Sometimes people say that water is removed from clothes in a spin dryer by centq a;cw6om8ik 42e jyfej w -s)w.-8nzsrifugal force throwing the water outwafs 6 -4qw jen8 ;mc.8-wkoasejwzy2i)rd. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a n:4hw,6uoqo n sharp curve at a constant 60 km/h as when it travels around a gentle curve at th w ,un4oq6o:nhe same speed? Explain.

Suppose a car moves at constant speed along a hilly wg8y26a sl1smroad. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hilm2 ays816wgls l?

Describe all the forces acting on a child ridindgy 949x a9bagh. 2kxfg a horse on a merry-go-round. Which of tfab 9 ygkax499.gx h2dhese forces provides the centripetal acceleration of the child?

A bucket of water can be wh5pbw : f:-modj +7v. 7c.dhmfix5 qizvirled in a vertical circle without the water spilling out, even at the top of the circle when dw ic.v j5h b7-df ::xq5+oz ip.mf7vmthe bucket is upside down. Explain.

How many “accelerators” nf+8f ik0ii7s s3 b(aodo you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they8i0s7(ofb nia k+sf3 i? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown ia76jm 1y)sjbak zh)y2 p7f bdybt,5l.n 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 hill. Explain this yaz72jft )kp lyh5j6a.,sb y7 b1d mb)decrease using Newton’s second law.

Why do bicycle riders lean inward when ro:dltbdk:2,fp xbl0m egu3k;2 unding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angletwzf7534xk2hs)o q ua given its speed and radius of the xftz w4h2qo)u a3s7k 5turn?

A girl is whirling a ball on a str tkquwzn)j lv1h +:m43ing 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 otklqj)z+wh 1vtunm3 :4her side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so6mtnfs l1nt: *, how large a force? Cons f*:lnt1 n6tmsider 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 Mx86;v ze-mn dsoon’s orbit be dimx sznd6 v;8e-fferent?

Which pulls harder gravitkoqasd;eaqqqfk g vn/q ;5 o3t/78;n+ationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates moren seq; n ta7v8qkd;qqg+5ka//q;o3f o?

The Sun's gravitational pull on the Earth is much larger than3tc 8u yczfdpr a0;u/( the Moon's. Yet the Moon's is mainly responsible for the tides. Explain.8 ad0;tpc3z /(ufu ryc [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the pu)7y4wg*imlv9wq k y5oles? What two effects are at work? Do they opposeu4w)9 5vl qy*giwyk7m each other?

The gravitational force on the Moon due to the Earth is oke22bqn fq *ol2yg*36mkwv 6inly about half the force on the Moon due to the Sun. Why isn’t th eybgo2 l6362vfni*wkm2q* kq e Moon pulled away from the Earth?

Is the centripetal acceleration of M p q -x.ww ,miovawfn84g1,uf;ars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Earthq,wawu.1f pow mgf-xn 4v,i 8;?

Would it require less speed to launch a satell-)cbve1yugkp3 xq 11kite (a) toward the east or (b) toward the west? Consider the Ea q -1kepc3kg xv)yb1u1rth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale iq tpmvjdz/k:),ukx(gw(, a h 8n a moving elevator: when ,:/,q x (pjhk wdau8kv z(t)mgthe 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 you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in otdh ;b)gf6orvd:obj, 7py y(f)ws 11outer space could be adversely affected by weightlessness. One wp1,wodf(1b)7 ;shvr6t d)o:by jy gfoay 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 experiences “free fall” or “apparent weighird82lk/f/p(naxnk 9 tlessness” between stepsrl(/f d8x92aipnnk/ k.

The Earth moves faster in its orbit around the Sun in Ja zg*gbdoe 42e-nuary than in July. Is the Earth closer to the Sun -ez2*g4boe gdin 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 its orbit.]

The mass of Pluto was not known until it was discovered to lc8jn1 t/5+bjd8sbj xhave a moon. Explain hj8+tx5db/8cj l 1b snjow this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th5s.d -kthyf 04biw.tke Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the othe4tyw0tifk5 .. kdsb h-r.]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 19xdqb vhef5:3dv x1ydb2 )p zu9.lf ,8u80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 thiskrn5vx*i4a:0)(s gtdceo 1 e 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 circle of radius 1.ga(5eiov1 d 4:ki srx0*t)s cn50$ \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 exefbx;7.xqezz7 m s hk,0rted 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 speedxq0mbs7zx h,k . e;zf7 of the discus.   

