Sometimes people say that water is removed from clothes in a spin dryer by cent*f8xy2p0t mve + lsm u7yt;3hurifugal force throwing the water outward. What i2fu3u+7 0ymt s8y;exm *l hptvs wrong with this statement?

Will the acceleration of a car be the same when the car travels arouw2pjzmy. ,1g nnd a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same sp 2wpn.,mjgz1y eed? Explain.

Suppose a car moves at spuu fo8 ij+3(-xj3os constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretc 8(pusufx +-3joi3sojh near the bottom of a hill?

Describe all the forces acting on a child riding a hoc c j4mak)/d-rrse on a merry-go-round. Whick ac mr-d4)j/ch of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water spillingmgef t:4 m:an2 out, even at the top of the circle when th emtan 2:gm:4fe bucket is upside down. Explain.

How many “accelerators” do y hbzai-iq3ned e0ko rq 32l)-l7j2h i4ou have in your car? There are at least three controls in the car which can be used to cause the car to q2 3h0)jhrli7 dqle-3 eo i2-4ikzbnaaccelerate. What are they? What accelerations do they produce?

A child on a sled comes flying ovg,09jp+xhr lcer the crest of a small hill, as shown in Fig. g +l,xr cp9jh05–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inxym;qo) 2ptu 2ward when rounding a curve at high speed?

Why do airplanes bank when they turn? How wouldifz:rfrsf; )x-ug)h: you compute the banking angle given its speed andf:s:)ufr) ;f-hgzri x radius of the turn?

A girl is whirling a ball on a stri) hwzz,s5fmn)1ax2 z /yc) htbng around 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 go of thezy 1 )wh ta)25smz)b,fzhx/n c string?

Does an apple exert a gravitational force on the Earth? If so, how large a f: .rb7c/jyxhye/j ip 7orce? Consider an app 7.j h/:ie7 pby/xcryjle
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what okdw ek/mn/)c )wb i;: (9eshkways would the Moon’s orbit be diwoe(w /dhb;cs n)kk9i:me)/kfferent?

Which pulls harder gravitationally, the Earth; yhln 7gq7rb0 on the Moon, or the Moon on the Earth? Which accel 7n7ybh0 lq;rgerates more?

The Sun's gravitational pull on the Eq3+ae9 +r tohm9/qo gwarth is much larger than the Moon's. Yet the Moon's is mainly a9 gt/3+o9e rqq mhwo+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 poles? What tbuy h5itl7y(b csy5rh,l2h;4 wo effects are at work? Do they oppose eachi4yy,5 shhthl ylrbbc u(725; other?

The gravitational force on the Moon due to the Earth is only about half tho/t)i+rbxax8xt j9t 6 e force onxto6rt/ xt8+a )ibjx 9 the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration x*7;hf:hwfgd*w / y b3ph2 jvkof Mars in its orbit around the Sun larger or smaller than the centripetal acce*bg 73*py:fhw kfd/hv2x ; jhwleration of the Earth?

Would it require less speed to launch a satellite (a) toward the /t)0tkisvi c 9 m1kt1ieast or (b) towar10)1tkt i cist9v/ ikmd the west? Consider the Earth’s rotation direction.

When will your apparent . cwh(khhpz::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 when you .:w(ph hkhzc: are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adverc+wv) fhss i:a);tfb 1sely 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 su s1f)+sv fiabh)c:wt;rface (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 :lbf er:, k-sa uy38yh+mq4ex experiences “free fall” or “apparent weightlessness” between s-h y+b:8 r:x4e ly fsuke3,qmateps.

The Earth moves faster in its orbihjo r 0njp4z:4-cv2: cqfl0.(a b a+ltvw3 levt 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 Earth’s axis relative to thea4 (40n ov +c zv:3pflvchb0t-r jaeq2l wj:.l plane of its orbit.]

