Sometimes people say that water is removed from clothes in a spin g8xb1 c /u*9ua9yce3y pc (mehdryer by centrifugal force throwing the water outward. What is wc8pue(xy*9h /yc13e9 abg mcurong with this statement?

Will the acceleration of a car be the sam pm(e/*v)wry ke when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speedykp ) /*wrv(em? Explain.

Suppose a car moves at constant speed along a hilly road. Where do),a5pz- ( 8le pc4ko l,zhgo 8sf/rtkgvwu/ 9yes the car exert the gk8k/ lr 5vg f9pgyt(l, a,- /8u)o4szczoe whpreatest and least forces on the road: (a) 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 child riding a horse td rmskd/( m 9bbzj7 0si-s0(oon a merry-go-round. Which of these forces provides the centripetal acceleratiotsbidmso r(0sj-k( m0/b79 zd n of the child?

A bucket of water can be whirledmzt (( jfvgg 0hg,/9wd in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Ex/,(vt0g h zwd9fj(m ggplain.

How many “accelerators” do you have in your car? There are at;f-p* uhs u 5r72(oztmcox iy8 least three controls in the car whiu r otfu-x;c8os5z7yh2(mp i *ch 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 th+yzgywj- te f(wd0q:8e crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease :08wq- zt+gyywjfde( 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 hir0q;o zo 7r 3y g:ryj:.nzvnt.u3f:dhgh speed?

Why do airplanes bank when they turn? Howu2 x2k2zpz0op would you compute the banking angle given its speed and radius 22x0zo kp zp2uof the turn?

A girl is whirling a ball on a string around her hek8l 4mthxj )+ f;z7ngiad in a horizontal plane. She wants to let go at precisely the right time so that the ball wil8g47fzkmhti; xlj)n+ l 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 soi,66 bp pyzw )rf4qw4v, how large a force? Consid646,) p wqzb iwy4pvfrer 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 M 23q-(nsm s09ifkly *shz/ jwlv0jiv7oon’s orbit be diff-j hl /fn9(2vy70q0sj*i wl szi mksv3erent?

Which pulls harder gravitatmlphe(fq +v)mu3c;1 wionally, the Earth on the Moon, or the Moon on the Earth? Which accelerateslwefu); (pm+1q 3 mchv more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yepqt 6,-ps5epjg0yh ;ut theeh05g -puptps y;,6j q 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.]

Will an object weigh m6j)o*b7 5v qa -aus(un:xwq wuore at the equator or at the poles? What two effects are ax- 7q :nuja5wso6(qvbu wu )*at work? Do they oppose each other?

The gravitational force on the Moon due to the Evb- *7wl d7;h h8gxo)tgi )rm9czo./ad iqc *barth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the dhr q-7wa c/it icdbmzho));. 9x g*8* bvlog7Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or swx7*:hafs skk3l5iwhd* cs5 1maller than the centripetal ac w7kxis5c3hfalsh5w:* kds*1 celeration of the Earth?

Would it require less speed to launch a satellite (a) toward the easvhzqc, e;674bp:hbmh45s g;ojg a we6t or (b) toward the west? Consider the Earth’s ; 4go meja q;c,b66hsbehv whzpg4:75rotation direction.

When will your apparent weir7dri0urf)1 y gj :b,mght be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, dg j i0fbu,7)my:rrr1(b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in out yvdw-58qb:f0sx1uxkh2l4iknpj g80 er space could be adversely affected by weightlessness. -bq8 jidhs01gp0xw 2kx5 k 8y4fuvln: 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 experienz*-fzq l :i)rgm8f-*fup7hu hces “free fall” or “apparent weightlessness” between steph- mhu*f7z zu 8qgir*flp:- )fs.

The Earth moves faster in its orbit around the j mr ,)zqkp*o;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 relati* z pj,rom;kq)ve to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a mog k;z+8q74r,fvkdsk w-5m,jb+aq lh vp *a;phon. Explain how thi wvlp7,+*r,f8kkp+jv - 45ghaadbsh ;;mkqqzs discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on1 koe diit ei +zu6+(-m5exo,y 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 side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a s kyod+ii+mextee-zu5 oi,16( peed 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 1980 ;;zm(b yb6 c 8(hwlysr$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 itb n ioy-p f2uku354yk2s orbit around the Sun, apyf3 i4 ku2ny k5buo-2nd the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N inrr pkl3olx ,4p2t )0as exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed oaotprrlk)320 4 x, nplf the discus.   

