Sometimes people say that water is removed 1x bn. -/para65r0mu9mekycxak1 r j6from clothes in a spin dryer by centrifugal force throwing the water outward. bykr5rmrj nu 1906. 1m/axe-6pcx ka aWhat is wrong with this statement?

Will the acceleration of a car be the same when the car travels around -wzg *ej w,0eba sharp curve at a constant 60 km/h as when it travels around a gentlzjw- eg0*ewb,e curve at the same speed? Explain.

Suppose a car moves at constant speed gbg6(u/gpg z1o /xxy 5along 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 thepg1o/ gg(xbxu 5z/y6g bottom of a hill?

Describe all the forces acting on a child rgb;z65yoe5w+d2;g jrd,b i6*naqi ye+b g. o riding a horse on a merry-go-round. Which of these forces provides the centripetal accelryg ar2 *+zbj q,+ 6dged;6; ebbio io55.ngwyeration of the child?

A bucket of water can be whirled.qf*,byj q c. :n)ynkz in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down..kc*y. z nb,:qfqy) jn Explain.

How many “accelerators” do you have in your car? gk-) 6x l qmcyhkvi,q.4sf e-3There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acceleraticmgi-vx3 ke k-.hqs6,)fq4l y ons do they produce?

A child on a sled comes flying over the cre *g3tofvjgbj4v,nb.q m, *wn*st of a small hill, as shown in Fig. 5–31. His sled does not leave the vmn ,gn4,j* o3f*vqwb*jbgt . 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 second law.

Why do bicycle riders lean inward when rou rgl04 n8h:ff0pafx1 inding a curve at high speed?

Why do airplanes bank when they turn? kj;qh :(7 3 n/tycogn7 z9sxp(s dr3qsHow would you compute the banking angle given its z7q 3/dx(o pyq37j;nc k9rgths nss:( speed and radius of the turn?

A girl is whirling a ball okpc),j/v ,yugn a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of thujc, ,kpvgy) /e string?

Does an apple exert a gravitational force on the Earth? If so, how large a forceu 593 ejx.9dyza( csln? Co9jl9 zn3udcae (ys.5x nsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass werem(h:f78 kk1m5s n3 kx5vaft(,2h ozwmhcr oo5 double what it is, in what ways would the Moon’s orbit be different m(3mkkarow2h (s71h:5k8v hczn f 55,oxfotm?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon 8zjae 0+ q 5ze;tlu5tnon the Earth? Which tz 58n;qzjt5 +l0aeeuaccelerates more?

The Sun's gravitational pull on thbcj p ; 1z +);lsn5nei:ksp0m,ujhun7e Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider th 7ejmzj+npkbscl1 ;,pnu5 ) h0i:;nuse 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 arbl (0l83rr sng,lw w1se at wor s3 1ln8gs l(wr,lbwr0k? Do they oppose each other?

The gravitational fokf3gdafhj9;98hfblri *fdj5( 7 r.kyrce on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why;9 gkkjhyi 8r5a3fj(f dl7*9b ffhrd. isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or s5:fdpc5 yl* wq.ua3vh) y 0pogmaller than the centripetal acceleratio:lyvyup* )ah5 5gq3 0fwocpd.n of the Earth?

Would it require less speed to launwa d8y/xf h79j/oipe0ch a satellite (a) toward the east or (b) toward the w y/08/7a9 oeph fixjdwest? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a moplk cuee1 8k4-ving 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 be the least? When would it be the same as when you are on the groun1k4e- ulpck 8ed?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods -a.( dh* / uvhy frkm1jyq+*jrin outer 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 hf-q*( avjjy +k.y mdh *1/rrusimulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiencmcpqsw814o b3hr 1ns*unm 5f+ es “free fall” or “apparent weightlessness” betweenn p5bhmf+qwsco3r*u18nm 4 1s steps.

The Earth moves faster in its orbit around the opxh s 4)0-skfSun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not musx-4kh pfo )s0ch 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 moon. Expl w5udr 7h,q-rvain how this disco 7dhrqru-5w,vvery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Ea0zjs2:yab f);sel( w irth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravita jf(bw)l;e0: s2zisy ational 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 19 kgrvm8, .+gxq80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around thel3-rf-6ufts o Sun, and the net force exerted on the Earth. What exerts this force on the Earthtof-u 6s flr-3? 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 on a 2.0-kg discus as654 1vnfkz xry it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discf4 6vynx5k1zrus.   

