Sometimes people say that water is removed from clothes in a spin dryer by c- e ):u6 uiilmz(td2abentrifugal force throwing the water outward. What is wrong with this stuum e(ad-zb i 2:il)6tatement?

Will the acceleration of a car be the same when thfk) j.uzgu wzzz 152z7e car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Expl2 zfuw5jg1.7zzkz u )zain.

Suppose a car moves g,9 fxy1os1vs at constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between twos9sgo 1xy ,1vf hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse 5pgfglgzyff( r;q , cb f* e7bo4a)v8*on a merry-go-round. Which of these forces pre* * g8fl4y(5rg va,zbf 7)bgo cfp;qfovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spillingf7pj ,rf0+:evcm dhmq0 2ax( p outpar ,7q2c0+demj h(pv :fm fx0, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in yx, r4xjioiby5):6w ekour car? There are at least three controls in the car which caky b,x 45i e6i)r:jxwon 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 orv(;2v rplp6al/hk q8 f a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieq vl8(vrakp/r6p h2l; ve “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 inwf0ndo4y;b 7 auux2pqqohd: :+ ard when rounding a curve at high speed?

Why do airplanes bank when l1 ,g 5 s6fwbbjfaky-0q7ev; mthey turn? How would you compute the banking angle given its sblf jbmk07-5;sa, fw y 1v6gqepeed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. no;tp 5o;-h8 tc -67 ih4jyev2znu fdnShe wants to let go at precisely the right time so that the ball will hit a target on the othe fo-8y2jhv5 z-n4uton din6c;hp;7et r side of the yard. When should she let go of the string?

Does an apple exert a gravitational +tkvcfqq6 h2- force on the Earth? If so, how large a force? Conqtcq+hk62 f v-sider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it il6i9n g0fxh m6s, in what ways would the Moon’s orbit be 96nl imf6hx0gdifferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on t5 d )(ytuvurx-vk6p+a he Earth? Wh5x+)t(d p6uv u-krayv ich accelerates more?

The Sun's gravitational pull on0 f m hjz43(tpzx;fo)n the Earth is much larger than the Moon's. Yet the Moon's t0f zx4hj (pmz; f3o)nis mainly 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 efa,h/yw::palen c 98mf fects are at work? Do then:,eal/fy 9:a 8wh mpcy oppose each other?

The gravitational force on the Moonv- lm.abh8 wj7-uk4ga due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pugja4m .8aubv-k7wlh -lled away from the Earth?

Is the centripetal acceleration of Mars in its orbit mefko( i;wq4 1;hpgc*around the Sun larger or smaller than the centripetal acceleration of the Earth;ghf 4 e* iq1k(mwpo;c?

Would it require less speed to launch a satellite (a) toward the east or (b) tr)aw30 d+0m0jqtop+jtr d+zsoward the west? Consider the Earth’s stp mzro0+qrd)+ +d 0jt wj0a3rotation direction.

When will your apparqh )r3aur *ro5; hlnm-ent weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? I*ramlor)-n ;rhu 5hq 3n 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 be adversely affecty1gijrg t(7 t6ed 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). igr7 tgy t6j1(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 629 rb 0mxw ;/r1a eyxovyp-sb“free fall” or “apparent weightlessness” between 2rbbs y1yamwrxve;o- x0p 96/ steps.

The Earth moves faster in its orbit around the Sun in Januhg.ela8/g t5qary 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 its h5.qlg/ta 8eg orbit.]

The mass of Pluto was not known until it) -l-rfic cloq);xzf1 sb n-t0 was discovered to have a moon. Explain how this di r-) ql ic1nflxs0t) ;of-b-czscovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational puqf a8l h2e2) beko6-jfll 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 6el2obq2hkfja)f-8e pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a 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 19p h80gnx31o0 x hhz:os80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Eawyao*o0qk 6jng3( ida8.f;p x rth in its orbit around the Sun, and the net forc3 xa j0*k8poiwfnq(6 gad;. oye 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 d*cj c8zd: ,mzcs:v h5miscus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the sm: *v5hc mj,d:s8 czzcpeed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth'sf+ tos ,shnn 3r6 /ssb(jwo3z+ surface, and circles the Earth about once ev/ sor+nfst,3b( s hzjw63+os nery 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 at;9eelur ngl+6 p m42j speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter n2;je+lte 9mp u4l6rg is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circle dx+kkcr9-b82 1tfywb of radius 72.0 cm , as shown in Fig. 529yb1+cf d b-xrwk 8tk-33. 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 round a turn of radius 77g+a:+vtbh j( m m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the m (+g+ha :mjvtbass of the car?   

