Sometimes people say that water is removed from clothes in a spin dryer5*o ez y s+n-0+zoeard by centrifugal for*-o e+ +zny0d5ozs arece throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the /dx-y:b gfe;. crnv )isame when the car travels around a sharp curve at a constant 60 km/h as when it c;fy/bxd: i )vr.gen -travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant sper* .lzkxkco) 9ed 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 )*9 kr z.coxlkstretch near the bottom of a hill?

Describe all the forces acting on a child riding a horsez*j:r0 a k wr6hykvq*7 on a merry-go-round. Which of these forces provides the centripetal acc wazk6 jhky*qvr 7r*0:eleration of the child?

A bucket of water can be whirled in a v fn+abxe.0di :d /8epjertical circle without the water spilling out, even at the top of the circle whe /e:8deapjx i fb+0n.dn the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Ther.e+boy*0yn 4yoo oi3sxn -sy9qrw,:qe are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do the*yowo: q3y9y x-ie+,sb.o 4 nr syno0qy produce?

A child on a sled comes flying over the crest of a small hill, as shown in il bno y))4zhtj36ta5b-k:rbhvsh45.4a nil 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 abjia4)isl:h.nb4v 3 5th-5 z l4tby)hon6k ars he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding9.zo -wkf* elf a curve at high speed?

Why do airplanes bank when they turn? How would you compute the biq);+6 j, leuldmvi0-r3 duom anking angle given its speed and radius of )iulre vli;3- mm+ ojdqu60d, the turn?

A girl is whirling a ball on a string around heyj mp):d)xby50gto 9cr head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of tpd yx )b)09o ymc:jgt5he string?

Does an apple exert a gravitational force on the Earth? If so, how labfsd*6/2 rfx0ks8n ic2j alu/rge a force? Considss * /u0rbkfj8xia2/2l nfd6cer an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would tp7s :dcie 8b8ehe Moon’s orbit be differentb d e8s:ie7c8p?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the dlglle o-cv3 5:k1so)Earth? Which ll-) 1l deoo5k3vcsg: accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon'pik7v/8e:s u1 u;quxps. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of th u7puskeq /p ;i1xv8:ue Earth to the other.]

Will an object weigh more at sy/ruxjugh5;+) x*pnthe equator or at the poles? What two effects are at wog ns p+*uxyr5u hx/j);rk? Do they oppose each other?

The gravitational force on the Moon due to the Eaoa3/k auavp3 i32am .o, j-dlgrth is only about half the force on the Moon due to the Sun. Why isn’t t3a o/gv u3di3aa- p.2o,aj mklhe Moon pulled away from the Earth?

Is the centripetal acceleration of Mars v:t*q; o tla+vxe)kr0in its orbit around the Sun larger or smaller than the cql)t 0r ta:vve*x;k+oentripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east orsarp/ e/c7wgu rjxp++ji6;s6 (b) toward t6 pxjr6ecs 7psiu /g+ra/;+jwhe west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale i45d 2crusqy f;n 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 ca cyq2 rd5fu4;sse 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 outer space could be adversely affected by mxm2(lewdx rv 9p *0;fweightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objectsr9mlw* 0 fpde(m;v xx2 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 u6n,,pvo6gp8 kb(p u2 6nd5a l vtv(xw“apparent weightlessness” between steps.kpa6,ug v685 tlxnv pwo2 6 (pv(d,ubn