  Suppose the space shuttle is in orbit 400 kmyo 7+ a:rlgeew4mqu u h8y5xxi4 (st89 from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the a8: 4rueqy tmw 9eixo(7xu 5s48gyh+lspace 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 speck of clay on the e)g6 cxulo00y tdge of a potter’s wheel turniucy)0 0goxl6 tng at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string isq2x2h9jcm 3 :n pdh-nc revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown inq:n2pc h9-32mnjcdx h 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 of radius 7 7mqn;h*pw:m zwl,/ew7 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the w*mqh;len7 :/,zwpmw mass of the car?   

  How large must the coe/a j,(kgojz h6fficient of static friction be between the tires and the road if a jjzhk,og/6a ( car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots 6re2 0 fou1ni+onz+ fbis 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 7.85 times e b2z nno1+ uif+o0f6rher 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 rotatiip ;t:mbc.u(.mp bdb9kkt-e7ng turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached akm(p-biebtd t.pkc79u b.m;: nd 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/ c-8lb+rjsb7 (rt )c(y nfscu when upside down at thebsyrtn/7rbc(+- (8 )j cslcuf top of 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 (including the driver) crosses the rounde5uavfx p/ yoldm(kd/f 6u wrm46:r91dd top of a hill (radius =96d r/w mfkd v upmx(91rfd64oayl5/:u5$ \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-diameten xk d- m(qy2kr-m5zm(x 6ug(vr Ferris wheel need to make for the passm yxm5(u2 (-rqzd(k6vgkmn -xengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m.t k+xe8c)4xkb34/cjslqq 9imx* kf k5 At the lowest point of its motion the tension in the ropf+jk5kq*tme4/ s)kqi8k bx9xlc43cx e 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 from the a +y(t.a ltpptm76y hpb;(i eh)y3oxa,xis of rotation is to experixtat;+mthp( bey7ipp(,a o3 6yy.h)lence an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a ca uku gwd 9y0otun58/)gep+x 6bd st))ornival, people are rotated in a cylindrically walled "room." (See Ftutk b )u8)n9 5oo/ wpd6xyeg0)ugd +sig. 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 circl :8j95k.vzj kma vhhgi) w;4aue on a frictionless air-hockey tabletop, and is held in this orbit by a lightzk uwi8 :k9m54v;jj. hghva)a cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not i )+i,y lge,j0lyxvf; dgnoring the weight of the ball which revolves f+il ,yygdx)jl 0e,v; on 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 radius .7m5mxc7/mzpmck+ gp 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 jgjsq03(6 x.bh w4aay+xl4d z $ 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 n3w.; eberb4kn6a(7 io jph1w310 $\mathrm{~m} / \mathrm{s}$ . 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 componen ovthe1u5b /(hts of the net force exerted on the car (by the ground) in Example 5-8 when its speed eu1 /v5bhh (otis 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates unifo75d qbf+xy) fnrmly from the pit area, going from rest to 320km/h in a semicircular arc witb5q) x7nyfdf +h 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 acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2 o: vo9+u3sqnyu xqh13.90 m . At a particular instantq s1o vhon3q+xu9u3: y, its acceleration 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 gra*r gfuf2sq: ,alvv3s4 vity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass *q,2rfluvgfs: v4s a 3is 1350 kg.   

  At the surface of a certs s4u; ;px;+ bsheles(ain planet, the gravitational acceleration g has a magnitude of; h;4 susxe;pbs+l(se 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 gravityr 2whibl5*j mtts..*e on the Moon. The Moon's radius is 1.7jeb*tl*t5 .hri.s2m w 4 $\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,; .:zrrrqfx c4:e z,ld but has the same mass. What is the accelelqzcrdr:e :x.4f, z r;ration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times rld8dsp/ x z*9that of Earth, but the same radius. Whd9*z/rsx8 p dlat is g near its surface?   

