Sometimes people say thatjd -t9dxtn d(- water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this -xtjdtd ( dn9-statement?

Will the acceleration of a car be the same when the car tra80*cnu3s4hh3 ) fi vu)ipa:rpekb ,ovvels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same spee)0or3u, kni v i3vph p uchs*)ae:84fbd? Explain.

Suppose a car moves at constant speed along )fo-z7a nr8v78ojb5s4sffzz a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, ( fsoz4bfra7zj8 fov8 -nz5s) 7b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-kwq .xq.w(8z*4mkdto round. Which ozdtqo w4mk wxq8.(*k.f these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a /:g kwjz3w v5y hyutc338i7y wvertical circle without the water spilling out, even at the top of the circle when the bucket is upside doytc7 53wy hzjgyk3uiv:8/w 3w wn. Explain.

How many “accelerators” do you have in your car? There are at least c *jsab;0sep j;ii3m(bl xf8; three controls in the car which can be used to cause the car to accelerate. What are they? What accelebfbjs m( 80s ljxi*e;3;c ia;prations do they produce?

A child on a sled comes flying over th 1ra9 e ffgj1v8i l4lp0g62vqke 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 normal force between his chest and the sled decrease as he goes over the hilr9ep4 if1 86gjqv0v2a1f lkg ll. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a cur3r 0wsdxct agw5 sq*b2hkutl+31-u,lve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle y0 (:fni 6fhnrygg(l.given its spe:n( gf(g6lyyin r0 hf.ed and radius of the turn?

A girl is whirling a ball on a string around her he *uwqc4m on 9k+hlp)q,/.ptipad in a horizontal plane. She wants q)u *qp iwntp. kmoc,lp4h9/+ to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitat2hh q6djq+z 0 snhp((h.pweb/ional force on the Earth? If so, how large a force? Considerep/+b6hswh (. d (jqzpq0hhn2 an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double wha*l7 njaxsux-1t it is, in what ways would the Moon’s orbit be differents71-axu l nj*x?

Which pulls harder gravi8j h(v upg/fb ogna;h5x w1,7ztationally, the Earth on the Moon, or the Moon on the Earth? Which accev1gf,zn;8bxgh 7hpw/( o 5ujalerates more?

The Sun's gravitational pull on the Eart)fdd9:4bw*m :k1-mi xtobk)ax q s/k oh is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one sid*)m / mbo)kt kqx-ka1f9 bo:dwd :i4sxe of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effectcn+0h 6isgjy( s are at work? (sng+c0 6j yhiDo they oppose each other?

The gravitational force on zc*mz*yb * -q +:uavu( bgu;3ab dxy;s1 qel;mthe Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from (vu; u yg1msx+;abq e:b*yzqd l -cab; *3um*zthe Earth?

Is the centripetal acceleration of 3vocdtyn yi( gq70,t. Mars in its orbit around the Sun larger or smaller than the centripetalnycyvt,. iqd0tg o7(3 acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward t2z cirp7,lf,jhe east or (b) toward the west7lz c jrif2,,p? Consider the Earth’s rotation direction.

When will your apparent3da *g3s2rm7fghulz7 weight be the greatest, as measured by a scale in a moving elevator: when t23g f7rhz sugad7 l*3mhe 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 out5s q8d+(/wc g 2qg 4*ucjh x dx+p:ktbft29liber space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shel b2txg+cfdj hduc*8q4qg2t 9b/sli(+pw:xk5l 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 experiences “free fall” or “apparent weightlesuy*.*.od iekwsness” between ste*.uk.w*ioey d ps.

The Earth moves faster in its orbit around the S q-vdl.h/0vyqo g(vnopx c( .3un in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor l((-.v/np yq0 oh . vcvqg3xodis the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was n*tlc9.ybqj r3b5q 7jmot known until it was discovered to have a moon. Explain how this discovery enabled 3.9lr7jytqmq b* jbc5 an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's.pf/:sr2s4wa. *s vbkuf; z glg x0unx ;9n,9lt Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 kxt* v0ns; l/4f;wru s9up9,l.nzgx :bf2a g s$\mathrm{~m} / \mathrm{s}$ . 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 ;ly a/r6i8 au qqh(zmfgm37 8d 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 centripetai/8en* b wooxrjeh((2-s - smql acceleration of the Earth in its orbit around the Sun, and tonqw ho ( miex-(8/s-er2j*bshe net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates unif6+r5dx 1)2y hlpaektd-8 r rxrormlrl1 5rk8t)d xxa-dr e+2 6hrypy in a horizontal 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 Earth's surface, and cirz1:8fu bp ved;cles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle p8 ufd:1ezb ;vin 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 accele-qs9eqvmw zz :u 2:e3sration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wvs qz:z ee3uq2w:-m9sheel’s diameter is 32 cm?   

