Sometimes people say that water is removed from clothes in a spin dryer by zyeg, b 59x/7z i uvk0jke(8kmtk:3ev centrifugal force throwing the water outward. What kekzy0m9ze vk8jt (e /3,kvxgb 7:i5uis wrong with this statement?

Will the acceleration of a cam;l hy5vkbw4bv8/) kf7cz x*fr be the same when the car travels around a sharp curve at a constant 60 km/h as when kv k 75f8wyhbz lm4b;x/ *v)cfit travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly roadq*n7-j(x n fu vrnb-oth s;4t;. Where does the car exert the greatest and least forces on the road: (aqn--*j;hst; uxtvf r (bnno74 ) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child ridiw pjxczo)*5g) ng a horse on a merry-go-round. Whic)zc jp)xg5*w oh of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the wal de4t 4ldiw8wob*6: yj 1q2zpter spilling out, even at the top of the circle when the bucket is upside down. Explajp*d6dbw2eq: t l148y lzoi4win.

How many “accelerators” do yog1-kay 4y3sre 54sxwxu have in your car? There are at least three controlsx gy135xsraeyksw 4-4 in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comesda;;ux v,5d m nfl7gp:zp 7m0v flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sl7 vz 07;d5mm:dxvfnpg ,apu; led 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 bhbc,h4l6sb5 speed?

Why do airplanes bank when they turn? How would x- )yuc o ks./w9trsjuj: nh+.you compute the banking angle given its speed and radwh tr:ouuk- jsnx/)y 9.jcs.+ius of the turn?

A girl is whirling a ball on a string around 4a/xgmx djff :8u5z 6p n02zyuher 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 of4mx5 f/zux8pz0yn fu:6adj2g the string?

Does an apple exert a gravitational (zczy 7 .cww j)yd-v;gforce on the Earth? If so, how large a force? Consider an ap zj- czgcy v7(;ww)y.dple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the M3 g(hy k sbp/kfy rzrob+ c2oh9oi/9),oon’s orbit be differ9grf) kk ,ho oh(+obpyirs 9 z/3y2cb/ent?

Which pulls harder gravitationally, the Earth on the Moon, or the Mw)fp1 a n7.xl1+bbtnt n39k b03truiboon on the Earth? Which accelerates mb3031+ 9 .tuwfa pktx1nl7nibrt b)nb ore?

The Sun's gravitational pull on the Earth is much larger than the Moon's9gx01i bk b m5bydb+-z. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differenm xbg+y-bi d bkb19z50ce 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 effe8foyf6 cn 76jj84k knicts are at work? Do they oppckof768 fniky6 n4j8 jose each other?

The gravitational force on the Moon due to the Earth is only np2d.lf2 5n/tpm7wugabout half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from tg2/ ut5wmpp2f 7ndn l.he Earth?

Is the centripetal acceleration of Mars in6,xu.x px7 ms ymmgs p8oz0/5d its orbit around the Sun larger or smaller than the centripetal acceleration of the Eary.umx/sm5x, do6psg p80 z7m xth?

Would it require lesau qim3t5whr5s .s k)k;x(xx8 s speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth) sh5.w5(ak3 k8i mtxxxqsr u;’s rotation direction.

When will your apparent weight be the greatest, as measuredid;vw m4h+jg 4 by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves h ;+dm g4wjvi4upward 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 lo 7gogk u9byf8dzl*8 8(l6i xaep;ml5ung periods in 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 walkingy(m uexaldig ; uk5z8op*fl 96lgb887 on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” behbfp/ l1pq+a7r-e;yr i fv :5ioe (l-ctween steps.vch75:i e+ob ;-1(pl-qia fr/ fper yl

The Earth moves faster in its orbit m3-zd*k fr:dtaround the Sun in January than in July. 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 Earrd: mkfd3z*t- th’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to havd rt w5ca*3rz.b )dxu. 09vflde a moon. Explain how this discovea.ft rcvzd*3rld ub w09.)5dx ry enabled an estimate of Pluto’s mass.

