Sometimes people say that water is removed ut:t lhctp;f7 t6z2r)from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong w:t6 h lfcp;)zt2ut7trith this statement?

Will the acceleration of a car be the same when v5r)-pyjq/ccem.,:dn5s tu(-xmwk i the car travels around a sharp curve at a constant 60 km/h as wwv5d .m-kqixe(y-j5 ,cc:p t)rsm/n uhen it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant s7fpn13c)s v aqpeed 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 ds7fc)qn 1apv3ip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child d2tu lx0 4(0c 9v8(epwkbxezbriding a horse on a merry-go-round. Which of these forces provides the centripetal acceleratio4e 8cu 9(k0wpvb bd(ezxlxt02n of the child?

A bucket of water can be wfdcr7v:-3;fha uy t nub/g26dhirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explain;tu:ahrd g7fvub- 23 d 6/fcyn.

How many “accelerators” do you hapzf jbd563:xy ve in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are thjp65z3yf:bd x ey? What accelerations do they produce?

A child on a sled comes flying ovx9w ,s*si* +qf (djcfuer 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 for su*w+d,ifcs*j xfq( 9ce 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 cu6g spp +gx f+7cx6dm8arve at high speed?

Why do airplanes bank 3ni ro03m2a xb.dzup( when they turn? How would you compute the banking angle given its speed andbd. 2xup (aor0m3 zi3n radius of the turn?

A girl is whirling a ball on a stri5 l.c +9 * xheni:wqvmd7mt(icng around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a tav:m lmwt(.idx * 5e +hc79incqrget 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 large a fu9e 30) gg eu /htbcb+v;tie6oorce? Con0eee;b6 9go+3tbhc )ui vugt/sider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were dl+cq z/8ikyv q90b/g aouble what it is, in what ways would the Moon’s orbit be differqil cba/0 gy8 9z+/vkqent?

Which pulls harder gravitationally, the Earth on thw 4dy p /g hj5d* 9epjf85skys.0r4yxke Moon, or the Moon on the Eart*g0 4kej5 k wsh/jry.xsp 9py4ddy58fh? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Mo637ela ktdyo 6o;seh *on's. Yet the Moon's is mainly o;a*yks d3ole6eh67t responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the polek;ux 5z7; fp t;nvl1zss? What two effects are at wornzztk5psf ;u;v ;7xl1 k? Do they oppose each other?

The gravitational fod 1d z* bdl-;yo2a14xh iolej*rce on the Moon due to the Earth is only about half the forc12 1*; dld jdohoe*yzxa4i-b le on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun r )qo 4 )2monxuajr,(elarger or smalleoq2r m4u)()nr,eoaxjr than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) +g (l/l-; u r3wx6dore rzdsw.toward the west? Consider the Earth’/rx6dgwzlru-+r o(ld.w ;s3 es rotation direction.

When will your apparentpn)6wrfk mj., 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 fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as whe6j.rpk,mw f )nn you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could ate 5d3m,+q. :cqh z2np 5pgn s3iqaz4be adversely affected by weightlessnes n gd3z3e ns42q5c, a:m.+5qpqapthizs. 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 of.

Explain how a runner experiences “free fall” or “apparent weightlessness” bebve- 51ogqy dia :.k:ztween steps.z .io keyvda-5gqb1 ::

The Earth moves faster in its orbit around the Sun in January than in July. Is e4-) o 0,hyrzyc joh6qthe Earth closer to the Sun in January, or in July? Explain. [Note: This is not much ohyh)oj zc ,qer o-40y6f a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered nv q*fa:iih x:( 1gybfr .2b3eto have a moon. Explain how this discovery*i r(v.a 2i:3fy1hfneg :b bxq enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the 68 cdwj8uuh i5Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differenc8 u5ij8whc d6ue 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 traveling3+f0o+y pbn ka exzi8 l0:zb.mte8*js 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of t smj9qces29qi.u b2zo02 y(fqhe Earth in its orbit around the Sun, and the net force exerted on the Esi9yoe9.ub02 sjqcm( 2 q2fzqarth. 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 on a 2.0-kg disrd d, ;..npnc7 vmp1iocus as it rotates uniformly in a horizontal circ7 .mncdr 1do,pv.;pnile (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbist1drdh,nkf (r4z b 16t 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your dt 1 zk6d 4sr(nhrb,f1answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of d q:7 dyjufw5*the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm j wdd:q 5uf7*y(revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of aq+u i0afz)td( string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5- +uaz q0it)(df33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with)*c ao 5lrpef(d -jf4 uin38k. lkpuga*7kz0s which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tire7 u)g3jf50 o8 zkl(ada l.nusikpc*4*repk -fs and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of bs vl az 1,:mz5 ap-h5wp ifo:4pc.q*istatic friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km5azoic* avpf bmzlq1h,p 5 4:pi-s:w ./h ?   

