Sometimes people say that water is removed from clothes in a spi(mk4 .tzomk6( bfa/wi.vw z8en dryer by centrifugal force throwing the wa.z w/k(w( em bifat 48.kovm6zter outward. What is wrong with this statement?

Will the acceleration of a car be the sam*uu lkb+bf)2qf+ l)*0 qvlj ufpf;f4 de when the car travels around a sharp curve at a constant 60 km/h as when it travels aro*u) f4qu;bfql +0*)plfl fv fjdub+2kund a gentle curve at the same speed? Explain.

Suppose a car moves at constant sozpjre;7es d(3q2y, p peed 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) a(dye7p 2o q,j psr3ez;t a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-r, g,zu02 npb;tmhl,9hns m5v zound. Which of these forces provides the centripetal acceleratio,zsn,;9 pl n,5mhuv2gzt0b hmn of the child?

A bucket of water caii-f(;l.n ;lt8ypvf7; uunq zjs) . kjn be whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is.vil( i yf s;jpu)tk8n;.;qzj-f u7nl upside down. Explain.

How many “accelerators” do you have in your cacq vb0k- t/q/uyw +*dmr? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerat wc 0+m*u/qqvdtby/k- ions do they produce?

A child on a sled comes flying over the crest of a small hill, as shown ipg +tk wjog a,o-:jk/6n Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he fee,gpat+ /o 6g :kjjowk-ls 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 sp2s;84 l1s suo.c(tyfbi:u ldw eed?

Why do airplanes bank when trdez+ho83 0j hkm- w1zel*d)whey turn? How would you compute the banking angle given its speed ek3wz0w ol-jhdm1)e 8* z+rhd and radius of the turn?

A girl is whirling a ball on a string around her head in a horvr pye 94d ,vowo63m+rizontal 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 svwpmo roed63 v,4+ yr9hould she let go of the string?

Does an apple exert a gravitr,vt hit .0ma.ational force on the Earth? If so, how large a force? Consider an apple t0hr.mia., vt
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways woun+nhup+ 0m lt4ld the Moon’s orbit be differe+ pu lnt4mh+0nnt?

Which pulls harder gravitationally, the Earth on the Moon7f(/kgk wjl ikur;j1-t7ri ;hd0ff q4, or the Moon on the Earth? Which accelerates 4rq; 7wk kfr gih-utf 1;j dk7j0f(/limore?

The Sun's gravitational pull on the Earth is much larger than the4 ianel1p.:z.x ns7 d c6zb lp1pq7hi0 Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider 76 .0 pqcnbezx4za:1ilp . 1dpns7hil the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equata,(udoy8 fl 4wor or at the poles? What two effects are at work? Do they oppose eau(awo84 f,dlych other?

The gravitational force on the Moon due to the Earth is only about ho255z s5k 6ean/8o1gyecwpb galf the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the cekpo5 ywe/ 5 sgoagb182n6z5Earth?

Is the centripetal acceleration of Mars in its orbit:cc )qf2uf* vav1; l .iffat*c,xyn :c around the Sun larger or smaller than the centripetal acceleration clxuc* f,acafv q2y)n*::cf1t ;f i.vof the Earth?

Would it require less speed to launch dq j :0 regd92(4nrr oxd2y8nya satellite (a) toward the east or (b) toward the west? Consided(qryy nj:r xre2dg9d84n0o2 r the Earth’s rotation direction.

When will your apparen5bhmoe*7g3c1b6d 2fgmk tv h*t weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free 7t g*m vg36hdb 2of*5m 1bekchfall, (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 lvq; kdyo3*7ahb0 wmi:ong 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 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 ca*yqk0hbvia 73dmo:w ;n think of.

Explain how a runner experiences “free fall” or “apparent wei y*hh0gp57i8puk p5 k10uyuglghtlessness” between steps50u0uppyk 7lhk u5yhg * i18pg.