  Suppose the space shuttle is in orbit 40 f3j uiit7k/9u0 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , 9i7 t3uu/if jkthe gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of 7jk:ph g(r.rna potter’s wher.(p7g:jkhr nel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a ve tdz7rcgj mk 5/n.9k7kflyg)7rtical circle of radius 72.0 cm , as shown dgy k7lfgr)j7/k.k7n5c9 zt min 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-kgo 4q rr* 5/vfuprju*lca*21 uh car can round a turn of radius 77 m on a flat road if the coefficient of static frr 5*jfrvu2 /* olcu*a1qru h4piction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static fric s bq(ns3/-jl90- tye5ebn7 dlp /c:bz;pcuxttion be between the tires and the road if a car is to rlqbse yn7b/u d39cz- te sp/blc;j5: nx0t(p-ound a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and 5bam fxuqxnh8gjc(s( j89)k4u os*s(jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the forco(gcxs4aus* s u( h)5b8jjnxm 89f qk(e 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 theb89 bu tsw bd6.is3w5p axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the cosptbs.56ud9 b3iww b8in 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 upside down ats uzab(x4cg2sl:p7g6lt:m v, the tob47zls( gs ,ulvc 6xapgt2 m::p of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the ke 9exv+l x19m.qmwi8rounded top kewq e9mx9m+i18.vl xof 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 would a 15-m-diameter Ferris wheej . f z31w kf,;/:msscudqy3osl need to make for the passengers to fe:3zf;y ./j3sk wduqms ,1cofs el “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.1en2ia 68o5xot 0 m. At the lowesoti62e8oaxn5 t point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a cenv*t,p7 jkq lk7q4pxi+trifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accelkq 4*,p j7xtlqv k+7iperation of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotatv + ef;x)4pjeaed in a cylindrically walled "roo;)e+vxe4j a fpm." (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 i 1r,lg6;c2:q sold 8 pkqq*akrn a circle on a frictionless air-hockey tabletop, and is held in this orb1k 8 d*pl;akq6lro:src2q,gqit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the zp0( ;bsjfo4rr:8c6-zcqxuz ball whichf46-rz b: p(uq; csjz8rx0czo revolves on a string 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 for a car traveling 751m ,1z relntr g6p7cp. $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masse gncc.k9c:gu9s $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically a8kafe/ 44an;elit pe+t 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net forceizx6 aar46gs q1 *vr+em66rma v;n/yc exerted on the car (by the ground) in Example 5-8 when its s6s czn6 xq/61e rvgrv6r;a*i4+my aampeed 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 pitjr25uv w)p 0hr;m8rmtj 1 li7rch +:ar area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determia7pr2m5 t:l w m0hhrr i;j+urjr8v) c1ne 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 ti 5cjp7k,bo dd j/5m5yikk8- a particular instant, its acceleration iyb/t,5dkjiojk5-i7 d58cm k ps 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 Earth radi.tq)rc,,p ) zs77*yrhyf1 *jy hkpyk qi) above the Earth’s surface if its mass isrqpt k,k 17y )rzy.jhfh*,s*q7)p yyc 1350 kg.   

  At the surface of a cerxg z;q)t 35 t):khgcz*f+ oenutain planet, the gravitational acceleration g has a magnitude 3tugz k)q+5 ;*zte x hnfog)c: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 Moon's radib+x 1vau(pyj l.l47i:xmpgr jyl)1 ;e us is 1.74igpxb xll:jy 47p )(l+11e;m.y uravj $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the ti .r3d 7)3h qs ur3 mj5ekmw7ng5hwp2same mass. What is the acceleration due to gravity near d2ng suwt j.k73)h5hmeip5 w3rr7 3mq its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but th)or( z-0vjwny lh -jy2e same radius. What (n ozh-2wv jyl)r-yj0 is g near its surface?   

