Sometimes people say that water is removed from clothes in ;0cfb 0 1jg1ynxuut6qa1gp3i a spin dryer by centrifugal force6g30jbp1y fgtu x a;n10i cuq1 throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travj ju9 wc24dkk2els around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the s jd jk2wk49uc2ame speed? Explain.

Suppose a car moves at constant speed along a hilly r vj++u/ jbyn-t kfl7e0w v8px3oad. 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 stretcjb+ 30eywpvtu 8xj l7/ fkn+-vh near the bottom of a hill?

Describe all the forces acting on a child riding a horse on;toz8ayz6cf 72j wzu* v8wp9p a merry-go-round. Which of these forces provides the centripetal zfw2pozwt 6 pv* z;8a97 c8ujyacceleration of the child?

A bucket of water can be whirled in a verdh* yx,s 5 /shs*thw0qncg :3btical circle without the water spilling out, e bqnsx h03/c5*s,g*thhsw:dy ven at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least t -quz /ljnay)q09nd0by 3,p hbhree controls in the car which can be used to cause the car to accel-aj,p 3 ny)/hqn d0b9lq uyzb0erate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a sm + a*oeab jql-8l+q0kgall hill, as shown in Fig. 5–31. 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. Expao0e8+ lkq-qjbl* a+glain this decrease using Newton’s second law.

Why do bicycle riders l(fy,9kpl /sqbq8w.nlean inward when rounding a curve at high speed?

Why do airplanes ban k0xz1,l3nk crj :u.dok when they turn? How would you compute the banking angle given itl30 ,dxjo cz:kruk. n1s speed and radius of the turn?

A girl is whirling a ball on a string around yq6a+*j.z . n mcybt1klovu7,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. Wh1+.ykql7b.v,cm o at6zj*u nyen should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so,2d3iwt4sc8c goylj3k7 ak:s( how large a force? Consider an apoc2t kiy:3dw g7kas4cs3 j(l8ple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublem4xs9 m;u)c(9m7,hj.ug miviq zr( s8cb-fwu what it is, in what ways would the Moon’s orbit be different?s7qv rxu.cg(m ,9;49w uzsi -f) uch jimbm8m(

Which pulls harder gravitationally, the Earth on the Moon,f zvgbae h ,,fir61a;q5hr(i0 or the Moon on the Earth? Which accelerates 6 rb;av e0hha1,(gr,5q fizfi more?

The Sun's gravitational pull on0rbl 8bxr w)d* the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tide8w*rlrd)x b0bs. 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 orxfsi)tl r0vu2 i;2ld t1e9v1d at the poles? What two effects are at wt012vu l s)9t dxi1vdil2 er;fork? Do they oppose each other?

The gravitational force on the Mooag (c*-akapydu + g5b(n due to the Earth is only about half the force on the Moon due to the Sun. Why i(g -(+bk ucypa5ada *gsn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Marsmtev,f *:lsy0 in its orbit around the Sun larger or smaller than the centripetamtf:,sy*elv0 l acceleration of the Earth?

Would it require less speed to la,iwxpc gob l6tx4-3t2 unch a satellite (a) toward the east or (b) toward tcwg-i4l2 xtxb p6o3t ,he west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatesmo :, k(ihxevxe -y;f2i0o n3st, as measured by a scale in a moving enxokf3(imoi2sh0y e ;-v: ex,levator: 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 are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space r d;z7e vqbta3;: d2efcould be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects2dedvearf; 7q: tb3z ; of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessnes; kkwd9oc3az9q f-wu v8i(+sxs” between steps.is q ;w+aw938z (f9okxd-vku c

The Earth moves faster in,ec8m 0nv ;obs p7h5irz tl)x2 its orbit around the Sun in January than in July. Is the Earth close0x)r 5omhv ben7p cz2,;t lis8r 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 the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a msd rn( /(9d,fu ,pirvjoon. Explain how this discovery enapvi frn/,d,(9rju(ds bled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. w)etbj (c:i )vmeeb)18x - nduYet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull fr x8)m:uetec)bb1ej d inv(w )-om 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 travelink6w4xd. lq 6ydg 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 accelhq) j1f-8dqjs- 2j sow9k6d iteration of the Earth in its orbit around the Sun, and the net force exerted d) qq 1d2s9 io8jh-fswkt-j 6jon 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 2.057)zceg99khr4kt*x ggpz* lt -kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate tr 9txg)p*4tlg57z zkh*gck 9ehe speed of the discus.   