The Earth moves fasto 7zr*kg2b ya6er in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not mg7ao2k y*z6 bruch 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 have a moonjm2 a(.mc:el1ak:u f w. Explain how this discovery enabled an e(k :ejm am2cu.af:lw 1stimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is m5hrauwg )5s -vuch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth t -5w r5vh)asugo the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19 eghuif)4 db6180 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 9kx 4. ;.(epgei khjbjthe 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( eg9kbj 4.iph e.;xjk 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 discusst08stjpl-wshby-//6 * 7t rr d:arye as it rotates uniformly in a horizontal circle (at arm’s length) of radiuht0jl t s7ysy//s8w -p *rd b6ar:tr-es 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth+obh+22mxt3pr; ,w qbeu 4vv v's surface, and circles the Earth about once every 90 minutes. Find the centripetal accelerathe,bbv;+t3q w vru+ pmv2 xo42ion of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitudap:2d47m daq-fo7g1 f:jlm af e of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is2dojdqf17:mm-a gl a ap f:4f7 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a ver 0y r xlbp9.sxd87duw/ ;bhqmk 3nj(g9tical circle of radius 72.0 cm , as shown in Fig. 5-33. Iug9rq.yj9psdbk h0 d/xl7(n; 8m 3bwxf 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 rkv w5rtin1s 9.ound a turn of radius 77 m on a flat road if the coefficient of static fr isvw1n kr9.t5iction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coes *-lc2 0tf4rxs fi;il2bz u/rfficient of static friction be between the tires and the road if a car is to round a level curvezxs2if0t cfui ;r*l2/l -r sb4 of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fividnw ug) fyvw8gkl(3-b h 49m9c5.hoghter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 gk .v(59d4mc 8-bnyui3o9)w wlh hgfvm . If the force felt by the trainee on her back 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 of a r 9iodp9+z3qxyotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turnt3 d9xpyiz+q9 oable 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 must a roller coaster be traveling when+zsp-: :gx;tn 2pdr bi upside down at the top of a cr sn2g;-:tx:bp+i z pdircle
(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 the2 tu o0wm9emw, driver) crosses the rounded top of a hill (mmt2o ,9 wu0weradius =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 otl+32u2ru dx gl/di6would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at o di2gurdl lu+3/ 6t2xthe topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a ve.3;iq a fiim3ortical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supportingfqoi. aim; i33 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 par5ulcdt6qe- ;c yq2fk2ticle 9.00 cm from the axis of rotation is to experience an acceleration of 115e2tcq ;uq 52c-l6fk dy,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" atm.7pnmff0lmb+ kz :z, a carnival, people are rotated in a cylindrically walled "room." zp:b7 n mkfz,lf0+.mm (See 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 ) isxzj6pgu9h 0p),ky 7zs rotated 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 ) throughp609szx pgjyh7)z,u k 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 the weight ofhuyjjui4vy+37;b s)f the ball which revolves on a str 73v4i )sj;byy ufuhj+ing 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked foa)x ii/fx +2jqaz aj*5n j1 sc*xpq84dr 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 massesfcyzte0nj d v 0m+g3):zt770a(yn ogj $ 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 *g4sbk*yv7evsc )j kjb/ bumt()q+ex:-5rp fmaneuver 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 ou1o q-clqn:. af the net force exerted on the car (by the ground) in Example 1cuq.- :ano ql5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit are7mz.a1eo 9o t7jvo+ama, 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 7m 7vote 1o+.maa9 jozthe 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 ofjkc 7zy5oy(il* vchz)/.w p,e f:e,q d radius 2.90 m . At a particular instc,e,wpel:ziyvh.z/j7 ko)5( df*y qc ant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravitqa*c( dcl) ozmm jhi 33(s3(eyy on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if i a* jlms(h3d(c z (3mqoeiy3)cts mass is 1350 kg.   

  At the surface of a certain planet, ( wo ( )iqv *w6u(yavge+k l/phhwdy:6the gravitational acceleration g has a magnitude ohupwe)l w k+vdgy *w(a(6v:q 6 o(hiy/f 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Mdn4cju 8mdt (l2m k2o+oon. The Moon's radius is 1.74 (2utc modd+mkl8n4j2$\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,g8m.lti sh d1 that of Earth, but has the same mass. What is the adgsmt 8il,h1. cceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.8;iag tuh(u: c66 times that of Earth, but the same radius. What is g near its surface? ;c(uait :hu8g  

