Sometimes people say that water is removed from clothes in a spin dryer by centr8+yp- g ypi(btifugal force throwing the water outward. What is wrong with thgypy pi(b+t8- is statement?

Will the acceleration of a car be the same when wo;/ nw( sem k9c9pek,the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle c m9cwe9;/o(k ewkn,spurve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where ;vkewe *7be4/4) 1se wlnrbtw9 9k zxzdoes the car exert the greatest and least forces on the road: (a) at the top of a hill, (b)wt 4;berl*zzv ne e9k7w1)k4e s/bw 9x 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 ridiz tda4/kg yw er36m1k5ng a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the zmke ta/4w6g31ry 5dkchild?

A bucket of water can be whirled in a vertical circle without thejcn g-pe ue6jgr)78r) water spilling out, j6rp 8n gu)-jeceg)r7even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least ttco6ik*hxx/ cy n2 ;w;hree controls in the car which can be used to cause the car ;nxxwocic t ;26/kh y*to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in F2 8( j rsg2d/vy1hyfvzig. 5–31. His sled does not leave the ground (he does nofhv/ vj(1zy22 rsg8d yt 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 rounding a curve at high spe(9a,- a4 blx hx7wai-*ld- v* nt3ybx*heuxfbed?

Why do airplanes bank when they turn? Howyn -2u; p9tjbo would you compute the banking angle given its speed and radius of thpn9yoj;-bt u2e turn?

A girl is whirling a ball on a string around her head in a horiz itgw+b3q- cv3ontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side3qv+ 3ic b-twg of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a forc m7x,vocqb+rhixh p0xq3//tank-- .se? Consider an hvq .q n,+/o/ m-ix0h3x pab 7rsx-ktcapple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doubl a8amdc5be9su/ +d+pcv;l- e ve what it is, in what ways would the Moon’s orbit be di5-c+cm9vvae;+sad8 dblu e/p fferent?

Which pulls harder gravitationally, th5gl7rs9,h 4, yz lxlbge Earth on the Moon, or the Moon on the Earth? Which accelesl9x rll57, g, zg4bhyrates more?

The Sun's gravitational pull on the Earth is much larger than thexs.ic,2m 8oseq; n sa( Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to thsss i eoa8(2c;mxq,. ne other.]

Will an object weigh more at the equator or at the poles? What7nh9eex6b y3 a two effects are at work? Do they oppose ea97eb6ya3h exnch other?

The gravitational force on the Moon due to the Earth 7h2ip9byrvb / : /-ec7s.yriolri6oe is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled aw/rcrh-ib l7sr y/.eib9ye: v 2oop 67iay from the Earth?

Is the centripetal acceleration of Mars im5:2xp56sobf0u iu :)rnhb kzn its orbit around the Sun larger or smaller than the centripetal acceleratiup 6fh5u:kmb2izor: 0xs )bn5on of the Earth?

Would it require less spexuvljfmwf5*d,id 8 *546cww8nh a)r jed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation divf fdw*8jua6n4*drcj i85w,lm x )5whrection.

When will your apparent weight be the greatest, as measured by a s8ypmlv nbmw1b/ -pm t0 lb-:s.cale in a moving elevator: when the elevator (a) accelerates 0lvm8p/mbn yt.mps-:-l b1wbdownward, (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 ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer spap2/fae 5dln;z,4i wv sce could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) ;p4al ef5 /d2 iw,szvnany other aspects of gravity you can think of.

Explain how a runner exp*tu qef/qf, rm07ke9oeriences “free fall” or “apparent weightlessness” between stepom* 0,rqueft9/ keq7 fs.

The Earth moves faster in its orbit around the Sun in January than in J be 1c3ek qw0dkb-2iq(uly. Is the Earth closer to the 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 or diw1b(-k 2qqe eb3ck0bit.]

The mass of Pluto was not known until it was discovered to have a moon59fu c*adf 4vf. Explain how this discovery enabled an estimate of Pluto’cf4av5f9fu d* s mass.