  A device for training astron r3tl3p:ayn4rp+q( ni auts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of rr:aqtn43 y nl(ipr p+3adius 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 vap3f blqe9m. .t)hcutd q .bs52y9n3pfriable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached )dy qn. qlbp h9tc3uef59 tm2fs3.b.pand the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller co 6yida +mbv)5,ak83 r o:jibvwaster be traveling when upside down at the top o+wy:ib 56od)a3bra 8mik,jvvf 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 (incxxjj-(saa: ky- bw+(cluding the driver) crosses the rounded top of a hj( yc-+ (b:xa sjka-wxill (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 woju ec. t(j6ry,wml-,l uld a 15-m-diameter Ferris wheel need to make for the passeng e c.,l ruljwjy,-t6(mers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is wx7lw0/7( dh,qe )m8isqbv zadhirled in a vertical circle of radius 1.10 m. At the loweslb,a(h7sxved8d wi/zm)q q 70t point 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 ,( t)2o;bjnrk0oqx wca centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,00bt0owco r;nk2 ,x q)j(0 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wall-xpp jsnf,-h1 w7 at2yed "room." (See Fig. 5-35.)ha-pj,ws2yf -p71x nt
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-hock/n lc3** yudcrvwh2/5i me9qkey tabletop, and is held in this orbit by a light cord connected ridmvn 5wc u 2ec*kq 9l3yh//*to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this;fygas/.vrg2q7yh 9 a time, by not ignoring the weight of the ball which revolves on ahyav a.2y q;7/f gg9sr 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 for a car tra0 t yle25uvw5yveling 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( x .y+,t,be+kgnna oxs $ 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 verticallrmk /sc6vykq5-.qp8 e y 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 components of the net for rj. fazlqs/65ce exerted on the car (by the ground) in Exa.s/ rl 5zfq6ajmple 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 507zcob r7e1v:n0 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide 1cv er77:o zbnthis acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a partic*- l s uc v5zy+.mmjp9(twvc9xular instant, its accele(tlzmjsy5u9- p cmv + 9.wxc*vration 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 spacecraft 1 4c) hf,av(d:;a cghac2,800 km (2 Earth radii) abo, c;hfc (caagv:dh)4a ve the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certainz orn 8n.ze4egpj*k4yd3+ kw0 planet, the gravitational acceleration g has a magnitude of 12 m/034 .*zzy ojnrp48dgwk+eke ns$^2$ 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 accelerat .h f;zqxo.)v ks/sa3wion due to gravity on the Moon. The Moon's radius is 1.7 z;h3 .fs)awxvskq.o /4 $\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 tcdx5iq- grge :; .a7fche same mass-dqc. 7 x5ie ;rfcgg:a. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1 (ge g 6px(pbtt vf5t9-9dd7ro.66 times that of Earth, but the same radius. Wpg76togp5v-d(e b9xrt 9 tfd(hat is g near its surface?   