  A ball on the end of 6 1lh qcw5je-na string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If i lnj6q 1ec-w5hts 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 as*ff anq yrjbn/ m53zq+4qs69 turn of radius 77 m on a flat road if the coefficient of static friction between tires and roadz+qs 6 bqf5ja/s3r yn4nmqf9 * is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and;x+ zvtzx msvw0n2k ;4up .;ft the road if a car is to round a level curve of radius 85 m at a speed of 95km/h ?t mtz;v4; 2.x knwvuzs0p;+xf   

  A device for training astronauts anxct h61) v op94ytjy7r;kd :obd jet fighter pilots is designed to rotate a traiyd:co 7py r6hk)tt;9 jx4vo1bnee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how 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 rot:49dz xdidy4 yating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on theyyxi zddd4:4 9 turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down atzm.(vzoclvb:7.t9:u3 tl z gz the top of a .v(tb: ltv uz97zgm 3:lz.zoccircle
(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 top q 8(ho1qo 04tp -usafwof a h t80f p (1uwq4o-oaqshill (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 .ip pk 4 6sk4mb-+lbfuper minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost po 44spfp-biu.+6 k mkblint?    rpm

  A bucket of mass 2.00 kg is whirled in aensc73o3vh0:fq +t pi vertical circle of radius 1.10 m. At the lowest st+vn f3i0cq7e3:ho ppoint of its 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 centrif8ipncfw45y (bfj b4w3 uge rotate if a particle 9.00 cm from the axis of rotation is to experience anbcb4ni3fw( jpf 58wy4 acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyli+/r :n3.duekypsl) c endrically walled "room." (See u).el+en /c3kyprsd: 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 ri 5x +yw4c-db1)iqg ypotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cqi5iw p4+1ybgcd) -y xord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the we9todl* h,m9pa xexq;4ight of the ball which revolves on a string 0.600p*d 9x9 lm4q e;oxth,a 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 off ty sxjo9l/xv idsa);1b8 s39 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 masset,fcqkyv:ia 6-fo2 t,s $ 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 ng 3xyfqy8er0-;8(*ik w rs fv3at5scby diving vertically 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 centripetal components of the net force exev 5wdr1i szvq+ 1 t;wv/-4qnqdrted on the car (by the ground) in Examp;5+vwdqn vq-tsr/ivw4 qd1 z1le 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 a2unp79qjh e4 cccelerates uniformly 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 acceleration of the car when it is halfway through the turn, assuming cons9uqce pj24hn 7tant 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 .dd) ei zjx ;mrl80(qd((xf0yb At a particular instant, its acceleration is (f8e;x (l(q mj)xrd0iybddz0 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’sa yeok c5qx/)* tlb7p5 gravity on a spacecraft 12,800 km (2 Earth radii) ax)eb7yqk o5c*lt ap /5bove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet,lqy:z (w7ae/(v sw(sb8 +ngmy the gravitational acceleration g has a magni( ng a:ss7w(/(8mvzyeb+ yqlwtude 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 dc axj/ 4wj8x.jb)md0Moon's radius is 1.74 ax wd/8bm4)djj x0c.j$\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 Earth, but has the sapci*jk r;m41dq b/tjhzz n (8 g7(cm(gme mashprtnm8cj (1;m gk c(g /*zq(zj74di bs. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has0j8 jlcnit84a bj/ /tdynoq +0 a mass 1.66 times that of Earth, but the same radius. What is g near its surface40djn//a8t+b8j nc yojqit l0?   

