Sometimes people say that water is removed from clothes in a spin d1)ur 9 (.jmlkcutl: d7hro(i lryer by centrifugal force throwing thu h(rl.)lrk1l(jmo97id u ct :e water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels b1w;d1wo 7jrtvd k.1beia( j9 around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speedave;wi.ok97r1d 1t(bw1jdbj? Explain.

Suppose a car moves at cj0yz- /*.jr ulfyot2t onstant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (jryl fyj2.u ot*t-z /0a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a chknc*a2.g,1f xibbo/ oild riding a horse on a merry-go-round. Which of the cai/b1no .*b 2gkof,xse forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical eeiyh m5c )+9acircle without the water spilling out, even ate)9 a c+5hyeim the top of the circle when the bucket is upside down. Explain.

How many “accelerator/wq r6ve8, pu;xi xuq75lnyv .s” do you have in your car? There are at least three controls in the car whn; rwxy/xq,ui6vu8ql57e pv. ich 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 hill, as shown r7 g6e 2cjnsr0in Fig. 5–31. s70 6cgn2rjer His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders leanx 2g7n+m)hmp9au ms m4:sqmw4 inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would youulg; h3xl+ 0s)ew;kza compute the banking angle given its speed and radius of the ta lgwkz e3hl ;u;x0s+)urn?

A girl is whirling a ball on 2rspt whg ,72ra string around her head in a horizontal plane. She wants to let go at precisely the right time so thatg2w2phsr 7rt, the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If sobu l9ak h1;d8:up,vvb , how large a force? Consider anlkb:d9 1uubvhv a p,;8 apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doxizo/n:0b8 n luble what it is, in what ways would the Moon’s orbit be n l0ox8:b/i nzdifferent?

Which pulls harder gravitationally, osxm1r snp n*y:lb0b69tg+;rthe Earth on the Moon, or the Moon on the Earth? Which accelerat * +grnpx;: lr1t69o0bmnbs yses more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet thz2-acuj2 . k2ulf ;ifhe Moon's i ;2 hijfc2u2zk-la.ufs 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.:;d v:qhut.fylrfa ) at the poles? What two effects are at d.:uvtf)ql .y a:;rh fwork? Do they oppose each other?

The gravitational force on the Moon due to thm7sodpq/kdw 0 x.9bx *e Earth is only about half the force on the Moon due to the Sun. xd.*bpdx0qswmk/ o9 7Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mxqijh:s;6ogl .x qs1 3ars in its orbit around the Sun larger or smaller txjiq.6l o3:h1 gsxsq;han the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (bkeq71y)y djj2 ) w*pak) toward the west? Consider t1ka j)qwd ey*kyp2j)7he Earth’s rotation direction.

When will your apparent weighmk2 0id yni3le/w u: 4b dsw*yi05jy1ldpv.n 4t 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? In which case would your weight dndi kyy35w i4pe:*vli4l/s .01ywbnum j0d2be 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 a1u a:6pzqya -b cgg8y7ffected by weightl ap yg87gcz-1:6qbuayessness. 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) any other aspects of gravity you can think of.

Explain how a runner r n0usjmcelyd9:sa 17.,yltdd( s0w) experiences “free fall” or “apparent weightlessness” between s0sw:ml.yd(ye1sd c u0ndajr,ls )79tteps.

The Earth moves faster in its orbit around the Sun in January than in July. Iqpinr6.a 42.ouzr9:-lr,c i8 (qokv+vhraofs 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 tilr-avnhr zi.6qkl94(2 i +8ooa:ovf pc,rr qu.t of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not knw5zfiyw xs wjdp508: r/sb62q own until it was discovered to have a moon. Explain how this discovery enabled an edwi y8 jw 6sr 2p05s:/5wxqfbzstimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is m.a.qrrm/ghs ) uch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Ea .)/sr qrg.ahmrth 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 so ufw1;1 evt-ul4v0 s 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit arou7;;xe5khf2fvtf .. kfdqecq6nd the Sun, and the net force exerted on the Earth. What exef7hf..x;e k5 k;ftqfed cq2v6rts 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 itxfvv ptyruso:h r6*8 06q0a3g rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the d hr*yov uv:6ftx8gap003s q 6riscus.   

