Sometimes people say that water is removed from clothes in a spin d1q ze6ev0vm1(m p bw3qryer by centrifugal force throwing the water outward. What is wrong with this stateme0q31 v(e1q mepmz6vbwnt?

Will the acceleration of a car be the sd8a8ap 0c req6y dz9)same when the car travels around a sharp curve at a constant 60 km/h asrqsc098 dapdz a y)68e when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at const myip9*w0 sxns/wu, +vant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near ths, p/syu 0+vin *wmxw9e bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round. Wezko;0lv)g p; pt+v8eb*l3e pd*;s 7.i vseky hich of these forces provides the centridseee8i +.p ko;*p;3tv lbp*s ;g0yk e v)vz7lpetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without t8 6eyz5bpae (ehe water spilling out, even at the top of the circle when the bucket is upside down. Explaizb 568epyea(en.

How many “accelerators” do you have z3ktc9*k 8jozjb( h cr;0kq.yin your car? There are at least three controls in the car which can be used to cause the car to accelerate. Wy0.83rz;*kok jbj9h( qt zckchat are they? What accelerations do they produce?

A child on a sled comes fly v *fgp: w0*ymtfi:n7oing over the crest of a small hill, as shown in Fig. 5–31. H : 0g foywm*i7tn*fv:pis sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders leanp g1by9:ds+xe inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would yo6 hn0p)j9wnt fv6:xuou compute the banking angle given its speed an nn6uj 6w90tvf)hx po:d radius of the turn?

A girl is whirling a1q*7cm1,ieta xe qho5 ball on a string around her head in a horizontal plane. She wants to let go at precisoq emha75teic* x q11,ely 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 ls79o).bx7(oaj3gf +gwwxhrw qg x (9karge a force? Consid)(f9xw7 gxo xawgshgobjr9+ w( 7.3kq er an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is,j6sjl8 k lcs ;9ua5et8o,s i*r in what ways would the Moon’s orbit be different? 5sjsit;8lucr jk 9,o l*ae6s8

Which pulls harder gravitationally, the Earth on the Moon, or te/1+,3v viw0) zxb c-b/5qakqs gdimwhe Moon on the Earth? Which acceleraw0bzqd5/ qwxei+,3i)bv m- akv1 /cgs tes more?

The Sun's gravitational pull on the Earth is much7t2+sp6 wzjg+.r osnohb0g 9f 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 Earth7norzg9 b+2oj 6pw s 0+stfhg. to the other.]

Will an object weigh more at the equator or at the pol n u*v 7qxffg).z vq;5l4ro4mves? What two effects are atqf4z)v r4 .mu7vn5;gvolq fx* work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only abopw m/kq *o5doyj *m9g1w (ue3vut half the force on the Moon due to the Sun. Why is13ou**py9 qmg5kmow/(wdjve n’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sunycz 4j 6- d/l4x9jw +sujofinbcj76m) larger or smaller than the centripetal acceleration of the Earc zjmb-6yx c9l4f isj)w6j +on 4dj7/uth?

Would it require less speed to launch a s7cm l yvshy/1ipy g;68atellite (a) toward the east or (b) toward the west? Consider the Evc8;s1ymh/lg 6pyyi7 arth’s rotation direction.

When will your apparen g r/k0araxs71 1yp)pnt weight be the greatest, as measured by a scale in a moving elevator: when ther7 ng0kpxa 1sp1)ayr/ elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periodvhd6ddxbz lfu 8, -r.7s 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 walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think zvd-hdf6r 7b8. ,ux dlof.

Explain how a runner experiences “free fall” or “apparent weightlessness” beq5bgy p61xk6 p m)l-pytween steps.lymbppg 6)p1q6-xk5 y

