Sometimes people say that s( vk0 a5je6rlf 7 yq*pw.f7clwater is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is 7 l.j eykcfar50v*swlp(7f6qwrong with this statement?

Will the acceleration of a car be the same .rh:r lm,m+xq;ds 9ki when the car travels around a sharp curve at a constant 60 km/h as when it travels around a g ,:xh9;d k sq+rmlr.mientle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where doe-gmv 7mv 8p,z5pe o2utrja72e s the car exert the greatest and least forces on the road: (a) ,mv emzp8 g7p7eoav5 2rut2j-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 horseiv 3 v:l/ve4ha;qst/x on a merry-go-round. Which of these forces provides the centripetal acceaqt/s vv:/h4xl ie3;vleration of the child?

A bucket of water can be whirled in a vertical circle without the water spillinmi;qbjos)4 p( g out, even at the top of the circle wheo;isp)mjb4q (n the bucket is upside down. Explain.

How many “accelerators” do you :ttbat-spy (,v59l 7 7m9mv ,kfzgozhhave in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What aremg: 7tbv5ha -o9 vtkt l 9(z,zmsf7yp, they? What accelerations do they produce?

A child on a sled comes flying over the cresz1xt zq5w zbek)*wv*,t 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,zek )w15 xzvbztw **q Newton’s second law.

Why do bicycle riders iam /pz n7d 8/n0nrs/xlean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you o/l, ,o;tt riemt*po9z,/dzdcompute the banking angle given its speed ,;o ot,me t9/ rilz*pdz ,dto/and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. Soj9j sc9ow.4whe wants to let go at precisely the right time so that the ball will hit a target on the othjc o9w j94.oswer side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If s0bumwm.zqe gn q01-v -o, how large a force? qz 1.mun e-0gbmq0v-wConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were douai .(5g qgv-lnble what it is, in what ways would the Moon’s orbit inq5-g.a vlg(be different?

Which pulls harder gravitationally, the Earth on thq2qo tqq(n57 le Moon, or the Moon on the Earth? Which acceleratesq tqlq7n(2 oq5 more?

The Sun's gravitational pull on the Earth is much larger than the Mlj y)r8dn.pf .xo -i;soon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider thyfox prs8.d)j.ln i-;e 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 twolgu/f kl)*dt(ic* u/v effects are at work? Do they oppose e(l f//tl *kvi)*udgcuach other?

The gravitational force on the Moon due+fa;7j qrtm .i)/ nxc/ xb)kww to the Earth is only about half the force on the M/rbxwa+i ;x/. )wcq n mtj)f7koon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit arm* q laxpczreht:v x0 (h:;*ll:6gn- round the Sun larger or smaller than the centripetal acceleration gr:*z;*qhcllp vlra6x t he0xn:(:-m of the Earth?

Would it require less speed to launch a satellite c o,)b72ccai-t), i7 gbe2wb gdctj/a(a) toward the east or (b) toward the west? Consider the Earth’s rotatigobc d,b2 i)7ct7a,2gacijc/ tew- )bon direction.

When will your apparent weight be the greatest, as measure vwzm-wy,6th; d 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 ;m6h ,w-wty vzbe 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 bf/ff4gt9w)f*v0 p7y7wsnb nde 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 gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any nw4fyt7ff)b *dsf0pv7n w/9g other aspects of gravity you can think of.

Explain how a runner experiences “free fall” o wuqy- 99ex d9l,;+mipbs4qe hr “apparent weightlessness” between steppbys49iu;9lhq+,ed9 ew- xqm s.

The Earth moves faster in its orbit around the Sun in January tln;l,cvi 0oc 5kd(ni).itz 7 rhan in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note5),li . n lc0v(nr;ictd7zoki: 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 untirwtm;q (hnbw+rit p-s (84s3p l it was discovered to have a moon. Explain how this discovery enabi q h3r4n8s(;srt(-wwb+tp pm led an estimate of Pluto’s mass.

  The Sun's gravitational pc6c nh,d/hvlkf(13 6pmf hw7sull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational 1k fc3psv7 fl66( dc, hwnmhh/pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{m}/\mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{kg}$)   

  A jet plane traveling 1980 ** c5/x:vbmoqwxg7 3gie5gz k$\mathrm{km}/\mathrm{h}(525\mathrm{m}/\mathrm{s})$ 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 a tuav(ks .y; lbi/0kb0-abw: rround the Sun, and the net force exerted on thbkuk s( avlri0-;b t.y:b0/a we Earth. What 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.]    $\times {10}^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg deo;o ,uma e +;gihi1.miscus as it rotates uniformly in a horehge, ;mi.ami+o 1uo; izontal 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 Earth's surface,uvg fgexmg.x -3 *+-yn and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express youuxgxn g .e+*3m-gyf-v r answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accz,pon rob9/h 4( 8xfabf-u ho-eleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions o(fx, -hz- nrba 9o8up/fob h4per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a stfk40h33 w ydcpring is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Figf p3hcyd 30wk4. 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 wit2cxo hcanb176 j:ein:h which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indepenj2bn 7: ahx1oci:c6ne dent of the mass of the car?   

