Sometimes people say that water is removed from clothes in a rap(bj0ui -l0p8j)vg spin dryer by centrif pul(-ji)0p0 j grvab8ugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the s3msoojji omzr/nyq)c, 265 8,ez yf :jame when the car travels around a sharp curve at a constant 60 km/h as wh ,of eiy 5)myro o/zmc,2jn:js6qj8z3en it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at co- ,ksin3/we teh7ez6i/x j7wknstant speed 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 hills, (c) on a level stretch near the bottom3zt e6 77iew/k -hjxk neiw,/s of a hill?

Describe all the forces acting on afktd r8b8lz8* 4qcnusbii7n*9y0t q 5 child riding a horse on a merry-go-round. Whichfbt ql9ykuz 0*87dbt c*qnn858irs i4 of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the waq0jlotzw j uo+u0( t0- h geo*h;6+ctgter spilling out, even at thjocu* +h0 u0-oe ;jwqt+gtgo(l6h 0tze top of the circle when the bucket is upside down. Explain.

How many “accelerators”f 6tdnu t.;c6y*/k fe7 pyoph9 do 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 are97d ;e pt6.kpfyhc 6 t*nyu/fo they? What accelerations do they produce?

A child on a sled comes flying oy ad c1o2,rbd-ver 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 hill. Explain this decrease using Newton’s ,ora-12db cydsecond law.

Why do bicycle riders leaol 8q0q ymx5-doea 2+nn inward when rounding a curve at high speed?

Why do airplanes bank when th+ u3jdtrd12jrfn3-. xwy,dwqey turn? How would you compute the banking angle given its speed and radiusdw+ 3qxw3d r2.,rn j1du-tyjf of the turn?

A girl is whirling a ball on a string around her head in a horizontal plan uujr+l2vd +-te. She wants to let go at precisely the right time v d+urj2+-utl so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, ho5b6(fk*i znv bqw(5ih w large a force? Consv5wih5k((zn6*f iq bbider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, rrf2+bdh1yt5 n8pez9kbihcy 5u* :* yin what ways would the Moon’s orbit be difb55t+21nd 8r c9*:hzbf * ky yepuihyrferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Mn2 zb rbn2 oh*cw 6h(pr;)szd*oon on the Earth? W 2hz)sr c b* 2obw;(hzpnn6*drhich accelerates more?

The Sun's gravitational put 2zf3:abb7xyr2n21 ibdwl+ pll on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Conw:bdft birx227+ yzl1b3a 2np sider 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 poles? What two effects areul. o7sla2 o;f0uvwzig* 8. pg at work? Do thego o vg; upl *08.uzlfi2aw.s7y oppose each other?

The gravitational force on the Moon due to the Earth is only about h x2ou 59q.ruujl p.*aqalf the force on thqx2ju9plouqr5*u.. ae Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or8*id9 ;x +o75,thw79vkoq zt5kwqmt l qhlf7 b smaller thav 958qtqt*mqbof,whh 7xli; l7ktkoz 5+wd97n the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (f3 ztj q-0xrg/b) toward the west? Consider the Earth’s ro3 zft grxqj/-0tation direction.

When will your apparent weffokl bm.910w hw q u+1jj5l7gight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight 7wj f jhfgb1mwq+.o1kl5u90l be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in out;f (oe4v zl4 erv:+azuer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravi;zu aezvf4l r4voe+:( ty. 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 weightlessnes8.h9: g *8bi *emha *pqrklvijs” betweenhv l9hmjg.:a8*k8iq ipr*eb* steps.

The Earth moves faster in its orbit around the Sun in Januo:g+tmb53 1mo* hpagqary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a ghab5o tm*g:m1qp3+o 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 discov-8/smv *i84crx*o6x parj ubaered to have a moon. Explain ar8*xu-mj8pa b *v4c xri/s6ohow this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon:nbf k ht,- 6j)ae1s q1qtkk:p's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the bnthp) esk:,:ak1-q1 6 fkqt jother.]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 txc .-zk;k3qfl e**ahfj21-qp9xti h1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 afdkr +z7q,u4ohkoqq ajh/ m a1+t3,e ,cceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. Woujta,/+1zhk3h qqmad,q+ 4oe f7k ,rhat exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted ffmh,k ;xsc, ns.q,7b7bkm6pon a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) ofmsn,.kxqbhb c6fk mf s;,p77, radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from 09l 1:bkkuh ndthe Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Exprhnb ukd:9l 10kess your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the- xbo:as .q*fo edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’sofo- .x*baq:s diameter is 32 cm?   