The Earth moves faster in its orbit around the Sun in Januatew)-r8dvze z jf70ba7 ug9r9ry than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a erj8ed-zt9z waf v70) rg7bu9factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moogn7h9 ta*yfyb 0 4qq2pn. Explain how this discovery enabled an estimate of P04y* 2t9qaq gpn7yhfbluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's h).r7aggt(* cxv bh4t. Yet thcv gr)tah7bth*g (4.xe 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 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 ragmj wtynn9;/9vms8es-7 5j $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 aroz1 20r1rv lfb4o )k(lyny4shhund the Sun, and the net force exerted on the Earth. What exerts this force on the Earthl21n0f1v 4h hrybyz lok( 4rs)? 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 rotates unifoy(p5+q 8qj5v3y bjyts rmly in a horizontal circle (at arm’3q58p(jy5yt qjy bs+ vs length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth'dr 9: jco*tzx.ac.2 eus surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration ex*.dcct a.j2z9u o:r 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 h8mb7u 3w(4mbj-d5tn5 svzk o the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if mn55zk7md 3jos-wh8 bt4vbu (the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical cowow o866dz:yxmi)1 wircle of radius 72.0 cm , as shown in Fig. 5-33. If its speed iso)m w6w1ixowdz8o6y: 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 rx 5 g6bdjvud96o 6h8qn nai1u+adius 77 m on a flat road if the coefficient of static friction between tires and roadd1 6+a 9io8uugv56bhqn6jd nx is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires6u:gbbh c b;3w and the road if a car is to round a level curve of rahb3w:b 6;gbc udius 85 m at a speed of 95km/h ?   

  A device for training astronauts an.zkpga18lrrgs3d+o plm0g0 .d jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the .l3ks. r1ozrgg 0gm8+0alpdp 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 variable speedm1y ej,r o3bw18 +vtp;xibk)b. 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 co +v11j8 yt 3biebbkp)rwx,om;in and the turntable?   

  At what minimum speed must a roller cv wp oetmz12u)h2ex1 61v lyj)oaster be traveling when upside down at the top of a cuwxy) m22 6)e1 vpo tv11jelhzircle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded toz(9ge ;xo2 oxcp of a hill (radiusocx(zoe2 ;x9g =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-diam./7kssnb( r nx,oo2aaqhsq2 5 eter Ferris wheel need to make for the passengers to f2rx ss7nko/(ba2n.qa,osh 5qeel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At l(h0vv vyz vw7jqqbl,+2 e +6xthe lowest point of its motiov+bv yh+v,lvxw0zqlq(6e j27n the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a pa yu*pjo*9cvftlk+q j2 m l1k1:rticle 9.00 cm from the axis of rotati9mj1lyq+jopf tl2*u: ckk 1v*on is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peo7 m:6, gupeumsbs:c h0ple are rotated in a cylindrically walled "rm6useug 7 ,:msb0hcp: oom." (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 jj)c1 3 8q 8t;zy2tioai-i7q9 smdigvkm1bd 3 ) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light c; 73d1 88 t9kbjijcymta3vq m2g1do)-iqsiziord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely ;p4s6cyinv/i2qgz a,(ru -abthis time, by not ignoring the weight of the ball which revolves on a string 0.6qu (p2-gci abz;4 i,vasryn/600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfect df w,yz63.du:2wu riuly 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 masse j2y)(be+n eb-txpr0zs $ 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 maneuve:+feypb4.y fl d4kep:r 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 centripetad)myqwx hz2o/u 5.j)jl components of the net force exerted on tdjw zo jx5)uy )/.2qmhhe car (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly b7h;38ryynha:qufkt2 hs29 bfrom 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 half7bu 3t2h9y: h8ysrfbq2nh ;kaway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal cirzg7xtx,f4 w .ewy,v3ehdx6y48x + ehlcle of radius 2.90 m . At a particular instant, its acceleration i 7 l8zx,, 6dwehx.tfgyyhew4+xe34vx s 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 spacecra9 nei +*i9ald5w7pow / e,t;zod nule4ft 12,800 km (2 Earth radii) ,* ud 4o/lpla7w9;w 9nieze 5tei+odnabove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certa4 fmz; 4(x v5(mwbqoaxin planet, the gravitational acceleration g has a magnitude of 14f(5b4;za x oqmxwv(m 2 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's ra hp-ws.uc. bo3dius is 1.74hw-sbou .3c .p $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planetv72rip7 4r tni has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surfatrvii4p n7 7r2ce?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same rad,+ ia 0wuf;,q luc+rsyius. What is g neariu;+fua+0 ,rlqy,s cw its surface?   