The mass of Pluto was not known until it was discovere b 4nqd /riqar.k,:4cj2)k qdbd to have a moon. Explain how this discoved,drrcbnq.a4k4i qj k)2/:q b ry enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Eartgv5 j2 d47ec ec58qdjwh is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. gq 4j8 dcd5wje572evc [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 1 zne: w7gux.g)980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around th*v:e sot)d3std,qbb ,qz owuc:77cp(67s raxe Sun, te7)zqqo3sbc*,: t(7dd v: 7 a6br pssx,uwcoand 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 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 21v; j ranc(4;ab0 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calcul;b (an av4r;cjate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from thelxxnm vrm 2-dy,oyxc6i 94c --phst64 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 answer in terms of g , the gravitational acceleration at the it- ,-lcynxx hm c6ov xr-449m26ypdsEarth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck oyly5) q*bg2 *hsefn9h f clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per min)lbh fn5syq*9yg* h2e ute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a v2m:b2x0zmq yn:zt ef5ertical circle of radius 72.0 cm , as shown in Fig. 5-33. Iftm5z2en: zfb0 :qyxm2 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 round a turn of radius 7amwi+ g4; kjb;7 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 carbimw;j+ 4 g;ka?   

  How large must the coefficientb0b 2 zi/yba7/ ;4,t ckkga/kg1sfpoa of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at 0 1 kg/b/t2 baiy 7/aa,sk;z gfpkoc4ba speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to ro82dnmnk.f.i kc zc )s99rm0 s )qxnd0wtate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own xsw0mcf)n)qkk.d98dn s9.2rmi 0 z cn 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 ro5x+.ktt 8jdg h j)k s.wc/n8dmtating turntable 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 reached and thew8k./ tx)kdd n8ght+.cm j5 sj 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 ,ix 0bv7/7n *n twmgnhtraveling when upside down at the top of a ciwtngmbhn *x0v/i n77, rcle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded top,cu9odx mp+s4 of a hill (radius =95x+,9mu dpos 4c$ \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 mi(n, v9qa ;arranute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost pvr nq ar9,;aa(oint?    rpm

  A bucket of mass 2.00 ka i9f4 xqmj89dg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope i9fajqd48 x9m supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotattt :z78kdr10-lw7ok 8 9yaj(cuxzocee if a particle 9.00 cm from the axis of rotation is to u1oaw 9k0-7xrcd: lo7ykz 8ce (8tjtz experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyl:enges lq 01*p- n8zosindrically walled "room." (See Fig. 5-s0gsq1 pen-8n l eoz*:35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey taasj) ov:vaql ,oz 0f 7ol;aa8ztb(+i- bletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hqio: v0zala tbv; 7,ao-+ ls(zfjo8 a)ole 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 , preciselom/ze wptl - ee.i)b 799qip7ny this time, by not ignoring the weight of the ball whib7ipo9tpme in97/leq. -w )e zch 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 fj 9l5ea9cq q/aor 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 massel b,m87s4hbiv s $ 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 evasivq8k+nnn2o , 6x eimqav9e0)ag e maneuver 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 centomg0hz93n o, 8db,uyjripetal components of the net force exerted on the car (by the ground) in Example bdmn,0ujy ,8o9h o3gz5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolisc5c(bau ;hv/ a 500 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 caah/u b(;v5cto 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 pak r3 )diwx1nh23 ndk5 m h,qr7*mc.mn.w3xuourticular instant, 1wh3. wh cmid 7),3ku.d32n rkn x*5qmxnru moits acceleration 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 12pj2lu--atr;rf9;bh cba; oh7h8+t mf,800 km (2 Earth radii) above the Earth’s surface if its mass is 1; +l2htbfbafao- h8m7;c utp9;h-jrr 350 kg.   

  At the surface of a certain planet, the gravit5 ;tli1rwo zm3(9 sghf qps.f6ational acceleration g has a magnituz( h 6wg.1mr i5tqls;fo fp9s3de 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.ox s+ 7se05: 5teddjs6nbm 5l:ok hna, The Moon's radius is 1.7 n 7a:dshm j0ko55ds e:eotbn+6,l xs54 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a ra bu5mk :7cc2idcz/ n+12mvno xdius 1.5 times that of Earth, but has the same masnx ick moucn2/cmdb+7v 2z5:1 s. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but tcy8 os 0)da57vq)fsyk39 ptuh he same radius. What is s59)yv)qt7a hoycfsdp 0 u3k8 g near its surface?   