  The Sun's gravitational pull on the Earth is muc1gf l *6faihe 0d(v1uo+ckr+ dh larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the cente cld(f 0u+1h 1dvgo6*kf ar+ier 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 1gf:q fl+ 92iyu980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 arpb7h 1pa me a6ib0d(:uound the Sun, and the net force exerted on the Earth. What exerts this forpe61udia hpa 0b:7(mb ce 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 5dqy xq+m0cy +hsq* r6s4rp 0d/ rp)h/f9gu byon a 2.0-kg discus as it rotates uniformly in a horizontal cir0qg6qsrq +rxy4c/5u0y db hdspp)*9/ rmfhy+cle (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 surfn3l2sd m zc 24xq6kh,pace, and circles the Earth ab2c npm,d26qhx4kszl 3out once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accel.3n:o9 ssu wqferation of a speck of clay on the edge of a potter’s wheel f9suon3. :ws qturning 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 un/fm4+u hgqi ab9m(z-,) ze5 (p pcjxjliform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speedzq()x m4u-fh ,z(jeipmb5 j+ c9al/gp 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 turn of radi30 skzisk:z 9cqdoh+9us 77 m on a flat road if the coefficient of static fric k9o:hic3sqzz9+ s d0ktion between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be betw+ azig-aq.mg6bhd i-n0;vkt -een the tires and the road if a car is to round a level cu0gqt .-nkzmi+v g-d i6b;a-ahrve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotate ssa49p)t;9jjrmm . qya trainee in a horizontsqam;)sjm4 j9 9rypt.al circle of radius 12.0 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 a rotating turntable of variableq8qn1b8dr3ht9 lpwg1-yx i+li.m-ud 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 coefficient of static friction between the clqrb1iw d h1. --y 8l+pqgtxmn9 3uid8oin and the turntable?   

  At what minimum speed must a roller coaster 0r;p(a zdou/wbe traveling when upside down at the top of a cio(z0udw/ ;apr rcle
(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) crossedou8iq.ajw 8 u*l)nb0s the rounded top of a hill (i80.ao u) q 8dbu*jwnlradius =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 wheel need to makebp(q :s.t pr-e(r8kmi for the passengers to feel “q(s.e:m -prr8k bitp( weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vs fi 0ti 1y.0c1c.fpntertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope suniysf c0 1i01p t.fc.tpporting 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 par kjp+c;o(e ua+ticle 9.00 cm from the axis of rotation is to expeeuja p (++c;korience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people ars/h9ye dk i4p(c3basx)/bcf a/oa ;) qe rotated in a cylindrically walled "room." (See Fig. bi 3cabka/s/ap)f/h c;e( 9)syd oq4x5-35.)
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 frictijs v3pbw/ xn2w1ha5g rm2b8k3onless air-hockey tabletop, and is held in this orbit by a light cord connected kvxn m2wrb/58hbjpa23 g1w3s 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 di81 +m5k c8l6yqgi:n/qcfg0rbrebz/ ug ++cthe weight of the ball which revolves on a string 0.600 m long. In partiqr0+g gncfrd y +i5egik q+zbl/8:6 / b18umcccular, 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 radia zfz(zed 6hgr: -4lu/us of 88 m is perfectly banked for 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 massezl(v ev *,-kaps $ 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);tcvkbb 9d* t4dtt-.o q,xvh 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 tangential and centri8iwrlqcv bk4 t4;v2(kpetal components of the net force exerted on the car (by the ground) in Example ;bc (q4i84 wkv2rlkvt5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from this 1le:j o0dj.t1.p fxe 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,1ot :0jxlsej1ipd .. f 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 k qzyq j*30 rc3oz*u7pa horizontal circle of radius 2.90 m . At a particular instant, its acceleration isjy3pq*3* cz ko70u qrz 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 12,800c (e 2sqid+42qfcjqmk9l9nx , km (2 Earth radii) above the Earth’s surface if its masssk4j 29qqfc2 n(emc id9x+ql , is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g i4iaqp3 4yjz z/y(3 myhas a magnitude of 12 m(pyz 4 y/iam3qzi43 yj/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 gra.k0zxm. .fjn tvity on the Moon. The Moon's radius is 1.74mx0..kf j n.zt $\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 xap18x w vkmq2*c+xhq8q1mh01 e5tvn has the same mass. What is the acceleration due to gravity neap 51q qx 8h8x n+v0 xhkqm2*e1w1mtcvar its surface?   

  A hypothetical planet haso 57*fstx yn)p6npp4j:a kes6w+,oe e a mass 1.66 times that of Earth, but the same radius. What is g near its sj,nfap ex*)o 5:e p6 4+s6po7 nksytewurface?   