  A ball on the end of a string is revolved at i(o1s3a+k 4eq9j7 ybw graoh4 a uniform rate in a vertical circle of radius 72. q+wb3ga97o4(ei4a hs ko1 rjy0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round mpj, yknp* :+pa turn of radius 77 m m p:k*pn,y p+jon 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?   

  How large must the coefficient of static friction be between the tires a)4,djys3se wn-po u o3nd the road if a car is to round a level cujpoo,3)ss 43e-ywnu d rve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is d4 ; ssd b+x rdqaxwn8f(jc9-ifj-*l, qesigned 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 hernxr9xjdc(j;i fb-*- 8aw,lsq +qds4f 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 spvsh v 3if/-ow n5y.xr0eed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a ryvf 05.irv-n /o swxh3ate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be tr5ri h/x 7 bga:i:z4hwj 3wyv,gw/ e ko/kn9;agaveling when upside down at the trhbe:kg;i/,3 w/w7ogk5ajn 4:i ha zyg/xw 9vop 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) cr-5bfc0 zlg2cz osses the rounded top o lcc2g5z0zb- ff a hill (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 wobyt l 2ko 9z)oj;lyd80uld a 15-m-diameter Ferris wheel need to make for the passengers to feel “wei9oo2tj l;8y)dkl 0ybzghtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1 z;c78,0 hk2cvj u2nygf 2mxaf.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 ,u2zfm2f7hykv0 a8xccn;2j gN.
(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 ii4cvn 28lu)me f a particle 9.00 cm from the axis of rotation is to experience an av l8)4 me2nicucceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wa . xmj6 8fzm2-/h*xonrb j(bkxlled "room." (See Fig. xjj86kro.bfhz */ x2n( -mbx m5-35.)
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 rotat2q o+k ouw3t:gwa8e:pqq;z2j ed in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m kq23qo2jz: +geow:8up;qw at ) 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 ignoring 9 t:pqckuth;g r83,mf the weight of the ball which revolves on a string 0.600 m long. In p3gpck8;r9ftu h, mq:tarticular, 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 banked for a car traveling -xu 22zek /s+8)hwq)mp qt dwhff*i.i 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 s7k-6.h tijqr$ 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 divino1:a-gwp m h(wg 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 centripetals. pllc* y8w+t components of the net force exerted on the car (by the ground) in Exa.cs y8llt*wp+mple 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accele65 9stsd 7bt qb /uvnz; -d6i:t1tgqxprates uniformly from the pit area, going from rest to 320km/h in a semicircular /tvst 6bsdbg;iun6zp9q1 x 5t:- dt7qarc 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 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 particulas vkmh+j8+) wrr instant, it8v m ks)++whjrs 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 Empi.,7l(sp:zi cfwh+arth radii) above the Earth’s surface if its mass pzp c,mwi +f l:h.7i(sis 1350 kg.   

  At the surface of a cv:1 eocrx0;vxx 4x/xm19ye rcertain planet, the gravitational acceleration g has a magnitude of 12 ox x;1:cxxxvr41 e y9/cvmre0m/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 Moonqiwcaia117zegh+4 - x. The Moon's radius is 1.7awi1ecga q z +x7i4h-14 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5t2;ku 3z6q;lxl3 g qzd times that of Earth, but has the same mass. What is the acuzkqtq3zx3 ;g6 2d; llceleration due to gravity near its surface?   

  A hypothetical planetsea)1(s(/ 4bhnh5v,i3fmp ki) mquym has a mass 1.66 times that of Earth, but the same radius. What is g near its s m 5( q vs)(bhuf/,shmy3pa nie)k14imurface?   

