Sometimes people say that water is removed fugtth ct;-m z2g3 1j+grom clothes in a spin dryer by centrifugal force throwing the water outward. What is w htg3;tgu- z gj+21ctmrong with this statement?

Will the acceleration of a car be tzewhb,0cl/q i rr ,5ov*1nhzrslc -25he same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at thesvl h,oi,/rc1zn lb2hz5* 0r5wc-erq same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does to vy72 ycie)ezg* ca*(bj8h a-he 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 7oc)v yec*ez(a i28 jh-yb*gaa level stretch near the bottom of a hill?

Describe all the forces acting on a child 3/vg hw ;yjvd2riding a horse on a merry-go-round. Which of these forces provides the centriv;2wj3 hv yd/gpetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withouxmn)0nw8wg u/ f/9qp vt the water spilling out, even anmw9 fw//8)xnpu 0qv gt the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in yopey i90p 1.b(2ndc zd)la ccsxhb.0e5 ur car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acccd1 dx5c)9n2 pzlpbh0cab.e ys0ei (.elerations do they produce?

A child on a sled comes flying over the cres7n05jxc2 3q/y :5x uitdvqiybt 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 n q5 /u5i:iqxt yd0c23xbv7 jythe 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 at high pazj9h/hu. s0v-h. u yros w,5b2 2ktmspeed?

Why do airplanes banetr83.s9 vgub jp 4ik, ft*d8ek when they turn? How would you compute the banking angle given its speed a93tev8fui 8sp rbtgd*4k. je,nd radius of the turn?

A girl is whirling a ball on a string around her head in a4 sakbidl *s;5c cp0+oa8fpx 2 horizontal plane. She wants to let go at precisely the right time so thato+; dib5 0ssa2*k xpfc 4p8cla 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?-w ,76zcxwkee a2v0n ,-syug k If so, how large a force? Consider an a6,-0av2nckey xe -wuzg,s7wk pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass werrcs 6wvrl419ht d ,di3e double what it is, in what ways would the Moon’s orbit be differen 9r3w dchitv4 d1r6sl,t?

Which pulls harder gravitationally9tf:eeopy+.qp h )rl*k 2i. oa, the Earth on the Moon, or the Moon on the Earth? Whe2y t*eko:+. fpio)ral9qhp .ich accelerates more?

The Sun's gravitational pull on tyr1mjyzb8 + )ihe Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference y i1b)jm+z8ry in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poleceqh5uc 4cu:vw2 g9*ms? What two effects are at work? Do they oppose each othce c uh:c* wug59m2qv4er?

The gravitational for-mmyg)db,18gch *fphxq da*5v i s61dce on the 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 frosc1* dfbi6p-dh d)xg8mvy, h*am q 5g1m the Earth?

Is the centripetal acceleration of Mars in its orbit around n+eb20rg.mk7mzz6l fthe Sun larger or smaller than the centripetal acceleration of the Earth?em67rn z+0k.l z2fbmg

Would it require less speed to launch a satellite (a) toward the east or (b) tx esb rfu/*9eft/u+8doward the west? Consider the Earth’s rotation dirf+ux9s /fete*d8u/ b rection.

When will your apparent weight b hin21c( b +cjr7hd,s zawn-h8e 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 whii +,rh( zdcc7wn1-8jbnsa 2 hhch 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 oute ;uh40rd64(zl npnso;+qqtelr space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fa4r+plzdtqu0q(4 ;6 en o shl;nll, (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 weightn6(yfwc j 7tigeddn1mku)b) h (a-0e6lessness” between y(c uamb wfi-6)(0n7h eeg)6tkj d1ndsteps.

