Sometimes people say that+ 5insgark s0( water is removed from clothes in a spin dryer by centrifugal force throwing t(krs s0ngi+ a5he water outward. What is wrong with this statement?

Will the acceleration of a car be the same c:wq10oxn.7j/aq ox6 xf5 iwcwhen the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.xwc:x co56i 1f7q.x0w/a qn jo

Suppose a car moves at constant speed along a hilly road. Where does the ca/i .(yzt f10s3f1 khjhwepo;qr exert the greatest and lef tq1031;ysw(j/zhpkfh . ie oast 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 on a merry-go-roue7*chl, n swd8nd. Which of these forces provides the centripetal accelera7,8ewl *hdnsc tion of the child?

A bucket of water can be whirled in7 06 x vraz;ib6jtg7gx a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside downg7tx zaij;7x 6vgr0b 6. Explain.

How many “accelerators” do you have in your car? / 7gvx fyc2+ff 4ggeb,There are at least three controls in the car which can be used to cause the car tog+y2ffx /4vg, ge 7bfc accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fiwee ynt+kil9c.62y( g g. 5–31. His sled does not leave the ground (he does noti2ln( ty+e96 kgw. ecy achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when t.m9 lfw7ny:l rounding a curve at high speed?

Why do airplanes bank whenrchmad3jb k):4 n( 2if:cx v;c they turn? How would you compute the banking angle given its speed and radius of the i:cadkm4( x)2c3; jh:vnr cfb turn?

A girl is whirling a ball on a string around her head in a horizontal pzo+1bw 0 xjh,d8h -cpqlane. She wants to let go at precisely the right time so that the ball will hi80 jzhqh, b-wd+1 pxcot a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a fipf h+;ces8g+p;e u*aorce? e u+i; a*spegfc; 8+phConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whzc( edialfw 3:z*zhqb * 9f35xat ways would the Moon’s orbit be b3a x d3fze:lziqh5(*wz9 cf*different?

Which pulls harder gravitationally, the Earcs u1 n9*kjmmw ,/6nzhth on the Moon, or the Moon on the Earth? Which acc1/ *mc9zs,6knhnmjw u elerates more?

The Sun's gravitational pull on the Earth is much larger than;zbehyb1b l+2gm-we6 the Moon's. Yet the Moon's is mainly responsible for the tideb l-bhze261 bg;ew+yms. Explain. [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 thu1/mcv mc8l.u1tgdj )e poles? What two effects are at work? Do 1u/1 t lm vmcg8j.)udcthey oppose each other?

The gravitational force on the Moon due to the Earth is only about half the y*gy5pqso6 x+ force on the Moon due to the Sun. Why isn’t the Moon o5pgq +sx 6yy*pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun l5/l ecu;k a5bdarger or smaller than the centripetal acceleration of the Earthlk c;5ad/5bu e?

Would it require less speed to launch p4i (h z,1dzq)yfo,(uzqpio.z(r em 2a satellite (a) toward the east or (b) toward the west? Consider the E(zo zpu iq(hr12,dzp )moqi,fz (e.y4arth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a +)kr ak9actuo:tv 0)7 t rv22pxw2ojrmoving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case wvr0ta+ t 2va22 okp)kxo u7) j:rtr9cwould 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 outer space could be advers r owv (m9.fy;8g-0g0czjfcedely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronautsofj0cgcv 9(gm0w- 8.d e f;ryz 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 fa3 oo3.m vb93sjngpr 3hll” or “apparent weightlessness” between stepvponr j3mhg3 bs.339o s.

The Earth moves faster in itiy .pc2vym j.r1j vqeaq-; 2-ms orbit around the Sun in January than in July. Is the Earth closer to the S.pyqv2emri .-v1m ;cq-jjya 2 un 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 its orbit.]

The mass of Pluto was not known untlq-0tt8aze- hra)7kwil it was discovered to have a moon. Explain hotw-)0z7hk -e tal8rqaw this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger th:n;kmv*4 xts5 xy v.o1ijvkm )an the Moon's. Yet the Moon's is .1 yonv :msvk)xkj5i* ;tvxm4 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 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 travelinwn x; phre.*m6g 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the(v9e hylw;*- 6k ualc-j ygy5a 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 r69jlyy-gu5h-(y evlaaw*k c;adius 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 on a 2.0-kg distn,of6t tr 2+y nkl5d+cus as it rotates uniformly in a, td +6nk t5tnr2of+yl horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earto.,u1 6:*+0ph eerfwlb syhxh h'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 g , the gravitational acceleration at the Earth'+xr yfbhh 6s:0e1ow .e,p* uhls surface. $\approx$    g