  Suppose the space shuttle is in orbit)pnb;* *py08 modj f+s1rezs wyvl(.u 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in itsfwopl)jsr1sv8.d*(0;* m ue + zbpnyy orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude:qbe v*m u j:7zgmm./a of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (re :avmmueq: 7/jg*.b zmvolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform nf +is8 ewx 7(rd4zq;lrate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. i;+8 ex(rw7lqf 4sdz nIf 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 spe 2c9 zf6hqhop+ed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road iq2c h+h6 9ofzps 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires an ( jmrfdym5-,id the road if a car is to round a level curve of radius 85 5jmdi, y(-rf mm at a speed of 95km/h ?   

  A device for training astronauts and jet figh4rvu *broak3 5ter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt r v*bku3o a45rby 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 ;jp.fdyjo79 j a rotating turntable of variable speed. Whenj7p.d;jo jy9f 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 between the coin and the turntable?   

  At what minimum speed mu)b xve7,gv(l 3 loav0rq01dwust a roller coaster be traveling when upside down at the top ofv b l3uge(vd,0q r )aol07w1xv a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg gx-pdjcun 0vo;w0)p - (including the driver) crosses the rounded top of a hill (radius = 0-c- v0gwxp jp)ondu;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 need to mi 0t 9(r-r7c,lvjepkm ake for the passengers to feel “weightless” at the to9vet(lmr pk0c7 i- ,jrpmost point?    rpm

  A bucket of mass 2.00 kg is whirled in 8 wbs4zj3v2 * w9vbgvka vertical circle of radius 1.10 m. At the lowest point of its motion the tensijv*b83 wzs2v v4wg 9bkon in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm f m/oih 8:vrn h(rxhy(5rom the axis of rotation is to experience an accelera5o8ri h:/rnxh v(m hy(tion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival:2mawc2ytir.i + g,a c, people are rotated in a cylindrically walled "room." (See Fig. 5-35.cay g,:2t +wcii2 ram.)
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 c jawi2*rg ;.rg6 puy+oc 05diair-hockey tabletop, and is held in5yrwi oc2*j0 .;adcg 6ug+ipr 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 tg /h+wd fvfmnp0a+4 zvgjg .+9ime, by not ignoring the weight of the ball which revolves gaj hf +4 n0+mgw vvzd.g/f+p9on a string 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 radiu42q .fg4tlc;x(c mzpm m* ji*zo5 (ofus 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 massey0 3er: qvp3bcs $ 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 /0 ppdom8 3odtdiving 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 ,p5v.6hytxju - up2sd: pkfj86as + fvnet force exerted on the car (by the ground) in Example 5-8 when its speed isp2u5pk p h6.js, t-ax:ysju6fv8+ fdv 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelced(cop/ grm 6q7ut 31erates 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 constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires andp ctodm (6r317g cu/qe the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal aowme:+ 9 li-yc-; zorcircle of radius 2.90 m . At a particular instant, its acceleration is 1.05 -r:ao w-c+y mei9ozl; $\mathrm{~m} / \mathrm{s}^{2}$ , 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 spacecraft 12,800 k6dnssx* o z8 j9u;j,dkm (2 Earth radii) above the Earth’s surface if its mu , zn9*okds68xd;js jass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelerati. o x)m)j9y:zzz(qci eon g has a magnitude oz j9 )yzcom( i:z.)xeqf 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 accelerationt2 d lkjzr2.:* o 6lwrft4q/mwvm(:sg due to gravity on the Moon. The Moon's radius is 1.74 2l2rmw 4j :f gdtlmsrt*/qwkv z6o:.($\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 time(: 4c1flhg6wy rg7h2hw 7g9cpkhm8 pbs that of Earth, but has the same mass. What is thgb (7 7hh1hr wpcchyl94k:mgpg8 2 fw6e acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth,ub2j-ci:zi)d but the same radius. What is g ij2 )b:idc- zunear its surface?   