  Two objects attract eacw yfkc)vghs:j1)5u pm zp/ g.2h other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective e,vo6 5n v+is,pk0x cavny o0-value of g , the acceleration of gravity, at (a) 3200 mpc50-aon i , ,sk0 ve6vvyx+no    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earthoej-; bux:bb/o7xa:xzi :w x5 where thegravitational accezux5ib::jo wbxa : e-;7 oxbx/leration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five;dq kvkzdu(0 + times the mass of our Sun packed into a sphere about 1kku(d; d qzv0+0 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average staqlm. :g,b7e.0gte jker 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. .:0 tmk.egeeg,ljq7 b What is the surface gravity on this star?    $\times 10^7$

  You are explaining wtla33a; og5fzf:zueve6 ik 9(hy astronauts feel 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 that it isn’t so by calculating the acc(;t6lkz5ev a a:3fuzgi93eo feleration 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 s+; l*pu vm *c)q4mfniside 0.60 m. Calculate the magnitude and direction of the total gravitational force el)4*sqn mc;i* +mpfu vxerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years m6sk8*x grmc n8ost of the planets line up on the same side of the Sun. Calculate the total force on the Earth8r6 ns*gmk8 xc due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleratios95fo3wrp8ab1 beu g;n of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Marw831b bgu ;ro5fsa9pes’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the q asnzzt,2ffby - 944wknown value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that o n 24zyfba9 tfqzw-s,4btained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sateeq,j xy5 i94ywp-lb 5wllite moving in a stable circular orbit about the Earth at a height of 360jyw9p il,e- q5y45wxb 0 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650k;f-ppv4 8c pv7v vib90)mvl c km above the Earth. How fast must the shuttle be moving (relative to Earth) when the releas9fvp7i- cv)4k;bvv 8mp0pvl c e occurs?    $\times 10^3$

  At what rate must a cylindrica,3ik2g a,fkkhe2 eyc1yw/q+ 4a)aa pfl 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 5–32.) kk wiqfa fe k e322a4p1hyc,)a ,a/+yg  

  Determine the time it takes for a satellite to orbit the Eart+(rw5*r dia7- ./wgbjaftlfb h in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very smdj5(l+a/ -gr wif7w .*rbftb aall compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal v56wyvkv i;p 3nq6g1 zielocity would a satellite have to be launched from the top of Mt. Everest to be qi1kp6 v6v3nz y;gwi5placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module contiohv,9*pm l:t)dn1r5 0 mi i1yy rhcaok)1pn4bnued to orbit the Moon at an altitude of about 100 km. How long did it take toky :ro19* in,1)md4av o5)0rcnylimtp hbp1h go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbi.x 9djqfrcz.p;j()yw t the planet. The inner radius of the rings is 73,000 cp.jx9w.; q( dfy)r jz$\mathrm{~km}$ , 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 rotatev5.ph*i dzd ln;f+ps1lav4l 5oo w74xs once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent we.hvo5z14 dplp n+;i4xs w5 lalvo7d*f ight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-k 5g u0z,dq 0a3uk)fsyyg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocit, gdf)u503 zy uaq0ksyy,     ----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 sta2s( 0dyf s5fi m+ct5n v,bm6nfl eti02rs of equal 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 t5( dci6m2n+5,0 0febtnfv lmysfi 2seach?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman)g juleh*1t, d in an elevator that movesh t*jdg1e)ul,
(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 hangulh *r3j4oyd +p2b:szs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum o u+rp3ljs 2h*zybd :4acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the s06vfd dt9tg-k 0xa2.pu p2npcurface of a planet with period T , the density (mass/volume) of the planet i2v d f.ptu 9ng-2c00padtk6p xs $\rho=m / V=3 \pi / G T^{2}$ .
(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 nnoiv6h5ph8b hn:j 1vojy 3 2)determine the period of2vjn8:hjbhn5p hoi o3v6)1 yn an artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acros6qs *hbh d:nz*s, orbits the Sun like the planets. Its period is 410 d. Whadh* nh :s6qz*bt is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of (cmj3m w 892zgzvbb r7 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 m:vue,vqu;vnm** - hg 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: Thmuv-e :g*h,vu nqmv; *e 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 t ;s/e ;w5.kl:xziie zahe center 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, pezglgbyh1e; 9,riod, and mean distance for the four largest moons of Jupiter (those discovered by Gal9ylh;ezgb , 1gileo 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 from( 6hyiwcwm) v. the known period and distance of the Moon. m(i w yh6)wvc.   $\times 10^{24}$