  Suppose the space shuttle is in orbit 400 kmgkt pajj)2xek ; -k,emfyk.0; 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 te2 - ;kege.p0;f)kjmajk,tkyx rms 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 edge of a jq au:hri0:2y potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diay:j:q 2a 0hirumeter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rato n9yvz,i.dg *e in a vertical circle of radius 72.0 cm , as shown i.*n zyio9v, gdn 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 wiol)7ynn / ;aos4lzdn7th which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car? o nn)ld 7l7 onyas4z/;  

  How large must the coefficient of static friction be between the tirej+tsozt4 3- ib5r+rohs and the road if a car is ro 54+obttz3hj+r- si to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to buat4mqjphs69 y nyw* 8n ;(:phlf17xrotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.l1698;tn4bph : *jxspu7n y(whmqa yf85 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 rotan*a6i /3 y)io.i;wz/oidye * zl;4puypibg8fting turntable of variable speed. When the speed of the turntable / /3oe u6z;n*zi8).gpwpb oiii yd;ya iy f4l*is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed meaa ww l;mqm0f5:sq;* ust a roller coaster be traveling when upside down at the f5;* aelmsamw:q0;q wtop 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 rounded5jro8 zje1c/usvsbd k:/ 0z/u top of a hill (radius =1u 8rsd0z/eu //j jocz:vbks5 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 whe478e.-co b fmpp wpbb8yew.7 eel need to make for the passengers to feel “weightless” at.88cpm4wwpbbb7 -eyee 7 fpo. the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical cihui7 pva00u:t rcle of radius 1.10 m. At the lowestpu07:0av itu h 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 rota s2/nl5aga ar ul7*21lxhq. kete if a particle 9.00 cm from the axis of rotation is l ar7ak hxllg5equ1 2ns 2/*a.to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a6q y925r*paksd6tma o cylindrically walled "room." (See Fig. 5-35.)ayd5t *rm62 9kpo 6sqa
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 ai-iadw7p ay0q 9r-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fw0ap 79dq yia-ig. 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 ignoring the weight or35,cqvjb:u;okg- trac(8x of the ball which revolves on a string 0.600 m long. In particular, find the mag g3rbua-c q:v5,xkj(o8 ;cr tonitude 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 myvi,. + )zj ztmn+ob7t1kp /gu 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 xhku9)l+7st5k gp i(oe z1v: a$ 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 ma aop(ma.7qhwi ;)smpd4boq : 4neuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerte)pmtz+ vk * 8b:9hjcqnd on the car (by the ground) in Example 5-8 :b9k+*nm ht cp8zvq )j 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 accelerateg/qw8xj) v,9tc-ifpq s 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, wh x9w,qjg8- t)c/qpvif at 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 z3uzj3og9- dq horizontal circle of radius 2.90 m . At a particular instant, its accel 3jz3-uq9g zdoeration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12v6szd f9*sa)d,800 km (2 Earth radii) above the Earth’s surfa dsdafs 6v*)9zce if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magn+ +zqw1pxhyl9itude of 12 m/ w+ hpx19qlyz+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 the Moon. The Moon's z5-l wd9obzsn; uzd 8koh.8 o1radius is 1.74 ;.85z on lzzoudo k hd8-w19bs$\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 tle01g42 8j5regw .ltxgn4 mb phat of Earth, but has the same mass. What is t 5w0l.rbjng4pel 21g8 etxgm4 he acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but mfo :**n i7wqdsa2abo 2g9/ajthe same radius. What is g near its d2jq:ob mig* anw/9 a2o7as*f surface?   

  Two objects attract each other gravitationally wi/)h0+xwlxuii wg 37hd th 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 accoh((tk +b3sjv eleration of gravity, at (a) 3200 m +k((b 3otsvjh   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centxw7vql77 e rq*er to a point outside the Earth where t7 q qlev77*rwxhegravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the r s;gpm9pwk ,xiz29(d-wc(demass of our Sun packed into a sphere about 10 dgpmk,9dxzc( serw2(wi; 9-pkm in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf mvbbxfjku*w) .n3c70 star, which 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 on this sj07kbbcm3 u.n)xv*wftar?    $\times 10^7$