  How large must the coefficientwaw,r8lm nfpi-0 d)ay2ev8zc x.5kz: of static friction be between the tires and the road if a car is to round a level curve of radius 85yrm,en8 a5wd0w -z clv k)8:.iapxz2f m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rota q1shz)l:mrltqs3 4 y5te a trainee in a horizontal circle of radius 12qs1 m:5rlh43y) tsz ql.0 m . If the force felt by the trainee 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 c8lk ta ct8d3jti38pw8 m from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rattdclta3 83jw88ptk8 ie 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 be 2bazv p -/.7:xgscoqs/ 8wh xl4fdkd1traveling when upside down at the top of a cir1.gl cxdfdxk8/vo 2- sa pw4b/ qsz:h7cle
(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 fz.3at /jfuy: the driver) crosses the rounded top of a hy .z/ ufajf:3till (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 needf4igvm/hzz f-b9 on ,mqkkl39 kd5:t7 to make for the passengers to feel “ n-4d7gzf :k9 f b3t,hk5vmok9lzq/imweightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a ver li(-z 3g4by0; a jm3ds1fzkyvtical circle of radius 1.10 m. At the lowest point of iygy3 (izal0 z1m-s;j34fvk dbts motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.o +099m e ,kl)+jt 70ypbtsn hmgk8htx00 cm from the axis of rotation is to experience an acceleration of 9t x btm8ko) he07t h9klpj+0msgy+n, 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotateo a5hve2/f z3.ltd1xw d in a cylindrically walled "room." (See Fig. 5-3doxh le/t1 w2a.53vz f5.)
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 frictioo2podb )y4 .msnless air-hockey tabletop, and is hels2)opy4o.m db d in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by 1d; hz2j 5xg8a5/ ygpvw:duknnot ignoring the weight of the ball which revolves on a stri5;pk1 ud hw:n5y/2vjad8xgzgng 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 rak+a:das u b6q;dius 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 massessfz.(6 im9r dn $ 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 vertl1knr i*gc .tamgt6,) n/,uupically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centrip1flsr 1uyy)h (9f fr) on6tp0jetal components of the net force exerted on the car (by th)9f)fo1ryf(t0 ny16uj hrlsp e ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformlyja3lo,e0i lx 6+hfmu 2jppw-3 from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial accelew j+h -l il6j32opu,3xmfpa0eration 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 9h gsf3/sw+,*/bz*hii wlo qm horizontal circle of radius 2.90 m . At a particular instant, its acce,h+bqf3wzwm */ l*ighi s9so/ leration 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 g +7noc f5ahbp*h:+n b0 xnq7bvravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass7*+5f nn qavxho bnbc7b+hp :0 is 1350 kg.   

  At the surface of a certain planeez(w(,pe1o y (q vcu,st, the gravitational acceleration g has a magnitude of o,e e (z,(uc1wsqvp(y12 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 rasgpuy2(i : 6ezdius is 1.7 (su6y2: zpieg4 $\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 k4ui5o vc20 (ig;7r wiccqiq- that of Earth, but has the same mass. What is the acceleration due to gravity n ciq -07cg5k2viuwqic r(4;oiear its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same: 8;hw c5g5tjgim1uan radius. What is g near its surfatjgc :m5n;1 wgiua8 5hce?   