  Two objects attract each other gravitlq j8d-vc 2r3bationally 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 dopx ;7 9)c0 bu:tmmgdxx3jzo8p-0htgravity, at (a) 3200 m g38)xtj7xzmcpup-od mtb0x;o09:h d    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center prl:g a+jv0-ato a point outside the Earth where thegrrag+ap :lj-0vavitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mas6 ;+kz 02l+b hli8rqbwz-sypws of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monsphwz2 wblkzy br6;++ -0li 8qster.    $\times10^12$

  A typical white-dwarf t;gjw 2mlv-3p- 4a4-lal heg tstar, which once was an average star like our 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 the smw -gvt4l pjt;a324h --a ellgurface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space0h cxnlid*6pz -9 dr:ok:pf0igi lv 5 f:i5r4i shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 k:p-c9 4zx vr0fo:5i idd60glfl i5 kih:*nprim above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at lxhs/cr vz), ,the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted rv,xc,/) h zlson one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most o8adphuyob rpq (020 s mb+iq(,f the planets line up on the same side of the Sun. Calculate the total f qhu(,pqp2sb 0+m0dr(o yb8iaorce 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 su2w w w1prd(e4brface of Mars is 0.38 of what it is on 1pwb(ewwd2r 4Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of th-agxrpk qa(06 3vddt 3e Sun using the known value for the period of the Earth and its divdr gp6-t3(xkaa0 q d3stance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving invz+ lplunx-z;5tx9m , t0hk5d a stable circular orbit about the Earth-z5p tu9m vnl;zk5l xxt +,0hd at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the /ym2 .fb8-d*d5jo cp efoq *ycEarth. How fast must the/*ybd.yeodj p *c2-8mff qoc5 shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occup -6jqas tf0yuf/ax(*t bj*g7sants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is67* ( x*-abgytsqtu/j0fjaf s 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 orbi6pe; o,k*geb *n8jxwbt the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result d** b6p,jb gknxo;8 weeepend on the mass of the satellite?    s ~    min

  At what horizontal vh 9pp+ rhlj4zkx*0wz0elocity would a satellite have to be launched from the top of Mt. Everest to be placed in zhrwhkj*0 4pz0+px9la circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module c1q( v6c vreok7ontinued to orbit the Moon at an altitude e6vcvo(7rq 1kof about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The ieyrrn+by 8 d** gy6gmm6hb7h0nner ra*6n6 eyb md7r0mgrhy+b*gh8 y dius 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 riyf121)n*x jugew 6f9w 6 grxaotates 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, and (b) at thj fgu ax)rewi w*6nyxg21196 fe bottom?
(a)    (b)   

  What is the apparent weiyf br8a;ub8bre+4 qu:0 e i(aoght of a 75-kg astronaut 4200 km from the center of the Earth's Moon in au0(ae4 rba b:i rfb8y8 oq;u+e 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 z)ol. almrb5 9v* kg+gsystem consists of two stars of equal mass. They are observed to be separated by 360 malo.vbr* g5 l+zgm 9k)illion 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 ut/,b rq fygw 1h2n(,qread for the weight of a 55-kg woman in an elevator that movesqfnu, tw rg,h2 (b1/qy
(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 su9x ov v,3w;mcppg )jr:*1qh ceiling of an elevator. The cord can withstand, p h)cwujvm o sx:1p*;q93rvg a tension 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 surqkuiehpb gf:f99*i6 4face of a planet with period T , the density (mass/volume) of the plap 9 i6k:f4bf*giue9 qhnet 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 perio5 ,v*iecn m-zaa p*r(rd of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very ne-r*invr map(* 5e,ac zar the Earth’s surface.    s

  The asteroid Icarus, though only a few hund:spod ;8tf,e rred meters across, orbits the Sun like the planets. Its por8tes fd p,;:eriod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of *9don e*/mda m4.5 $\times 10^{9} \mathrm{~km}$ 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 rough4fmrb uueb+.. ly 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 the comet from the Sun. Is . f4r+umbu.e bit 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 cen6ox x,w c8h+ vzh7cok*ter 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 distance for the four la,zp3 wlh9 ckc(rgest moons of Jupiter (those discok (zlc9c,h3p wvered 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 perhyy/e(ge( /g-e wutl4+u9npaiod and distance of the Moon. -l/t/y9h ga gw((uy+e 4ep eun   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moon5 ci7nidu d14is, using Kepler’s third law. Use the distance of Io and the pern i5c4u17id diiods 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 fragme lj 8,whxbkp5* 4hi:hvnts (which some space scientists think cab8*iwx k hjv54phl,:h me from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "pq we/-qdf krx((oe3,j lanet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and thatqr-3e(fewq / x,(okd j 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 (Fig.tilq:xl0 43: u 6few00cr zsis 5–41). If his arms are capable of e630z rs:w0ecsxtui4i :f qll0xerting 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 of gravity be halhb43oeynbi 416e7 p)u pidacq62ikd,f what it is on theq41p ,2 4nb 6iadie duy eb)hk6cop73i surface?    $\times 10^6$