  The Sun's gravitationaa91pf:,a egral pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from p1: agaa fe9,rthe center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980 do .o/(lz 2 z1kp:rwua,8z0rpzt7b5( pxjjuy $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 the Sakwv ta*c*8d 8uwt+ + b1roh+eun, and the net force exerte8+rtwcwao *ae+tkv1 * bhu8+dd on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted f p+qnj+xk0, gon a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.gfp+n+k 0q ,xj   

  Suppose the space shuttle i3 jhrvpbs g4/;p*i7vcf-c5mds in orbit 400 km from the Earth's surface, and circles the Ear*ppr ;h 54mci3- 7dgfc bjv/vsth about 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 acceleration of a speck of s( b,a8 v ou7/ )lucryth98qtvclay on the edge of a potter’s wheel turning au8s8vq,ubr(vyc9/7tl oh) t 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 akt 9/tgz2me+k uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spe 9z/e+t2mktgked 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 rounryg0ls .s+d r.d a turn of radius 77 m0r g d+rsy.l.s on a flat road if the coefficient of static friction 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 bde8iz6opfo /(efd e w5x/ qx/)e between the tires and the road if a car is to round a level curve of radius 85 m at a speexo/(ox6i 5e ef8dwzq/pf /d)ed of 95km/h ?   

  A device for training astronauts and jet fight9o jfhmacg (1p*v*zi( er pilots is designed to rotate a trainee in a horizontam(1pv a(hf jzo**i9 gcl 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 rotatiuf4kerkka9p(u 8jk26ng turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntab6k 8fp9kkje( k a2ru4ule until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coa6/oi4uaay9 crster be traveling when upside down at the topur /a49ai 6oyc 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 ((sqngiuerk3 bsp0 .hg*o247z including the driver) crosses the rounded top of a hill (radiu74*sqp( 3 s k2r0oh.bgi genuzs =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-dia4,oil 5 cap ge*ry --mwa+on5fmeter Ferris wheel need to make for the passenfagi-pe5rwcy * mo5a+ -lo,4 ngers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radrh rd ;9tbiu0s7p0:nkius 1.10 m. At the lowest point of its motion the tetn07 ;:iur hks9brdp0nsion in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a par-y0xuav0n aa6 +tcic*ticle 9.00 cm from the axis of rotation is to exa*u itn6-av 0ca+x0ycperience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are ro( f1kzkp 7 e bwbu2j9o5i:fss3tated in a cylindrically walled "r1 w5 okz:9(2j7kpeb bs fiufs3oom." (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 rotf:na(04 of(c;zi7x ghj hwk u.ated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a .f0hwcuj ( gn(i4hz;:ox fak7 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 q+c v/v+azlq 9weight of the ball which revolves ov +vqa+ /lzc9qn 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 radijvi )2lq5m-y-;qc.fr4*yucq;ylpib 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 masses f6f:eqz- 4xn wx,;ycq $ 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 vertical*vp,z8qek e8j ly at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal componea/ 3;vk8knalx 1k v3nvnts of the net force exerted on the car (by the ground) in E8 vv3n3v;/anaxk1 k klxample 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit ao vd2xior68 q)l:/,iwzh5ua jrea, 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 2)h/,vod i lowqzx au5:8ir6j with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular inhk pnke +0t*u/+5.exiq3e tke stant, its acc0eh* et+/en 5ek k.uki3 tqxp+eleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a udh/ twvj ;lh oez,8s3uf78k*spacecraft 12,800 km (2 Earth radii) abdw3,;kesuhofu8l8h /7v *tjz ove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain pla b(ib ijb ltc9.:k4x7f8yk,axnet, the gravitational acceleration g has a magnitude otjb fa:( ylk,4 .xb kc78iib9xf 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 rbo-9 sjiej w il0f3.wm:at sc. g3n)/the Moon. The Moon's radius is 1.79. isgib:c0t frw3am -. 3jwo/j lse)n4 $\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 t5ax8(;ibq oo:) srrpvx, :fwnhe same mass.;r :inoxb 5 s),a:qpwfvxor8( What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same raorntk,9p1lh rsq d) rl qdkd(68 1j1g-dius. What is g near its sshk rp) r6-k1,jdqt1( ld nrlq89ogd1urface?   