  You are explaining why astronauts feel weig z2zptc0 q4p3bhtless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yoursp3bctzq4 0 pz2elf 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 at thel 21 xrl e v,abbi idl;fu/odb.v19y.2 corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the ot;vlvr .di9fbdab,o11lyx/ 2.ul ib2eher three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the s. bpcck0x0wp6fk .pxs+ kc)+a ame side of the Sun. Calculate the totakkc pp6+ xwa xk0.sfb+c0.p)cl force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 vqxdrlm)(:k 4) j -pucof what it is on Earth, and that Mars’ radius is 3400 km, determine the madk)v 4 :pr-q)ucm(ljx ss of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the mti,0ae, pba: spdvrj6153dag +m swa,n3y: qknown value for the period of the Earth and its distance from the Sun. [Note: Compare ydnmgi:50,jp,36mpeav:r3ab, ads 1+awyst qour answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stabl mpthfjq)2y9 5/9rhv me circular orbit about the Earth at a height of 3600mt 9py2h rm)5j/ vhq9f km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbr*aeuo s1av7w7-d6l ehokad 4klg/:5it 650 km above the Earth. How fast must the shuttle be moving (relative7*oao/ s-v6dd 4:rlwuh 1 a7ee5kaglk to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occjac5f+skgidc/+l 7: aupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed fo/f +i7j :ck5 sgclda+ar one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit t0fp ,ooow .*s*a hqwm2he Earth in a circular “near-Earth” orbwfoo ,o** h w.0p2aqmsit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity wou6d okp- x8q/8xif7nw vld a satellite have to be launched from the top of Mt. Everest to be placed idnwvpxf 6q o 87/i-k8xn a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module co9wtq1q 07qbnz26kqxcva y5 :entinued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon oneqcazyqknx5wbv q26 7qt 109:ce?    s

  The rings of Saturn atb09hsq 224ea rfyu *ore composed of chunks of ice that orbit the planet. The inner radi9*t4s u2oh0y a2fberq us 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. 7 gaavm lk +rnotl;5 h-w3d8;y5–9). What is the ratio of a person’s apparent weiv-ahw+73ko8y ;rm;5 dtga n llght to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent y 4;z+idfp)o ts68uyz weight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a spay +dyo z 6tpsiu8;f)4zce 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 consi;h 00ji t1+by4mjhv,kq(asfy sts of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is thyt4 ajq;hb(y,0m 1 f +jikhs0ve mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg wxi(fgei np y pz63d:64oman in an elevator that movi 3dpgpix6n4(e f:y6zes
(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 poafc1z;*i o7 tbs)z8of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What wasio1oztf a)p;c7zb8* s the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface 2ekjvt6s 5we0 of a planet with period T , the density (mass/volume) of the planettjs 6e2wvk0 e5 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) tij:e8r. vuc fb( r .h/m5uxf ltj+ep+7o determine the period of an ar e/7v um.f(lrup:it+h frc 5.ej+8jx btificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a +sh( 6flgogz5c6uol ,/66l k1gyxjn qfew hundred meters across, orbits the Sun like the planets. Its period is 410 d. What,q h6of lkc/6 (ygg6x1 j6nu+ 5sollzg is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance u13dd ie 1 ;ajl:ubhwc:o 3p562qrwlnof 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 yearswi qq ,btgcv3.y q 1yb5ff6aw5dkg7,0. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean vc70bg qkqy36yqb id1t f,w,gaf5w5 .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 of6 s28yxa afz/ne;h +as 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 four largest mo225l1gh3 zktb 8jo rmmh)i z3uons of Jupiter (those discovered by Gal2jh2 )i r gt31k38mozbm5 lzhuileo 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 Ear8pc1hkwy5ifx /q th .qgk-0g*th from the known period and distance of the Moon. *yf g8q1w-.pxthk/05ihcgq k    $\times 10^{24}$

  Determine the mean distance from Jupiter for each oga pk 73oov2l7usv:)c f Jupiter’s moons, using Kepler’s third law. Use the distance of Io and 2:p7ls uog a3ocvkv )7the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (ws6:4hgqod0zf9 - wanzhich some space scientists think came from a planet that o9-ango q 4h6z:z0wfsdnce 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 idjd5m-vhk8i)xt 32hrtelc*p)6 n) qqcy*o 0 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 quc -c6*mipn*y2 j 0eto35hd)v )hidx8krlq t)qickly 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 swingighryd9c7rpl90h m5brghf-)0ng 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, what is the maximum speed he can tolerate at the lowest point of his swi0 75rr 9fbyp-cl 9rgmh0dgh )hng? 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 fkf) 7vji k)d -iiz*5lbe half what it is on the s-ikk*)vifjl f57izd) urface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin inne01qx7gn2,q :9 a /li-kx zwmlrn dq0 a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pu q,n 7d09/lqniaxwr gnzk1lm0-x2 :eqlling on one another?    $\times 10^2$