  Suppose the space shutokme j1 0as6y)yh 72mgtle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttlh2gj) 0a7y1ky ms m6eoe 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 acceleratio-4vg;zwe./5n kb:j mxnhomc*n of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revol*gj co -n/:m5;z.bhn kv 4xmewutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is wi o7jz7x:k63d x ( ef-b.2mmf j:gltqrevolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If im m3bjz7q : -e2i d7fflgjkt:6( woxx.ts 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 77uo(;o2.kxj yy m on a flat road if the uoy(2k;yj .oxcoefficient 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 of static friction be between the tm9gj*;-wwnc o fis)iqn4(w s4 ires and the road if a car is to round a level curve of radius 85 m at4 qi)n; ss*wmwo-f j4iw (9ngc a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designe)auwn m+ xhdpd/mbok 6z1+f6-nzv.3 ld to rotate 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/ohx+u6znmpwfd l+a)v -b1d3z.kn m6 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 rc )-aant73dm1kzxt/ cw 8 +ue;0o vtmjotating turntable of variable speed. When the speed of the turntable is slowly increased, n;7u+o)mwt-m3k1dxct/tv jez a 0c8a the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveli/e r3o;w 0p 8aciz+ke)n bm-atng when upside down at the rkca/pabe +0)w3-n8io mz; et top 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 r6wi(5.p uoc7qn0mib:rs * t3afndd: aounded top of fan tin*pdr:3. 0:cb sai(o5udm67 wq a hill (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 g4 ht 1g./upecneed to make for the passengers to feel “weightlet/ugp.ec1 h 4gss” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radh/zn 0cbymz x04bfyz6 x:k1f5ius 1.10 m. At the lowest point of its motion the tension in the ro/kmzfy 4yb5xz0xcf :bh10z 6n pe 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 rotvcrx zfdc5v830pj gv2 i4tv4m c8o-5nate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,g85c58j t44npzd2rc3 f0- c mvovvvxi000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, 7m2u *fxr wp)opeople are rotated in a cylindrically walled "rooo 2 wm)xrf*pu7m." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey )md)srzb 9 s1ctabletop, and is held in this orbit by a light cord connected to a dangling block (mass brz d)mcs)91sm ) 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 ignoring:bl ox)jl (ov( dbyru+)2kyq 0 the weight of the ball which revolves on a string kb)xo2 +q( byy)u:o0vldjlr(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 traveling 75 aktvmins:z3(xfaau9jg97 u32a h7 f) $\mathrm{~km} / \mathrm{h}$ , 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 massex ub2u-f*9m 1,s;mxgdbh7 vynt j92e ns $ 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 divin o,/n mlbwt+ls2 9prk6g 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 centripetal components of the net forc yg;2bi1:7ywj t3yeq tfa9.z ce exerted on the car (by the gro2gt9 3tj;ybiy.7: ywcaezf1q und) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly:;asl(beed: c 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 (e bs;a:celd:the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius.sp r 6nv2xuy,6mbif rg96;df 2.90 m . At a particular instant, its acceleration pvd;u6nyr2,f6fr si9g .x6m bis 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 f,jzm 8tf)w.axmvu14on a spacecraft 12,800 km (2 Earth radii)w4.m ft z)ja 1vu8,fmx above the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g huauh6 k zf128kas a magnit28u kk6 1zuahfude 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 *. f(ckjzoe9s due to gravity on the Moon. The Moon's radius is 1.74f k*ojz9.(esc $\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 op y5i mj qua/pu*21y+wz+ f-zsf Earth, but has the same massmuyq y f-z+j 2uw*apsz/5pi1+. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius. +i5w-rvnp ty5 u5 y82ksi7q( qlabke;Wh wlni52apv5+y;qr ebkskq 875i - ytu(at is g near its surface?   

