Sometimes people say that water is wd/ 0pysd6i/+l 1bo:y bj.h ucremoved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this 0/u6c1jybiwoy pdbs l:+dh./statement?

Will the acceleration of a car tz k gkp1*4oi6fspy 97be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentl4 pi1o t *79zkpksgf6ye curve at the same speed? Explain.

Suppose a car moves at constant s j0 -8b2tknvtj;b- rdipeed along a hilly road. Where does the car exert the greajn;0bjt -t d8v-2kb ritest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on lwytpj ;6k:04,bidpfm 6j:v:xz 2kfx a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of th:jlwi xfy,:ptxkk 2d;zv46fm06 b j:pe child?

A bucket of water can be whirled in a vertical circle without ti m2 j3tps5h-f;nfknwt3r. b)he water spilling out, even at the top of the circle when the bucket is upside down. Expl i)t st.5;r - m2nhjp3w3knffbain.

How many “accelerators” do you have in your car? There are at least three cll2f:8fwcu xp/,a4 m0f.af w wontrols in the car which can be used to cause the car to accelerate. What are they? What accelerations do.2 , fl4fmacw:/wxflw8puf a 0 they produce?

A child on a sled comes flying over the crest of a small hill, as f6 h4t21hctpd oxlsvt vj s62h:2k+n-ph7k s+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 th - 2+j2k knh4htvsfp6d:sxc7h21ls op+vh t6tis decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high speed? sm 0 ;spk35+kgotc)pc

Why do airplanes bank when they turn? How would you compute the ae 9pksx/wi8;banking angle given its speed and radius of thex/9a;e kswp8i turn?

A girl is whirling a ball on a string around her head in a -zkkq +ichj.+horizontal plane. She wants to let gc-ik.+h+jq k zo 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 the string?

Does an apple exert a gravitational force on the Earth? If so, how lar,-eg( a8,3 fmiu8xvdcv8 yq rv6.ps pyge a force? Comey.-u8igypxa3,v 8(vqsrv6p cd8 f,nsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would thm1 nb *hfiwcmp. 24nu:e Moon’s orbit be differepwufh .*4 b1 cn2i:nmmnt?

Which pulls harder gravitationally, the Earth on the Moon, or th*hv +v)*xwqb-n9r f)rf gwbo ;e Moon on the Earth? Which accelw *;n9+-g )ov wb *)qfvhbxrrferates more?

The Sun's gravitational pull on the Earth is much 4ll2hu d20s kj(yypc-larger than the Moon's. Yet the Moon's is mainly responsible for tdu-pslkyj (2yc 2hl0 4he tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Whaiv mc,d*q 0cw4t two effects are at work? Do they oppose each othemqcc4d *iw, v0r?

The gravitational force on the Mr e ue;)fe4( (doiqv ,x jk.n0y8cch-poon due to the Earth is only about half the force on the Moon due to the Sun. Why-xe.cj0kqfio ucye 4v() d(8he;r ,pn isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration ofg0fdti0+ki+s , aq0 ek Mars in its orbit around the Sun larger or smae00+kfqi sgdi0k ta,+ ller than the centripetal acceleration of the Earth?

Would it require less speedp-yud, 7bo4s0a l3je f to launch a satellite (a) toward the east or (b) toward the west? Consider the Eart-j e,d3s pa 7o0flbyu4h’s rotation direction.

When will your apparent weight be the greatest, as measured bkdl*w :iuan*f .u9+ t5azwwy;)4sw,tngs h 3cy a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates n zt+d ywswiua;*hwa)5g., *tnc9f43 suk l:wupward, (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 ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could bc o*htc lhggpc 6yod204jo:6*e 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.h6 j6c c2g0 *tl4:c*ghdopoy o 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent we msizmw2e whc77 8px;8ightlessness” between s z 7h7eiwws2cmm;p88xteps.