The Earth moves fast9gj+p0(sa fwfer 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 producing the seasons — the main factor is the tilt of the Earth’s axis relative tof0( wjsa9+fp g the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explail*r, ymx qxq:(n how this discovery:q* r,m qx(yxl enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Ear0)f n7l5h vvmyth 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 side of the Earth to the other.]A chilv)l7n yfm 0v5hd 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 0g) .uig p1yplm.b i/f 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 itrn4p miki99er1j ; uo(s orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orim9 4ikj1n;p(ue ro r9bit 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 gl 80 f;:4nlibqyetr3exerted on a 2.0-kg discus as it rotates uniformly in a horl3r :tgqn 0f8yel4b;iizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is inrshxu * ,x2k+t orbit 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 its orbit. Express your answer in terms of stk h*x2ux+r,g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of cla 1vjh mew1u ha8/ksx14y on the edge of a potter 8ajh4s 1/e um1vhkxw1’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is rb qq3.5onjg--3 s zyrlevolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. Ify -35lbqn.gj r3szqo- its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of c8 f g;/xv8yyoradius 77 m on a flat road ifvcxgy;y o88f/ the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static frvr+; c:3gr2 ckn o8 km+qbx4xbiction be between the tires and the road if a car is to roub+roxn38bk q;cm2xr4g kvc +:nd a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is z70c0+ljqi 9*s(5xi0zqs q vm(tkxcq designed to rotate a trainee in a horizontal cir7 isx0* 0j(cs (c5vk9qlqzqt q0xi+zm cle 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 rotating turntable of s3ao;ftro 0 t-variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable untits3r0oat ; of-l 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 dowcga5 btwt+( r86qq y4j fxf cr0p+0w:fn at the top of a ci y++8qgf(t5f:c46cwr0p a rx bfwjqt 0rcle
(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) crossesy+ :.a5 ,ymva6pa ms2btyst0 j the rounded top of a hill (radiu a:2tbyyvm0+ a, tmss65aj. pys =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 p cno(93wabtq *er minute would a 15-m-diameter Ferris wheel need to make for the passengerqb *wact3 (on9s to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cirug1o+x.g hsusqbe )2+cle of radius 1.10 m. At the lowo esx)u+u1+ bqh. g2sgest point 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 particleof-jpe 3 /2uqs 9.00 cm from the axis of rotation is to 2u/op -jefsq3experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peoplfv.zdf,axfa4 8.wk9*m 0ha hng5 fp9he are rotated in a cylindrically walled "room." (h8ph.z4nf*w, ha f 0afv59 g fmxkd.9aSee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless acu:e)*uxack 6n)xbi( ir-hockey tabletop, and is held in this orbit by a light cord connected to a dangl*xakb )c n(ci:)ueu6x ing 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 ig) -o-znn o rkluz5s.i:f.v.ninoring the weight of the ball which revolves on a string 0.600 m long. In particular, find then .-.ofi )n i-r vznlzkus:5.o 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 of 88 m is perfectly banf bq no.q2g-3xked 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 masseaa0qi3eve wz f4 v545xs $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at 38 y6a*mqeypu0 rt96ue10 $\mathrm{~m} / \mathrm{s}$ . 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 foqj2ii:l xpmv b/9t1-xrce exerted on the car (by the gxip1l 2i9/qm-t: xjvbround) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 achg,upi7199r /t gwdr -r3wl imcelerates 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 coefficientlm rwg3ui9 hiwt rgp1 9/7,rd- of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular ik-kjt/xj u47u nstant, its acceleration isu kk-/7u4xtjj 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 12,800 km (2 Eartsixtp v56;h:*ej at,eh radii) above the Earth’s su ;tp:i,*ta 6s evexh5jrface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has af8mig5;yen/ ohxhwl .l7 (6 if magnitude o;m eo lg/w(f6yhh n. xfii587lf 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(p.jc6xg .oip gravity on the Moon. The Moon's radius is 1.7 p.g.6( jxcipo4 $\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 sac)gss ylns ld*a zq vx2-56h-3:dc4knme mass. What is the acceleration due to ca-yq dhl:z)s265 c-vsd4kg n*x3lns gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Eartzezppr68 xe/*r 5k8ec h, but the same radius. What is g near its z* p /e88r65eckzpexr surface?   

  Two objects attract each 4 2jf7hbtmk.1 mq;uvhother gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accelerati+m0b.n m d3rppgn:oc :on of gravity, at (a) 3200 m:drog c3m: nnmp+.b0p    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to qq-ezy+-8wsr x,vz./ bja a0ba point outside the Earth where thegravitational acceleration duaz zv. ,by0-/a +-qrqxs8bjewe to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the masse6 dxw*ubl+.i,ozb0fl g-zctkrs+5. of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on x,igkc rlzw0b-.td e .bzs5f6o*u+l+ this monster.    $\times10^12$