  Two objects attract each ot4:k ax q-t f/6josrq;rher gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravipqi,o 4c:m604yo -pd .ewrlltty, at (a) 3200 m -dwp e6l oq4 m0p,ry.ltoc:4i   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from thee.v2r mc(gnj 3)k bum ;ulwvs(-i.f-e Earth’s center to a point outside the Earth where thegravitational acceleration due to the w.n( mvu;23vsfcke-e.()ir m l gb-ujEarth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has f w( wzw;qnz37r-1u:tgc lm k-hive times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the s7twz3n kq-lgm-;: c (r uwzwh1urface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, ;um lahf8 5dr+which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surfaa 5ulr+hf d8;mce gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space s7.0 zcz;*.3ggi s*y zo erpwpghuttle. 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 the acceleration of gravity 250 km above the Earth’s surface in te73owey r*; p g spgzz.zg0ic.*rms of g.   

  Four 9.5-kg spheres spp85z7:q oknib kv()nd6 z0ware located at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the otn)dwv :zzs(k 5p7k6oqinpb 08her three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the pla3mnwx0p5 g t1qnets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses arm5wqg 01xtp 3ne $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 su3tasstt:3d,rl dnz2 .rface of Mars is 0.38 of what ittzd t:3s .tard,n sl32 is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass ofup /0d, bm(.lcrh6cf v the Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained usingl br0 .(phcvfmuc 6,/d Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit odk*4k mxcu42 g0szw, s4e-ngabout the Earth4m2gs-*ekdzo, uk4g cxnw 4s0 at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orvwqv jcg)9 s;yonzt,+j( 8 slh*u16prbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) whens(u6,)jno;q*p9vy vw rlhs1 +j cztg8 the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experiel7vv :gpw-,wvc1qc t *nce 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,-vw1pcg qlwv7*:vc t, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “n*w9hqh;lo2q:;(cju qhuq g. gear-Earth” orbit. A “ .*gqcul ;gw2qhuoqhj9q:h (;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 satellit. b7b3arq1.nab 0xddhe have to be launched from the top of Mt. Everest to be placed in a circular orbit around ther hdbdab n 7bq0.13ax. Earth?   

  During an Apollo lunar landing mission, the com j 7w+b,af8nrtmand module continued to orbit the Moon at an altitude of about rnj+twf7a ,b8100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that: wpmnls37xl. lq hk)7 orbit the planet. The inner radius of the rings is 73 s3k:7. 7lnhll pmxw)q,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 o/fl 1l- wrzfvcm* ,2rmht(,tonce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, a 1lh/-zl2cov tm*fr,t(rw fm,nd (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astrk/qalge(; ca12tj.zs onaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velsaz(k j l.ag /t2c1;qeocity,     ----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 saef 2 0c.;pb)n/vjipzp -nm+rystem consists of two stars of equal mass. They are observed to be separat/)znjpr f .ie -apmc02pv;n+bed by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in 0bu9eqca*vg n7ny4t6b j(h3g an elevator tha( 34*9v7 0egybq6hangbntjcut 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 ceilgcfd4x ld*jvc5 7-pq6ing of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? aclf5 7c4p *xv qd6gj-d =   

Show that if a satelgae,hs5;o mm4 lite orbits very near the surface of a planet with period T , the 4;ag 5,esomhmdensity (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of 2b4 ;wj-tqvh pthe Moon (27.4 d) to determine the period of an artificijt p4bw hvq2;-al satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits tht8u a;e9ic 5y9,etlnye Sun like the planets. Its period is 410 d. What;n,cu58 yay9et i 9elt is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of+t:vs oz hx;g zwe:x4. 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 ever8 tfom-1lla)cmk++wef kw82 iy 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 orbit is nearest when it is+ffm+2 81ltkeao - lk)w 8mciw out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gala3qqoue-a4umvf0g3 r4f0 p dj+xy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 moonse) b1c7s mn1c*x7quag of Jupiter (those discovered by Galileo in 16xung)cq1a17 bem 7c*s09).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period an9wfvltbi .ve**2yz7 cd distance of the Moon. *92wcfbeit vlz . *y7v   $\times 10^{24}$

