Sometimes people say that watn8+ai7nvv ui4) g2et ter is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with th +4vnv ei2tn)u 8itag7is statement?

Will the acceleration of a car be the same when the car travels around a shakn+8z;o j5l6oz)f*mb jmg+w r rp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.+ rzomojz6)m+g lk5*;8nfb jw

Suppose a car moves at3 2vu:b mb:apk 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 two hills, (c) on a l2a:k: vb pbmu3evel stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round xs2t4l2u ;j5ra onlbdevs89,. Which of these forces prov es85n ;o4xa u t9slvb,dl22jrides the centripetal acceleration of the child?

A bucket of water can be whirled m yk4asd*bv) 5.p9pu4; mjxq5j 1q wvpin a vertical circle without the water spilling out, even at the top of the circle when the s4.w a1d4 q mv)5b9pxvy*qj5 mpujpk; bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at l /)lwd/8q-qtao5 l waseast three controls in the car which can be used to cause the car to accelerate. What are they? What a8/d llaq a5w -wt/s)oqccelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fig. bhr(3pj/y yr9 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force / jpr3yb9hr(y between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at7pn)0crmrv px gu/x6 ) high speed?

Why do airplanes bank when they turn? How would j+;qjbfvy h0te; ka ).you compute the banking angle given its speed and ra.j; f;aqtbk ve0)+yjhdius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plan9czk;smg+:eww7.oo e 0s pzqnfa1:c 8e. She wants to let go at precisely the right time so that the ball9:s;ao.kcw+:0zw oz pm8ee7 sfgqn 1c will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large aas8- y +3b+23- mybpx; ucuhly*fehur force? Consideru;e -38uya* 2p h3mlf +-yu rbhbcxsy+ an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbits m;x/tch5hm x-jc9c ( be diffe;h hcmtm/5sx9 c-cjx(rent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on n6iuduysm *27 the Earth? Whic*76ms2 ydui unh accelerates more?

The Sun's gravitational pull on)c ao vw .jdm65nsc8(,b5mtaf 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 pull from one sideaco )5v,c.m f8t(dw6na5s bmj of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects +mxv7ury3 8rdare atr3v+r8u 7mx yd work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is on:.0pgpk z4(fm(ujo 8 cha fxh.ax-+x kly about half the force on the Moon due to the Sun. Why isn’t the Moon pulhxjkf0.a4 mz ph+pu c(x8 ogf:(-ak.xled away from the Earth?

Is the centripetal accelflb76 yoj+0k:fh :nrp eration of Mars in its orbit around the Sun larger or sm 0 bo+7fryf:k hnj6:plaller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the eas6: f tqa2r9wfr-bi75zthx if5t or (b) toward the west? Consider the Ear69xb : htwi-5tfzfqi5fr72r ath’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in lro 7om cxj:mh ;gp,rswr1.t x;y m),-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 be the least? When would it be the mrr1; oxmyoptwcx:,g7hlm.-,; r)j ssame 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 adverseljfaprypj, nyse6x 4ud-;-6fq70 t0n ;brr0g uy affected by weightlessness. One way to simulatu e7bq f4-;r y- ay utn,0f;g6jrspnrp06 dxj0e 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 experiences “free fall” or “apparent weightlessneqae+,)jfcg7w7dcm ex:c 9 kdfld6+n/ss” between stepsgda)7ckde:jdce+q/f9m l6fcw,+x n 7.