  Two objects attract each g3 jtm0: rzc:zother gravitationally 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, nll4a7z*4m+fdt9 ibe ly; w2mat (a) 3200 mmllb7z;+de*92y 4nm4 wla f it    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where tz3xh 3 z,ixh4ohd 5yf:hegravitational accelerdyhoz 43 xx:zh,35h fiation 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 mass of our Sun packed i;bs3 gle oa*4onto a sphere about 10 km in radius. Estimate the surfa3g osae *lo4;bce gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average sta;n8x3mr a 9(.p+ axs4jhygq wfr like our Sun but is now in the last stage of its evolution, h y+fsmjx arp (. 3nawg9qx84;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 w(e3 zkfi q9wf/31 o:x:au8z2 wq/ sgpzpkj; ashy astronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the accelera q:8f( // x3zoeu p13spiqwz;w :a9jgf2 zskaktion of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are locate,3 acdyl-iw,el:vl,g d at the 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 other three w,l,cd lila,v-:y3g e.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years *+*rnokas. v fmost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Frs*a *nk.fov +ig. 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 acceleratf0hkmo4y-yu qje 304wion of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ rj3e-oh m0w4qyk y uf40adius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for th q)m7,nv5zto tk-s 6xe+q wp z7kbeu((e period of the Earth and its distance from the m)uk7be 7o xe,6q-n p+vk5(wt tzq(zsSun. [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 circulank6wh/rad/i ie:m 8y 8r orbit about the Earth ate/i/86h dy8kan iwmr : a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the sq 55jpjib z:5h+ m ;-ycgul4v-4zxx mEarth. How fast must the shuttle be moving (rizbg4vy -zq ps4: mj+ hx5cjmx;5l5- uelative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupantsl;bd, ;jxe(w o 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 for one revolution. (x (dew;;,blo jSee Question 21, Fig 5–32.)   

  Determine the time it takes for a satell9zve 9 nb3h5np4 sa1unite to orbit the Earth in a circular “near-Earth” orbit. A “near-Eanbszp4uh 9nn9 5e31v arth” 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 wevsasdj(gcz(x, o 26 ,ould a satellite have to be launched from the top of Mt. Everest to be placed in a circxde6 (o2 gvjszcas,,(ular orbit around the Earth?   

  During an Apollo lunar landiy tvxmb9(b; l,ng mission, the command module continued to orbit the Moon at an altitude o(l byt9x;v ,mbf about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are co7jguh m pk5zs0t0 6ho;mposed of chunks of ice that orbit the planet. The innh 500sju6zt; hk7gomp er radius 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 diamjk. e 8h-qaomvj;d8n-0z jks*eter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bot8n0q j8v;.-d a j-*ehks kmzojtom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut )ckarsbv; 93bj dr, j hdc1)s-4200 km from the center of the Earth's Moon in a spcb39r);skh,ajddbs 1)v rcj- ace 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 coe dtx5i//a0d8m 8fx0z epwd.insists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 dmt08xw. x/5idae /i fze0 8pdEarth 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 weight o3wi(c8ox 5pyd g(d t-kf a 55-kg woman in an elevator that movo iw(t83p(y5dcxg k d-es
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an u ig/ 4 a7l7v 1c7(ehviibop6jelevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directi6lh/ujc1avi 7ibepo4 v(g 77ion)? a =   

Show that if a satellite orbits very near the surface of a planet with 71rdrg 4w lmg*period T , the density (mass/volume) of the m 147rg*rdglwplanet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine the period o)c97g5pu h hmiy4uh -lf an artifigly -9mh4ip)uh5u7h ccial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters wdlk)zr j8 ./ydf wn95across, orbits the Sun like the planets. Its period is 410 d. Whatlf. w5r8wykn / d)z9dj is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of oa /uo:4+nykg 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 i5az/x7 yat ,c*ed:glthe 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 nearz5ayc/ 7, :ig*xdal etest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cenb8 u*no)jb5axter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moons ow p7-d6:s qn(h(i xmhrf Jupiter (those discovered by Galileo in 160 np7w(-dqsh h(r m:xi69).
(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 know)2kg vpc6.b ayn period and distance of the Moon. c.)vgp a kb26y   $\times 10^{24}$