  Two objects attract each othxsbm ,;k jo;t/er 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 q(vve;x)pa.w93 g(vw v6 cu6pu(si w vacceleration of gravity, at (a) 3200 m( qv w ipswc9p;.xgu3v v)a6uve((v6w    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’g6 or0:, os nnl69ayzb.v*yfa s center to a point outside the Earth where thegravitation.y az :r*oalsngy0 6,bo96v fnal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star hjm2l ;zw 72yxzuj55oc as five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate tj lx2mz5c2z7o;uyw 5 jhe surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star,;iunjs- qgt4 2 which once was an average star like our Sun but is now in the last;ijqu - tnsg24 stage of its evolution, 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 feelkfxc.u7g.e z9gs oj-- 2hj2as weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up f2u-k-9sejg s g .7hco2.axjzthere. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located x 1*bp 3ow9 vhj n(w. n7p.k:cgoh;gv (ruysi3at the corners of a square of side 0.60 m. Calculate the magnitude and direction pc.v(soj hb3krw gi;o w7:hn. 9n(31ygu*vxp of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line 8bj iofj8;f8u0i ektqt -ol.,up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four plqio ,effjti-0 k.l8ju8b ;8t oanets 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 oq7twmz3 th:dt;9xhs 4(ui c5df Mars is 0.38 of what it is on Earth, anut:dtqh d t;7sh59 cm 4z(3wxid that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using thwy)fll2/cd*cei1 /mcc 1gn d,e known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s l* l/ lg d dyi1cwcme)c/,fc1n2aws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satelildy 3;k,uw0cb r01 ,vvsfzy/ lite moving in a stable circular orbit about the Earth at a height of 3600 km. , 13,/v zl isrycdkb0 vy;fwu0   $\times 10^3$

  The space shuttle releases a satl8h3ss,vbhu , otc t 2j9n9/keellite into a circular orbit 650 km above the Earth, jh9lhuvebnt3s9, ckot2s/8 . How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship 5m158b u:e t oh5o0 c (ununwlns1d+wqrotate 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 Question 21, Fig 5–3estbo 5n+u8 1dl oncuwhqm15(:5 nu0 w2.)   

  Determine the time it ap :ps-)ud l5kdg69oftakes for a satellite 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 is very small compared to the radius of the Earth. Does your result depend oa )f5gdlk6opp9-s:d un the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launche s:htb7,tpj b;5qf5p dd from the top of Mt. Everest to be placed in a circular orbit around the Earthp7 s ,:5bpb ftqht;d5j?   

  During an Apollo lunarzq sqq kx( (4k:k,/ozw landing mission, the command module continued to orbit the Moon at an altitud:(/oqk q,wx4zkzs (qke 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 thelz ejs . 6lz0t7v 4ge:nqf9/:8ghg.z vqo;uwl planet. The inner radius of t: 9/.6gg lzoslne:glhv tq4f78z jve .;zq wu0he 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(. d7lajd 9jv32jvnft in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent (va.3dj jvfj92tdn7l weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75ko*tmlah .27 t-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant vek27 htlato* .mlocity,     ----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 otnpkh)8l;o3 stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orb38ht; l)nokopit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for t4u. ut zkn xdhybsc;vr*(.29ohe weight of a 55-kg woman in an elevator that94 (cdsob* v ;.rxu. t2zhkyun 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 elevator. ftmmle-2 ev.8 fah0jfqs(/ 5nThe cord can withstand a tension of 220 N and breeamv/sm tjffe. q85(2nlf0- haks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planykj* 0v4jz9yu1m g g)iet with period T , the density (mass/volume) 9kzg i 40 ygjymj1*uv)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 of the Moon (27.4 d) to determine noj* ks7d4a2a the period of an artificial satellite orbiting very near the Earth’s surfn2k4 a*a osjd7ace.    s

  The asteroid Icarus, though only a few hundred meters across, o-0g6ds hl.xh pm6 xjc-rbits the Sun like the planets. Its period is 410 d. What is its mean dmc6 0 h6-gxshlx-.p jdistance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of r 3tmpvs7t;2hko+j/sg g+ lq6 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 on++)wuardx7s n*:j to3 -v3v2y e qovdrce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s ortov* )7 2nvsvyeq drj-u3:dr++ax3 wo bit 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 cqsbdwo+ epo(+2l4my .w w:n-fenter 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 d2muu;n( ) uwzmean distance for the four largest moons of Jupiter (those discov(2uuwuz dn; )mered 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 Eart;r8vneajs8st:9r / 78 zbnrjch from the known period and distance of the Moon. jj8nan8sr:; 8tz/ b7c sevrr9   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiterd: ,c 4mucnwfqp) u54gj ,kzn*’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Comp np f:qj ,uz 5*kn)4mucc4g,dware to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (whic (yj,jlpt1 ,3uetzu t0h some sp y13tje,l ( ut0uz,tjpace scientists think came from a 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 ofdnv/: nb82ykpa e;x/x a band completely encircling a su/de8y/2 v n knx:ap;bxn (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the 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 swi*4vr07fnrm bvcp, mjx.pd 3dom u5-t)nging 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 jcupt.m-mvp 04mrrd)ndfx5*,v bo 73speed 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 will the acc 1)yiu5bie0i,q 0/pp jsdyg2yeleration of gravity be half what it is on0sei 2)5 pg0pud, 1/qb iyyjyi the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in2q tar*z vb* x+pr3m: qb2*afp 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 pulling on one anoth2*3 *pfbbap:*rr2x qma tq+v zer?    $\times 10^2$