The Earth moves fastewo lrs;3 jr*vwe z/e-3r in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in produ / e3jzerro3 ;lw-vsw*cing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explain m aa+/.) v wuwx7-nvlwhow this discovery lw -7a wwn)axvv/+mu.enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet 3cn, u 1m69c 1)uf9aqyvo hj+umo+lc ithe Moon's is mainly r6u9cyl uvhm 1a3c9n + c+i,om)oq1fju esponsible 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 $\mathrm{~m} / \mathrm{s}$ . 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 19p3 7:jot+fy fu/nd:af80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 ie)qyfx830x2oz0 y.isdte1 c fn its orbit around the Sun, and the net force exerted on the Earyyz .edtcx3 fe0) 2iqs8of1x0 th. 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 exviw,pj7nmvj(-8z nmwim+/2hj /l.- k ct 6dclerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle i np82m jj( m6tw z-chwkvnjl/i+-.v, dml/7 c(at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in or0t6p4pu gy l 4qzkd-zvxr21(c3dr ne*bit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the1 6cql4 3(uztxdg*ven4rpd -pz 02kry centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a sx,)4jv qbcbf.peck of clay on the edge of a potter’s wheel turn)jxqfb.b c,v4 ing at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string ik- vtf99lau(r s revolved at a uniform rate in a vertical circle of radius 72.0 cm , ask-vfut 9r9l(a shown in Fig. 5-33. 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 1kq(tmp,+gsjaq ,*7nasyo d 6of radius 77 m on a flat road if the coefficient of static fricj * 1o(6adpsa tn,+ksqqm7,yg tion between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction bzon-8of 9pe)z e between the tires and the road if a car is to round a lezpn89 fo)-eozvel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pi(m;rf +j -h)r jwgws(clots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7( jfwrjrcs-gw+h ;)( m.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 theu0oc::n ucm4hs i39v r axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable un49h3c: icvr 0ons: umutil 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 *,q(wj 5mnv lhohm /r;at the top m*5q r,jlw(mvo ; h/nhof 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*gig51 )ekzjp kg (including the driver) crosses the rounded top of a hill (radius je5)gpk1* gzi =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 make 7 q)0j7rr e: cxuzcl+ 94j+xoi;sxnon fore)+nx 0jcnorxu7ox:7lsq4 z+c9; jri the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg 02q8gd3vn4slf(fgd sis whirled in a vertical circle of radius 1.10 m. At the lowest plsdv s2(gdqg0nf8 3f 4oint 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 centrifuge rotate if a particle 9.00 cm fp21r5vf gev (wyml d-2rom the axis of rotation is to experience an acf2m lpevvy5-wd(2gr 1 celeration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated82a si ver1a5t in a cylindrically walled "room." (Sa1s 28v tr5aeiee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictnljo z ) vz a)94vio3*dfok1v:ionless air-hockey tabletop, and i :k1 )n vo9 voao3zlzvjd*4)ifs held 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 ti 5) dkeahq4xkhe 3)qo9me, by not ignoring the weight of the ball which revolves on a string 0.600 maekq)h3k5xe qoh d94) 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 radiu1wfc7sg,aec3 eay89b s 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 masses ;qz;1rs xubb2 $ 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 dixks- 16dwo/cf,s za9r ving 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 exert;oq6c7 og+hko72hqqv-8z a qb ed on the car (by the ground) in Eogzb 728c- q ohh+qvqa6q;o7kxample 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 unif 3w gtwoq:c,ohf9x 8 5cz;kof2x iq4e2ormly 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 and the road to provide this ecg,ww4qoxh 5zq2;of9o :k3 2f8xcitacceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of r bmc)hc-gm0( it c7:h 2o.yiaxadius 2.90 m . At a particular instant, its acceleratiom :-thca270hoy.mcc g)ii x(bn is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 1 55u,pwj:tgu b1 i3sfkz,syj92,800 km (2 Earth radii) abo 35s1 gijykt 9,j5zwufbpu: ,sve the Earth’s surface if its mass is 1350 kg.   

  At the surface of a clll9xse7zn4 7poubqy645 8pd ertain planet, the gravitational acceleration g has a magnitude yud4 lpx7l9b4 6z qeo5ns87lpof 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 tm99 - hhocp9+wl7r6j ors4e n)qkxet6 o gravity on the Moon. The Moon's radius is 1.769 ns4e kml+phxwj-e or9o6h7qc 9t)r 4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radjoas96 3b r8prius 1.5 times that of Earth, but has the same mass. What is the acceleb a6r9rspo 83jration due to gravity near its surface?   

  A hypothetical planec9:(dip2 y-m:kwq zlgt has a mass 1.66 times that of Earth, but the same radius. What is g near its surf2mwi9 q :g -czkyd(pl:ace?   