The Earth moves faster in +l7r sdtm qtj3b,o9- jits orbit around 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 Eartj,-btjr +s9 7l3mdqo th’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until i x7 2n:p-mvt/d+o itgtt was discovered to have a moon. Explain how this discovery i:v2pt7o/nmdgt+t x-enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the0 bqd6h: p-uqivf- vis-y a-*y Earth is much larger than the Moon's. Yet the Moon's is mainly responsible fo-f-h 0q v d-su6i p:iyv*bqa-yr 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 1980r u;3q7qj u.o(lbrv26 r.no v8unr:qd 2lw z6c $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centrip m* iqvgi-i(+ bae18gietal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.5gi1v+gi -im eq8bi *(a0$ \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 uniforml:r7 ; zywk r pvo3hala-*lj5g5y in a horizontal circle (at arm’s length) of rahaw;l rjl * p5kzg vo:35-yr7adius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km fro jtc9/a9k pqag(. .fdhsv0.dwm the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Expr9 dq . dafpvh9tg/..sa0(jk cwess 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 clay o3xot6; ls(vyn.i5w +bsz pn5 dn the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm? lit wo; n6z.d5 sxpsb+5v3(ny  

  A ball on the end of a string is revolved 0cto 08x(e+)f1y*k bevgnphh at a uniform rate in a vertical circle of cyeft+0pnb8eh0*1koxg(v h)radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum zqdt (tdu3 +cv7bid.7si.l v1speed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static fric v7us .dzbli7v(+d3d1cqit t .tion between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of st/toe/jl9k n0b atic friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed ten9l /k 0o/jbof 95km/h ?   

  A device for training astrm9h-vrf1uz +, pry-4 ,1 aa2qhrwhy(pkfint)onauts and jet fighter pilots is designed to rotate a trainee in a horizontal circrhq-h,2pv + ),1nt-far1 hw imyrpf(azku y49le 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 variable fj( ,;xc;slku speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable uns(f ,lxk ju;c;til 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 coaster be traveling when upside down hbuqxjrz)3f/fr5 9af1h,m6b at the top of a cix,6hrf9 b/mu)zrf1ja3 qb5hfrcle
(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 drivebm7o n7nqym/ *dbx2s2 r) crosses the rounded top of a hill nms/7by722 xonm dqb* (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m+ vo;nkuy*r )ygha1( t4up t*p-diameter Ferris wheel need to make for the passengers to feel “w4 )v;yphtua r*n tyg (+1uopk*eightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of s wsjn g)h./bf1z7g q,radius 1.10 m. At the lowest pointh w)fnsjs .q71z,gb /g of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuo0p+t4cmu *l;f7dc q kge rotate if a particle 9.00 cm from the axis o+d0q mtlpfcc4u k*7;o f rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically waln j6qz9y *j:rjled "room." (See Fig. 5-35ryqj 96jn j:*z.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey tab):t:q7uc.us njev+b pletop, and is held in this orbit by a light cord connected to a da:t+: pecu)7bqn sv. jungling 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 tim ne+us g4 wyhgl.kq4*m80(etc e, by not ignoring the weight of the ball which qtg4y0n4s*elk8 +mg (wcue.h revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked fohr6na+abl 6n;oc6n b:r 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 fyx7,dma+3h.l la4vm $ 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 maneuvhjzo vl*,dn p/)3 3.,xbmw vgxer 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 centrvgx o:h0 e82 vlbehkp+s0 1wz3ipetal components of the net force exerted on the car (by the e:0hhowg 8x0 s2kev +p 3lb1zvground) 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 from the pit area:)y.uyzdm9c y, 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 t9uy. m cyzd:y)o be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a pa g.b78;uo (t m;gy *eondird l0a;hmn2rticular instant, its aa(n nrmde0h;;7td; g*i lob.y2u omg8cceleration 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 Ea(s8b3f sj wq7zrth’s gravity on a spacecraft 12,800 km (2 Earth radii) above thefjzsq ws7b 83( Earth’s surface if its mass is 1350 kg.   

  At the surface of a cert(r d3 ndsvw8,y rso q/s/z+2ezain planet, the gravitational acceleration g has a magnit,s23 odrsw /rys/zd(qnezv+8 ude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius ae :b/no1wo6o: p h*rnis 1.74 abhpoen*/ nw 1ro:: 6o$\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 thy.ye s1mj8r *sbw+v, u0xidmm*kxl 7/e same mass. What is the accelerat+s 8*/xmb r0.ksu*xy,mi wvj17eyl md ion due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 tihffjm ,3c;m/r mes that of Earth, but the same radius. What is g near its sj m;/h m,rfcf3urface?   