  Two objects attract each other gravitationally with a f xx2k./kjsdyf+ mnnsof3. +8unl,t x) orce 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 gyzwdsmo.lhrgkhn6 2qq+f k95/i(ah ln-8, (o , the acceleration of gravity, at (a) 3200 m .s-k 26n/qiqf9,dg a8zknm5l((+hor loyhh w    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth mp oy. n4uv6faa1+wu 1where thegravit 1op1wa6au nmvy .+uf4ational 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 mas4: du,flr8new m /be3ps of our Sun packed into a sphere about 10 km in radius. Estimate the surface ,d/bw4ele frp8m3u n: gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like oury0 i z pe,bo2fp:pm)2ci-y;aweo8* rf 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 gravity on:0 p8 zayee2ci;iprf2wm )yo*,- o bpf this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in th ;q n9- p4fczao(e+cbpe space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating cb-oa ; pzf+(qep c49nthe acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are lo m 8p.j,yonhz4cated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravm,hno8.z 4 yjpitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years 2it5c hc0a g *kyilt.1e/d;fvmost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Ju.g2 iyc1 ;akchd v/0tl t*i5efpiter, 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 is 0.38 of whay rgp:222c mket it is on Earth, and that Mars’ radiuskmp2cyg 2:e2 r is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for th(m .s u*yfkw2ue period of the Earth and its distance from the Sun. [Note: Compare your answer to that uf 2 m(k*ywsu.obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about thdb( h:onoaz;vj r/c0;hx2l /ke Earth at a height of 3600 km c/ kohzj/o:h02;l(;xnd v abr.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit z x-i6tfu6n*y 650 km above the Earth. How fast must the s-n6i6zxfu* y thuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylitc 4zh2f0 x.fn,h wj8bndrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? An xjtb4hf0z2,.h8 f wcssume 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 Earth in a circ xbc)t/n +py6yular “neatyxc)y n/bp+6r-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched fr(lvc 44mn a/zs hwoe31)a kx0zom the top of Mt. Everest to be placed in 3m) k ha4zazxc0( le/wovn41sa circular orbit around the Earth?   

  During an Apollo lunar lan7)n qu :h2c;fni u-ov )wamwcbc,:.ndding mission, the command module continued to orbit the Moon at an altitude of about 100 ,7 w)odbnf2wcv:q;n-ncciau. m:u) hkm. 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 planal + dj/, -ade/tc9djget. The innecdt/ je ,dad/lj9-+ag r radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates onh 4dxxu.,0ndkl bk.tn +a7mx.ce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weigh.kx07.x nk.u+mx ,anl 4ddbtht to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center obw7uho mf z*m k955te-f the Earth'smuoz5fh 9- temb5w*k7 Moon in a space 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 sxk6g z2yv/*kptars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit aboy 6k/2pv*x gkzut a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for mly 1rs x2(fr;the weight of a 55-kg woman in an elevator tha2(rm1x ryfl;st 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 a cord suspended from the ceiling of an elevato 3wn(rynk9s (h3ln i-uz: n*mfr. The cord can withstand a tension of 220 N andsunr(kw *i :(hnyn3 z3f9 lnm- breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits v e3-yql ns3bxbgzc, :9ery near the surface of a planet with period T , the density (mass/volume) onbq -, 33ylbzs gx9ce:f 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 anu)7mv ,kg867 zxtnrcb d the period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very 7rcvmx6), 8z unbtg7knear the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lxpvz9hu 1+9a,ig q4 fnike the plf+np i4u 9ha1 q,zvgx9anets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average disd x7s7 np bpq;6ej5*wtc5j4fgtance 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. Itip,dp7z1b, 2xt/8 k:srklmt x comes very close to the surface of the Sun on its closest approackp1 / pdt,7kizx2l,bsx:rt8m h (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 farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center0ixv)m:*l dc0dz y4zn of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moons )u-vrs6 9-spo+pow68c cggksof Jupiter (those discovered by Galg89 )6 wgvrpopsu-6+ c-sso kcileo 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 f9e16n02cjgj3du+bm /r(at ixowu yz* rom the known period and distance of the Moon. i*t3ya/ezju+co1ur dn9 m6j( wx2g0b   $\times 10^{24}$