  Two objects attract each other gravitaticpj9mul/cv8vib0a : 4onally 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 gravity, at x m-w+uzpddpyb7lvore5,;4/ (a) 3200 meuy;dm-7d,lrxob v+45wp / pz    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wh,8;fosplld g3ere thegravi,fs l3ogd8lp ;tational 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 mass of our Sun packed into +y6aluqj,26pi4kikgt5z 4pz a sphere about 10 km in radius. Estimate the surface gravity on this mo piuq4ajk4lyig2p+ z6 6 tzk5,nster.    $\times10^12$

  A typical white-dwarf star, wh8jyep/z01 )bi/yv dyc ich once was an average star like our Sun but is now in the last stage of its evoluti zid0cy j//8 1pvye)ybon, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitinji +hk sarra40 z,pq:61o 3exdg in the space 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 acceldzqkp eio4j03 1 a:6s ,xhra+reration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Catk2 kc ixh0aqxy1w.)(qn syxy4u:l04lculate the magnitude and direction of the total gravitational forcy:4l q1yw.u iy 2athxk0 )40k q(nsxcxe 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 theh q jock x5v67ruzo4l-,zd(f 0 same side of the Sun. Calculate the total force on the Earth due to Venus-zhq c,4j(kfo 706urvdl5xo z, 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 gra99 apentle5)j -ua*rv vity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is)ut enj99-*r5ae alpv 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass o6vvic((u3 ypk f the Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]p ki(vuv3c6y (    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit ax bzsw), f yh*a-8lafck.g.7 vbout the Earth at a7w-a8xba* s l.h.vk f) zyf,cg height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circro 2-frys37x)4tyn *wt w w b:k75vvgdular orbit 650 km above the Earth. How fast must the shuttle ber yr2yfg-xk nvb4dt:3*o7w7 ws5)vtw moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotatn01tupnaha g1k/,5 xte if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–35 1u0at/n,x 1tkgahnp2.)   

  Determine the time it takes for a satellite to or5.xiqnnx+5nyl( i (tv/-l xolod , j;fx/k,s mbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a;- .m5,x+ xqf/njtl (/,oylxidlk5oinn ( xsv 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 laund4:ks84icl rla1z.ck ched from the top of Mt. Everest to be placed in a circular orbit1 :84lackz4 ks ird.lc around the Earth?   

  During an Apollo lunar l(0kyz /qvdc0q5 6j(um :0w.ormtba mjanding mission, the command module continued to orbit the M 5mr c0qbm/.(qtj vawd:y(zjo0mu6 k0oon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of cht.stf 5opt3 ;yunks of ice that orbit the planet. The inner radius of thet tp f3ty5;.os 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 dia;xscxt 1i9 ijtq) 7izwkcky1 5i+ m11nmeter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weighix 1)xiy5+t;1 cc qknkwi79s miz1 t1jt to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight oibxxub v/5a 81m8f6 ruf a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity,a5u6uv1ix m b8rf/8bx     ----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 systxw.m w9df6i1v4z t2 xlem consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway betweenxt1v9w. xm6f dlwiz24 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 t1 *g:(ie1d l/x to6o;0xn;dyjymj yks hat mov/s g 1ny;djyy61;motxxjk0o e *d i(l:es
(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 hang 0 *y y6whbh* ue.ju5bc55mgnms from a cord suspended from the ceiling of an elevator. The cord can withstand a tensionhn5. hb*5e6muwy0* gmcb5 jyu 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 neard5l 6w z qaamox5q(;;g the surface of a planet with period T , the densi;aaqol (dz;g6 5mqx5wty (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 period of the Moon (27.4 d) to det80cy+sc1pbw- 4vfv yyr rg l.l)o 8rm(ermine the period of an artificial satellite orbiting very cc8f l0)ov.myg1+vr48 rwyl p byr(-snear the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meterp1fbd0w8 4;s-ydw 20 csm uvdjs across, orbits the Sun like the planets. Its period is 410 d. What is its mea-f c ;w 0ddpuvs1dbmj8w 4y2s0n distance from the Sun?    $\times 10^{11}$

  Neptune is an averagevkj,6dl.emslgok j5 9 n/u+0zs jvzv3vb9; g5 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 roughly once everh9k:xpg,b0co1oswq ( 8yv: 1 k rddj2ay 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? Wha(82kyop ks1:dx,h9rjoqcb0a w gd 1v:t 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 aboutt:7 h/ln :jkrou0f6mzvwy*5s f : bbv) the center 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 mds i68v)kl f-w3qg9m bean distance for the four largest moons of Jupiter (those discovered by Galileo in 1609) g 6il9qfkwb3-msd8v) .
(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 te9pyl3j n27c7tjw b a8he Earth from the known period and distance of the Moon. c3ljwt njaeb729 7yp8   $\times 10^{24}$