The Earth moves faster in its orbit around the Sun in January than in July. Is)0dpngti7u3 56vgflofi6(v m the Earth closer to thn0go(3ffli u 6t7mp5gvi) vd6e Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not knk wgw za4j 80onw(n-oikr32(sown until it was discovered to have a moon. Explain howwojok2i3 0a wn4n( w- (8rkzgs this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitatio)g aoj5uzdpwj9-xg) . nal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible fgdgp j x.5)z9joau w)-or the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane travelinh1wlek8 e-( nkg 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripuniv+(8, m q)wfush/retal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. Wha+8s fv un()muhwiqr/, t exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it hgiiu fo(piawh:l9g,t j/n5 2/b e;/ wrotates uniformly in a horizontal circle (at arm’s lengt /g l:e5piiojafh/w;wn ,2ti/ 9bh (guh) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's szopkc,** kc*l ulrf y+99g7hd urface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer lc 9cf* l ykg*9krhudo7,+zp* in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edgenpmcll8 .// ygm*re afeh1e1q5pjx .8 of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is . .cemql je/pga*l8h1rypm1/ 5e8fn x32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circle qg50tj(m/ldz of radius 72.0 cm , as glzq/tjd m0( 5shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a tu pd2-sls0twk. rn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the m2 k tp.wdss-l0ass of the car?   

  How large must the coefficient of static friction be betw o(xb2orn,+xp) ra i4qeen the tires and the road if a car is to round a level curve of radius 8+2x o4o(pnba)x,qi rr5 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots sy x l4c36s7adis designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weigh 3467ydss calxt, 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-ts+s cgeozd -k8l* c7otating 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 coin slides off. What is the cz7-8gt+skod*lc -es coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside do 9mr 9y28rp rkvhj4*kaom wr-2, dwq+lwn at the topkrwkj4yr 2mw 9l-ahord2 mv*rq9 p,+8 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 ked7*xlob:zp54gtz*v/k fzf-e4 6qlrg (including the driver) crosses the rounded top of a hi:l tv6ob5e4xz lf** 47rz/fzk dpq-egll (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 Ferr5cdy+tw zwa2 7hm5fn 5is wheel need to make for the passecn7w2 dy5 mfthazw+5 5ngers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a x d5edwv5r3z+ vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.5 e+dxr3zdv5 w0 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 centri4sixgycwy((q4 u4t1b 0o6mbc fuge rotate if a particle 9.00 cm from the axis of rotation is to experiencqcs1b6(o4uwt 4( mcgy4yi b x0e an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated vizffotcwa1en9tm6 i s9k++ 1y6y.n 0 in a cylindrically walled "room." (See Fig.tmeyz i syt9c1on16+fa. 9+vfkni6w 0 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless aij t lpqai9(d02r-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) throug0aq(i 2l9t djph 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 , preciselfi 57b 5hlcmieg,+tl9 y +:txfy this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In pi7gt mytf5lb f9i5,c:e+h+ lxarticular, 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 huam6 55m 1uxbfor 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 masses5k (7hktq(f5ve*rrfof;5vmcc4 n cs , $ 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 eqju j)+jl.o2bk 05yvx vasive maneuver 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 tangentias-fxv1dz *q0y a5*b fgl and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its speed is vf5-ba ys1*q*xzdf0 g 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uvx43m * :uwdh,f z2axw1gstny(kd s;.niformly 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 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 slippizs; dgw,sky1dt fwvh:uxx(243m * n.ang or skidding? $\approx$   

  A particle revolves in a horizontal cir,awhqg2 85ble cle of radius 2.90 m . At a particular instant, itlhgew,8 bq a52s 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 gxx(sy c12rh 2vravity on a spacecraft 12,800 km (2 Earth radii) above t 1yvxrh22(cx she Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has)8p tvc9au2mxq+(bkc a magnitudvk(2)tq9 acx 8mpb+c ue 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 accelet4 v c vxz)kd:2ym)va/ration due to gravity on the Moon. The Moon's radius is 1.7vvvz)):/k a2 tyd4x cm4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 ti*1li74stz;qiw ibh 8n mes that of Earth, but has the same mass. What is the acceleration due to grav7q8wbh*i ; lnz41s tiiity near its surface?   

  A hypothetical planet hl;rjphenq-)j5-/e xy as a mass 1.66 times that of Earth, but the same radius. What is g near its surfac/n;lj-x)yj hrp-e5e qe?   