  How large must the coefficient o a*4wo ywudu00lzf;7pf static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of uyo7 *pwf0u4;w zl0 ad95km/h ?   

  A device for training astronauts and jet fighter pilots is desiafce.,8ce;: :tzm me qgned to rotate a trainee in a horizontal circle of radius maq c,ze:em.c8 f;: et12.0 m . 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 (jfs :4 t9wylll04sfwa rotating turntable of variable speed. When the speed of the turntable is:9fwfjstwy 4l 0sl l(4 slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when uy aiccok0uu g o.gju+/0ke;// pside down at the top of a circl uo/0/iucc e;/.j ggyu+kao0 ke
(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 drivbdu xapcn15u- r07;ig er) crosses the rounded top of a hill (radius cpxg n5ur0du-b;7 ai1 =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 woulf1ut rubfuyk7j k x9-7g*th78d a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at t9 kkhgj7tub7f1rfu* tu-x8 7yhe topmost point?    rpm

  A bucket of mass 2.00 kg is whirled int26 moil qp8;c a vertical circle of radius 1.10 m. At the lowest point o;top il2 8mcq6f its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from thxafl9,w)jl: hfyqg- 1 cyc 0.re axis of rog)rlf w01qxhyjfc9 :lcy -a.,tation is to experience an acceleration of 115,000 $\mathrm{g}$'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindry/g hymm d;/ icq35t,va,)hky ically walled "rmdhy yk/)tiq h,5y 3 ,v;g/cmaoom." (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 ) is rotated in a circle on a fz c)(vtg5 pk f- fy+fbs5(br9mrictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 59grfyf(t) 5-m(b+zpvbsc5k f-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{mgR}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring theoc 2co/d5kfq(gef67 i weight of the ball which revolves on a string 0.600 m long. In p6 fkqgic(of o c/e725darticular, 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 tr1q/9i - tnrradaveling 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 masserm; 0u gvipj 7t6rfwqyta+ fq+63j27ms $m_1$ 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 c(;beo1,cblavertically 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 tangenti t3p8lua14xgw v25 leeal and centripetal components of the net force exerted on the car (by the ground) 2t4w ap 8evell gx315uin Example 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 accelerates uniformly8lf ;+ 6hbh: erdqgg(vyi*j+i from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the c*b(6qi+; he y8h+jl vggfrd:i urve 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 f63am;2dr9 o mu w9:pnsacg6ao) iyt:circle of radius 2.90 m . At a particular instant, its accelera) uc: sd3ta6pn; y 99w6fo2gaa:m imrotion 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(uw6lj1q -g hx 995sdhke:crnk-a-jx km (2 Earth radii) abovehr6 :cjwxu-k 9(glnjh x-5 d-sae9qk1 the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certac s; sjfak6wd lfk9)93in planet, the gravitational acceleration g has a magni)j96skl sfk ;cwfa9d3 tude of 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 Moon. The Moond 6.jr .bdodlt: q8jo7's radius is 1.74.boqrdj8d7d . jlt:6o $\times {10}^6\mathrm{m}$ and its mass is 7.35 $\times {10}^{22}\mathrm{kg}$ .   

  A hypothetical planet has a radius 1.5j1o v/ iu ng-i7/p0m1h1czlm o times that of Earth, but has the same mass. Wh/1nguml/m 7ohicj v-z 0po11iat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 tho1uh.m-g )iad p7hj-imes that of Earth, but the same radius. What is g near i1u o)-i.hdg ajhpm7h-ts surface?   