  Two objects attract each other gr(dv*j3kuq nt ,avitationally 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 vxmw9,;6k(u,n qvrfwsi0 .cd aalue of g , the acceleration of gravity, at (a) 3200 m i90 dcw xsu,ka,n 6mwqfv(r ;.   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where tdrr s,vvh, 5a;tqpa5(hegravitational acceleratipars5(qd,t,; var v5hon due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has m5nkng2 89lbq8b fxl 9five times the mass of our Sun packed into a sphere about 10 km in radius. Estib gn88q99 lnfmlk52x bmate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like odad) hj*92xmcur Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gr djh*2adm9)x cavity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the - x -kgjf 3czqz)k7xq/ akh5x-space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them andx-hq-c3kk zxj zg )/fk q7-a5x 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 3fktt7c( j+l(7fj*,a- hetv3yqhgrp t the corners of a square of side 0.60 m. Calculate* gvftqjeyk -f,t pa73ctr+3 hl7 (j(h the 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 most of the planets line up on the sameh.km)a- bxv-z side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, m)-zb.-hvkaxassuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity a z;oureg:+h .lt the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is.zr u;ol+eg :h 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value f kp,iz(x4)r aqor the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s la(r,zpi )4x kqaws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circularc:+kld33s nhhlw6,fv orbit about the Earth at a height of 3600 km. 3:cfs 6d lh khwv3+ln,   $\times 10^3$

  The space shuttle releases a satellite into a (i3ivx w1p.awcircular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) ii awvp1.(xw3when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants arewuu: c(ahou,0; d3bex to experience simulated gravity of 0.60 g? Assume the spaceship’sewx hbac; 0:(uud u3o, 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 a sateld bvo;vl j.j3.lite 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 r.o jvdv;b.l3jadius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the topq; +(knq l og;8uz5.opu5- lhvolc a5d of Mt. Everest to be placeoknap- zu 5 d5( 5olocu8qqg+;v;.ll hd in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command2*rd)b ,hywr v 3t8nwd module continued to orbit the Moon at an altitude of about 100 ktd8) dr,y2 nbw3hvw* rm. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the plan2pn6 ,ryb3xeb60eho p kuhfa1q)s-j0 et. The inner radius o rhbeb2 0h-kpo3nq06)jy, uxs1e fap6f 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. 5–9). Whdg+s 0+jcgea8at is the ratio o8j+gad ec+ gs0f 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 : 1r wm44tt p:qx8exggof a 75-kg astronaut 4200 km from the center of the Earth's Moon in a spacg1 8 :tpq 4:exwtmr4gxe vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal m5 muh*b9 :np -ac4dulvass. They are observed to be separated by 360 milvcm-n5 b 9 pld:*ua4uhlion 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 f6v 0w/mb8bni 4plbim 0or the weight of a 55-kg woman in an elevator that lb84iw/bvn6 mbmp00i moves
(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 elevator. 9+x,tize 6n9m z0ey zuThe cord can withstand a tension of 220 N and breaks as the 0 +z,uznixetmzy9e 96elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of n9q9p;; -4r puqlgjt ua planet with period T , the density (mass/volume)-uq9l9unj 4;;p tgpqr 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 dz) ed6/hto y(metermine the period of an artificial satellito d)ezym/6 h(te orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred +zndhc9ca q33meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun? 93acn+q hzc 3d   $\times 10^{11}$

  Neptune is an average distance of 4.cc4m,va dw6t)dx4s l75 $\times 10^{9} \mathrm{~km}$ 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 i5yd(er3k.u lroughly 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 e ld.5yu( 3irkcomet 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 centell)we-d:r 3lga + a(dnr of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the ci muxm59a i8ce2hm3u y 36q,afour largest moons of Jupiter (those discovered by Galilmqh,2a ym8e 3iu6x3cc9m u5aieo 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 lnii s sq4d9i w2)+a2mfrom the known period and distance of the Moon. nwil4s2+s adi9 2 )qim   $\times 10^{24}$

  Determine the mean distance from Jupiter fo(wck:lz(( qzpw*rzu x;b,6bl r each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in thl zzq 6wwr:p xu,b*((kzl(b;c e Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragme:dele p 5p rkn-w22yx0nts (which some space scientists think came from a planet that once 2e-p 2xreplw0: n5kdy orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes ih(* *v2ikl 87wuwv:.)kk or5st rvbman artificial "planet" in the form of a band compl7k v r) wbk:*v*tvw 5iku.28 mo(lhirsetely 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 Earth days?   

