Sometimes people say that water is removed from clo c/:r2 3c ygnh7/ifqbpthes in a spin dryer by centrifugal force throwing the water outward. What is wrong wit 7//:3p2gyqcncbir hfh this statement?

Will the acceleration of a car be the same when gxcs,l8p7.1cte/ bda the car travels around a sharp curve at a constant 60 km/h as ax.s bp/l178g,tcedcwhen it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along ;3 j6ju.b nlema hilly road. Where does the car exert theb j le.n6m3;ju 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 the bottom of a hill?

Describe all the forces ac4id+ vv;i)ci dting on a child riding a horse on a merry-go-round. Which of these forces provides the centri idd ;)ivvi4c+petal acceleration of the child?

A bucket of water can be whirlaxhj 1cne89.g ed in a vertical circle without the water spilling out, even at the top of t jga98c ehxn1.he circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Thered2 ytkh p7)vz-f5y1vh are at least three controls in the car which can be used to cause t 2z-ktv1p hfyy7)dhv5he car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a ne7kdfewd 2:s55ukk , small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels thedsk5uwen k5fk ,:e27 d 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 inwaritmi8obo c(57 m05 mysd when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bi8b6 ksm qaf(o)4fb05eku 9pj anking angle given its speed and radius of tfb(a kk6 89qsf5jb0)oie 4 upmhe turn?

A girl is whirling a ball on a string a8+e0 r6y2w,kbw okpmzround her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let gwm02yb8rze6pkko w +,o of the string?

Does an apple exert a gravi jqg6c8 4k-ljf i:;ulktational force on the Earth? If so, how large a force? Co6klu lcjk-4qi 8fg; :jnsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moorvfnns5r zh)mv 04:b +n’s orbit be diffe 0bvnr4zvnrhm )5:s+f rent?

Which pulls harder gravitationalsfpq 1 w35j ti5c1khx.ly, the Earth on the Moon, or the Moon on the Earth? Which accelerates cwih.5tq pf31ksx 15jmore?

The Sun's gravitational pull on the Earth is much larger than the Moon's. ir3vof-n8ox5i7ut-p0+ 5 lz t/ sifbm Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differi t+ znp0r/5o8t b3-isf7o5vixm- uf lence in gravitational pull from one side of the Earth to the other.]

Will an object weigh mor yjez.hdnw597 e at the equator or at the poles? What two effects are at e yjz d579nwh.work? Do they oppose each other?

The gravitational force on the Moon due to the Earedi xqm4-8n)qexm m* +th is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulle+dme-qxmenxi* q )48md away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun largermc(3- zt; gmx9gg ndt+eq-bm6 or smaller than tc 9(gegtq;b 6mmz 3g--tx+dmn he centripetal acceleration of the Earth?

Would it require less speed to laun flzz.l+ pjeev-eo 7)4ep16pych a satellite (a) toward the east or (b) toward the west? Consider tz .-7jllzvo y 6pepf4 ee)pe1+he Earth’s rotation direction.

When will your apparent weight be the greazc/ykwi e/hfh9j4wt:+ket 4,test, as measured by a scale in a moving elevator: when the eli/ k9ze +hkw: 4t/tc ejh4wyf,evator (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 perioix;dhrnj t;6y2emp83ds 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 f t6npry;3 d8x e2m;ijhorce we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “frue img* y01d5f*huoj: ee fall” or “apparent weightlessness” between stu* ogh*0f5y1jdi me :ueps.

The Earth moves fast86j wavr8t+swf ;u7m 3bye kj:er in its 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 ofk 8+8ywm7jsu6 b j3e fat:wr;v the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not know d-40kzxvopuriu /po+ uq: j(:n until it was discovered to have a moon. Explain howuzxo 4(qikpj : vr0+/od-: upu this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much la k q k195n0gh2:pqxmcmu5,sr drger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merryr5m1,: 90d mngck2qukx qhp5s -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 19 qp).rnf ;mtsalv0jfo 1k2a,(80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accel5nr9 cuuaj* jojt/25j eration of the Earth in its orbit around the Sun, and the o5jt9cjn u ar5/*2jjunet force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a r(cq5mr-v)s x 2.0-kg discus as it rotates uniformly in a horizontal )x (srr -cmqv5circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shp46w0 b3pu3so0tzi tsuttle is in orbit 400 km from the Earth's surface, and circles thet4 i6w0pos3z3btsp u0 Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of cla+r afvopp /(6krccu59 y on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the ror9a/v6(puc 5cp fk+wheel’s diameter is 32 cm?   