  Two objects attract each other gravitationallyvm4f1 5jynac f,*p x2p 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) 32d 7(8pg rvtv9s00 m vv87dt rg9(ps   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outk4 *sx0zkqrt4 n81jksside the Earth where thegravitational acceleration due qnxks 1k0 jt4 ks8*zr4to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times {10}^7$

  A certain neutron star has five times d gmg2;p3bi0*2b wxbjthe mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gra32gdxm b b*ijwpg;2b0vity on this monster.    $\times {10}^{1}2$

  A typical white-dwarf star, whicuwaev 7yl( (x0qv*a/ z5jags )h once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravitye0)(az u*/ (xawvjla gqsv 75y on this star?    $\times {10}^7$

  You are explaining why astronauts feel weightless while oymidn;f -c58ufqcd r 843 c+qrrbiting in the space shuttle. Your friends d8c; d5nufq cfmqr8c 4ir+y3-respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square oft8.b;jrtsm:t*3 d jz x side 0.60 m. Calculate the magnitude and direction of the totalmjx.;8rdsz: t3 tjt b* 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 lin1-dpipt8f wsf8)oq 10tp 9d p3xg0b socaw-h.e up on the same side of the Sun. Calculate the total1)0poxps 1h od0p. f cab8tqdwfi9- -sp8 w3tg force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815M_{\mathrm{E}},M_{\mathrm{J}}=318M_{\mathrm{E}},M_{\mathrm{S}}=95.1M_{\mathrm{E}}$ , 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 4d/1 zh2 mehtfMars is 0.38 of what it is on Eart hh2/ eztmfd14h, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times {10}^{23}$

  Determine the mass of the8lit y2jh cjkdh0s81d u9) v)j*x4uhh Sun using the known value for the period of the Earth and its distance frodujhdx h 9 ckj) lh)82u s4h08v*iy1tjm 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 mo 3sme6/)9jjt enhmb+nving in a stable circular orbit about the Earth j/n9em3 hnbts)+me j6 at a height of 3600 km.    $\times {10}^3$

  The space shuttle releases a satellite into a circular orbit 6502qs db0pw(z0 a km above the Earth. How fast must the shuttle be movis2bpw0 0(adzq ng (relative to Earth) when the release occurs?    $\times {10}^3$

  At what rate must a cylindrical spaceship rotate if occupants ar)phobo asju*+)ur9d7gg b2 .ne to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time ne7juog*) n+ubp9ag rhsd. 2ob )eded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit ba:46sntksj0 ldjz- y6 sl ;jd6 k; e0vjzeu+5the Earth in a circular “near-Earth” orbit. A “near-Earth k;eej: t0-ykdsv0ll+bszj6aj6z5;u6 4s njd” 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 velocime8xexv:/t0:1w osl q)0im v uty would a satellite have to be launched from the top of Mt. Everes s080qul/xt::mxeomi e)v1wvt to be placed in a circular orbit around the Earth?   

  During an Apollo lunar lang (e(9 fqt9r)yh-khording mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it takh(gehoqy9t(9)- r r fke to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbittpfus.z efo we(0x l7c -u0i84 the planet. The inner radius ofcu-oxupw t8.f(z4f 70sle0ie 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 gx)ol /sfsl(ff h76 wr/p;;fbFig. 5–9). What is the ratio of a person’s apparentpgo;l( hfs;lffwbr76/)xs /f 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 qi8fmodwn-7j h7iu9 j)n1j w 1astronaut 4200 km from the center of the Earth's Moon in a ow9jfnij7j )n7 wm-h 1iu1qd8space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{m}/{\mathrm{s}}^2$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of ew-8laj.x2r-tp z h3edqual mass. They are observed to be separated by 360 million km and take 53x-8.hplw-taejr2z d .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 th70q;9txdxcn c e weight of a 55-kg woman in an elevator that mo9xtcn qxc70 d;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 ceiling of an el93w;,x gz z8kraj5bby ksja 7/evator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a ba7 jasrkx zj59;g/k 83zby,w =   

Show that if a satellite orbits very near the surface of a *ksjl7mk8-iw n.ss4xplanet with period T ,n8*s7 kiskw4m jsl-x. the density (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 6w8age3zmq - dv81kog the period of the Moon (27.4 d) to determine the period of an artificia6o13qmggw v8 -eadk z8l satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun linb iii+b,ja 6m*oxcs1gm7z+ (ke the planets. Its period is 410 d1g s+*b o7(,jc 6mxazii+mnbi . What is its mean distance from the Sun?    $\times {10}^{11}$

  Neptune is an average :woo yh9vuv1-9 ;h( sg) hgpu2xfi+vedistance 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 the Sun roughly once everyvq ft(o/(x h9ljj:70qktst 0 i 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39).jjq( 7lstxt kq:9/fvi0o0th( 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 distance from the Sun.]    $\times {10}^6$

  Our Sun rotates about the center of the Galaxy 0f44lj o.vbh :kn93atrkp a*x$(M_G\approx 4\times {10}^{41}\mathrm{kg})$ at a distance of about 3 $\times {10}^4$ light-years $(1\mathrm{ly}=3\times {10}^8\mathrm{m}/\mathrm{s}\times 3.16\times {10}^7\mathrm{s}/\mathrm{y}\times 1y)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times {10}^8$