  Determine the mean distance from Jup2bb/p 8 mg+1zrm- rhmbiter for each of Jupiter’s moons, using Keplerzp+/b8 bm-rm1h2gr mb ’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars51)iw3q m-gq-)vryy iuj6zsrj ;;mco and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyed).q5i;)s;q yy io -v6c)mm zug-j3r jwr1
(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 q xy4im3 e(p.c"planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the m 4ce3.qyixp( inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanj *28l6o4fesjzc oj)d8ap +vnging 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 d aclpj*)f 6vo neo2j z8+sj84lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surfaceogt c)*y2d*,b*notf: qqn1j2xb5u yh will the acceleration of gravity be half what it is on the surface?co *bd*2hqqy txjg5b1)nyu*f2o,:tn    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin mu1qr s5 q;9xwin a mutual circle once every 2.5 s. If we assume their arms are each 0.809qu q1xr5s ;wm 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 apparen6xgj rat5ji0v++bc :v t acceleration of gravity at the equator is slightly less than it would be if the Earth gjr5vjt :06+icaxvb+ 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 Eil f5 0bqk50zox9h xe5arth to the Moon experience zero net force because the lfx0o b hi5q95kz05exEarth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass iobwvmi*9b7dq(m,q;w dfk2d ln yf/)/s 65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the e9q 7mln)kv fdi/(dw2 m,f ;b*/wd yqoblevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular t)bv:.e2v5cx6db-8 ah bks rj iube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to graiav) r5kxdj .8sb e-:26cbhbvvity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft inpc2h .cx3 d4oq 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 of a planet in terms of its radius r, the acce3t8r.6labn wu 1g ;sclleration 1lc. sngb6r lwta ;83udue to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertick32xgd n44avaal by an angxk 3na 244davgle $\theta$ 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 ofzmq16 it;*(u:vtardm5 dmp9 z If the coefficient of static friction is 0.30 (wmztat91dv (udqzm ;mi 5r*6:pet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at thln6n v 3)oi5yym.ory0 e equato6mv)yr30.nniyl oo5 y r were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain6li)mhcr-if9) y0k ws 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 atdm(blwltnhmu(fqk : .f 2l;+3 a constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angllbldmu2hm:.(f wf(lq3+tnk ;e of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. xp f 27vkqj.p1rx; fmv63vwe *Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter s72 1 .ewfxpvvq3 p*rfx;6mvjkince 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 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an9g4/ rwv/o yze extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light o9r/ywve / 4gzescapes). 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/n.qro q 2x8a(ida3ka;q. vg ;g4zbkwown 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 wo8x.d.oqk2 gv;qga3k4q w ;aa (rz/i nbuld 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 ,zaxn.n w,j. la group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth c.n.wz,jnx , laan be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), af9i)km*i9plib tkz(v n c .t4cr+76dkdter traveling 2.1 billion km, is meant to orbit the asteroid Eros at a heig4mzd()i9i nd7k+tpl6itcvb.k k*9 crht 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 satellite in 1s4xk(fja uya cpg8m/ ik)z4,need of repair. You are in a circular( 4)f y8ckjzxg s,u1ik4/maa p 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 hawna7i6qrm1) tkqx(r: s a period of 3000 years. (a) What is its mean distance from trn6w 1)(k ix7q:tmqrahe 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 pur-/zv 0mios lh (n2/to be if you could actually "feel" yourself gravitationally attracted to someonersnzh0 -ov ilm u/p(/2 near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of tht6*l4h 1zaeq1uf p5w5 xb vf1fe Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 lfp uh16f145 zw5f*ate lxv1bq ight-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 l7bg ib jo4z9q+( rje-corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitationag 4r ie-7+ oj(qjzbl9bl force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kywn ,j z-i ni a,s0krtp941+tgg 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 sec2pzb3n-g9 qm 0ilqb*jd sg 3xip 8x6y)ond hand on your *q2miz0ls 8yiqjx) dpp-3 bx63 ngbg9wrist watch?    $\times 10^{-4}$

  While fishing, you gq2u 3mj (k(aafet bored and start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes u(jq23( aa mkfa 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 radius R in a new9z +w 0g gj7uf;,wbi.r(g:z yrng*i yr highway is designed so that a car traveling at speed y0r:rb, 7.i zyngrg(9z; f+w g jw*giu$ 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, utiliz7vfrkfxy* ,vmyy+ x7 1es tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train px r,y1vf v myxf7*+7kyassenger 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.$\approx$    $\times 10^2$