  Determine the mean dyc:5) ryrcjbh 2h 9b)sistance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and thjc:5hbbsh)y2 r) yc9re 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 o7fffwf mr3 d8tznmcu/1y81(x3u 3buaf many fragments (which some space scientists think came from a planet18rfm/3udu1 yx73nm8wfa u fftb cz3( that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in th7 ; g r32qqpthjox4+xfe form 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 cl+h32gq j txfr;4poq7 ximate 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 gorg5;ci)6i e( 2q7pzmm izkony*nenn 5xn )8t9jze by swinging 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 swing? His mass is 80 kg,n2 emqxinzo nn6kt8)e7z zj ycpin5 9mi);5(* and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half nc8ut/ hxz 7g)j mg9;jwhat it is on thehn 8gxjg9 t c;m)z7ju/ surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab haz 4m,:vfq9r vonds and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individualvvzm or49,q:f masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rota1c vkluf4xxm4d5 7md( tes once per day, the apparent 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. What fraction of g is this? (fxv d4x571d4culmmk   $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelin e)i2s5/)vz3lu y dna(vf:ek m:mzhj,g directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppvk32z f,a) ij ud:vly:sz5 hem)ne m/(osite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an elez/q 5st )vx2esvator, it says your mass is 82 kg. What is the acceleration of the eq)2 tzsxe5v/s levator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate aboua*bezd6j(nqeaao4 3vx yky0; /yt *b9t its center (like a tubular bicycle tire) (Fig.bbzn 3ojdya6x*yvy * a0e/4e;9( qatk 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 of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical c ega msj.dd1zv1 8b9*loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accelera tdlq 8wl9rjlx:sf122-6yc q0d/um qztion due to gravity at its surface and the gravitational constant 9: q/d -wxdlq6jf cqml2st 821yrulz0G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical byfgye)urz od.v+9 -. gv an angle+ dvgeo .ru9vf.)y-gz $\theta$ 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 ban9czg(e0x/ 8 avk9 yc7ww.heatflr- l 3ked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what raaekv htf.3g c9yawlz 78c90welxr ( /-nge of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating9fjm,8u) gb)k14os ad*q7e9nkv z abh so fast that objects at the equator were apparently weigsq d9uf7e*)4kn1v bgmobh)a,8zkj9 a htless?    $\times 10^3$s

  Two equal-mass stars maintain a co ew*6xad+n;esvg sfv ./e(l:jnstant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constantcgz.ok 2vij2 h lzm518 speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17 mlz 12.2ovgzcjh85i k.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 czyndw4r4-c 7 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 cyznr4 4w-7dcof 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 Hgcqe:c:ws 8bjv4 f5x1ubble Space Telescope deduced the presence of an extremely massive core in the distant x1e:fs8wb v4qcjgc5 :galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it t e,8 cj6rlho:praverses 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 losi6j8c,eolh p: rng contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satelliewy-6et f6jh (-wfd5stes orbiting tedsh(yw-6 f-6ft5w j ehe 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 “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.+w* . )rtqer bsxg8zr31 billion km, is meant to orbit the asteroid g38sb t.*r) wx+reqrzEros 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 thet// 3db0eug cdg bwj kpj.99:e space shuttle pursuing a satellite in need of repair. You are in ad: p9j/gtc0ejgdb 3/ub.9we k 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 kh3(:c)lcrf: f*j )gzpv x ,agis its mean distance from the Sun? h , :p(:*)xcvfk clr3gj)gf az  
(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 wh.cd n/*6zoc4otd 3b usvz,+sould need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonablen3z 4+ cv*cz6suo ,h/bosdt.d assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig.+ //cernqan z: 5-46) at a distance of q:nen //z+ acrabout 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each sidv h9c c,c3k,aoe. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at k,a,cv 93coc hthe midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500ks1pyn3 gp2)b kg 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 experienced byx x-k:n3kki)y-z h kp8ee/(bl the tip of the 1.5-cm-long sweep second hand on b- kxpz8 :lyi)he 3(xnkkek-/your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swi3-vgb ups 8 ,jj0t25nuud(ccsng 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 with the vertical? [Hint: See Fig. 5–10.] d -utcus0bngj,8spvju3 5c2(   $^{\circ}$

A circular curve of radius R inhp .mt-8:wg(f+ sre*f skj4bg a new highway is designed so that a car travelingw :tsb4 f+*- rmjkhs epf.g8(g at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the carjsdjq4d; ..ebs when negotiating 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 passenger of mass 75 kg if the track is not banked and the train dd.jd;4.esjb q oes 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.$\approx$    $\times 10^2$