  Tarzan plans to cross a gorge by n*yhr ;v(r +et2h /tfeswinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, et;vey /r(+n th2f*r hwhat is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half what )ac-tez 1oo(4:xjtznabhn( (it is on the surt c1)(bxo-nt(:e aoazj4zn(h face?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spintu 8dvzye,* g, in a mutual circle once every 2.5 s. If we assume th*8uev,d tgyz,eir 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 acceleration of gravity bob1p)/,4 k7zf0 rrzlwuh r *rat the equator is slightly less than it would be if the Earth r 7rhbrl zb ruw*4z/)kfp10,odidn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth willr:bpgg:;owycj w3swy;w. 19 v*c*a7 isfrv/ a a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and M y9rf:3jwbs v s1:gyrpaac wg ;w*/iv7;.o* cwoon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in ansf mnvjr4:l*v8+2 8 twyijh/e elevator, it says your mass is 82 kg. What is l84jrntev+mjwh: y/vs28i * f the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station c n5v/1tz9 jrodzv5-fjonsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tu dv95ofjvzn 5tz/1j-rbe 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 a qxf1 h ;pvs1:,:mxs( jt8)geqvj,t air*j6awircraft 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, :uwf g06+hp/if(nexp5g oh4 zthe acceleratifh:hg 4 wxuogpi+/efn 0p6(5zon due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m h2:-pciuk 2b6 zxw bq-tanging on a string) is deflected from the vertical by an angw kbp q2tui 26bcz:x--le $\theta$ 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 fo58 q rgalm52v pw8jwd8r a design speed of If the coefficient of staticqdpj 8rw2w mg8558val friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at 20 yco;x th;1enmi( qkthe equator were apo ; 2tqhny0 ;ek(i1xcmparently weightless?    $\times 10^3$s

  Two equal-mass stars maintainngu)+wipm02 acuq + 6ut :gsl( 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 3p3,oj(tv4plsgy)c x t m b7 p3k8-skeradius 235 m. A lamp suspendppjs)b38ytce o 3(kklvtgs p mx43-7, ed from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claimed th)y j/o8ts+tiybnp:- 3 u snb8qat a person would be crushed by sq-y 8t+ 8iu)ny/nb p t:3sobjthe 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 Hubble Space Telescope deduced qb( kx mu3,g7dthe 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 gaxgkm q du7,b(3s 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 speezg;z1emzg iy 8 m oxndioq9v595/x+,hd 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 do the normal forces acting on the car at A, B, and C compare? (Which is larz5+eid;1oo5zhmqx vzyg / 8m99 ingx ,gest? 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 (GPS) utilizes a group of 24 satee.va ku-ob 8d9llites 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 navigaboae-9. 8k vdutional “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)kg(-pgv suc( q+ ,u3pg8zp*lp2 pb6ou, after traveling 2.1 billion km, is meant to q 6zc 8 suu*,- ppgob+p3(u2glpvp g(korbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttlegkdc7.z5 oxq w7 g:qy- 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 g7yxc.qzkgd q5o- 7w: 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) Whd w,z gd8id.:j, k.inpat is its mean distance from thedi.w:nj zkd.8p d, g,i 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 -mpuo)yj)qi -:vp+ s g3dxaw5"feel" yourself grav-x)i pjyosp+m3 vdqawg-)u 5: itationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around twcph -blf )vf / :/spy0lq z1nj/yo 5vaw):h.zhe center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-yearvp.fqf- 5cl b/h/j nlh 0):apy)szw:owyz1/vs 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 0.5z6ld :5o,+pnw8t6hfj 7qay +mxi9u bj0 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side dxfzqhiml5 9np+6 6o ba: y, wj8ut7j+of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits.q4b qbf 85y g-k5jwdz 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 7 o(pymnro1/c by the tip of the 1.5-cm-long sweep second hand onc(7ryo1 mpo n/ your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cirsm5 piq3uztx5:a9qcm v7hz 4o+a)qs+cle below you on a 0.25-m piece of fishin5spc+qm ovaizm u )t+9qzq x4573ash:g line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car tra -peh *z gcmlq2p9ks3 x3+g dx4ult1w9veling a4gpepql9 s39wlh2x c3d + -xu 1gk*ztmt speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when n:lr ica02o:h(jk3 dg;m-gdihegotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, ko igih:ml;d2h3dj0g-(r a:cto 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.$\approx$    $\times 10^2$