  Two objects attract each other gravitationally with a force ya0l 5o ;k+5w6ij5 (zlxuebynof 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3200 m8w kcfrp:vh-l:o 9st1vc 1wk hlf o9:t:-rps8    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth where *xxo+3 yt/sgu( phok: thegravitationkyohuo+g /3(px*s :t xal acceleration 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 packxz mp3n::yi:pi+ *akued into a sphere abopz:a+p:*yn:3 mx iuki ut 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which j0dfgvo* k7i;+ cn4.g(waq cfnn+vb4once was an average star like our Sun but is now in the last stage of its evolution, is the size of o; +nfkga f4vvn7 o d+0(c.iwg* nj4qcbur 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 weimnha-s z:4 e3qghtless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yours hnm-e z4q3s:aelf 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 lotylr26btnyu5)/ n+mkcated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitat/)ymlky 6n+2bt5nu rtional force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planesr,2/hkdi fx94w /56hj oyx :jqts7nyts line up on the same side of the Sun. Calculate the total force on the Earth due os4 6 5 h/x,t/j:di2wq7yyksr9njhxfto 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 gravit6 )4 1hdt.tgv 8)w(vie1(wfqvd slz gpy at the surface of Mars is 0.38 of what it is on Earth, and that Mars’(4 h) qlvd186( tzfsi vdwgtv w.1epg) radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value fe, vlg 0)ib a0su+aul rj+x,x c5;vdi:or the period of the Earth and its distance from the Sun. [Note: Cov0g ;e,di0ul,a x+x rijvl5s:ub+) c ampare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular ux;7oavxipkz7(x wxha-2 l 73orbit about the Earth at a heightoau7p hx(ix7ax-xvwlk 2;3 7z of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite ingj h1hcjamio1 ,doxclr );607)u v1mhr1k f o;to a circular orbit 650 km above the Earth. How fast must the shuttle be moving (rel)0l1f dxicu6hgk,7r o;j h mo1a;1co m rhvj)1ative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experiencexpb) ,l:w0iy 1ml8vh z simulated gravity of 0.60 g? Ass0yml1 vhx8p:l, z w)biume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Ear7ecg;q u(l2i :q:ghgh th in a circular “near-Earth” orbit. A “near-Ea:7iq2g:( clhhggq;eu rth” 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 velorypq91tr )fg my.jmvw6a)a 8)city would a satellite have to be launched from the top of Mt. Everest to be placed tv)a.r gyjfry 8)91) apmm6wqin a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module conpfasv 8y m 7j-1nvh04ptinued to orbit the Moon at an altitude of about 100 km. H1sf 7ppvmyv0j 8n4h- aow long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the 6ln8yhro,br g;n4 h+uplanet. The inner radius of thl oub;r+6ngyh4 n ,r8he 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 Figeup 6. hfp;*e)4 y6ckg/wkaac. 5–9). What is the ratio of a kepkua*h acp6.4fecy; )g 6w/person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weioi4xwb 7fz ea 97j6lk (2xk 487r bzjz(j6ijtwght of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at co264bi a(bj o8j 67ew779xjkk l(jztwfzxiz4 rnstant 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 eqf h qf)xqf8o6.ual mass. They are observed to be separated by 360 million km and takeh.qfx) 8 6qfof 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 wei:p c z7)b nuncc.4u(joght of a 55-kg woman in an elevator that ncup )c ou(z.7:4ncjb moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from at)jpj tmvmb3g2ca1kgi2 1-p 7i j.f3 v cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevatomca)ipgp-3ft b3j ktv m21ivj12 gj7. r accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near tj;fbj.pubwk 6 a:h 7,fdp,2wr2;rwn the surface of a planet with period T , the density (b6whnk , jj,;.u2 rwd7;a ft bfrppw2: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 an pvw8b0t,u/t rse;p4h d the period of the Moon (27.4 d) to determine the period of an artificialet , su;wrp8hv04bpt/ satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lif (g0w/ ahwd 82dxa:pkfb -:jlk(2 -/ :dph ajflxbk:0wafd8 wge the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distan 4p0sff*lz 5l+ ofptql2bk(4lce 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 tc(p)ef:w gkz29 k f-ayhe 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 p kc:) 9w-g2afe(kyzfcomet 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 th*0xg zyc: f-i4xipk. ke 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 for p4j7wbc1k6s 1w3fptothe four largest moons of Jupiter (those discovered by Galileo in 1609w7kjb6o ws 31p f4ptc1).
(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 Ear.r7 b 8(xaxd5q3gscs vth from the known period and distance of the Moon. qg r a3csbx5sxv.7d8(   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupitekl;dz-bd :k*uvw hhic95a f /.r’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to -5d/huaw* vbh;kc z l9if.dk: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 5cl 07oq3h 3kre;nj vkJupiter consists of many fragments (which some space scientists think came from lok3750 kqcvr3;nj hea planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a band co:aajcbk r53rqoda - 1b(8zj +jmpletely encircling a sun (Fig. 5-40). The inhabitants live on the insidz:aaro3(jc+-8 rb1 kjbq5jdae surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging ,rbm ebz i0/ 8e(uiv)gin 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 maximum8e0gb)m , ibzvu(/ ire speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface willhanbj,ql8ee g(r tf 3n-. rt43 the acceleration of gravity be half what it is on the -nq8rh3elf ,(j 3er4tg.tanb surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a : tq1o k(m dmvs.jyh),mutual circle once every 2.5 s. If we jsymmoh,(.t)q: v k d1assume their arms are each 0.80 m long and their individual masses 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 gravity a8 oaybvghh** /pm(w:kt the equator is wam:vp(ygh/*o h *8kbslightly 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 Ea.endz3bx)u gstb7;*v rth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon .z3etbnvu *7)bgs; x dpull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when yxrpa .3wb f4+bou stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is thwf4prx.+ab 3b e acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a c3vwgwf,a 0oj ,ircular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tubogf3vajw w,,0 e 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 inoybqf17u 9-ptwm it ;(8;s iia a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass)qvq+9 j1/tzr sd px3a of a planet in terms of its radius r, the acceleration due to gravity at its rzjt sv 91qdx p)a+3/qsurface and the gravitational constant G.