  A ball on the end of a strinqw0cug:1)n hr g is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as showguw0 h:1q )rcnn 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 speed with which a 1050-kg car can rob7kt3m 0qx:dco ;qa8r c+ epq3und a turn of radius 773 pc7+qrc:e3;80q db taxmo qk m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient 3j2enk gc)a*g*k,o5ygskfn *of static 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 95kmskyj*ogng5*k*3f g )nak2e c,/h ?   

  A device for training astronauts and jet fighterc tq+tkehx. /pyk (;l2 pilots is designed to rotate a trainee in a horizontaet/xl .+ h;(ckqkp2 tyl circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turr/ht4u;bn ye9 ntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is rea b ryhe;ut94/nched 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 dow7f+ b 3e0iqr-lcoq l5h3tuq(in at the tr hl0e735iubi(qft+ oq-ql c3 op of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the ro4kw x3ud; q3u+5 jax4ddc hr(ounded top of a hild3(u ho kaw3 4+5rj;cqddxu4xl (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-diameter Ferris wheel need to make zc k 5pwaqu+d(q1g/dv5- qml+for the pamd++-1 q/d5 (a qlkqwpuv cgz5ssengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verti30by9aqsp 3zlb79d wr cal circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the 70 3brzwqd bs39alyp9bucket 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 rotax2v phei 2ter 30lk l;(;gckkuoi+16mte if a particle 9.00 cm from the axis o uvek1xkrg; i3( hopl0 ;6+mkc 2i2telf 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 (ur6 +gzcy;wo7e lrm5cylindrically walled "room." (See Fig. 5-35. 6gywc lzu7me5+;o(r r)
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 tabhl9 1bz1aueegb46b .xle.ez bubx94l1 agbh 61etop, and is held in this orbit by a light cord 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 this time, by not ignoringzf3yuy9y dv ))4x(kwg the weight of the ball which revolvy3 u4wk)x9yy()d g zvfes 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 fordoy9 9r1bgrv k8ph;b8 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 massesfsiq+n.k5k) : (euozo*zej 4f $ 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 vertically at 310 g1r du/-zp/i5b;8:ft9 hs8 7 n4 llsny krzlxe$\mathrm{~m} / \mathrm{s}$ . 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 grn +q5q + tq2tc7y o.skdxnq v,z-;y-the net force exerted on the car (by the ground) in Example 5-8 when its speed is 15 x5ny+r.7 dtqt- s+;,qc2ngkq-qyzov $ \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, g er4 oiclq0( m9c7voj1oing 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 t(ov 01qmli97ocrcje 4hrough 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 circle of radius 2.90 2ex8l:/;h(zui s m(m rwfmt2lm . At a particular instant, its ach2x/r( f :lutmizs lwm8 m;2(eceleration 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 gravnpwt6zj gq;/) ity on a spacecraft 12,800 km (2 Earth radii) above the Earth’sgn/6 ;q )pwtjz surface if its mass is 1350 kg.   

  At the surface of a certain planet, the q hg qqrs9+z75*fy7 lqgravitational acceleration g has a magnitude of 7*qq lqy gr9+fsh7z5 q12 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 gravi ,+9ni,qkkc0f5tkhuk ty on the Moon. The Moon's radius is 1.74 kti+hn 5q,k,kf k0u9 c$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius thbr3(: z.bnaih fst(7;2n ud1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity na.nfb(b i(27rz tduh t; s:hn3ear its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but th 6rcmmv*-s8 n89pqwjze same radius. What is g near ij * zm6q8r8nwsv cpm9-ts surface?   