  Two objects attract each other gravitationally with a for/bc dh7duf0nqq2 ro n.4i5 -tpce 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 d0zo01 xvthw9m 5n i8 -isz.ndg , the acceleration of gravity, at (a) 3200 mx mv-siz8d 0.w1t noh9idz5n0    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from tdvy(:2wacpmf w.74 -f;xdex ehe Earth’s center to a point outside the Earth where thegrace-wdw 4d (. a7pm;ffvx2:y exvitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five timbp(aquu) ,3 bmes the mass of our Sun packed into a sphere about 10 km in radius. Estim(q 3b )umpbua,ate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averagesiu:)6 ;o) rh*nlemrj star like our Sun but is now in the last stage of its evolution, is the size of oulos)6:hr;i nr)*e jmur Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining whrpja:qiqb2y p* 2.v e5y astronauts feel weightless while orbiting in the space shuttle. Your friends respi v . j2q*yb2p:earqp5ond 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 a ks)7kgyetp30t the corners of a square of side 0.60 m. Calculate the magnitude and ks0ke3t g7)py direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the sme 9cc9tq(ub6- 4d vytame side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in - t9vbyc (t4qucmd96ea 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 s5uw me-vxpe1h qt27h,urface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 34texp u-h q1ew25h,7v m00 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Etihk-po2 *2phfaz +p10 ( 2jqz2h yeylarth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lat2 *0p -p2 y2oi+h1lhy afq2jz(ezkphws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite mp8m v4 jf:q7eensi25c oving in a stable circular orbit about the Earth at a height of 360 fqj25 cm 4pe7esn8:vi0 km.    $\times 10^3$

  The space shuttle releases a satellite into a tef jxor .ao8rbuhz5l-ek 8wk t; +..5circular orbit 650 km above the Earth. How fast must the shutt b5ta-xr5r+k8ef ;k.lowt. uj z.he o8le be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spa)1kmcd lr- 316tyey) i- hvk)b 1wikvbceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, anl )1 e 3md-yv-1 i1bick6wbt)rk)kyv hd give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a ,h 83 yqmwp *-:qwnsnvmvb2x* satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the svq*nh*mb v 2x3m-8qswy,p :wnatellite?    s ~    min

  At what horizontal velocity would a satellite havtya j 03 )lprv pkvz.2gc oy;iv 0fk7lgg216,te to be launched from the top of Mt. Everest to be 0lt fr761g03.yv y iackpt,k 22gvzglop j )v;placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command modupnf2qv6hu-/j le continued to orbit the Moon at an altitude of about 100 km. Hohp6/jnqvu2f -w long did it take to go around the Moon once?    s

  The rings of Saturn are composed of zk.ybhlwl/0+nqz ox1f 1 cg*8chunks of ice that orbit the planet. The inner radius of the rings is 73,.w*cxg0 1/ fkqzb8 loy 1hlz+n000 $\mathrm{~km}$ , 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 srwc jtxo9+tfg ft/( 1* (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) co tw*f 9g(x/fjtt1+ rat the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weiprxt 1c,x0.jfght of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velrcp0t.jx,x1f ocity,     ----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 mass. Thea4sdrc- y 8y))7hptt(x .qzvry are observed to be separated by 360 millio .zsp)va y84d trhtq7-y)(rc xn 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 2d 2o 0zc(zmeg0rdl1/knp)hpwoman in an elevator that moves n/2l pe2d 0)g(1zrhdkomcp0z
(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 suspend*lxnr:gm+zyl qn.u+) ,w8 i mned from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks uy+l x+,gn*m.qnlrnmi w:z )8as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbit6qw dxq9b29 hew)fn, us very near the surface of a planet with period T , theqh6 xbwq e9w2,ud)9fn density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the pe acdyt535+ rwm /ahp;lriod of the Moon (27.4 d) to determine the period of an artificial satyhc+3ap/5 dl am r;5wtellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred mebwc 96biu:+ps ters across, orbits the Sun like the planets. Its peric: w96+usbp biod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distak:fee g0vyl1l(n, th. nce 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 rexwh amc. 3:o2oughly 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 it still “in” the Solar System? What pla 3wahcx:.o2menet’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 ag8ugg(m ckmcqzok 316+r 7t/ y*wei,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, x- h2i9b jon-2rbsxw1and mean distance for the four largest moons of Jupiter 122x-rhxbibnw j s9-o(those discovered 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 Ear+5ow gu+ew se8jz 1sm+th from the known period and distance of the Moon. uzge+wos8wme5 s++1j    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kepl6vr :eo+qv2, xp,zvvwer’s third law. Use e:vp xvqv6vz +o2,,rwthe 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 frag(oh90wp+yeva ments (which some space scientists think came from a planet that (wp9h+0oeva yonce 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 descri;pgq.)c r1:f sqxjs (qt/o)b wwg.n(u bes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, ub )s.;/ofcrgx p1jt()qn q(s:wgqw .in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc f zpaykfk 11py-a5q(2zrom a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m longqz2 ( ya yzkk1-afpp51.   