  A typical white-dwarf star, which once was an 8fxlr2n* 9rorzw z );laverage star like our Sun but is now in the last stage of its evolution*r ro)w8rzzx l2l9;nf, 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 weightlesh,zm +l;u.snvwv)z4m s while orbiting 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 acce;4umzvls ) vm.zn,+hwleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at qhuok(mmhov:h 13c):the corners of a square of side 0.60 m. Calculate th1uvk:(hhm ):m chq3o oe magnitude and 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 m 6r5xwgw,8nqs gspe0.s*fp1 uost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 1gn8. srw s,u5epfsq*0wgpx 65-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is o/gk/rp+p+tb 3txt0mf* 6wqh 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determib +o03pmt*/pfq/th+ tkg6 wrxne the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the E3v+( avylk+ 83 *pcf/awvc tgkarth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws,kck+/ f vaa(p+gyv3lvw*c83t Example 5–16.]    $\times 10^{30}$

  Calculate the speed of+2 :k:blcl pe x;p/f5fflq1m 1 k3ejae a satellite moving in a stable circular orbit about the Earth a lxje b/1epffk+ 5cqel23kl ;:afmp1: t a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 k )iaax-9kkpoh y- os48m above the Earth. How fast must the shuttle be moving (rkko8hx4)y aa is-p- 9oelative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotjv1cp4 qce-w;ate if occupants are to experience simulatp qe1cj;w4-vc ed 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 5–32.)   

  Determine the time it takes for sl8x.vtjv1kuez r ;y3+tj )n*g.2 dila satellite to orbit the Earth in a circular “near-Earth” orbit. A “nearijj+el3lu ng1st.t;8 ydrv *. x)vz2 k-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 satellite?    s ~    min

  At what horizontal velocity would a satellite havnvej nlb zw+ t3vm9a8d;c.(a9 e to be launched from the top of Mt. Everest to be placed in a circular orbit arov3nj9.8(9adm c ; zwebal nvt+und the Earth?   

  During an Apollo lunar landing mission, the coi7. gdr/e0wh z2wwlm,mmand module continued to orbit the Moon at an altitude of about 100 kd2gmw ,ez/w. 7 rlw0ihm. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed ofn,5h 3y6*e;rrba5 i tq)l hvqb chunks of ice that orbit the planet. The inner radiu*ya6;hqh ib5 e)vb53qt r,lrns of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig+)ae+ ;+rg w 7fswvgsj. 5–9). What is the ratiw7gg+wr f;as+ sv+e)jo of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-y/ 1rx-ax1 xvh)98ko ic8s0z dx*s6/e wpwlezkg astronaut 4200 km from the center of the E k)l6z1ore*dxhisa-8p 0yzex xc 8/ wv1w/9s xarth's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star syste:og,z txjh i, +7;(ibc0bh arem 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 a0c,(bjg,oxzr 7 h+a;t:h eibi point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman inimd/q5afv1*+ x a;yd m an elevator that movesq;m+y/i 1f*5dmaaxd v
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an eleva s/j-x/yb xu(utor. The cord can withstand a tension of 220 N and breaks as the elevator accelx(/ j-su/uyx berates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period T4 3lcj+yig,u :z4.tpwv.dkx(vwp k6u , the density (mass/volume) of the c j.vtw.yx w+v 44,(pgk3lki6u:zpd uplanet 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 gt :sfm la0)(md) to determine the period of an artificial satellite orbitf s 0tlg)ma(m:ing very near the Earth’s surface.    s

  The asteroid Icarus, w eco/3 h8d.vnf s 8k+2u *x/etpmpem3though only a few hundred meters across, orbits the Sun like the planets. Its *k/expfvw3t2dp+ m3.h8s cn eomu 8e /period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averag*3qmh45rtxj ne 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 o lm5s; 0jxjiln -/t:ionce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5nslm/i; j0itx:o -5jl–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxyr/ ig7 pl q a;zw:w0ugo;lph60 $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, peri 7iip)cc3z*c jod, and mean distance for the four largest moons of Jupiter (those discov)ij 7*zci c3pcered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of tw0r.,a h jyb9che Moon. yc wa 09rbh,.j   $\times 10^{24}$

  Determine the mean distang : ccix+)gf;uce from Jupiter for each of Jupiter’s moons, using Keplefg+:g xic)u;cr’s third law. Use the 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 pnps* 7irn6)mk0rai3 of many fragments (which some space scientists think came from a planet that once orbited the Sun but was 6*r7nkr 3)sam npp0iidestroyed).
(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 0l +pbr g+8g3o30 jj1ufbtspoartificial "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, in Ef0up +gob1obl 0p +8r3gs jj3tarth days?   