  Two objects attract each other gravitationals5x .+ibh6.pq+ d zw,b:tcr dsly 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 f xq*pv8zx1,ko1r )q ag , the acceleration of gravity, at (a) 3200 mpq8qzkxfv oarx)1 ,1*    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Edfc:do d(3bws7(l88bt b2v klarth’s center to a point outside the Earth where thegravitatio8obltl:8 dbsfv (2 7d(3bdkcwnal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed q(n q4e1lk hs4ea ,mi)into a sphere about 10 km in radius. Estima qk44sm)(e, liahq1ente the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, : 5x /vjz:qduiwhich 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 surface gravity on this sta/xq:z:5 v diujr?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting ikohk08 29mosi hla o/.n the space shuttle. Your friends 20.8as/ k9ohhlom ikorespond 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 terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calcu. 7m*/9gehjug 0nnfpfq x4vi 9late the magnitude and direction of the total gravitational force exerted ofnq9j79 iegm xvuh/ *gnfp04 .n one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets 8.y-tin,vok*n oax/f 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 (i /tykfx vo*n-oa8,n.Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is m m.py 7sta, 0c :bxvge8rm/y30.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of :87, 0y ms.gpcaxv3mye/mtr b Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of thena;:g ( xs9 bqz0*wiit Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example x(nwsz qti a:b9gi0*; 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite 2jt.1qks cw6a,ptd 2 smoving in a stable circular orbit about the Earth at a height of 3600 km 1jqk2t, wdc psts.6a2.    $\times 10^3$

  The space shuttle releases a satellifo1ds(0,ze xe9nm;x j te into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when, xeeo9 ;xz01j(mdnsf the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if of 64 np s5o,eu6uq)bpvccupants are to experience simulated gravity of 0.60 g? Assume the spacefq)v4s 5o,nubup 6pe6 ship’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 circ6y phf2nror9)ular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to thfy )h9r p6orn2e radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a sa5q qqom*zi02 dtellite have to be launched from the top of Mt. Everest to be placed in a circular orbit am2o0q* q qdz5iround the Earth?   

  During an Apollo lunar landing mission, the command modu 8lqm2.zxro*)okh9s sh+ p xy:c a4)dfle continued to orbit the Moon at an altitude of about 100 km. How lo x9rh):qsdhp8o+ys.)komxc* l2a 4f zng did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet.jsb)mvl3p dlc* * k 3pthtt29/ The inner radi3h2dj *)tptkm psb*93 t cl/lvus of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every c3 n-z j9lu4ja15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight -unzj c9al34j to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight c4 dj2svvr03vtkpwfm7 k v , )l8alj15of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a 5) tsjvl 40vw13 7 rclvakj8 fpk2dmv,space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star syst*m1(dl8o txiw)9gunn.w/msq em consists of two stars of equal mass. They are observed to be separated by 360 million km and dqt8g1o(s .win)l9nu* mm x/ wtake 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 rea7)hz,s fi3f3jg k0(j v/ yenz7ujx a4td for the weight of a 55-kg woman in an elevator that h4,vnz3s 3/yeuax7) gjk0z(jif fj7tmoves
(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 ceilintm dc:. kipp*-g of an elevator. The cord ctd pi:k-*.c pman withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satelliq9ib btuv6n 58te orbits very near the surface of a planet with period T , the density (mass/volume) of tq5i6unv8 b bt9he 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 the per6j- io :ay1a o96mnyh)lcb*kpiod of an artificial satellite orbiting very near the Earth’s surface.1oy a lb yj:in9pm*hk6c)-a6o    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun liy mivj xl,a(0;blti p1,i5ea6ke the planets. Its period is 410 d. What is its mean 1a,6xyt,ilbjmii0;v5la (ep distance from the Sun?    $\times 10^{11}$

  Neptune is an average distaht,o yhe: i5hz 2(o/5oqk7jcnnce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very c ft5p6 xfs0h ,k8c3nxulose 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 Kepler’s third law is half the sum op6s 3 fhkuxn,f50cx 8tf the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the ceg v-*.gg/s qg nsbps*6nter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the fco0xvb/:py wm7(weu- our largest moons of J:xw-obmcy(u7v/e 0w pupiter (those discovered 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 Earth fro(lt;peygm.x)rwz *9pm the known period and distance of the Moon. *(t x9)plze.ryp;gwm    $\times 10^{24}$

  Determine the mean distance from j1a 879rchz sp 1qz:udJupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io ans8:7pcqa u1hzrj 9 d1zd the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter ;wyy,q3 zkwbgb- +o6i consists of many fragments (which some space scientists think came fromo y-,zi36gwwb ;yk+bq 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 of a band:ubm0q yo+zk2b g)q 3 jzabt,3 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 same as the Earth-Sun distance (to make the climate temperate), and that the rb3,jz ma3zt qy2:uobkb+) q0ging rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. c,c vx 1 u6r6p,yh-wwj5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his yh cw,, -ux p6w6vrc1jswing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity b w(wrqc02j0:egh1hy xe half what it is on y 21xjw(hch erqwg00: the surface?    $\times 10^6$