  What is the magnitude of the acceleration of a spej rz k lt1sq24a:ky+o)ck of clay on the edge of a potter’s wheel turning at 45 rpm (re:rk+q4jzksla)2 yt 1o volutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a mu v;x1wjgt:x207bf.q *k ek n 4djar;y6k0fovertical circle of radius 72.0 cm , as shown in Fig. 5-33. d;:4gb6 ; fm0ju xvtjoyn*k fqke 7ax.0k21rwIf 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-kgol9bvr30a/w o 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 t9 al0 /3obvrwohe car?   

  How large must the coefficient of static frictiodk m*1f d6/ bzijvo ooe5gh:fmu3mc571-wtl5 n be between the tires and the road if a car is to round a level comgoovl6 t d d5 m-75iem1uc3z* 5fk:wfb1hj/urve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotatea g-ctrv2e+s 8 i7tl;t a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her btcg7l vts a-8r +it;e2ack is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis o.,fss ,tcg s5gf a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of ,ssg5.gs f ,ct36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsi 0p;*q ;xaff( ew fejwy0t(u/kde down at the top of a0ju(/ tfkp fay*(; e; qxww0fe 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 (includin 0 9iyaj)pl87ltom uk+ln5a/eszc48vg the driver) crosses the rounded top of a zj5t0 vclsmka8ioype 48 7+)n/lula9hill (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 whe(3wm)ynx whwv vs.em8 d/gxr )oe 4*w*el need to make foreyhwwxmdnw ogrsv )vw x m*e4)*(3./ 8 the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle o ,;za vw,y 3jn:cz tscsf(01itf radius 1.10 m. At the lowest point of its motion the tensiov,ijz za:fsy,s1c nt0 t;cw(3n 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 m6: iglsr+ag; particle 9.00 cm from the axis of rotation is to experience an acceleration omg:+ga l6 i;srf 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotag+g :xk ko4s 03lhep)uted in a cylindrically walled "room." (Se4 l:phkskg+e0u xog3)e Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey tab y5bby3w; ri; 07otaxuletop, and is h7obai 5b0y ;3u;ryxtweld in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignorin,s,t),stnii jg the weight of the ball which revolves on a string 0.60 sis,nijtt ),,0 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 of 88 m is perfectly j*y mx2fmc* :ybanked 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 masse ;*py)i jqot7is $ 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 a)qxsnbuj 6b*6t 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 forc;uy/4q0( 9uj -vd hclzhb9y)tw0qt pl e exerted on the car (by the ground) in Example 5-8 when its speed is 1yjw; h dyh c9l)tpq/0( zvtulu0qb4-95$ \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 arl.t-q xv5 hw c.;qc6tyea, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and th;h5cqqx t.- cl 6vtw.ye road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2g.pw7 g:eh 0ld9r8doi .90 m . At a particular instant, itsreg8 wd:9h0po l7d.gi 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 gravity on a spacecraft 12,800 km (2 Eartfxjgr :e35x1(6 uahnv 8xskh)h radii) above the Earth’s surface if its mass is 1350 k 5fxh ghax (36 er8:sxu)n1vjkg.   

  At the surface of a certain planet, the gravitat duoasp0*;l el) et+p5ional acceleration g has a magnitude )l *s0oudelat;p p+5eof 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 t (9wxr6r d7foeo gravity on the Moon. The Moon's radius is 1.7w e7fxr9r6 (od4 $\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 Ea wt0axkk *dg4.3xl xa/rth, but has the same mass. What is the accel xx .wt4g3/ kl0xdka*aeration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but naei oq: eod4az r4gb-/c(2+xthe same radius. What i a e4(o/rcea4x2nd-g zoq+:bi s g near its surface?   