  Because the Earth rotates once per bk+/*nr( vrgmv0t mp3on3w4u day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rot+vmb /t0m*r4pwgn vno3kr(u3ate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft trayu q./jb1r7( );6vcf ggcydmiveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppositem.i)/ b 6j7rcqu1v;y dg(fcyg forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand ol 1mnp1(lz0n rn a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction? z1 p0 lmrl(1nn    ----待选择----upwartddown 

  A projected space station consistsd2qj a6 ey 9 4ulrp1ush.2d9tw of a circular tube that will 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 surface 2hquwd.94sy ad jtul r6 12pe9of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fi p-ogx(ib )fv :g(hmewvp,d: 9p2pn(v g. 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 o8 p,phx mts9; lijzrsphj7/-*f its radius r, the acceleration due to gravity at its surface and the gravitational c z/*m8; s-l jh,ppihrp9tx 7sjonstant G.

A plumb bob (a mass m hanging on a string) is deflecte8ik(ds., g boqd from the vertical by an angle (gqdi.bsk ,8 o$\theta$ 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 banr /u/lio p1wb)mv4 ,bcdxww6.ked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range/uv.d mw4,ir w/o16pl ) bwcxb of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fa 6mgk.d kkut r0f./ta ,3l 2jduni1cvwl/ *nu8st that objects at the equator w / lkd l3vt gnru2.itu*k.8a0dj6nwu/ 1k,mcfere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dist4.btrl0p :-rplrvn a/ ance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A la4b ckvi)zv nd61/z4kqmp suspended from the ceiling swings out to an a)cq4i 1zv /kzkv bdn64ngle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 ti9l q *shvgywf;1ze)+c mes as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few vwf91;ce+*)g lqsyh z 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 the pres pxz: zim.,+ 7zrsu cp6: urtntr1-0xaence 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 0.-6upuairrxxtzs,+ t: :z7z mrn1 cpmeasuring 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 coe n8hdnp.)nefm+,* t jnstant speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill andetjdfnn)hn*p8+ m .e, 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 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 satellites or.1tcfa 4i1lmdg. t/ gow(5dtc biting 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.c1gaw .4l dtf(to5t/m d gci1 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. x4.z fhbefmd98uh72 c s3c:hl1 billion km, is meant to orbs u x hfb87zd4.flhhc:2ce9m3it 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 shuttle pursuz*kk+bf.w4ta hr/l :ting a satellite in need of repair. You are in a *lfb tzw r.ka/th 4k:+circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean dis e/yg 2)k:zc6r0ddoows c42mk tance from the Sun? o kwrd4s:6 0 e2)dmco2z/gkyc   
(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 bees)-rg w7ux. r /rcs8+ x;sajm if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, l/c8js s xg)7ur.rwm+s-x;ar eike F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milkj h 25libthxfv+r )7(cy Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the(7hjl brf52 vi tc)+xh center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each side. F)mr/: bvakg8-k): /cp( zjlpsiyh*r1 c wl8ntind the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midp:-pmyt sk8wlb))aprg *c c(:1zlj//8khr vnioint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg ouutmk2n1 (ca+f /dt , 7rbdmw1rbits 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 acceleraksaj50.phmc 3y 6-n d2 hld4qmtion experienced by the tip of the 1.5-cm-long sweep second hand on yona6mh-0 s2y53d h .mj kpqdl4cur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sgq+p7v vz821 cbs0 loae6cx w bnp.,v9inker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makesp2v v,8.lbwq9gn1z0 epc7vb6 x o+asc 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 highw0q8wi 8gw9v (bj cir2tr/e p+hay is designed so that a car traveling at speedii hvwb8/90q 82wpc+rgr (jt e $ 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, us wsz yai5a6)yo;. /km9s p4dbtilizes tilt of the cars when negotiating curves. The angle of tilt bps)zy9i /a smok.ady4w 65 ;sis 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 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.$\approx$    $\times 10^2$