Sometimes people say that water is removed from clothes in 09po wg*vvl 0jl6bzw7a spin dryer by centrifugal force throwing the water outward. What is wrong wi9v wzbp v*w7log0 6j0lth this statement?

Will the acceleration of a car be the same when th+ ( ij)yy gtfpnnux/:;e car travels around a sharp curve at a constant 60 km/h as when it tra; g iptnjn)f:xyuy+(/vels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant sp . eptzv.6xh ))z*9p53 kswjxf8mf lfbeed 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 hilfe fsbhmt *98p vx5xp3zw6jzk)f. .l)ls, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merrm2-oj c9qb bb4y-go-round. Which of these forces proviq 4b2 omb9j-bcdes the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the eon/dkyrkg7 -8 (eyfjpi9 w 60water spilling out, even at the top of the circle when the bucket is ups w/d07 eon8 6ip-rf k9ykg(jyeide down. Explain.

How many “accelerators” do you have in your car? There are at least threfi.uk9 8myfb)e controls in the car which can be used tm. ubffy)k 8i9o cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying b 4-u92p-m ibwvdsbr-qw;s ;pover the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hupb 9 bmr ws-sqd;--pw4vib2;ill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inv17w: up vu8 b1qaya7oward when rounding a curve at high speed?

Why do airplanes bank when they tuyvcpf5reya14d9) 7g:ia c +jgrn? How would you compute the banking angle given its speed and radiu 1yd cvf cjy7+eag54)9p:ragis of the turn?

A girl is whirling a ball on a stringlyg1bp1 rmxu li.c 7f/;6 .pow around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yaw.x7pom6/ u1.lyg lb;r f1icprd. When should she let go of the string?

Does an apple exert a gravitationaluy4pyj e9n3 o2y6j g6t force on the Earth? If so, how large a force3et 6j24o6nyuy9jpyg ? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what u;4p+f.v )uub qtkj-uways would the Moon’s orbit be diuuu) f-p+k .;qu jvt4bfferent?

Which pulls harder gravitation u2hgb(i7r4z;8zv2jqz-/ada y w f7qwally, the Earth on the Moon, or the Moon on the Earth? Which accelerate7427i2gzrj/q d f(bvzaauhy-w ;qz w8s more?

The Sun's gravitational pull on )zngeu6ai-o0the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difiuz0g-6 oen)aference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or o ae8+x /45y+prts0w-nphjkp ftm :o-at the poles? What two effects are at work? Do they oppose ea+ /oj5xo p tn m pk-ret-8aphs:0f4+ywch other?

The gravitational force on the Moon due to the Eapc:m ,ocm- ocm*vm w0r.xd1b4rth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Eart1 o0 cxobm vc-:.,cmwmmrp4*dh?

Is the centripetal acceleration of Mars in its orbit arouqwe bxu wp38e8bn( h*e2tx:7 bgrq1e) nd the Sun larger or smaller than the centripetal acceleration of thqenbxe*8(:he eg b3p8b)x 1wrwt 7uq2e Earth?

Would it require less speed to launch a satellitfx-f wlj(m98we (a) toward the east or (b) toward the west? Consider the Earth’swl 8(mfj w9fx- rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a mrgxpa *4 womhr s85j;7oving 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 same as when you4r5 p8x;*h rm7gsojwa are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in ,ehst7);n +esq *i liwouter space could be adversely affected by weightlessness. One; *e)hsnl q,+ieisw7t 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 exper8m*bsputehn; 6ugx 8 6hk bkj2v+e.1v iences “free fall” or “apparent weightlessness” between steps.gk m2e8+ejxt 68u b6vvnhh.p bk1;*su

The Earth moves faster in its orbit around the Suh)u b0*dk gtf87mta 4on 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 to the plane of d7 )tg4*hombftua80kits orbit.]

The mass of Pluto was not known until it was discovered to hav8z.e9b ds q7j*fs5oj fe a moon. Explain how this discovery enabled an estimate o7*jzffqs bo5d es.9 j8f Pluto’s mass.