  Two objects attract each other gravitationally withv a(:8q1den 4ad;wr0k+xs hv k 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 effectivep+ s v3sdu05jc9 alst4 value of g , the acceleration of gravity, at (a) 3200 msavs+3 lt59dc0 sjpu4    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cn*4 p5z7hcdgys sip);enter to a point outside the Earth where thegravitational accel5igs7nh;* zc 4p)ds pyeration 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 81wiz :ddi pfy f499uypacked into a sphere about 10 km in radius. Estimate tuwypf9:4f1i diz9dy8 he surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like3zk74dp/xr.3 xy p +jic cr8vo 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 st r3pxjd+vy8riop4ccx3/ .7kzar?    $\times 10^7$

  You are explaining why astronauts feel w418 rg.t-xe c mnpqls1eightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by 4 n -plsqc.r gm1e8x1tcalculating 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 siaeg6nah1 8au 8de 0.60 m. Calculate the magnitude and digaaeu1 8 a68nhrection of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side ; i4f:wz8hwzr 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 m8fwwz ri h4:z;asses 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 tv i;n*z 0mo*hmh6 j5rihe surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine tho hmr5i*v;h jiz*m60ne mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known vajv;h m 5xn4xlng h)9f0lue for the period of the Earth and its distance from the S n;)x5gvxnmlf j4 90hhun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a *0n ck 6qs18,:+eil*gj osz,euzgc iesatellite moving in a stable circular orbit about the Ear0*:skcez 6sn1u e* ic+giez lq,jo,g8 th at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a s t)7*2cs hzlq( q1ih9t evpmf4atellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the rhe (qzht42*lfsp7)m9 ticvq1 elease occurs?    $\times 10^3$

  At what rate must a cylindr;ci, .p7eunsx/hm) 9st uywh4 ical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5 cshmtx4 ;uhu.7y,/ p sn9wei)–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circulasiu4i. 6jtu 3z9huyo9r “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth whi9s9iz ui h4 oyuuj.t36ch 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 tcj xa bjt59g313 j+ v8uux(pfsatellite have to be launched from the top of Mt. Everest to be placed in a circu 139aupjfjgx8ut5c+ b j (v3txlar orbit around the Earth?   

  During an Apollo lunar landing mission, the command nd9l63c);a46va ryyyjp pkd b3.q l)ymodule continued to orbit the Moon at an altitude of about 100 km. How lo c3n6l; dy 3ypvy .ld)49)kryp abajq6ng did it take to go around the Moon once?    s

  The rings of Saturn ar sy)b:kn4h5pz5qv loc.25r jme composed of chunks of ice that orbit the planet. The inner r hj:lqby k5n) o5ps m42z.5vrcadius 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 15.5 s (see Fig. 5–9).ac(e4ban;. h p 4a:q2vbvl3u m What is the ratio of a perso a4(:3p.2 ane b;a4hlucmvvb qn’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of iw +3jv-pi62a 2 dhrgga 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a)2wd+-6 i3jrgav2ip gh moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of e vgwc8. xt tm608 tecd-3h/vxiqual mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of eam ctgdt-0 .8w3 x8ixv6c /hvetch?    $\times 10^{29}$

  What will a spring scale read for the weight of a 5 w*,zaug yu.pr9n.. fc5-kg woman in an elevator that moves g pa,.fzw9.ryu.n *cu
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an jo+ji h0ocs; -elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude andjoho+sc j -0i; direction)? a =   

Show that if a satellite orbits very near the surface of 7: 2xr wc1sdz ro6gd0wa planet with period T , the density (mass/volume) of the6 201wdr:c wd xors7zg 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 q:g:3 tch-imv d) to determine the period of a:v-ct mhi:3qgn artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hu zo7u, fj+szu(z6si .bndred meters across, orbits the Sun like,os.z+ fuu7zi6js( bz the planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average agx;sip65m15b s:qnr distance 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 cl60(ffh qlz5hsgb 2 eyn.+ x*jyose 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 ther6 5f2gz0f(+ bj.yhhx *e lynsqe? [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 Galaxy 1bj r4igmuf3 u6 x4.5 fu7apjg$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, anq i; aqhh2fru0*i0pmj9uz-v3 d mean distance for the four largest moons of Jupiter (those discovered0;v-3f zhui r *upqaqj2h 9i0m 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 Earthh 2989nzzwa mdc-3y kb4* peyd from the known period and distance of the Moon. 4wzhybcd*yd9pzk 239ane8m-    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usinla+ 8q(7q royxg Kepler’s olq(y7r+8x aq third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between n su).e2 )5lev2erkhzb z6 v3yMars and Jupiter consists of many fragments (which some space scientists think came from a planet t6y .2e)5 l)hke3znru2 vszbevhat 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 15 801zuq5 l*ruc*z bjw aaqdrof 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 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, inqrz8ujw bl5ua *0*r d5z1caq1 Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc frzny+9qt9w lb2yjpq s( 52i cp2om a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the macbnp2s ljy99wqz5t2y i(+ 2qpximum 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*th.zr zh3vd1’s surface will the acceleration of gravity be half what it is on1vzhdz th. *3r the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin inxeph8; i+q1sv)krx1a a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on ones ;exh+8ka1 vr)1ix qp another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of g rqz93w:tf bz5ravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude qf9 z:w3rb5z tof this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling direcz evc0oe:4 nu;tly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal a 4neo0e;:u cvznd opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scaks m3)(d53(k-amhoz up):yr j dw zd,t-c :rzele in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directio,csd- m)tozz3a:w j(:z)p(5yk 3rkmdr - euhd n?     ----待选择----upwartddown 