  Tarzan plans to cross a gorge by swinging in an arc from zfk i*+ly;x l(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 pl(y* fkix+ ;lzoint 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 gravus r0d/ t1syc9ity be half what it crdu/ty 9 0ss1is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass1 l9.sj pd i .hqduf,32facn81 ycr1im grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual 291hi 1 afp3,l.8 u qfcdnjic.m1d yrsmasses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent jh bvoo a;swq .op275:1w4zdaacceleration of gravity at the equator is slightly less than it would be if the Earth didn’o;b:15.pjq aw ohs4 dw 7av2ozt 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 the E 5hnj z i hzd4fv.(yny k7(b8zo5haw3+arth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces? v3 owh8za7k+(5nj.yib5n(f 4 hzdh zy   $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom s (p 799pcp 6:ts:acsl(n uvgmacale in an elevator, it say( ap v7cp6 mn9::cg( us9tpsals 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 abo+n*5j u4gl2j 2ocyr r:cu js,mut its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Eartunj:c 4rmurcyj *o+jgl25s 2 ,h (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop y,np 3k(gkpbk,i02buq / /eoj(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 accele2iyb w+vkff8r2 d,de7 ration due to gravity at its surface and the gravitational v yw2ke2frdd8i7f b +,constant G.

A plumb bob (a mass m hanging on a string) is defy6qk i+ywv1 s:lected from the vertical by an angle y :w ki6y+1qsv $\theta$ 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 *s0 5; gi2a,wgs*f .mf-jf l wqtv.xpzis banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safel*w ssfp; *aqzxffm.l,jt2v g0i .-5 gwy handle the curve?

  How long would a day be if the Earth were rotating so fast thaybycr ,w5vn l;/+4ytkt objects at the equator wyvt;+wrlnbkyy ,/c54ere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apaq 8p3jqy : e1fa/g-celrt 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 constaos z; )w chuo9howr*21nt speed rounds a curve of radius 235 m. A lamp suspended from tz;ohw1or9w2)hcou * she ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as th) )qv iw8y2ufcqd s3s lt2j ),uj c1r)6(dvvabe Earth. Thus, it has been claimed that a person wouljq d2dru6l)yu(8vc2c ,)1tb v )s fa)viqj3swd be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: 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 H k-.g au9tps+lubble Space 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 by measuring the speed of gas clouds orbiting t+-l9.g p tkasuhe 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 1v3mv olell4mct:a) 2valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where lvm:3t4 o2)a me lv1clwould 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 (GPS)7vw+ ylae9 d8ktu) x2w utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these sate7+8)kd xl tuyww9ve2a llites, 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 (NEAR), after traveling 2.1 billion km, iuwp )ps eh:u cm+7r; jmp;d:c*s meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughlch+ )w: pejdppc7m *m :ru;;usy 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need ovp 19:fd zo-nw+ fh7esf repair. You are in a circular orbit of the same radius as the satellite (400 km above the Eartv7nf:hp fsw+-oe d9z1h), 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 perqak db,5a1(pwiod of 3000 years. (a) What is its mean distance frad1pwq,kb( 5aom 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 b o/j s6m-c4tulx39nt would need to be if you could actually "feel" yourself gravitationally attrat6jscmx9n3lu 4 /tb-octed to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cesg isnwt hxf*f-7 ,d-1nter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cent,1fdfi*stnx - gws7- her $ \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 dfnn 3ic)s4 x3f.qx o5square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the botti3) fondqfc x.s53 n4xom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the E/jdi (0p-awh-li (aw-j 5licp -vej:aarth $ \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 j,g k 0n6kazw:h ix(k5by the tip of the 1.5-cm-long sweep second hand on your wrist watx( h0naiz ,k:wk6kg5jch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around inubh7lk 9i e8f6 a circle below you on a 0.25-m piece of fishing line. The weight makes a 768b fue kl9ihcomplete 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 (s6/dj* xdvnfka a-i ,highway is designed so that a car traveling at speenad6f/ k xajs,*idv(- d $ 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 theqj//fp*i5tski6a z,b - a(w ivfu:t8fkql53 e 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 mo w*lt:/ fq 6zka5isk/t ,(8ubjeva q5-ipi3ffre 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.$\approx$    $\times 10^2$