  Because the Earth rotates once per day, the apparent ac/ 6txi 8aymd;0e 7fxqdmc2ks.celeration of gravity at the equator is slightly e; k7.xiaq6tdmsdc/fy 208xmless than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth wqm0wa; 2n 4w,k0(-sxad nhac till a spacecraft traveling directly from the Earth to the Mo(ax-a 4ntdasn0 qh20kwc ,;mwon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an eler(4r, c(m ooujvator, it says your mass is 82 kg. What is the acceleration of th( mro (ucro,4je elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stationpcpegr m:15+6w x-0w 8ylfjp d consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diametpcw jr-x1e:l p6f gmyw8 p5+d0er of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–rrq eesu+0qtx -/1 /zr43).
(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 plancm7+d/; ezickoc )zi6 et in terms of its radius r, the acceleratizi 7+k; icdcm e/z6)ocon due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from thezwqm.yu (4yu7 vertical by anzu.4w y7uym (q angle $\theta$ 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 5 q9wgft1w(vhhjh- 6 .zuyllrr66un)of If the coefficient of static friction is 0.30 (wet pavement), at what range)fur6h n66t hyv-9wz wjqlgr5.h(1u l of speeds can a car safely handle the curve?

  How long would a day be if the Earth 3m 7vg,ax4, ;)zqdxv ntf zkj:as,4o uwere rotating so fast that objects at the equator wg3n,,q; xo4jsm a:d 4tv 7uf)axv,zzkere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant;; cv2 :uf:qovg 0knsm distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 8*o6e s9tc9 g6 s5eppvon,df vc 3h*yqm. A lamp suspended from the ceiling swings out qtph e e6s,scdp6o99*5vg co*yvn83fto an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as thm*z -,v h6bvggr zyvch/)2 7;gcsf,q sp,e.u pe 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 6m/pcr2*q hu-gv;b cvz ,.g 7gy,esfp)vhs z, '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 Hfrv;n3oj +k4o:- q ar7vq5 +ur ;jkyozubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (fr;rvnk -f; q +vorzo+45:joa7q yukj r3om 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 valleyw(2mza7 /vnfq -avhb 7o2eso7 shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and ov7wn 7/- vaz2e b2hm(sf7aoqC 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 o 8.gym7m tq-gof 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determinedmqtg7g.y o8m- 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 d7hdlbjh1 v8) (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km7l)vjh 1b8dhd . 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 need ocdl odbxl 2e(*g;+zk8f repair. You ar2g; olcxbz8+ d*(dekl e in a 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 ku+ l)hhawvf8)j wzynx45 06 f;xamg;is its mean distance from the Sun?;lun0z8mx v)fjk6+) w ;xa45yh fawgh   
(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 l:u r3v+t6pvv you could actually "feel" yourself gravitationally attracted to somru: vl+t3v6vpeone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way ; .os7 e wfp,-mpvn3pxGalaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center m3vp-.f, p7w xs e;pno$ \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 j3pq0 qp9-vjxthe corners of a square 0.50 m on each side. Find the magnitude and direction of the pqjqvj90 x- p3gravitational 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 kg orbits thecge 9g- 29t djr4ht,*9m sgrdc 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 1y(o n1lfv s2t7.5-cm-long sweep second hand on your wrist watch?ol7y12(t nsfv    $\times 10^{-4}$

  While fishing, you get bored and start to oe,s:4:dx . fnjy:hfln ul)i0 swing a sinker weight around in a circle below you on a.xln:f 0yu:fdl ni)j :4seoh, 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car um b. sk/: i:0zn/ulz:+vyuprtraveling :rum n0l.p:/kvsi + uz/uzby: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 th)y87 asnczk kl8 u68s7j0xl zre 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 passkz rz78sa86c8 nljky)xs0 lu7enger 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.$\approx$    $\times 10^2$