  Two objects attract each or .;yk32qklj 0(bbfjlther 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 grn3h4kz 9kbnof-b+kohp3h k/w; czl j5 5f0y3aavity, at (a) 3200 mzacf-n43n k3hoy+bp50 l;kh kwbk9o f hzj53/    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the0e- (xu3qyzt0 fpyssc+6f /ka Earth where thegravitational acceleration due to the Earth fy0 cu+(kpy6 se-0fz/xqas3 tis $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has dy9j*:7igvjz dl4 0 fxfive times the mass of our Sun packed into a sphere about 10 km in radius. Es9* vgdy4lzj:d0fxj i7 timate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like ourru, oea0,:vh(x w*kcb Sun but is now in the last stage of its evoluo 0ca*,e:kxu,w(vb rh tion, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless whilr7iecdmy 6o aom z1k(w3/u64re orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince themokui4 mw y6ze7o 1rd/r(c 36ma 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 corum)o210: 9c yh2ud,l xbfa etfners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the othuyl fuc)tbx2mo10fa:h ,9ed2er three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets liej it5b,9oxcp-*eqdqoa togpezo y , 8-9t. 2)ne up on the same side of the Sun. Calculate the total fory9-,8b9e)tjezec -,otpxp togd .oo2*qiqa5ce on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars iswq5yd 9t2q *xk 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars. qw5tk 2dq9xy*   $\times 10^{23}$

  Determine the mass of the Sun using the known value for the peroqa:*h48nfn(:-afb/ xh6 2ffvc izub iod of the Earth and its distance from the Sun. [Note: Compare your answer to that obta:f/b f- n4cax(i268zo*bh qa:nf vh ufined using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellixs )gl/z7h e*ods.hs ,te moving in a stable circular orbit about the Earth at a height of 360* .le),7hzxdgssho/ s0 km.    $\times 10^3$

  The space shuttle releask6 nl hz-pb+v)+ cjiskqf g,:5es a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving vf+ b i,pznhc-k+5q)slgk:j6 (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rot .7rcvjlkp j2p .ti0q7ate if occupants 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. (See p2k 7.cvpqjr.j7l0it Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite(yt.)j- uz: f1nolzo evc:dn8 to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which isn1 oz:).yd(f- 8:uoel czjntv very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched fy/ti *b ;9gtj*i7uyrarom the top of Mt. Everest to be placed in a circular otita r i9g*/yu j7*;byrbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbd9/xx bw uc8z*it the Moon at an a* x b/uwzc8dx9ltitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The is tq2agw+d/0 frny.:anner radiusqdwa0y r.t2s a:g+n/f of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once u-wki9l5zo-tk-l(jez5 z*aj every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) akz(ljow 5ut95-e jz*l-izk-a t the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronau,1qul c+3uyy zr ih)e;t 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant vc31h zury, u;e l)iq+yelocity,     ----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 equal z40k;vmfpr/ 0hmaqi*1qeiw k/ s.-c n mass. They are observed to be separated s4kii apqw*z1 nk.vf/hr0 mce -/0qm;by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman i+ ;yk6 y1isy0klp/d gen an elevator that moves ey;y s 6ik0ly1p d/g+k
(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 t 4.azb4 zwb-bfdtt 8)r5h 6fbohe ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directidwbf5z)6. b4tbb8t o4zr-fah on)? a =   

Show that if a satellite odb k*i:( mk d qt:dos4:gd7j6prbits very near the surface of a planet with period T , the density (mass/volumk6dtm:j:7bddq(pk:di* o 4 sg e) 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 o85x f-v 3espsfzco /ge5wj42wf the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near th5swe4cgvp5s8 ofz /fe -x w32je Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun liq v/vu uh/ hj4h8*7ih:swc6drke the planets. Its period is 410 d. What is its mean distan hh/vuhq874 sc:*vrdw/uh i6jce from the Sun?    $\times 10^{11}$

  Neptune is an averag 1g6s0pn4sr dfe distance 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 every 76 years. It comes-p v ca1in5lr(u q/st) very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and far) v-15suqr (cipl tn/athest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about 4ekqmzgo1 m z21m . .s4orqz3xo1x 7mgthe center 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 f g4msbhs+;-ud1 uik;jb junvht+ 3 ia j(i5)a,or the four largest moons of juitb)a+g umh5sj+j iv13k;s , bdha;u -(ni4Jupiter (those discovered by Galileo 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 dikiomr. vb;/ymhw(bl /k.j/dsx( zn71stance of the Moon. 7o1rklzb / .(myj(ns.xwhv/ k/b;idm   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupite o(*od/prgz tpb 75)ae3yx2ezr’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Tableo * pt)a5rde2/x 3yozz 7pbg(e 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 betwo nmrb48,bi) rb 6h9jween Mars and Jupiter consists of many fragments (which some space scientists think came from a pla896wr, )rb 4 hobjnmbinet 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 talgs0 4pt ws.zlmch. :f(kb+s;te describes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surfa0stl m4wg. ( t ;z+ssk:.phbfcce (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 gorgexcwd3-azp b-xg m4iohnj; - ); 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 a)x- b;m w3goixcn- d4p;-hzj is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s )me iuw :1y)odv+jvcyn: 8am5surface will the acceleration of gravity be half what it is on aiu: w:85m+yomdcvj)nvye )1 the surface?    $\times 10^6$