  Two objects attract each other gravitationally with a force of 2.5+-mr.e+tpx z yuw;8lc $ \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 xct ts(c7+wf 7gravity, at (a) 3200 m7(+ws t7x fcct    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wk8fcxnyg27ec:) l+jz here thegravitational acceleration due to the Earth i l8n+ecgf)kzxcyj:2 7s $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has am rgwbhj0b67)gg /t5five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on 7tjr0b5g)h/ wma 6g gbthis monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun buwlmi6rwu 8)bw9(qe6 a bi 7jz4t is now in the last stage of its evolution, is the size of our Moon but h 7u wa6r4zj6)iem9 b iw(ql8bwas the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while hv*u(unib x6r /bp )v;orbiting in the space shuttle. Your frie) xr;u (v6*buphbnv /inds respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squarer :ik);c7 sbc86a 4; czmeqc t)b /tnunb91ohd of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on onr;6k qcdh:uz 4cse1 ;8n m)bta/ bci)t9bon 7ce sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the h +el5zd 4k5dx-dq-e zplanets line up on the same side of the Sun. Cal5d5zl+hk zd edxeq--4culate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars 9q5roks4lghy+ smwj uq606a/ is 0.38 of what it is on Earth, and that Mslqmh6 w ksa5urg/4 +0yjo96qars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the peri6g oh-w zmk+3wod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtaiow k+3z6-ghwm ned using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satelli 13v kx;xcaeu*te moving in a stable circular orbit about the Earth at a height of 3600 km1ex;xvka *3uc .    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Ea1icfkttc+; m /rth. How fast must the shuttle be mk+ /im1tc ctf;oving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupantsndaxl nm95m;i +6 2ldu 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 Question 21, ;m ndlmu9 ial2+ ndx65Fig 5–32.)   

  Determine the time it takes for a satellite8*xot2 d brl.vfk+xu p51c ku* to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a vo.fu21 kd x k*5xbpu+crl t8*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 frza v epfl2u1.6om the top of1au vfe.26zpl Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to oh;,p vxq vp*5.vnthd*rbit the Moon at an altitude of about 100 h t5qvh*x d*. pvpv,;nkm. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that ooppcrl9: 5ha 3rbit the planet. The inner radius of the rings i:ca pph o5l9r3s 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. 5qev3.d;78 ctxc j ;y43e xtzu(ni hdh1–9). What is the rah 4tx yte7zc 8;jvxend3(ud1 c;3i.h qtio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight no(7y bb71*u) 3dcwd,orsofm of a 75-kg astronaut 4200 km from the center of the Earth's Moon inrb mdyoow(s c773b fdn,u*o1) 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 equal bn(ny1j sdu l7u.2s yoh019k eizma2*mass. They are observnehzs d.lyso1m71un9yb0ji 2 a2u k(*ed 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 an elevator ). bq4)e8wwy8v pclvxn;y9pb that movespy e9n.88vv p)yl;w b)wqcb x4
(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 ellu,z 1snf 23psevator. The cord can withstand a tension of 220 N and breup2z1n ls, sf3aks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits wb;olpb,0q 138ywq q maz*.c qvery near the surface of a planet with period T , the density (mass/volume) of tm pq 8l,* 3a0q1;qqybwo zbwc.he 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 th/a99z b)ubr etw:7ob roq*(ym9n mpi0e period of the Moon (27.4 d) to determine the period of an artificial satellite orbitinbu9w *b (zt0 bm 7 oyro)p/:mrein9q9ag very near the Earth’s surface.    s

  The asteroid Icarus, though only a few ht8v v4wbrzp (:6imiwh kt:ry-cau de534gm,(undred meters across, orbits the Sun like t(vvrtpw:m,-3ucr: zb4th 6g e m(k iyi 4wad58he planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagsqdfo4vu-gf ,5ir87ye distance 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 roughl 9w yvn+l+t1+*3xq ujsx .otuqy once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of t*w tv.tjsnxlqy+1x u+ +93qouhe 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 7v54exf4ll+ gyegnt1 of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 distog4 ;w)lp/cat k;klh1ance for the four largest moons of Jupiter (those discov/gh4 o1lwpka ;l ct);kered 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 distanu l3 rs9nd*w*7boek kk7tf (h+zn6uq,ce of the Moon. ,(k6* dzn7br3 9+k 7k tnlofhuw *ueqs   $\times 10^{24}$

  Determine the mean distance from Jupit *6wzlg7pwjrq )9o3iser for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Tablq*93rs7g6jwwzop l) ie 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 Ju5gs7(dz jc,oi*x dq6n piter consists of many fragments (which some space scientists think came from a plgx d*zcq is6(n75j, odanet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tas*rp h1w;kjhws ;;87ap8av c ble describes 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 distans8* v8 ;jr;awp71ch;a b spwkhce 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 inb-d x:cb;l,5ky li2-ghtxt,a1 cm*oz an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerygh1tb5tmcad:2*i oxl -k ,;- ,zclbxting 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 acceleratis1 to+0jmuz e,on of gravity be half what it is on the surface? eso1um0 jt,z+    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin 65*x apohj0z din a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulli6x hp0o5zj*da ng on one another?    $\times 10^2$