  Two objects attract each other gravitationally with a forcf ae2c2 hpyj/*e 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 accelerati1w(+ ahv 3bdhu0zl,omon of gravity, at (a) 3200 m 13zb (h+woamlu,0dh v    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the (n7fyrdv -1vd gtk.x,:(gyqwEarth’s center to a point outside the Earth where thegravitavn tq (ygydf.,wd 7(vgx :-rk1tional 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 0pkj70 yfjfjym:t6d 7mass of our Sun packed into a sphere about 10 km in radius. Estimate the syy7 fj06d:fjj k 07ptmurface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like ou wlu/ d9l/krz9r Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass ofz rlkud9/ 9wl/ our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel )lws;raob)m6ki2,yp weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself w2;)syiplr 6 bo am,)kthat it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at t8*nwbm. d9ozdt4qn9 mhe corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by98oz w4dnqn b mm9*td. the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side/rrq gws a*wg/:um0ft*ux,4 hfs / eq0 of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line /*srm,0g rse* wagt q:x/ufw hu0/4fq(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 acceleratiomu;z,++-oxpty7 nbz afo5z xxnq.;j/n of gravity at the surface of Mars is 0.38 of what it is on Eoa,-+mx+/p foyztnz;zx.b5 u; j x7qnarth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of w/ +jda6pc p)mu;.llethe Earth and iw.d lpue+mpaj/c6l ;) ts distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the E;txaxl* hzag4x7rco qr )*yb/-hb7 8v ar tghzv* oxarx 7lc/y;r7qb *4a h-b8x)th at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circz4: q*so1gyi h 0bh:dgxqqiq59av y/8ular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occ/qhgdgsy: 8 z qqb5*ix0v4 9i:oqa1 yhurs?    $\times 10^3$

  At what rate must a c00cwd 2fidwh v)e.lz2ylindrical spaceship rotate if occupants are to experience simuv dedhz2 c.)ilw00f 2wlated 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 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circu egmk5to: r5y :csv96d(- b+ fkup6sxwlar “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth whic(g 5vs k6tmed x6:s5fpk:ro cy9u-b+wh 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 r,n 8qh4ws4*yg nfq)h have to be launched from the top of Mq4h4n8wnr fshy,q*)g t. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landingg/my7 tvkk f(+ mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long didvkmky+ (tf7/g it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice tha0*a* o bkxr3n s)k;jh s:9ncltt orbit the planet. The inner xs; hk)o9cb: * t*r0lsnna3j kradius 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 rotate l9nxwdr /gy-vr2hx;6 s once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her rv;y g2-r d9xlr/6nxwh eal weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astrongac1e7 m0)qdwqi -: hnaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constanth ea0 1qmwc:-d)ni 7gq 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 consisjmxx2beiv(+( yj o57xg3lyru j..2g gts of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point +7.xrvjl o(y3(ju2m 5b g yggxx2. iejmidway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight ofsa auzv :.63a9sen e,t a 55-kg woman in an elevator that movsavs63 9ut,nz aa:e.e es
(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 frif9 u x:rk0 : hla2hysf4ny+g5om the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the e2y iknshl 5 :g0rf:9fhux+a y4levator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface dqj6m5 jp 9y(- mmtod;of a planet with period T , the density (mass/volume) of th(d6y5p-q m o9jmt;dj me 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 (2/*x/x3-dlu- 3 ofxpno / xvlgw7.4 d) to determine the period of an artificial satellite orbiting very near the E-/3xw/xfnlol*dg vu /o-xp 3x arth’s surface.    s

  The asteroid Icarus, 7r-edffc(x tc8ussp..ts45r though only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distancp.8t7.f (druef-5ct sxr4c ss e from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5m ;j6j-s y cl.rlsp0j3ngc1q: $\times 10^{9} \mathrm{~km}$ 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 e 1,d;cy2urby+( cuoadvery 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 out there? [Hint: The mean distance s in Keple, ycur1dycbdou;a+ (2 r’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 Galaw7; k8.+lj mwjs.zn jtxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 me/d8y ) ofve9yxan distance for the four largest moons of Jupiter (those discovered by Galileo in 1609)8fvo9)dyxy/ e .
(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 thekq98p xlme8-qkybl0o 6-ua ,a known period and distance of the Moon. pbx-6oaqu8e 9l km8a,qk ly0-   $\times 10^{24}$