  Two objects attract each other (fjkvv-* ,bws i;xg w0gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3200 sc:b+) cr8,a+exoa py maco:ce ar),8sbpy++x    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Ebgriig+y5 k0s *5tfl 9arth where thegravitational acceleration due to the Earth t+l5* gb f5k0syg9iiris $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed i ufgtzr xg-0s,. 6wjn0nto a sphere about 10 km in radius. Estimate ug t-z 0.fgswj6,x0 rnthe surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averpqh4vvcc80,)zg pu,te.a;atage star like our Sun but is now ie8 4g,pahc)., ctt pazqvv;u0n 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 star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space sh43u z 2nv.(zpzdeu x fv88jh2tuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calxzvp23v2j4uzfu8n(et z 8.hdculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squarz8h:,fk kzc /*vmj g(/j1vzoue of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on onhvk vk zjgzcum,8o / 1/z:j*(fe 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 same side of tjtxf8 v;jd,nws-skadza48rl / y+v - ,he Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The m8 ra- kl v4s,dj /x-ajd;fnw+v, yzts8asses 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 accelerationx dtik2d4v a*j aljpp 4uw)qx ;kb866* of gravity at the surface of Mars is 0.38 of what it is on Earth, and that 4lbq w6*j 2ki4)t *dx;6dpaj8pxva u kMars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valuerjwmdcr nu2 . * ut;jo,ex5q1. for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example xert ; 2rm wu*q ncj.uod15j.,5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable mwr,50 v4 :dj km-yqkrx7hfopl;h:, m circular orbit about the Earth at a height o45 hh,;mo,k-vm7fp:q kmj: 0wxrl ry df 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abzu3 ux +psv750 z1enmaove the Earth. How fast must theevu31a7um0+ 5pz zsxn shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to ec5j, *+ yzcr42mdm e*y im+h -rqjx)waxperience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–3*5jza )-dr*+chy +mjimw2y4 r xqcm e,2.)   

  Determine the time it takes for a satellite d r 6piree)3 zhfc;i3*n+s 9ffto orbit the Earth in a circular “near-Earth” orbit. A “near-Eaf3+)s*9z 3ei6 ei np ffdrc;hrrth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satek6k c,fbv5 9vbllite have to be launched from the top of Mt. Everest to be placed in a circular o6v5kcbbk, f v9rbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit ue,o4;bhzr0b)hz zu7 the Moon at an altitude of about 100 km. How long did it take to go around tuh,o7zrez 4;hb z0u)b he Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the p9(mp3q0wp ebulanet. The inner radius of the rings is ( pqe 30pumbw9 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. 5–9ssb0g0+ond5rg8dj r ,g1upx 2). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at rg+sbro0pdggu 01 nx5sd 8j,2the bottom?
(a)    (b)   

  What is the apparent weight of i huk isim3t sfrpp4zvru *cg,02ln;3h46j*2a 75-kg astronaut 4200 km from the center of the Eart26 i2phz;p0ujcv*3 3 4 i,fiks*tnhur slg4 rmh's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two starv/;ln2k1t i*mzb .arls of equal mass. They are observed to be separated b;irk1atmvl * .n 2bz/ly 360 million 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 for the u,hfg, 1o xf) w6mf)fbweight of a 55-kg woman in an elevator that, ))wff,fmbgx 61 ofhu 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 suspec0bnb1p uh4j 0. /shgfnded 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 (magnit1hbhu c4sf 0p/gbj0n .ude and direction)? a =   

Show that if a satellite orbits vecn(u5o 3wf8xli7 27ecawp gp(h k9sz1f 6( vnlry near the surface of a planet with period T , the density (mass/vo c(cgnoz ilf6w a83 77p5hxsv (we12f 9nkplu(lume) 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 dewq-2 nm+br6mz/t .ldstermine the period of an artificial satellite orbiting very near the Earth’szd rtnl2b w6+m-qm/s. surface.    s

  The asteroid Icarus, though o4 omo5voqy;45e ok 6sfnly a few hundred meters across, orbits the Sun like the planets. Its period is o5 qom64ofv y;ek s54o410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancefo) 48 k3otcgw of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits t.de9;n 1cnxl*o *( . mqbmztv:9obgnhhe Sun 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? 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 eqz. 9*: n cmn1bnb .lvt o;xm*dgoh(9distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of th;uy5z /pa erh;e 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 9 cwjv,, ;fdl8vdqb6d distance for the four largest moons of Jupiter (those discovered by Galileo in 1609dvj9; bl qdfc,v,w6 d8).
(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 dis v2jzyex+:hyuy* (r)jtance of the Moon. x*)2jyzrvjeu :h +(yy   $\times 10^{24}$

