s u.z0v 3(zphswatellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earzp szu3vhw0 (.th?   

  During an Apollo lunar landing mission, the command mk mp,dl99dqn5b c6)r todule continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once?,ndmt599pk)lr6 q dc b    s

  The rings of Saturn are composed of chunks of ice that orbit the planet.+.on 1nvk uax0y ha5o( The innervo aa+xn1(hkuo5.0 yn radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (seespc y4qll//b+y/rq 920lks 4f5vxnnz Fig. 5–9). What is the ratio of a persqns 2l/+br04kq9 zyvxy/5/4ll csnf pon’s apparent 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 astronan*-qb0(jd j,d- v.lncp1 wbo tut 4200 km from the center of the Earth'dw lnj t-b pj bc(.,dq1no-v0*s Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of e i 0tqo5bar/r ntv.:z,u hgy0(qual 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. What is v noz05qrb0h ytr( ug: .ta,i/the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 5 4(x,n6odo wjm 0r q;shlhz*e25-kg woman in an elevator that moves rxj2o4 weol 0q*(hsz 6dh;,mn
(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 fr mjwtxf*qy; 6s8bcy ta:i87p,om the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accele8 7*yj m86aqifwtps:;c,bx tyrates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits v0lz 9f4eah;beery near the surface of a planet with period T , the density (mas0l ;94bahefezs/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 tk i1 q7rf0wp-vhe Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surf-vrk 1f70qipwace.    s

  The asteroid Icarus, thoug.p bqwa r4/u6 tq*t, ,88ud x6qjisingh only a few hundred meters across, orbits the Sun like the planets. */ut ajuindqx6b,.t4qi8 8g6 srp,wq Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.55vh ;;zle5*4es wenq ftomrebvv;) 9; $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comc (6*kv4s4wru9ow o xpes very close to the surfac (ru496so xk4p wwoc*ve 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 the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxyg7czb,fl+ s1y lrbwxn0olq8u8632 fy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest m0d,y 8 bty7b b2cwcnuro*a()aoons of Jupiter (those discovb ncbcwda7a)b 0ut8,2(o *yyrered 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 period and distance of the Mooe5i..f/ancs(vqar ,n n. .nvfn/ (ecq.sia5 ra,   $\times 10^{24}$

  Determine the mean distance from Jupiod t ukng*car2i:7961 l xt)rwter for each of Jupiter’s moons, using Kepler’s third law. Use wn au2:* tt)9xoirkdlg67 c 1rthe distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragment my7kq4y5pc) 2.llbt q-8rm7vsss;dw s (which some space scientists think came from a planet that once dyl7sr.2t smyqks-c ;p v58)ml7bw4 qorbited 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 d:o vbebez70kjmq,1e ec:c0 nipo,-e5escribes an artificial "planet" in the form of a band completely encircling qe70i-kcem,one: obbv c0z1j ee5 ,p: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 by swinging in an arc from a hanging vine (Frol301n 2n wlu+5lwwz ig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum spen51nu llw 2w3rol0+wzed 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 gravity be half whxx e h 3+k,c+mhls7o:ha4ju e4at it is on the su+:7k he3ehxa,c+ju4 o hsmxl 4rface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circliluq h) 9azr7t*aq 7roicivo qz,*m): f:9 st:e 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 are they pu)a t t,7s*lm r7fii*z ::voq9 ci q9u)hra:qzolling on one another?    $\times 10^2$

  Because the Earth rotat ,j (guxd,ft :gc; podw9jg1hwgd*b5 muk133oes once per day, the apparent acceleration of gravity at the equator is slightly lepfdwhg: w9gx1 dtg(d35,ok 3c*muj 1j gu;b o,ss than it would 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 tv1vct.k qw)9 c1 hoif2he Earth will a spacecraft traveling directly from the Earth to the Moon experienc.c vf) i1 t91v2ocqkhwe 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 b lk.l6y *a+it*( u4q voz*db6pmsmj ,when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in whi+bm.s a ,b** 6p6imlk4uoz(y vl*jdtqch direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that vozs 3)l9 ucrca j75c.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 (revolc u.rvoc) 5cz l793asjutions 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. 5yb3 s;5dvbeb6–43).
(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 pvu/c)9it hj ,v31 bkrilanet in terms of its radius r, the acceleration due to gravity at its surface aijv)cr/vh9, tib3 ku1nd the gravitational constant G.

A plumb bob (a mass m hanging on a stril* g kga-b7up3ng) is deflected from the vertical by an angle bpglg-7 3* auk $\theta$ 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 (1vyn.pthzjs. 9 (u2m0vbsg bcoefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car sa( mj.pugh.2syn vb19tvb (sz0 fely handle the curve?

  How long would a day be im /n *0i9qgymmf the Earth were rotating so fast that objects at the equa i0mm/y 9gm*nqtor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart o/9p*rjxo9k itgacn7y5 td 8) lf 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp suz1f5 5cr g*tzoxm qr18spendedrfc5zmgxr811 5qtz*o from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been)id k,b5e y 127z47lqx3 cwhszr9kxhp claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: massx9pqw723khb7 lc,1erz z)h k si5d 4xy =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 Spac-px:ao48 scb y5rn+li:/gmeu q-k 3iue Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be isb: i-+nxk:/5e-m38auguco 4ylrq pa 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 vx m(.kmde4wo 5alley 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 can the car go without losing contact with the rx4em5wk (mod .oad at A?

  The Navstar Global Positioning System (GPS) utilizes a gsnv ((iut e2sm 3yz19troup 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 t sy(e9i3st m1(znv2 tuo 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 Rendezvoux , :7yo1c4dxsvwmyyg/g cg8 e7 t:3hcs (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid : 7yy8co vdtgxsh 1c e/y4cgxm g,w:37Eros 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 satellite in nl1d bih/h6f )ceed of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behindc)l hd 6b1h/if 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) Whimm 8tz /976bldm6irmat is its mean distance from t9 6mbl6trmd8m/i7m zihe 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 actua*uqjk/q tr0ps83 g:bally "feel" yourself gravitationally attracted to someone near *g8:jartq k/spbq 30uyou. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the p;kiwg2:c;io- o bg- tMilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-yi-;i gcb; tow g:2ko-pears from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on eachq whk*t aj 1kl3/gcr*/ side. Find the magnitude and direction of the gravitakc/j3aqlth*w * 1 gkr/tional 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 5yy3: xl cl4qdb09roy6y o)uk6500 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 l4ip (soz2e* fpc 15zbthe tip of the 1.5-cm-long sweep second hand olp*o e2pzc 1sbif 5(4zn your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinr/2cdysr17a mxubli gng: 9k9/b9 o.gpgj - +kker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a comp g o1-jkb9x:.guak+r cpd7 glb9 /s2yinr/9gmlete 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 that a car jh9rf7fj52fev x)mrzyz6 7:v traveling 67e7m)frr5fj9 zz: hxvy2jvf 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, utilizes tilt of the cars uj0rnn79z qiax75o y 4when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal accenn70izox a4u95j yrq7 leration, 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.$\approx$    $\times 10^2$