  On an ice rink, two skaters of ll: bh3,xtx0ab9b:q zequal mass grab hands and spin in a mutual circle once every 2.5 s. If we assum3t z x: l:l0bqx,9bhabe their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparen,j(oq6(ch1hs x7vm 9 )oebrnlt acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude o (o ljvxmh1e ,q67)(nb scrh9of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the Ea /zc6p qmdi0s75 nzom;rth moi; zd7cnp z50 6/qsmto the Moon 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 annqh n3 h9tzqp 0si.*i; elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and izq h*n.n3sq;90iip ht n which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube t+yqa2.8xs t 4xb6qt,o i22 n/rj nkaaghat will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of abt+qny s8 t,62 xbajigrao4 /qxa k.2n2out 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 aircrd i g+ o8dzg2ia7p1ck x*9kt,saft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass ofsg* ak 3pn o7x8sr v/0oe+wo2u a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravit8eoaps7 o x0nou rg+k*/vw32sational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertt dxo6hohw0 -j6d*,neical by an angl*oo et0j-hhn d d6,xw6e $\theta$ 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 67fwb x,kyi,)f7hoh16x m is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds,kx h7wo fi )h,f1yx6b can a car safely handle the curve?

  How long would a day be voak .p(pr- tyla4d/ 1if the Earth were rotating so fast that objects at the equator were apparently weipaa( t op4 /v-.ldyrk1ghtless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 scwpuv lkf.d h 9/qt: 65v-b0x$\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 rofdj-af p; p1tq/zh 2:junds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle of 17.5zd paf:ht12j f p;-/qj$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mas5e+p dl 8id6osg +uok;sive as the Earth. Thus, it has been claimed that a person would be crushed by the force ofsgd+dpl 8;e+ui6 oo5k gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , 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 Hubble1pahctf v9 55ovr f30z Space Telescope deduced the presence of an extremely massive core in the distanta3p zcr0ofv 5tf 9v51h 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 .),3bc,z ry pkq-eqe6a(gfjf 0p.o vm hill and valley shown in Fig. 5–45. Both the hiqfv(.)c.m0p,ayzkeo3rbef 6gj -, q pll and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Pos,,,l*4wwxvpvq l/d+ f9wvt .v5*ogc 8ta znozitioning System (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 evenlfg.dl*tv , wvnwlcvpq5*9a ,w+vx48,toz/ z o y around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billifvo 1fqt w*f6t).:o; itj auaj*z 0/rhon km, is meant to orbit the asterottjfhq6twf*1 z/ foa ;io* 0rj.av:u)id Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuingw9j :i5tl 7yxq3oxu 6v a satellite in need of repair. You are in a circularo:t3v9i7 w5xj6luyxq 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 3*8avx +c: lg +)hsdgqa000 years. (a) What is its mean distance from the x:hlg+ac g* sa)v+qd8 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 neeosztn),+3ty;mrg b(y : e4 gted to be if you could actually "feel" yourself gravitationallyn,g(;ybz)toe4 gs3te+m r:t y attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Ga p3ytjn) y/ 7(*xnbbxblaxy (Fig. 5-46) at a distance o/y3x)btpnjby n 7( *bxf 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 locfv2g* fkbl*kkel2fk(jv f*9 +ated at the corners of a square 0.50 m on each side. Fi *kflev*lk+2f*g9k v b 2f(kjfnd the magnitude and 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 orbwrm.,ad)z)5on rkmh+u;slcl2 w+u. 8qqnu 6dits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep second gb+tyu)n.v 2ga)j tq(ht) b gq2()gu.jvn at+yand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a : fh5mk01c63rkw7y;h wn+mes;y rg qrcircle 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 the fishing line makes with the vertical? [Hint: Seemr:r r;k;ekfgq c675w+ syh 3m w0hyn1 Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new 4n jy wmxxqs4 2-roh5+cwv+p.highway is designed so that a car traveling at speed .wxnc m5xwhjq2 4opvry+s4+ - $ 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 A1 x7uy, uznz7mcela, 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 knu77zx1z, mu yg 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.$\approx$    $\times 10^2$