  How far above the Earth’s surface will tf b 1wrayr8z u(9y6 +bx0qenu*he acceleration of gravity be half what iqwr (0nfxe u+ rbu8a6b1y9zy*t is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin inuk kxo7 0+xgx0 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 pulling on one another? 0+ oxu0gkxkx7    $\times 10^2$

  Because the Earth rotates once per day, the apparent acomk;zi 7*r +fpoc*,lqceleration of gravity at the eq *; oziko+cr*mp 7fl,quator 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 directly from theo7w 8deb6vonv05-u(iw bovr9 Earth to the Moon experience zero net force becauvdw u owio0bn-5e vrb8o7(v 69se the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you s2fkk,xovds ds 94m+b78 ke h;gtand on a bathroom scale in an elevator, it says your mass is9f kkb;hk2+x 8s,dgemo4 vds7 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 tubb* vj-rd*)6zvt0o pxje that will rotate about its center (like a tubular bicycle tire) (Figt6 x*o* z0 dj-)rjvvpb. 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 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 8/ccl 6s-mtk:coq1f,c1a ngo(Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet eu , 4)xnie9s4s hz)irkq2,m ein terms of its radius r, the acceleration due to gravity at its surface and the gravitational constantm, z9n2r eiu,e ihqx4s)s4ek) G.

A plumb bob (a mass m hanging on a string) is deflectedx o.;avoxac,q4i:n c2 from the vertical by an anglecn, xxa;v4o:2icao.q $\theta$ 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 ban, 40 eyh3xcl( p:ba scv9l;,b zws)yzxked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handlexv(9epw:lcz),,yc0ly h z4ba3 ; ssbx the curve?

  How long would a day be if 6 n4 q4-kdcflntm/ x(ithe Earth were rotating so fast that objects at the equator were appard4k-x i(n 6 tm/nc4flqently weightless?    $\times 10^3$s

  Two equal-mass stars , whjnyrf) l 6 bf 6:n5hkox9qzbyq),9maintain 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 rre-+7 am4f2m,dk e vzcadius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.5 fkcemzmre4 7,va 2d-+$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as thr2hmtj2jzb+ ; *.lr kee Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of gkr. *lzhrjt+ m;bej 22 '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 pk:tqroi;z63 Telescope deduced 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 br:i6q3ptz ;ok y 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 xo)uq5pvdgn-/bim 3 klj4:cpn0 : yp1 as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How -)0 lmndv4j3o:n5gc1:ixpp /pyk qbudo 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 Positioningg +7.n1dhw+xd xzw3* fz6wxi a System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and s3 xfxhxd ww i*6a .7dg1+zz+wnignals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEnf1q yv )mc 0zpepoig-e)1g (4AR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros )mfpeey0gi) v 4-g1(qnczp o1is 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 ixzn,c/d(s2 tra4o b3rn need of repair. You are i/ s3x4o drr ct,anz(2bn a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What m,9 .hm3+,fvn,zq rami,zjwois its mean distance fromhwvmzmn,o,.93a m i, zqjr,+f the 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 actually "feel" acz2+s;:dtc k yourself gravitatia2 :kdsz;ct+conally 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 Galaxu5 /b, 6ivqglyy (Fig. 5-46) at a dista,bi5 /v gyqu6lnce of about 30,000 light-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 cd.l;5v.2cmgbjrj2 u2 g q4 sxjorners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational f2 v.q .j5rms242lucjbg dj;gxorce on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg dhdgsu.84 knxs6 )r8uorbits 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 accelerat4m g)v9gg0j hwion experienced by the tip of the 1.5-cm-long sweep second hand on your9wvhj)gg m0g 4 wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and st sms6 ft3 6saghz-)clior*t26art to swing a sinker weight around in a circle below y6otm2gcifsr ) t*s6lha3- 6zsou 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 with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius Re ad;uor3vgye 4 04q0q in a new highway is designed so that a car traveling at speed o43rq4 d eea0v0gqy; u$ 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 whe ci2i8xn *tkt.n 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 for 8t*2c xiktn.ice 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.$\approx$    $\times 10^2$