  Determine the mean distance from Jupiter fogjdva40w *3m gf) amk7r each of Jupiter’s moons, using Kepler’s third law. Use the distance)j*3wdg4fkgam ma70 v 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 fragments (whi ci 9ch(v6;twjm:5ryhch some space scientists think came from a planet that once orbited the Sun but was destroyed).5 cjhy(69 vtr cwim:h;
(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 des gxtjxzm0q55h td-u75cribes 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 t 5x uzg7 5-qxtmd0jt5hhe band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hang m 3(q x/.zj gmugpbettov;/76ing vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N onu /jp7g3t.mb 6xgqvzto ; e(/m 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 z0yx/dyd.b ma* e5b-wbe half what it is on thday ybw d*em.b/50zx- e surface?    $\times 10^6$

  On an ice rink, two skaters of equa:gts)1g;b f nal mass grab hands and spin in a mutual circle oncegn:a;gt1b f s) 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?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratis-kb7+. a5 9q-cl rwbieycfl(on of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate thilabysq -9wc 5cf-k7.+ (rblee magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will ip+ bn+baw)1k a spacecraft traveling directly from the Earth to the Moon experia p+)ikb +1nbwence zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 ky18hzx8 -hmut93j.z d mcnf9 ng, but when you stand on a bathroom scale in an elevator,mfz99z x8-81y . jcumn d3tnhh 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 station consists of a circular tube that will rotate a8i hog i aj+guz6c5h;(bout 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 t;ujz8 ( 65+ higigchaohe surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his ai25g r byl; qm ahecsp)*17 pdv(b9oh0lht54sn rcraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accele3 bj)v8dblihx5v om12 ration due to gr18jho) l2x3 v5bmbi dvavity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected froty ;9x .ss9ao:ggz0nj m the vertical by an anos:09g yj nz.;9gx atsgle $\theta$ 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 dizqlne;l f0 ik8- - 1llumy.o0esign speed of If the coefficient of static friction is 0.30 (wet pui0 il;l8nll.qz --m1o e0k fyavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth ;y lh+tehg)zkz5m/*9m r;q qh were rotating so fast that objects at the equhqm;l;rzmkhq*z9/teh y +) 5gator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distanc5pkl7 ,90ox7klc w1akj o3pqpe 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 235 m. A lamp ss - 7 :)3xjf)h.xt7g -twpnxsoj(lymguspended from the ceiling swinxjl-txj7n3):psg7x)-o(.s w ymtg h fgs out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as m2u mgvgz wferb:s;c4ci v)xa;: y7d99assive as the 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 g 's a person would experience at the equator of su a ydw9 )ebzsm9v g7xi c:c4f2;;:gruvch a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an esbzd 0kwzm-09; ee2t:p 6w zorxtremely 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 measuring the speed of gas clouds orbiti:-2 9z0rbwz;etwk p m0oe zd6sng 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 sgnb -79m )c astd-s1i( mzbef8hown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largescbifm(9dga-t-8s71)n zsm eb t? 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 System (GP n dax6h4f8/.jk na8wlS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approxima4k fln6h/w 8d8na .jxately 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 traveling 2.1 billion km, ia on5 luc/rfi2qo;4q5s meant to orbit the asteroid Eros at a height of about 15 km . Eros is in 5fl2aq /o5uqor4;croughly 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 3vyz hqxmoeqrb *)ll683b0g -in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 0emrv- ghl qq*3zl 8b6y)o3b xkm 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 ha g aautoz;-*7xs a period of 3000 years. (a) What is its mean distance from the Sun?ut ;aa* -g7zox   
(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 spt/ ulyq2f a a+xf- is3020brG would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Maky2sq0rlifx3af u+tas/02pb- e reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy l4siv, (ww i ( vv5f1fq*np3v:refu-pv(o 3 yr(Fig. 5-46) at a distance of about 30,000 light-yearse5fv, l*iivsfypr1opw-furq vn4 w :v( ((3 v3 from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m uwyvehfl3r)s)+i, c3on each side. Find the magnitude and direction of the gravitational force on a fift lf)viyswe)ru, +3h 3ch 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 kgs 2* ybtsr2qh,vsh,h, orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-ldaasu: pv,9 v g26)hxoong sweep second handvx:duo,g sp629 v)a ha on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinkel t8fqefwm8719yv;qam8:/cni2j v x e r 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 with the vc nyqf8wxeq1ve; l:9 7ivj82t mma f/8ertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designe :iwub 8n:unm8d so that a car traveli mb8u:n uw8in:ng 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,t-py3pc gs9;g utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on theg -g 9spc3;pyt 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 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.$\approx$    $\times 10^2$