  Two objects attract each other gravitationally wi b si-f/gb , azu u,sfavrl*z9m/kbqf0.w*47ith a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleramft o9-hqn s,(5 n*gljtion of gravity, at (a) 3200 m l ,hn 5j(nst9 q-fgmo*   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsi3hd77zwa edbz0, erd bv.1+l:*oe qaode the Earth where thegravitational acceleration due to the E7vzdqdho a:+owdbeaerl*zb, 0 .13 e7arth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fivi01px ccn31:o w8e xlse times the mass of our Sun packed into a sphere about 10 km in radius. Estimate tnxiel 8wc: 3cpxo s101he surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun buteea / *jdzhpa)l7(fp; is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What ie pa )/;a(7l e*fjhzpds the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while 4bi trqt93fip44o si1(q and ,t(cl s(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 acceleratiob t,d3(a1q(ris( tfl4 4q ipno49cs tin 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 ng4 f qc 4tb2syj,:wq2rqz18n m. Calculate the magnitude and direction of the total gravitational force exerted on one s 4qw:4r2 qg s2 jcyq8nt,fnz1bphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets li*/*wh;b 3brx wr by5u kr,ix6bne up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturbb/ hku*y 5,;36i r rwxw*rxbbn, 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 acceleration of 8+5p2jp e5v-2jmyg qp ,g :3 lcpak,0olacdfqgravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 k80 gagk 2f-v,,3l jepc+pc:qjqd5p myp2o5al m, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known 9 s*amegc*sqv600 2 esavu0qf value for the period of the Earth and its distance from the Sun. [Note: Compare your *avc 2eg69q00e*fvum0s asq s answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving o;ppe;l1hmd 1/dmr6t)xo3ndy3 y 7qd in a stable circular orbit about the Earth at a height o3y;dm/1 po d7h)e dy x;q rtp13ndml6of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 65- k6vle-7k orge)uz 4eo/ix3k0 km above the Earth 34zekx )k /or-vk7g-eilo6ue. How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants arz55w h52 ptajn50uaadf xpn-)e 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 revothpjn2z awd- p5550u5xnfa )a lution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth ivc3a y. yt hnpccxe kmg-)59,4n a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of thn)ccm t-h5.vp 9k gyay34cxe,e satellite?    s ~    min

  At what horizontal velocity would a satellite have to be laun 9. iolqx/gc(i 7ahk,p:rrj9mched from the top of /,7 (. mk lxjqirca9i 9gp:rohMt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continux/y (orxy:u1z/wmdmle b5*d 2 ed to orbit th1b:/oy*y mxdr2wdx m(z5eul/ e Moon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of ch( lolk,l9-hh*g(vy eiunks of ice that orbit the planet. The inner radi*(hih- ,o l y(vglkle9us 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 xo;;xq66zq8 aa*rudj once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bott;zxaxq*6 dr u6 8;qajoom?
(a)    (b)   

  What is the apparent weight+kpu3 . ;*ky- kdqsgag of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) qkugks+3 k .d;-yag*p 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 j 6egomvr mkv6c53*g-d55coqequal mass. They are observed to be separated by 360 million km and taq-cgm6c5m drkeg v 3v6j 5*o5oke 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman0sq kj-en )up5u5kv3m in an elevator that mov 3v0 um5sq-k) kpeunj5es
(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 gz80t8m5ex/nry.: 2xywe wzs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelera exzx0y5rm2w:.gz8/wt es8 y ntes. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with pe lm 8mkts;hn0 iwb+8x0riod T , the density (mass/volume) of the planetxk8;ti+wsm00mb8 ln h 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 f07pfm sqrv 9y-w-sg(hp/ 9gdd) to determine the period of an artificial satellite orbiting very near the 7yqm0 -s9v9 /g-gspp ff(wrd hEarth’s surface.    s

  The asteroid Icarus, though o s v4i)7t5gzn6/ ey,dy:ihvz knly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distancetv:5s4y ,iveny7)6k/ d zgihz from the Sun?    $\times 10^{11}$

  Neptune is an average k)k0jqaz6 ( ipdistance 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 roughm 5q d;u 2 ifqsc48p 2mj3a5r6yux;mobly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar 3oa26 ir4qmm;f5ujcpu2mxd 85; sbyq 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 of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the G;7mif6tl6/v0:euof(jn acw salaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest mot.mhrtwbr3*sq 7 x3c7ons of Jupiter (those discovered b7 rc*7 .hxq3wbts3mtry 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 from the known period and distance of thenb1v4- tnb zx/g6rt +e Moon. +nxe/ 6n4-bgrv1btzt   $\times 10^{24}$