  A projected space station c,q7vq6- rk9f b ix7ycuonsists of a circular tube that will rotate about its center (like a tubular bicycle96quxyf ir,7cb qk7v- 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. 5–43).r7m jqw9bljjmz zv mig-t9i/*:; ,ix(
(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 iz1kx. .(shtegom 5in(ts radius r, the acceleration due to gravity at its surface and the gravit ez1mti k((.hsn.ox 5gational constant G.

A plumb bob (a mass m hanging on a string) is 3ubn)zz *xb1f deflected from the vertical by an znub*3fxzb)1 angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is bank(:n i e:h.ogv *6qjbymed for a design speed of If the coefficient of static friction is 0.qhbv6*g ejn (: oy.m:i30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects afs3i0 86 6pjkml0qx.gea6p fbuz c57 vt the equator were apparently weighlfpxiq5k8vu6zmj cfa.g0 s6 0 3epb76 tless?    $\times 10^3$s

  Two equal-mass stars maintain oe, oh-um:mqbew 7 9j1a 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 spe5f3mk mqf4ik*ed rounds a curve of radius 235 m. A lamp suspendemk fq5 im4kf*3d from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320s z8p6ucd.tc2b rb6/c times as massive 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 ect6bczbcds 268 u/rp.xperience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of g hj:flo lk m)s6 wf1j,6,*/9rhafk ls4ak3 ujan extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed ofakh/l3m:h6gkjjak9 f ,*fus,4r6l)j1 wls o f 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 cons/ws09rzz,o s .+ avsbglf8 :gutant speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting onusgsar +fg /,zs8lb z o0w.v9: 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) utilizesgr*t xos:yr:lf 6(dn3 a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a res nr*gtdl3( 6oxr::fy ceiver 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 11,000 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 billion 1q,bp 1thcl,cv,no*gq -t-d 4 j 6prfxkm, is meant to orbit the asterxd lnbqq-gtp,6r1 vohc,,*c p tf1-j 4oid 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 purs iib;ztu +,rm :nfj rt)gci(2.uing a satellite in need of repair. You are in a circular orbit of thertiui.,nf2ic;j+(rz :g tbm) same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean xmmx 2 ,ut 9u9a n*-afi/zc0ccdistance from thez9 m/cfm-xauc0iuax c92t,*n 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 valu(gt6fqw p lh u8il6y4wq3b24ye of G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptlyhwpu64w82g tyqiq4 (bl63fions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (F7;+py7:yyt h( ;fpgy i,afelgwij 5:xig. 5-46) at a distance of about 30,000 light-years from the ce7itx,fwiy yg:ey(haj: ;pf7 +p ;ygl5nter $ \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 5z/ .t .ba hne :okiyh(i7tra;located at the corners of a square 0.50 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 bottom bhat(z .e ki a:ohyi/;.n tr57side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg084kwc2 gqn * 8 d(4 mc/ucsqbrshiic7 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 u2dju rpu p5/l)vy,,nthe tip of the 1.5-cm-long sweep second hand on your wrist waj)5/un,puudy,vp2 r ltch?    $\times 10^{-4}$

  While fishing, you get bored and st,erjg2ppmh w.-a6 8 xiart to swing a sinker weight around in a circle 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 vertipw68,pr j2-egx .iahmcal? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius Rf5myx ums0a. .a+y *zs in a new highway is designed so that a car traveling at spey uya.xm 50safs.m z+*ed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utix h)s cmt)j4d37 ijp7mlizes tilt of the cars when negotiating curves. Th) xc3mt4dms7hj)j 7p ie 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 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.$\approx$    $\times 10^2$