  The Sun's gravitational pull on the Earth is mv hvt(1 enl3yax +g2c.uch larger than the Moon's. Yet the Moon's is mainly restnay(v23 1xc vegl+.hponsible 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 sk)w* lxh0cu w .7 ff,mx7xik.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 orqop8qr8d6nxa117he yk2 a k :f the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a q1o adxk1eq8p7 8:2anr yrhk6circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted ;fd,nv q x-79 n1d)iq ew8znwnon a 2.0-kg discus as it rotates uniformly in a horizontal cwnn) d v9eq- n7,d wn;1xqfzi8ircle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 4cro.xfpc/wc7 ux0 7yk/3 0mgz00 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 gz.f/p/g0rk0mo7ccxxw7y 3c u , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay c 0cn1 ncv 9g*(fqq*/ooz(ishon the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?cz/cqh( v1ng iqfo* 9n0c s*(o   

  A ball on the end of a string is revolved at a uniform rate in tvy12z0gwqll* u) 3 qza vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If itsq q z130y)lt 2zvgw*ul 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 -r,dn1aqyfa *os5sulf( id:+-kg car can round a turn of radius 77 m on a flat road if the coefficient of static s* -5fsra lod,n 1+:uqdf(iya friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient ,t m6y13ebnsp of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speedy ntm 1e,6ps3b of 95km/h ?   

  A device for training ast7afm y(fy ;v-rronauts and jet fighter pilots 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 7.85 times h(f-y; 7ymr faver 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 variable sdo:1-1e* 4ddsgyv nma peed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between t o1yam*sd vd:-edn1 4ghe coin and the turntable?   

  At what minimum speed must a roller coaster be travelr( )j0g7f liju1bx- cuing when upside down at the top ofbuil01c ujx rg-7()j f 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 k;c xcmv s ix(m 1+xgaj.w9g9n1g (including the driver) crosses the rounded top of a hillvcjsc 9i+g;9x1m axx gnwm1.( (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel neeq; d b..pq*nzud to make for the passenge qbpqnduz;* ..rs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cvt giioa-9b o4-9s5a6bl r)z vircle of radius 1.10 m. At the lowest s-iv 4aabg99 zotb 5ir-) 6lovpoint 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 from the r jmwv1f-ol1 i.7fn. uaxis of rotation is to experience an acceleration of wlnfm-.u jvr1 .f17io 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in nn y,i1;td, fserv6)7fosy;l a cylindrically walled "room." (See Fig. 5-35. y;r t76n voseds)fl f,n1i;y,)
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 air-hockey tam46u, r 7otgvubletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole7 vtrmo64,gu u 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 , precise5wf+3mpk,. k xgjh4ofly this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitudm j f3kop+g.wkxf5,h4 e 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 banked for a ca g536yiv499mgfwlm qztd6a q. r 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 masses1xh;p6ie zp2xfwox m 8f4j1 3n $ 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 31045b *. )jrp lvdu-saix $\mathrm{~m} / \mathrm{s}$ . 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 cz *1ag 57ozsnkomponents of the net force exerted on the car (by the ground) in Example 5*oaz7ks 5ng 1z-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 uniformly from the pit area, go92ocs yke--5 e c +6bu5w.skj (gdagmwing 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 hgjswu-(ybgo mc9 a .k +esw-d562eck5 ave 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 par3ngv* astqb,ns0 mc 0(ticular instant, its accelera bs,3 q0gscn*nm(avt0 tion 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 spacecr;yzxhp mw+/3kp4( oqnaft 12,800 km (2 Earth radii) above the Earth’s skwo/h x3;y+q4( mp npzurface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a maj *dy*:.knsob x*6ymjgnitude of 12 xnsoym* jby:dk*6.j* m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on thoz.)q9 yu)t1jur g-yu)bn o-i e Moon. The Moon's radius is 1.74 yg q)ou9j- iur z-u))b1y.nto $\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 s)vd+xb/pl g4y 26p rufame mass. What is the acceleration due to gravity near its s+)xgf/l 42uppvry d b6urface?   

  A hypothetical planet has a mass 1.66 times thatxw:mmy)2 dzv ) of Earth, but the same radius. What is g near its surfamdmy:z2x))w vce?   