  On an ice rink, two uq/m 2 m40xdgkmi.p,z skaters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their .mqpd,x40kmmg/u 2iz arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotat10hgw uw u g/ :.ztz5*,yzkrfxes once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effecf*/wzztz hk:xgu5, .ur1y gw0t. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft 2 lp9hx* (hmczl.sv z3traveling directly from the Earth to thzv*p(m hxl239. cs zlhe Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass isy5m f wqv3w6 n .vz4o68yordg9 65 kg, but when you stand on a bathroom scale in an elevator, vy6w9d5monqw 6og.z8 ryv3 f4 it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space statil/en4ahb . .mshq*cmy+(ulx 4on consists of a circular 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 effec* b.(/cqlxshuy+n4hel4m a. mt 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 vertical0r f1 aiglcjtf88a+*m 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 vy/+ ,t;bi5 mvwgyoz(mass of a planet in terms of its radius r, the acceleration due to gravity myv5w yg,zvt(+o b /i;at its surface and the gravitational constant G.

A plumb bob (a mass m hangi*ua*l4uzb. hoh ut1.lng on a string) is deflected from the vertical by an a4utz.ul * bh*1al. huongle $\theta$ 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 ba , .1 ej2l(hehe6jzvpb.i r)yoec4or6nked for a design speed of If the coefficient of statjzo c,6lyv h 1)i(ejr6re4h ebo.pe.2ic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast thatn ycp/+1u3.+ vo0zkno g:3blkw dewg3o cv6 (l objects at the equator were appgc3gul3b +:kovo k3nczew.w10vo y lp (+6dn/arently weightless?    $\times 10^3$s

  Two equal-mass stars ma(ni0w+s k 7pcvn.i(ufintain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of 4 d+n ao4sste*radius 235 m. A lamp suspends4n*so tda4+ eed 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 320l3 ,) wlslwcq; times as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the sizesqlwl;w3l) ,c 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 presencwa w+7fkubolr:3jm1h f wi6i4i6 tl,6e of an extremely massive core wi:ta6rkj6o w 1w,u4ii6f3hlmb+f 7 l in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant spfebv3.jb.y *rnd4 8dz),x u uqeed as it traverses the hill and valley shown in Fig. 5–45. Both th8d*v dyfr), j.bnu4u3. xezbqe 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 Positioning Syste2+4 i x2j.bm4la9n ol0ashb0s(e c2zu haqq4m m (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 centijbz 42o2hs0 h uxqnai04bsa4ma( lqm e29l+.cmeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after tr d dp7rdliw/e*9w;k85i )sc cwaveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is ro ;9)ww 7wdelc8rp sdid/ick 5*ughly 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 pu5 o9ws5ju owadh 9ri7:rsuing a satellite in need of repair. You are in a circular orbit of the same raddi :r j957owa5h9swo uius 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 mhoy8b1:e 0hr. (a) What is its mean distance from the Su0h1 mbhr8e: oyn?   
(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 p :c6j3nfmpmc*-wfd1v6+bx q +kjije,* p cq*actually "feel" you3+b mmq16f *vfp*x:jjnc+ek6 *cdjppw ciq- ,rself gravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at/p4 h6q.-t yyj)q epvl a distance of about 30,000 l6)v4ejyp/q .qpy- lthight-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 the corners of a square 0.o- s cvv cajz(w4u-n*050 m on each side. Find the magnitude and direction of the gravitational forcnvwzsvc0a*co -(- u4je 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 5500gxy6h /hh.t r3*f y5nen8q+dq 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 u9vo/1hss c0jr.1hz p+vx3fzof the 1.5-cm-long sweep second hand on your wristujchvz hvofxrp11/ z39 0s+ s. watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a siyxm.9g) 2v7s4-x avlxj,qkqrnker weight around in a circle below you on a 0) 2ql4xx q skrjma.yvg7v 9x,-.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car .8t zr5 0op-u3:hiay llmh+y vtraveling at h8+o5l v0yht.rzyia pm 3ul-: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, d1m4b vu u5ry:utilizes tilt of the 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 friction force needed on a train passenger of mass 75 kg if the track is not ba4v5:y 1brd uumnked 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.$\approx$    $\times 10^2$