  Two objects attract each other gravitationally with a force of 2.:kr* o1zebd8 v5$ \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 accwar jic,yl5lpx/upd 7).vel;+.pq: ueleration of gravity, at (a) 3200 m dpl.q;,cx+/iu wa:leyu 5rv7p .)lj p   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’sy/j 7z r9zbr-g1sof2qsa/6 rm+ qu3qt center to a point outside the Earth where thegravitational acceleration due to the Earth isqqt rybor/2z- 9/3qjgs 16z r7+safmu $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the maiw:d9m8v9w -crn fs 5ass of our Sun packed into a sphere abmn9ia8cwd- s 9:v5w rfout 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star liqlp1e1 m:ak w/ vdqd33m bn;au819hwike our Sun but is now in the last stage of its evolution, is thedp bme1h :k u1w1q83qd/ ;walnami9 v3 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 astroho ep /01 (5nqt;denlhrs,1d knauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince k5s tnhrpe/0dndho 11 ,e;( qlthem 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 located at the cornb5b) 0x eq5iqpv5 dk,jers of a square of side 0.60 m. Calculate the magnitude and direction)kqei 0bjpbqd 55 x5,v of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line p9n w *4ol57u;ln-dkb ki:zltup on the same side of the Sun. Calculate the total force on the Earth due to Venlk : l4nzn;l5d9w oubp *-t7ikus, 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 lmigwzem)pu )8t2h6twq8 o )gd3 6-m yMars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km,8 qemm)y owm)p2g h)6 dtt83i6l-wzug determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the kn: /rixhgm s0z3dnu9z.own value for the period of the Earth shu/zg: 0 rn39izdm x.and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit aboj)wc.n4x/f gput the Earth at a height of 3600 kjc)/ p g.x4nfwm.    $\times 10^3$

  The space shuttle releases h6t8py vjk-/ ia satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Ear-pyh8v6t kj/ith) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to expe:/qqyp.mgjj 3ycx(2srience simulatedyj /3(cmqp.sjxy2q: g gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to o)iapz4 -dzxzr * 55.cwfl*zerrbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Eaid*rwf5 lp* -xza .)zzrz4ce5 rth 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 vw015i)wdzjpx(1m o l celocity would a satellite have to be launched from the top of Mt. Ev1zpci)0djl(xo 1ww 5merest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mi+hq8widietnse k. wmfhj-x ,qs,(9).ssion, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moxtq,s-qkfwemwji .dh,) +i8 h. n s9(eon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the pla9 q9jo8eozu hd,w*s8fnet. The inner radius ojso9f8e w 98ouhd*,q zf 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. xxmyhyi6, 0p +5–9). What is the ratio of a pe6hp0xyixy + m,rson’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km8uyy3z6vye 3 q from the center of the Earth's Moon in a spac ye38vy 3zu6qye 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 ofxy.g5qm6xr e)u 6oo:y equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to or6:.ery xox)6 ym o5ugqbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an eg-ytf1r r v*-8gtvu 4kt,c+h glevator that mo uc-4 gy+th 8*vrfvg tgk,1rt-ves
(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 ceilingvixza4 ( r;ch3f9h:lu of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerurfa4vhiz:h9xc; 3 l( ates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with perjt(hc;-ui e /kv(c u;viod T , the densitv e-t(/; j(h ucvucki;y (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 (27e3 rk3wttkxvoo-r ,9,y 6nfdu/bx( *j.4 d) to determine the period of an artificial satellite orbwtu3r*,kv3-(y/6k,edo9jtxx nf bo r iting very near the Earth’s surface.    s

  The asteroid Icarus, thoug3f,twcp 69pu nh only a few hundred meters across, orbits the Sun likwpf, 3t9ncu p6e the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5iyt7po ( 5;yx;tm.ikww )z :up $\times 10^{9} \mathrm{~km}$ 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 years. It comes very close (x mf0*dqcp5 * a5gr23 c faq6g*vgfzzto the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greates5zdc0cqa grf 2fpvxg(g*m3*aqz56 *f t distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gapgkwai cr 68o hl2.y,prm 6:i*w6i/ ullaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 largeb49d +lf/n wgqcl4 -gest moons of Jupiter (those discovered by Galileoew4g bgql n9d4/fc+ -l 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 distancu.z 1ls 7xr8z5 ulyr5po..msk e of the Moon. u5 lp7yu1l ozk.mzrs8.sr.x5   $\times 10^{24}$