  On an ice rink, two skaters of zxc7 6opz vo/3xt:q0 r47z9n lynsu0o equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they roo4 zxc v76z tq9osu7y/zlnp0x3n : 0pulling on one another?    $\times 10^2$

  Because the Earth rotates once per delupm 6gpg 76k56l4jday, the apparent acceleration of gravity at the equator is slightly less than it would be if e6ldp 5 lp764jku 6ggmthe 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 spacecr,z 2 m4v1vignn :q)wew 9ogof:aft traveling directly from the Earth to the Moon experience zero net force because the 2gw n9::of mv)v iq 1e4gnz,woEarth 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 yr-ep ema4l3it0e :*l in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directtlm reep*- a4:3iyle0ion?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate aityoh7wx1y j,(iyxg, tm6--tbout its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) gyyw t-7, -(1xjix yhmt t6,oiif 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+0 +dona avw(s. 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 run1 :9jeb 8hfi, the acceleration due to gravity at its surface and the gravitationju19bfehni:8 al constant G.

A plumb bob (a mass m hanging on a string) is : *ne1 mzfadwuij r66dw8tsf,l- d 01ydeflected from the vertical by an anglyia,dmw 1- 8ts1:ju0 6dzwlf6refn* de $\theta$ 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 If the coe8 rj6n u4*.cxvwwrp3hjm ,3n5 jgo fi(fficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safeg.3pjww,i fr m(rh3 c5*on jv64u8 jxnly handle the curve?

  How long would a day be if the1dtt49yo xa j+q5 jpd7 Earth were rotating so fast that objects at the eq1dpdtj47xo 5 jq+t9y auator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars ryzb y4bk-q24mducs (40krd: maintain a constant 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 -czqk:vu44ofnr3bo( * a5inr(ky 8pra curve of radius 235 m. A lamp suspended from the cv ru8q:n3crioy4 5 kp-((on kr4fbaz *eiling 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 Earte(c/ t1 pe vy5d.fh *bokm80vqh. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can'ke . 0yo8c(he1 md5pvv/ *bqftt 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 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Tcecoa6 1 a/l5welescope deduced the presence of an extremely massive core in the/cec1 aola 65w distant 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 traverses the hfe 2 ka,z,*vlqfe65qiill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal 2f z,ea vkeq,l5f6q*iforces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites eq kt 7k6jtc hv:: zs;nf+5j2jorbiting 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 around7j5: j6k:t eh+t ckvjnz;2qsf 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 2.1 billnm )j ivyd37e j62fwi6tm 6.9cbf zrb5ion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roug)d9cztf6 . 7b ib3m52e6j 6wjfriymnv hly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttyimagb .,(,sow:d m:ele pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but ay ( :og,.imwbmde:,s 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 0p9 mzju c e0r;1mc51-msywbcyears. (a) What is its mean distance frb- sm0cz1r5 eymuj m;c91 pwc0om the 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 could actually "fy:p 1apluv-n-ku9da zp(ijj:*-psu , eel" yourself gravitationallyp j(vn:zpj-1-*dp uu,sy -k uaai9pl: attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy bs 2mgh(gh srp+(mmn 3 9-eqk:g-(so f(Fig. 5-46) at a distance of about 30,00os9e3g mf mrghk:2b h-g(s(ps-+(n qm0 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 si2 ;6)no otggequare 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-keg2ot 6)o;igng mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits th q us-r(psq10vlmo 48lfrz-fj*w.b pn 50mzf4e 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 by the tip of the 1.5-cm-long sweep second 2*hp0 hl z(k (4lravmdit8 mw6hand on yourp0hwkz *(a42r m(iv6 m8tl dlh wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinke8)6+ngi+t ksz/b anl .umx 9nkr weight around in a circle below you on a 0.25-m piece of fishing line. The weight makeskxanz k/um +)98s+.nbl g6i nt a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of r.9bu knc9. p/a )ywgsi xb/v*9 u(mqykadius R in a new highway is designed so that a car traveling at speedbi umvu)wg.//k9q 9( sc.9p ayyk* nxb $ 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 traineaae.h x/kb99, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjust9eeaa/k9 hb .xed so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$