A plumb bob (a mass m hanging on a sihy:yq0; y6k htring) is deflected from the vertical by an y0: ik;hqy y6hangle $\theta$ 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 desiny+k/jfhy l4 4kx2b 20ap h(lwgn speed of If the coefficient of static friction is 0.30 (wet pavemefy2(jp +kbwkllhyn0 a2x4h /4nt), at what range of speeds can a car safely handle the curve?

  How long would a day be if tez xrd 1q h-m;kz3 97o9)hmn4)tj planhe Earth were rotating so fast that objects at the equator were zplx ) j1 doh ;a3z-hn99n)mqt 4r7ekmapparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.z7m-3 t4e4m yyq u+two0 $\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 spdv6nz1l q; m5)efa4 xy20fi lceed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to 2mxq f6ec0d n15iv4lay ;lfz) an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 m7( que/txhby.5edn n1vsb18 times as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 1u51yeqbx ( nbtv n7s8./mhde$\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope dedqn agf zes)77*u:ev a-uced the presence of an extremely massive ezue*g7: n -a 7saq)fvcore in the 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 hill and valley sh .qy nq914vv7ld)h qis xa( tm,5x-nwzown 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)dz-n 5vlqxxv 1t9 wqs4hynq.,7im( a fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Sysh ap b67u7v5j;ssdj0q tem (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 navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of edsh0ajb7vj; p 5uqs76ach satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after travelie/vq*qu q+n wtrjq*52 ng 2.1 billion km, is meant to orbit the asteroid Eq2trne+q *qv* uw5/jqros 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 the space shuttle pursuing a satk;a,b ,czjp5ujoj 3j-ellite in need of repair. You are in a cuojz3j5ak ,p; -jj,b 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 i9.aarj:o. rmw z6.h lzs its mean distance from tm69awa l. h.rozr:j .zhe 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 o clo 5crv2wsz52 asnu9j.0r5af G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptu5a9own2slacr 5 c 5s j.vz2r0ions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the zws;mlzi 97517dn spg) /l lb5lj9fu8s2e v geMilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-yeafss)5eje z lv1g/gu7 b9n9ls7mil 52lwz; 8dprs 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 0.5h qb e/t-t*fv:0 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed-q*ft h:/t ebv at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 554u6 jqkgf 4kg/+u kc+v00 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 by the tip of the 1.5-cm-long sweep s+lh3(t*.nddb+ivq z kecond hand on your wrin *dt lzq+bdki v3.(h+st watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing 6ghyh4 7(s4j9p(nl jbg-dslh 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 sjs6b ( 47ghjl n hph9lgd(4-sy. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of ** ;frb(d v2nut fu)6icte/gmradius R in a new highway is designed so that a car travelingt(b /emu;fcgivr6)2*dtnf *u 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 cars whenokba-i21p 2vi6sl o 2i 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 (approximatelylo22 sp 2o-6aki v1ibi ). (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.$\approx$    $\times 10^2$