  Two objects attract each other gravitationally with a force p+9au gh n gof2*p2l,yof 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 accgq4x01na*zv fyf;fr 1 eleration of gravity, at (a) 3200 m f0vfrq*zag 1 1x4fyn;    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from tg9k9v nj3t7d the Earth’s center to a point outside the Earth where thegravitational acceleration due to 9 jvk g3n79tdtthe 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 intorrky2 7wnyg69s; nx e9 a sphere about 10 km in radius7w ny ge;r9629nsxk ry. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whis72iez4ht;:hqs6 w44pyb a ktch once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity b 4zst h 64pikaw4 y72qe;h:ston this star?    $\times 10^7$

  You are explaining why astronauts feel weightrgug2*zke)r6) 3cbq. 2 jyklc less while orbiting in the space shg6ryz3c)q)krcj lu2k* e bg2.uttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are lop/lm4ihhwwv g q3k063 cated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on o6/w g30pqk lwi 3mhh4vne sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planetsr(aic 4y/vlrv9h2 *pa line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Sat/ la49v*rrp i2hc(av yurn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of what itnxz;e3*jn * bxrwyfs(h5w1 x+ is on Earth, and that Mars’ radius is 3400 km, determine the mass of(wrxyhs;3 1*xb xzn5 w*ne +jf Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for t9l/: ;il f.ynr*u.mprd yds,the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lf/.ldy;tm: .9* y, slrpdnruiaws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abom9 *yl f1hu(axjyo29yut the Earth at a height of 3600 km. (1ojlym 92y*yaux9fh    $\times 10^3$

  The space shuttle releaseskkvf*e l 7q,n 4aln,y0 a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earthe704vnk,n*ql y,af kl) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occufigml3 ww 3 76df0 vpcfew4l)+pants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter vdpfl 3c64 ifwg+l f073ww)meis 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circfvirxxu a /q:aoxrj u 4qzb 7y80/9q +4bw/be-ular “near-Earth” orbit. A “near-Earth” orbit q7ux+u/ r r4qy/4qv/:a a90xwibzebjox-8fb 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 woul7jzws6ozc+ n *d a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around thejzsz6wo* c7n + Earth?   

  During an Apollo lunar-5j2 y+mpa0 k-vyru p(tgxt5 o landing mission, the command module continued to orbit the Mr (t5+y5oxt pa0 ky- 2mpuvg-joon 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 +1sl rty7so dq3l:y6 gchunks of ice that orbit the planet. The inner radius of the rings i7sls+q o:t1 lgyy6d3 rs 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 mni7h u nplc ((o1h68 gity/ 3qinyo10y in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at (o/i yh7(un6 t10n1nicpy o g3hiyl8 qthe top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cente;q lpyzxg ds4 kl11i83emz,gwg14 -yfr of the Earth's Moon iny q18 g44l3mlf -w1i,pdsexkgz; g zy1 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 system consists of two stars of equal *djob.8d:dc h/w 4hlo:b f qq;mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between th./db 4;h odhqw :c*qbo:df8ljem. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the mv6/(cd5h o ff2/dy ckweight of a 55-kg woman in an elevator thahvd6 (cdyfc5o/fm2/kt 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 fr*+d+5odo 5p cro o5dpfom a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and dirrooop f+ 5o +*dp5cd5dection)? a =   

Show that if a satellite orbits veryugjxzy:jdn jqr 1r8(k z7n6m65sn,:q near the surface of a planet with period T , the densitnxnq8jk(dz6yj5 qm gzrn:: 6us7j ,r1y (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 determine the period ow: vdkm p5t-a:9oea(yf an artiav: y5 dekm:wpat-(o9ficial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, th2z mduc;lma l0,mr,/ wzyy fz+ x)8d)vough only a few hundred meters across, orbits the Sun like the 0xz)wuflm ry m8m+) ,y;v2a ,lzcdd /zplanets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5x lqg.ul7j/ 7jdbe8th7-y . 0:snqpz w $\times 10^{9} \mathrm{~km}$ 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 -29emh u8j 3 wipwcbh4Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? Whai4hewp- 28m w uj9hb3ct 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 centpgwa9fu/mo)x(r v (o5 e xy;4;+wjljcer 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 disq2ou9 szjke0(tance for the four largest moons of J(uo02e9 kz jqsupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Mnfwtrjr nm r(268em5 +oon. r rrj 5emf8nntw(62+m   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usin : qlg, gce*5ahnr0uw.g Kepler’s third law. Use the distance of Io ancw: ,ur*q0a. l e5gnghd 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 M;5u am4tn/4 e:4n3ah8cjf an-scgk)k q d5ehoars and Jupiter consists of many fragments (which some space scientists think m 4 /:-4neckf shn 8)jne5d4tq hcga k3oa5a;ucame from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a band pk9 s wb5jsi,z3cws(a/ 5s:db completely encircling a sun (sis dbjcw/(5sw p k,5ba9:s3zFig. 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 swinging in an arc from a hanging vine (Fig.4.)0wfuss3ayfdlf7 h 5–41). If his arms are capable of exerti l03s uafh7w y4s)fd.fng a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s s3kqwqpw( 1u)nurface will the acceleration of gravity be half what it is on the surface?npw 3(k )1uwqq    $\times 10^6$