  Table 5–3 gives the mass, ax+ jaltv) mj.;f .ii/period, and mean distance for the four largest moons of Jupiter (those discovered +) maiia/.vt;lj. xfjby Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\begin{array}{c}\text{ Jupiter- }\\ \text{ Io }\end{array}}$ =    $\times {10}^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\begin{array}{c}\text{ Jupiter- }\\ \text{ Europa }\end{array}}$ =    $\times {10}^{27}$
$M_{\begin{array}{c}\text{ Jupiter- }\\ \text{ Ganymede }\end{array}}$ =    $\times {10}^{27}$
$M_{\begin{array}{c}\text{ Jupiter- }\\ \text{ Callisto }\end{array}}$ =    $\times {10}^{27}$

  Determine the mass of the Earth fr iq, l*lx 6mt0tott12-epikf3 om the known period and distance of the Moon. ltfitk*m-i20q1el3xtp t6o ,   $\times {10}^{24}$

  Determine the mean distbnpctuid h6 ulw1p ippsl9 ,**(0:s3tance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distanc **u9cns1(pbliptp u t, wi06:pd ls3he 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 okaiw 3 awk k-8ie6z-c(f many fragments (which some space scientists think came from a planet that once orbit-z(6aek8 w3kkia wci -ed 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 describex0g0zlv: *f qvs an artificial "planet" in the 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-glv:0 zfvq 0*xSun 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 2:p2zd7zjo t ) d 7jv 1k4,stdhc4zrbsswinging 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 tole h4d: djp7ztdoc4z7jb ,z2 ss2tk1) rvrate 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 surfacg/vj) kgvr+ kwv2us99i 9m/wie will the acceleration of gravity be half what it+mv9)/ 9/wwgrgj ik2ki9u vsv is on the surface?    $\times {10}^6$

  On an ice rink, two skaters of equal mass grab handbhe3 z47vks4 ts 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 massese4bt ksz43hv 7 are 60.0 kg, how hard are they pulling on one another?    $\times {10}^2$

  Because the Earth rotates once per day, the apparent acceleration of gravitnn* ko-0quvr 87k/k- 3v5xgu1v jwzgry at the equator iuzkkvvq 85onu1v wkj0g rx3-nr -g/*7 s slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times {10}^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the ok.+ban2ms0x 5f9y sk bshn52Earth to the Moon experienc 5s+sxha9kf2. k2bm ob 5snny0e zero 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 in an e 9 b:/g uik i(cxg):4vggm9lhzlevator, it says your mass is xgcgv:b (gil 4 )9z:hik/u9mg82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists otz 39pkdw(qd1cg h9gd7akr2( f a circular tube that will rotate about its center (like a tubular bicycle tire) (Figg t(2dz 9(cadh 3 gkp1r9dk7qw. 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 loop (Fig.2l e;n 9ekkawg b1mk64o3h0dm 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 rl; wb )jk /5h;s 8pahwam5*oicadius r, the acceleration dueh o8w;bi5sjc)a/ a*l;m5hwpk to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a okcp3dn5dok9 p k6h gs*5rd+ ;string) is deflected from the vertical by an angd59k3;65opp k rhsn+c d*odkg le $\theta$ 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 Im8 45i-jwd e5dgmz .enf the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safel5.gw8de- die5 nmmz4jy handle the curve?

  How long would a day be if the Ej)en1po 6 ab x2,4bn7km yw d59/pgvtzarth were rotating so fast that objects at the equator were apparently 1 75p,jdxayz9 pkt/e6nno vw42)bbmg weightless?    $\times {10}^3$s

  Two equal-mass stars maintain a constaz,ek gvk2v*zerc36z *nt 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 constant speed rounds a curve of radius 23/cgmvmju0 (w3k ;fh8g 5 m. A lamp suspended from the/gkg8 mw;(jcv hu 03mf ceiling swings out 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 her0 p4 +sip: yu,m(gqras been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since ,:sep+ gpu0q( irmry4 people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times {10}^{27}\mathrm{kg}$ , equatorial radius =7.1$\times {10}^4\mathrm{km}$ , rotation period =9 $\mathrm{hr}55\min$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the preseyv8+zia9t1 oatub2 s/ nce of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light esc92t/zuio a+tsbvy8a1 apes). 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 $(5.7\times {10}^{17}\mathrm{m})$ 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 :.zy kud,f.0ae u+1ds sa6tsxtraverses 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,1k .da6, us+ztyusdx 0a.e: sf B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global P8 mfv5kjdvu gqw0m 73,ositioning System (GPS) 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 navigd05 3kuv 7, fgmj8vmqwational “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