  Determine the mean distance from Jupiter f/4vbck429szekhh: 1 3jey xcbor each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and t941 cj/ h2kk3becxebh:y 4s zvhe 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 consists of many fragments 7ehh5xia+4ynxh v 2on0 r3o,j(which some space scientists think came from a planet tha 7hn hj0i evh+ax4o2rn3x o5y,t 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 "planc f n6ufkk6*0het" 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 same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to pkfnhk*6 6f0 curoduce 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 iu mx/*la0uzr6 n an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what mlrx6 u*z/0ua 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 , s x-,ay-l7,ukjf4 kbg fj.bfacceleration of gravity be half what it is on -,k 7,kylfba xf,4g-jbf us.j the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands p :tej13zpzu1and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0 1p1 ep3jtzz:u.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 apparent accn ;q)v/hg5 urz+dk0,-xgmo rbeleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is thzr/,qmxrdv+ k;g-h5)obng u0 is?    $\times 10^{-1}$

  At what distance from y +jkmeim35h + u)2nruthe Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forcei 2)n5mh3+u kr+muej ys?    $\times 10^8$

  You know your mass is 6 6gbm)i2mf. wy5 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is thei2m)yfgb 6 wm. acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube tha 2b 8:eyvy5wqst 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 rotatio :8qsywb 2ey5vn 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 (df1zgm( mr*5qjh z:x mma 2c(+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 terb* sr 66op-ml,zf,dmrms of its radius r, the acceleration duez-*b66 lfrrd , s,pmmo to gravity at its surface and the gravitational constant G.

A plumb bob (a mass ;vgrx 0584oib on,oeom hanging on a string) is deflected from the vertical by an angl80x e,o nbg o54io;orve $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speedo20s teu 4*3i acscwq: of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle s4s qco*c0u 23 :teiawthe curve?

  How long would a day be n+y r-uauc1y3ametkyf, x2; 2 hgun7 4if the Earth were rotating so fast that objects at the equator were appareny7 h2 t3fuunx ,+n;rma 2yaeyg4k 1uc-tly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart z*joxod9a (xr*l .v j avqe)g+f/;i.wof 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a cu uq.-p2z q0csqrve of radius 235 m. A lamp suspended from the ceiling swings out to an angle o p.qs-0 u2zqcqf 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earw81mb, ra1 mpwth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1w8b pmm1,w ra1.9 $\times 10^{27} \mathrm{~kg}$ , 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 Hub b sbz10 x8uuri8 ro-o)-wwu2kble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from whi )ubur8-8k102or w bsuowzx i-ch 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 traverseyr f7muw; sq 0+y y,4h;watm3ks 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 on thuw ,rsq04+;mmyw k7 y 3ft;yahe 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 fr0k) lz(fxfd24t s*,s;- d tiaru9ts 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 uris0zr9;ft l4-k(t,2s)fd*dfs ax tan 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 km, ivov x/ ui7oi59s meant to orbit the asteroid Eros at a height of about 15 km5 oi9xv7o uv/i . 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 shuttlwreo yg2/ v1yf81fuc.+k; alwe pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satelli lo rewaw28 uf11y y/vg+cf;.kte (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 oc(rcznc 2i7d 08i 7kjqf 3000 years. (a) What is its mean distance from the2ic(nrq cd8j7k0izc 7 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 "flbn.k) j5 qdbt3 fv5+eeel" yourself gravitationally attracted to someone near you. Make reasonlb 5bjnf.t3k 5d+ qe)vable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center o: os+j-e hfchy/vs(s.f the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-yef:eh oy -s.s/+sh(jcvars from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners ofjtm++ zjss4s g;4hhxt0rks9; 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 side of the square+;k;+hh js90t r4stz x gssmj4.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earxjkq4; yrt rv7mb+ 74uw xx.0o2fe0ykth $ \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 cl ub-*/v+wc9 tvf,pm the 1.5-cm-long sweep second hand on your wrw v-*p/mc9l f,vt cbu+ist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around x;tl*j4r,ji min a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. W j;l,ir tm*jx4hat is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travelvw+y l1,ko7(nkwr bz 3uu 7ae/ing at speed+o3r z /v17 n k,ul7kwyeubaw( $ 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, utilizeswn9y2t+gk8pw qq2v2r tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, 9 22rqwtg2 vpqyk nw8+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.$\approx$    $\times 10^2$