  On an ice rink, two skaters w ieh45f, 4e vosk,2zy9pk6 bwpsv:7 nof equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each4,of syh epve6n97 4 w2w5zk,vipsb k: 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 pdt godm4no2 15 +h-tsapparent acceleration of gravity at the equator is slightly o24ndmg1-pt s th+o5d less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth w4r77szrefmjxde 39si 4ci (6oill a spacecraft traveling directly from the Earth to the Moon experience zero net force because the i77z9 cr4eidjre(6 s4m ox fs3Earth and Moon 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 an z-4m m l+fx 1f0hpx)zhelevator, it says your massm lf1f+hxphmz) z04x - 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 w) -.serhy6/hpum u36tm4ekzk ill rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surfa4p uym kmh )/3s .ztkue6hr6-ece of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a verticaljt c,pexk1bd;e,c-.r csar+ nf )u/ 7w 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 s7 7/ns07z f9a +nl+ajqmn( f sne7fpkplanet in terms of its radius r, the acceleration due to gravitaa7 + 7 jlnks+p7 q zfsn0(nfm7sfe9n/y at its surface and the gravitational constant G.

A plumb bob (a mass m hazaqqp:ginwv/ (..j ; wod s8m4nging on a string) is deflected from the vertical by an .qw;pi/d osjw.q(n8g4va : zm angle $\theta$ 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 design speexeg.5vb9gz ,cc lys)-gl-n oft*ifnj 917j,od of If the coefficient of static frjgtc9y.jvl-)5g fcl-7 ogeobn9fs,,i z*1n xiction 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 objec5) (udyc:4g8koi hmxi ts at the equator were apparently weightly48 xk(5gc )umohdii:ess?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of j8mwt,aiuzt0)i ft;- 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. a1w( +sx nz+yuphi/w constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angwsu(i1 p. + /hy+wnzaxle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 timest ry-)okn(um7dk, 1yme(zs4*uubx3 h as massive as the Earth. Thus, it has been claimed that a person would be crushed by thmuo-13k nsd7m4)(hxby tukr(,*ze y ue 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 Spacexsok90mhip:7tl :f ;h Telescope deduced the presence of an extremely massive core in the distant galaxy M87, m:hl7k p0:oh9t;xif sso dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill adc*qk8 l1v2e;hg;c km-ayag 8nd valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do thegq*; d- k2yac8l8v hc1e;gkam normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group o8( (ondud+o7 ;ens8u:prtlfkf 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 navi ;8r(uklt87of eonds u:(dp+ngational “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, is meo6k ny.(e6cgik,h g f)ant to orbit the asteroid Eros at a h g66 cfe(y,nkh.) iokgeight 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 shuttle pursuing a satd*;rts0gr x;g baf2j1ellite in need of repair. You are in a circular orbit of the same radius as the satellitr xgs;t12d0j*;bagrf e (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp hassgh9i+g o.+ e uumdy0klnn-bq55 x-2k a period of 3000 years. (a) What is its mean distance from the 0ghy.ke5-u5mxun qig -+kb9+ldsn 2o 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 0rv:bg a:dy k* would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make revrd0a* ykb:g:asonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at aookh*.26l -qx 5ffn sb distance of .sn hk f -o6xblf52q*oabout 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corn4hp l5 :o-r lbuth0j*rers of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fi ljho:0 r*h4 urtplb5-fth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbi )p9z/s (wk yu mx28zrotgtugci ,)()kts 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-long sweep secondkrw.r9c1kndif)j ,r,2zhf+t hand on your wrizndk29+h,w rr1f ),ticr .fjk st watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in rpc( c 2(tg*ed*jex4ma 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 vertical? [Hint: See 2gmt(p* r eccj4*ed x(Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway idb*..g li,6jb o8f yao6eu2eis designed so that a car traveling at speed,fa.yu.o6o* g8ij be e26bidl $ 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, theqnsopzb 8s/; v 7e /ra/cj(z0c Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, ise0 zsr8ozsp /;/v /a cbj(n7qc 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.$\approx$    $\times 10^2$