  Because the Earth rotates once per day, the appare i:b6y-fi0o b*cndeg( nt acceleration of gravity at the eqb( idog 0fne*b- 6icy:uator is slightly less 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 the Earth will a spacecraft traveling directlg es)mlq 8xk86,pm5sm8kwv 2uj )qo:ay from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite force5wk 8 v2om)sk:)qgx8su l8qm a6j ,pmes?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathrt g o, ymw(pm9,x00c)s8uqsm hoom scale in an elevator, it s t x0ops0g) m,m8qy(c9,u hmsways your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular*am:+8is g0i.vcg ipt tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the : i g*p8cm0svt+ ga.iisurface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fi*4f,e 1jubyoug. 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 its radius r,0k3 .mlxc4 xd y/pzfmf5-cs8g the acceleration due to gravity at its sxmgc c 4/f5 lks.-3mfpxy8d0zurface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected frk, s4r:tae thrza .3q7om the vertical by an angle,zktt7h4sr r:.qa3a e $\theta$ 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 coefficient nvcb 5heb- ;4iof static friction is 0.30 (wet pavement), at what range of speed;b4hnev5bi - cs can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fastc0h-oo hk 5uqpw k6m40 that objects at the equator were0kw qm-okph 5u4hc 60o apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dista 86c oqj:e2b5bwd2 (u xpxkh9i4-gbntnce apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 2hkxo 1p -wzgdxj) ha3m,.7y,h 35 m. A lamp suspended from the ceiling swings out to an angle oho a1 d-x,7yp.m x)h3kzwjg,h f 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Exu z2e) 0ga3yddf bg6y96in/c- )jjzk di7*qzarth. Thus, it has been 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 dafyk -*dijz qa6g)u93dc)/gx 62izj y70bez dnta 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 de vx3iq;)cw8g vduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by meicqw;3gv xv8 )asuring 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 if psw+ oryodl+kyf-3 nxr+ s.:bpi76c6 /hm- in Fig. 5–45. Both the+m66:.sikwylf7b ry fcrp-p-dn /siho+ o x+3 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 road at A?

  The Navstar Global Positiozvb:+dc.ti as oj)29bning 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 distrib 2bbzo9 j:)i.s+vtca duted 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 Regr:8:2hcp0jaa:in02qbtf z -te n gx,ndezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the aster:nzgr0na ic8 2t:g t-a2qfephj :b0,x oid 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 s x7l kcm 9lib05tafbx//o4fiief4 s+8pace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (xb8kf sm a4flifc4o 9ixi//l+705t eb400 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 ewyb()pxv*i1 0kny 7+ b3ki gchas a period of 3000 years. (a) What is its mean distance from th1pc 7ie*0) kix ynby+wbv3 (kge 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 bcd2qy d .88, kdnx)anxe if you could actually "feel" yourself gravitationall2.) 8kad 8 dxqncyn,dxy attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of th 5cu0wgbg (1(jk htuc nxukc3, 0 29jjytl,sc/e Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 lighkltxy1 cuj cug,gw9/0t3kun,bs (h 2j5 c0(cjt-years 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 thvj*ct sk 28:sue 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 midpoint of the bottom side of the squars2*:ksj t8 uvce.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits thctl tr 7ye 8gwj)igy748 gk5b5e 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 thenbgrk jt;s) ;;xx5ephw ) h)e3 1.5-cm-long sweep second hand on yokgxsrxe ;))hej3; hwbn;pt5)ur wrist watch?    $\times 10^{-4}$

  While fishing, you get bor0.mhbps nn4n h t 32qa2yk.w5ued and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes wwu0a2shp25n n4.mkq. hyt b3nith the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highwab/6dbbm(/3 u9rgda: axfstn v4b6 g u;y is designed so that a car travelbd/m 4a/x sdg;btb g9auv(n63b6 ur:f ing 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 up,n6eh7sn nwsb 7n .1the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the frict6sbn n,np7.1shnw7 euion 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.$\approx$    $\times 10^2$