  Determine the mean distance from Jupiter for each oftcz6b,p+tu t8emj 2 g -rpst:6 Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Comp6s+8tt peg6 j u2,tr-czt b:pmare 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 betl97.nc v3 ,dnxku(pls ween Mars and Jupiter consists of many fragments (which some space scientists3 ,d lnk9upvsn(x. c7l 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 descri i +5ywjtnyi3xb4)r) pw bt,2ibes an artificial "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 own, that the distance to the band is the sameb, it inw42)px5+wyr yi)b j3t 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 )p3jehrua( sfl()vwp5*6m /oq7ur f warc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vif( u53(/wv)smr ) wl qjfr7ph uep6a*one, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of g +ewvrq 8j bc:6o*ljc4ravity be half what it is on the surface? er4b6:q8cj* vjw clo+   $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mu;jt+ ve t..gpqz hc7:b:mv/aktual 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 hagavzc t +.vt m7:hq:/bke p;j.rd are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once peaz9 3q1g1 d(6cmno ijqr day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude ofio3j9 (qn61qd cgaz 1m this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacektm gya,amw0x -sr0g1 s8h ils/3;3pucraft traveling directly from the Earth to the Moon experience zero net force because the Earth and ghug;l/smrwpx3 mti, a31yk8 0-ass0 Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bh,v1:sl;yqq aut when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, vsyqha,1lq ;: and in which direction?     ----待选择----upwartddown 

  A projected space station catt9d0n; 1 t-4q zpkoconsists 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 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 (1ctt4n;z t1p90dq k-oa.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vert d+4bhh/ehlh;u edln7..p / gqical 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, 0 1;j9yxy)iuzr1cb sothe acceleration due to gravity at its surface and the gravitational 1)z910 yox sjcuriy;bconstant G.

A plumb bob (a mass m hanging on a string) is defld1b ei,f oxj39ub4 xn, (n)enjected from the vertical by an ang)n x41jef ,xb d boin3(9jen,ule $\theta$ 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 gsh-m al-s*5g,psn) da design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a c-pgs hasd) gs*l-,m5nar safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at u5p in,6ru4lw-ay9t;xj )i mlthe equator werxu jmtn;5 )ui6wr a4ipl9,-l ye apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a const6o ac qk;6vk0lant 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/+ +lhnya4gls a constant speed rounds a curve of radius 235 m. A lamp suspended /hgns4 l+ya+lfrom the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mas33zo gpa 3:tphsive 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 eqz h3tp3 ga:p3ouator 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 0)mx w2 l(ejewpresence of an extremely massive core in the disw xjwe(02)me ltant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the (wq2,xle (eu whill and valley shown in Fig. 5–45. Both the hill and valley have ,(x2qwu(l weea radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites qivc/2t+k) xjorbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,00k2 vj/tc +i)qx0 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km .roj4ewel g fe os7ce)4.13tf, is meant to orbit the asteroid Eros at a heighe.te sef7w eo4 .jc4orgf1 )3lt 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 satel;do/tisgscb-xy4 )kssyx1)8 lite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km b84 scsysxobsk gyd-t)x1i /);ehind 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 oz:e sl05hg:y29tuj daf 3000 years. (a) What is its mean distance from0egy d2 ua5s9z:lh jt: the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" yo73l +hp(b1u-yxbvc dwurself gravitationally attracted to someone near you. Make reasonable assumptionw+-cb3x1p( udh7lb yvs, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Wayv;w6fdxxoj:t t ; cn /4u(lj3j5osme* Galaxy (Fig. 5-46) at a distance of; j:x6mcx/; 3e*5us(tl nwj o4tdofvj about 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 loca-xchhbx7gnt x2(xule;; . p-mq3jw8fted at the corners of a square 0.50 m on each side. Find the magnitude u8blqxg;h(hpx nxe .- w3;x7mf-c 2tjand direction of the gravitational 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 tnxjt5 h z:h5;, txij4izwu/7yhe 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 acceleraqof)8 ewdjg.h ix(8n-tion experienced by the tip of the 1.5-cm-long sweep second hand on yourxw.-i(nf)jg8 heoq 8d wrist watch?    $\times 10^{-4}$

  While fishing, you get bored d-xxysu(1u4m and start to swing a sinker weight around in a circle bexmyud-1 (x4us low 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 the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway uyrk,s rf:g6j49 )dv fis designed so that a car traveling at spee46frug9:f dvk, jysr)d $ 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, thum qid8 w5)p:3htpj 9fe 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 speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and h3f) 8pi udt: m5jpq9wthe 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.$\approx$    $\times 10^2$