  Determine the mean distance from Jupiter fop9, /z tjlk*wzyui4au .x2 (8t:qqfxjr each of Jupiter’s moons, using Kepler’sljqp/ u. qt9t:2 zw8za*xifky4,u( xj third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (whcz42fenn )c+ef2: xvnich some space scientists think came from a planet that once orbited the Sun be+c4xfvnez2c:nn 2)f ut 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 b+g ,rvh e yqff-h: j7/c16ooppand completel oy6,rohhgvj+1q-7f /e:pp fcy encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in anr m1d+k-lr3vw 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 tolerd1 lwrk v-m+r3ate 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 ie z/ kdbv v6 zw*rlf-(/a3uujli5 )/nbe half what it is on )a/ ni 6 z/juzdf kvb-w3ur/illv(5e* the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin iny p:xn:4/kn ww+ py-mz4+ gojo a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual m pw 4w xm4kj:o+-yzon:pgy+n /asses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelerat)7ay -k3jl 9xl ,ulkgmion of gravity at the equator is slightly less than it would be if the Earth didn’t rotate.kum9,j-37klal lgy x ) Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling dit lnj+ysm w-ea4c67)nrectly from the Earth to the Moon experience ze4mjy+e6nsc- ltnaw )7ro net force because the Earth 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 inj)g5 luliw+)l an elevator, it says your mass is 82 kg. What is the acceleration of t)5i lluwl gj+)he elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consishee0s0ac r)y3 *jkq8w;fbzu .kj *y 5rts 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. Whk;yj0k.a 5ru3fb* jyq0e)h8 z*we rscat 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 aircraft in a vertical loop gfxzfzju su4/)n (bs 46uv8r1v gzv+/ (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 i0,8vl /xun0h :p 2 jhz9jejgsof a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravi/v8j,eznhp gux sh9 0:2 lj0jitational constant G.

A plumb bob (a mass m hanging on a stringbu)dj+l ob (6ukk*,.4 ay6 fwv ezvw4r) is deflected from the vertical by an .akd6ewv 4b o4rlk6 (,w+yjv zb u)f*uangle $\theta$ 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 speed of zwfuq o4fv,r):wda1j* b(d 5r If the coefficient of static friction is 0.30 (wet pavement), at what range ofj( o w:5rawdqb1zfrud)4f* v, speeds can a car safely handle the curve?

  How long would a day be if the Earth we ak1y:qibo(m8c5 clhhvk ,asr+(4 b;s re rotating so fast that objects at the equator were apylo;b+s:v5ch ( q41a(8si rmk a ,cbkhparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apar pv8po8: zrc*z.cdkcc.cba4hd 6/a; dt 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 rx-q kxbw-lgd;.(g7y c adius 235 m. A lamp suspended from the ceiling swings ox(l.-d cbgx-;w q7gykut to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been claime 1q yeb l:t5na6qpx hq5b315nzd 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 p3 btl qz5n5 e5q 6xp1anqy1b:hlanet. 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 b(ublp3;)3t/avkkej ;h31 a+xwcydkdeduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by 3;(xet1 dpkua;bhkl+ )acybj 3w3 v/k 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 d8e8 s7rx(1sqvy vldm *6uy d,the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the 1(7*q 6m 8yyld8duevss x d,rvroad at A?

  The Navstar Global Positioning System (GPS) u,squbg5ejp s.m-um0 za-(2,kxx e4r utilizes a group of 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 navigational “fix40 (-psm ,5e,m q-egksxuzuuaj2b.xr es.” 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 k13h rmwtew:o. m, is meant to orbit the asteroid Eros at a height of about 1. 3rmhwew1:ot5 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 duww389u1mh i s5pw 9uthe space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abov3 iwsuw8u mwu199 hd5pe 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) Whar)q t6)g9ru7d9l 0ba:j w xmmxou3/uu t is its mean distance from )bx l3 gjur6m 9ud/:maow97 tu)0urxqthe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you rzsy -fpo-vv5 e)+hp ,could actually "feel" yourself gravitationally attracted to someone ne5,yrvf- ) vh+-ozsep par you. Make reasonable 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 ay ymm68tmg p**2ryvw 4 distance of about 30,000 light-yearsvmm *8t pgymw4yr*6y 2 from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m j ;lbke1 6) tm/ idbnwe*z)ll6on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottoe6jlmk) /n *)b lez tb;id1w6lm side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg ; k1yhl3m4/g: wpfmrg 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 experiencv rr 0:9mxrzw2ed by the tip of the 1.5-cm-long sweep second hand on your wrist wrz rmrx2 v:w09atch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weighz j q613/x6y-6xlp p ybyuihb/t 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 with the vertical? [Hint: Siyyzyx3 6hj/x q ub 6lp/6-pb1ee Fig. 5–10.]    $^{\circ}$

A circular curve of radiusrmv9o;ogf )8() prg. ,mvlz my R in a new highway is designed so that a car traveling at s mml)p v(m,zfg 9y)gor 8;orv.peed $ 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, utilize()xx eg m/l67n,fp8crn. t yxzs tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passeecyml7g,t z rn(pn )fx/6 .x8xngers, 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.$\approx$    $\times 10^2$