  Determine the mean distance from Ju2r- sj 1qf 9s9jh5p zg*rgntsy5 -q0fdpiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3.g9r h1f 05*jz2t pgqssf y9j -ds5-qrn 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 ;4k5) f+qyridyuse l, and Jupiter consists of many fragments (which some sp 4ieqr5kyldyfu;+, s)ace scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describh*j3 nobh2d4 e0h7 f/(w7raf mhof:dues an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on77of*ho:d w3 me h(uhhf dr2/4ab0nfj 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, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from 80975us9bqz,dz z j0ns ctbska hanging vine (Fig. 5–41). If hiss jz k z5s0b90nsqbd9z8 7,utc 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 swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleratio f bm1k9lsd4d 6a1,rswn of gravity be half what it is,r6a9s dwb1k 4sfd1ml on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spinvr * (r1iiid9i in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one aniiv1i *ri(r 9dother?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accepqo;s;lf1g53lapx:e0n + okmleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effec1nko+3el0pfgq ;;xpml5: ao s t. What fraction of g is this?    $\times 10^{-1}$

  At what distance from taidu8sx 8p.9 bhe Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth. 88sdu 9ipbxa and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 pc vm(x;ee*qz yqh+evx :3+n 5kg, but when you stand on a bathroom scale in an elevator, it sayc nehm+xv ez *:q(3+5yp;e qvxs your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circulaw4-p+nnfgog 3r tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tuben +w-ggpo43nf 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 vertx2o ,fbbo*kd)wdih5k6 8v2gcical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the acceli)dsic y ; -ji(sxx+n5eration due to gravity at its surface and the gravitational constantxs5 -cinixis(y d;+ j) G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical bsc sz5zr4l8 )uy anl u 5sz)s8zcr4 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 bav/ r-ifwlv k(26u+lgt 5zp2fgnked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), atfpigz+5/vw -tkufgl2( 62rv l what range of speeds can a car safely handle the curve?

  How long would a day be if the Eaa:/.z9 (ythyqbpn pd(rth were rotating so fast that objects at the equator were apqy. zb/p9 na:d(p (ythparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apar97+y1awtdzz- /*; xtwgaq v+wny/m rct of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A .tz lg8k5 tw,ilamp suspended from the ceiling swings out to an angle ,g85w.tlkizt of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times af8d zi7a w r 2y03z5nmwp2fb4zs 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 a 0z 2dniw8b23p4zzmywff7 5r 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 Hubble Space Telescope deduced tltqf 05e 5)xjghe presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escape)l0 xj5t fq5egs). 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 ,-byyr dn p6ck+jwm)(speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley hamry- 6j+bny (kdc w,)pve 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 Positioning System (GPS) utilizes a gr9 jm (lo( :8g)nupp)tqld 0xjus(6i fyoup of 24 satellites orbiting the Earth. Using “triangulation” and signals( jsg(06 )f(uutlqi9d : ypmjl)x n8op transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 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, is mev8aby guplxxi x.1at n*7*kp:eca .wb v(*00 iant to orbit the ast:v c (p*l1 8awb.aa x.e*vt0xgp*biki7y x0uneroid 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 pursuing a satellite in need oer7ka 9f5nb8qf repair. You are in a circular orbit of the same radius as the satellite (400 km above tka58 n7r9 qfbehe 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 *emrh x2vh; 3e1g vsqfpd 5-f.mean distance from the 3 2mhd xph.fgqfe1vvs-* 5;reSun?   
(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 kl*8lgml zm2. would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, likel8mkz2m. ll g* F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy i0vgicwro+cs -rt1+ szs2z /6(Fig. 5-46) at a distance of a6ot0cswi -rzczrv/+sg+ i 1 s2bout 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 locawqiez : v*bi+zoj4l/5ted 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 siq4 * iiojvw+:elz5bz/ de of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg or 1;wi t7t)tc gz1oknd6bits 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 theb:;(4 chz crp7 llqk-u tip of the 1.5-cm-long sweep second hand on your wrisl:kuzq-bpcr(7;c l 4 ht watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a dlp(gm s9//fb sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a completel9md(g ps// fb circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway :o,a7z)atf -o m bhmxm;gg/ 6bis designed so that a car traveling o:tbgo z bg;mfmahm- )a,/ 67xat speed $ 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, utilizes tilt of thtgs,edt(1irc2( gtizz z 2+t *e 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(* r1ggizt2(et +i dzz2 c,tts 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.$\approx$    $\times 10^2$