  Determine the mean distv*vpz, h- xowoe:-)n tance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the p,v nph)ve:xozo -- w*teriods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragfdb( z /c7sy ( mwu+*hv2;gvcfments (which some space scientists think cayc+u( fvdcw*hv fbg 7(ms;z 2/me 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 aq,iet n)md2*c rtificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our owntecnd* qi, 2m), 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 oubyx)yi---agsf (n1from 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 speedx)(a1fno y- bi ug-ys- 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 y*ev *1(wnx.r x6mbh nthe acceleration of gravity be half what it is on the surface? nv *xmwb nx hr1.6(*ey   $\times 10^6$

  On an ice rink, two skaters of equinkl;pbpg (,*al mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how ha( bglpn kp,i*;rd are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleratio9g 2y.k)d sdq0nu n*bqn of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. W bq.n *d9uk)ngdsqy20hat fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling djjl9s f.: 0wn ppif+9jirectly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opp9nw:+jijslf 0pfpj 9. osite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you)tnf-u5 at20i fsav i+ stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in w avfu0+f nt )-25isitahich direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube tha mt7:gbyxoe;j)e lng -:z*: dat will rotate about its center (like a tubular)ge n l-e;d*o :ygzbmt:j7:xa 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 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.6 om xi:yyh4m3 s8r5ir 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 7 aq(ji.m*v r)dyli( 3boy.lsa planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational q.yid)s3l. v rml (by jai(7*oconstant G.

A plumb bob (a mass m 7acm8- j)wt fih lfi 79wg-a3nhanging on a string) is deflected from the vertical by an angli7w- j7tgfm8fw -hi9c3l a)na e $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient of s-/rugqx5bh)0(2,2c1ado k:aky ubk b7 c kv jktatic friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the cgdkr2 ax7khb) k ucyb2c: /oj0u-5bk q,(avk1 urve?

  How long would a day be if the Earth we5*rmn4 dekz1m re rotating so fast that objects at the equator we45ndmr1k e* zmre apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain ae)o7kjwtah8p)z z.l3 1;:zh 6vvzhil constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A ll ) bn(c+6u d:dolvrb1amp suspended from the ceiling swings out1 b6o (n:bl+dvc)urld to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mas 7 eo-9iy6abmp4z;ze.s q(bqzsive 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 dat(;7qzo6qs z ip b9yee4.zbm- aa 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 presen8w7uqy4+kxx05 zaw 1z;nb ugw ce of an extremely massive core in the distant galaxy M87, so dense that it could +1uwawznx4bzwu; g80k5q x7y 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 vxo o r/ ovob()p.as 8a5td t;2)zip)nyalley 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 C compare? (Which is largest? Smallest?) Explain. (b) Where would the drivyxsoozrtb 82);d aopp)a) t/i5 .(onver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Sy qnqp;xmnn lc+5kq( xg1wb4 4+stem (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 + nm4xbq cn1q+45wn(l;p kxgqan 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 Rendsmmx8o:qn *4 a5 . kbhkc(u;efezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is 5 xkmm4ne s. 8*;bfch(q:akuoroughly 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 pursuim uc zy/d0ws7*ng a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 27z*mws/ycu 0d 5 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 is its mean distance f1 ypv6s: dhts*ro1t*sp6 : hydsvm the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need toruu.y1fh1j gy (+qcsmt4 (v0p be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptihpy11fcvg qru (ju 04tm.s+y (ons, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a disa;v6tl i/wse3 tance of about ia3 v/st6w le;30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50./z1qi ym*r 2i5a mccv m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the botiqym/ma irc 15c.z*2vtom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5 riba*y:vqrr1;)jq+,hik8fz 500 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-l54a o ;dgmqt1z 6vmmq1ong sweep second handv1t4 ;mqzm6o mdqa 5g1 on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a cn(zxigfj 0nv68 ,d 8wmircle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that dwf6g0m8ixnnj,v z ( 8the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway 94yvy:juw f mz4d6a( uis designed so that a car traveling at sdwz:9 4yau 6y vju4m(fpeed $ 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 t )xw+3gw5ca vnrain, the Acela, utilizes 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 spa+5 3v)nww xcgeed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$