  Determine the mean distance frjkxcj w1;h 9 oavh961l06e sbgom Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distancsoex hvgja9;b 9l chk60j w116e of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupitk)gj 6*ktvpqd2.f8q;5i2 x9mh0wjkdy cln4 jer consists of many fragments (which some space scientists think came fromkikwjm;*.d ) 4qpkygdnq6j 5j h2 c08lx 9ft2v 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 descrir0:azx.;pft4 sx kk z;bes an artificial "planet" in the form of a band completely encircling a sun (Fig. 0;4zrzs : xk ;xaftkp.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 ,j+7 9 yoavfqwcc;+6wpvui-/t5fwlmvm )0 gzan 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 spe7wg tcv+/uz -yvm9;jf0)a,wiwlfcv+o mq56 p ed 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 whj)4vhdvefiam ;/-/kx at it is on ;-hk af 4vvedmi/x)j /the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass gra cp8oe.j k* 7z 6+pvuw/ 4qoyc1utsxg6b hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses 4.gyjw ctsk76u16qzx*opup+ce vo /8 are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparen3 ,6wou1 t6 odgclh1vgt acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. Wha g6ol o6c1htvwg31d ,ut fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directlnt)y)nlw4 (ffy from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forc4) ln)tn wyff(es?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a batl(; q lm3 s elqs(xs3(:tlxex9hroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and x9e l :((sxlqxtl m;lse3 (s3qin which direction?     ----待选择----upwartddown 

  A projected space station consists of a circultgy ho(xf00*rg; 4spwu4 dl5g ar tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tubesl 5owgfg; rtg(* y0x4u4p0hd 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 aixr*)b4qj q8ag w+oc8 orcraft 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 i(um66o*z 9 oba)xm)iixfen w9ts radius r, the acceleration due to gravity aewx99oam6o)xb u )i6z mi(*nf t its surface and the gravitational constant G.

A plumb bob (a mass m hangucni ao2xz99 n4q9u( aing on a string) is deflected from the vertical by an angle a9iuz2 nx c( u9n4aq9o $\theta$ 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 gau,ylow-f8z p t22w h*02fgy a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what r2 ,wfatg zhyu2p-o w0*lg2f8 yange 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 b* a44ih8n4mvb rmt/y bgf, n25ghsm+the equator vsh+ /4t,bm 254rmy4 i*gabnnfm 8gb hwere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of -7tphu -b sv7 ;7sgngmh3 k.zc8.0 $\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 m6*mycsw )p;mn . A lamp suspended from the ceiling swings out to an angle of * wym6mpns) ;c17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive a x d jc;;gb34kdocw ym thdpq4fg529s:ec*i.; s the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =d2 dw cc 4cx;g.o;jsd53 :ptqy4mig bf;ek*h9 1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extremel8 ) ry.+b yjw;zlru+mpy 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 wlrp +m.j8; uz b+y)rymeasuring 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*g1k/xs layn2 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 largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losnl2/ x1sg* kyaing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites yq9-gnh-3ev jc ltb4j46t -w5e5jhj5kd hra, 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 ba h5q5kj j654rdh4h-ctye - je-,wgl39vjtnare distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Ren*v -4t*xu8pq;/xvl8l ffenr f dezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros x;l/ve8*xvq tl fupr4n*f-8fis 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 satellite iy,i2x 5l*nrg4k6fvvjcr 1l4s n need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km b jg15x si46v, rkcvr2nfyl*4lehind 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 pk.*e3;ra 4le)g 7i / lqiphbfyeriod of 3000 years. (a) What is its mean distance from the Sun?3 ibh) el/4.7k;lgqe *rfi ayp   
(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 vv 0(bvbjgo ps ,:fl3-need to be if you could actually "feel" yourself grapjl:v, v gso-(30fvb bvitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cenl c*jg;aiesf,b 2mnpr6 )y*,jter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the ceng* y*j,p csfrlb maejni 62;,)ter $ \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 cornerqxyulp3 +n;b 8/u9m rts of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-yum b9px83 ;/lnu+q trkg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kq;1ck gc:z8+hf* bbdng orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experi88cgj b1x qdqxe/bq/ddo62z iu 7c )f) ihjm9-enced by the tip of the 1.5-cm-long sweep second hand on yoe/d bdmcx -oz8x96i/71)hqcdbj q2g8j)fi uq ur wrist watch?    $\times 10^{-4}$

  While fishing, you get bore6ah+rkdic+dozog t8g8 n q/klafmc5z* 5a5( -d and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes wi(zc k*g 6 ktl5dg -+r 58z/m5qaon if+dacoha8th the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of r 3p:w.ws s8 pgv4y+smsadius R in a new highway is designed so that a car traveling at spw8g.ss: 4sy wms+p3vpeed $ 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 negotiatitfli7*u6l;k z vc( )kgng curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling 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 pku i *fkvlz(lt;c7) g6assenger 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.$\approx$    $\times 10^2$