Sometimes people say that water is removed f8 sj 3/itl1d j;fb/521.uaqe scp gushrom clothes in a spin dryer by centrifugal force throwing the water outward. What i2; f3uj/jp. ss1edl8ibac1gt5uqh s /s wrong with this statement?

Will the acceleration of a car be the same when the car travetw+w ,g4krialp8wbf 0- ba29gls around a sharp curve at a constant 60 km/h as when it travels g0w ,r-+ p4l2wga9f 8wb baiktaround a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car oy-suokt38./rt:f ii 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 stretch near thtii f or8y-so k.3:ut/e bottom of a hill?

Describe all the forces acting on a child riding a horse on a7 rwxzmuk mauzdl2;7jie)t9,8c+ ;m b merry-go-round. Which of these forces provides2zura,;m 7w)j t8 im9;lmb +kduzc7xe the centripetal acceleration of the child?

A bucket of water can be whirled in a .v c/s:/sgwv vvertical circle without the water spilling out, even at the top of the circle when the bv/vv:w gsc. s/ucket is upside down. Explain.

How many “accelerators” do you have in your +:1 8al9-uy)l px.rolucm 6ll3ci s xncar? There are at least three controls in the car which can be used to cause the car to accelerate. x31ro6.lx l)l:8ccn+ u l-y9 plisamuWhat are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a smallgzy4(a(s:.-0 ydm ur;duum uj 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. Explain this decrease usin d(g0rdum; ym.ja-su (zyuu4:g Newton’s second law.

Why do bicycle riders lean inward when ro8xwk / m ninmjz.w*l4-unding a curve at high speed?

Why do airplanes bank when they *ah;g zbj1d fr5c,6m )pxhj8 73nfhhv turn? How would you compute the banking angle givhf m a3cx5 7,jh f 8vdpgnh6zb1);j*rhen its speed and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plan.my*sw ,m65n f9w6wpfs*zg e de. She wants to let go at .5 p*fne9fmywzs g w d6wm,*6sprecisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large q(34y3lgvf um a force? Consider an appg ulyv4 m(3q3fle
(a) attached to a tree, and (b) falling.

If the Earth’s mass wet1f/ zh xc(f8cre double what it is, in what ways would the Moon’s orbit fx h/(t1c8fcz be different?

Which pulls harder gravitationa3lkki )/ puls;((wvvhlly, the Earth on the Moon, or the Moon on the Earth? Which accele;vw)( u lsi kpk(/hlv3rates more?

The Sun's gravitational pull on)n2v o chc)e5yygzvtw0782*vj( tug y the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pocvjv n8vzyt 0h 5y2)g7tu )c(e2wg*y ull from one side of the Earth to the other.]

Will an object weigh more at the em,6 ijfhg9rgr 2 t))bbquator or at the poles? What two effects are at work? m rh)f gjr,6tb)2gi9b Do they oppose each other?

The gravitational force on therxrreexp ,e (xas 8.p05 r9pq0 Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the Ear0pq r (s905x peer8axxp ,re.rth?

Is the centripetal acceleray- ,h.j5xy4 j0i,yrnsbsg.gd tion of Mars in its orbit around the Sun larger or smaller than the cey4d ,y5ry - .s g.xbji0,nhgjsntripetal acceleration of the Earth?

Would it require less speedtg 0qohs 8w()a to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotatio(ot h08a) gswqn direction.

When will your apparent weight be the greake19r,r w;7nh:em y xx( e:mmatest, as measured by a scale in a movinemwxxmeryh7,a ;(: 1: 9k rmneg 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 are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be j1h5bkvym g2* 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 m2 j1g5vyhb*k 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 23d dl/.lqe v+okft9xexperiences “free fall” or “apparent weightlessness” between steps. f3vk l t.ed/2lo9+xdq

The Earth moves faster in its orbit around the Sun in January than in July dl- :b7b:h)w.tkqv*fytx7vl hg y 03bq fw6s1. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in produciwgtwvs*6 ykt qblbd7:b-vlqyf .1: h 7f)x03hng 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 discove6jfiu7t+ eteh 9(3ig nc *qoa.red to have a moon. Explain how this discovery enabled an estimate of Pluteeot +ii*nj ftgq.( c 3uh7a96o’s mass.

  The Sun's gravitational pull on the Earth is mmn. +kpgme0( duch larger 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 merry-go-round mon0gm+.m(dek p ves 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 travelinghf33/9 xnq gzm 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 centripqy jefm v1ss7fow:vv69z( p5-etal acceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that thq6e(yvv7z 5-wmf 9p1 o s:vsfje Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus ai+i8h:.rd5q eog r( th )mrx/2fqth3as it rotates uniformly in a horizontal circl(o8rgr3tix:5a+hhhe .r/f2itd q )q me (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbih8j / .xgp).rx lcup7bt 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravi8g. /.hc pjubxxp7)lrtational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelenab3q i90rr 2sqh)wsg/ 9nfn8 ration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minnr9s3q8a g/ w9n0)hrn isb2qfute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform uir5ozi k;,9 arate in a vertical circle of radius 72.0 cm , as shown in Fig.or; iz9k5aui , 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 roun7g ,i msb,nbrs10t nk*d a turn of radius 77 m on a flat ro ,ks1,nstg0rbb*m7 ni ad 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 of static friction be between th3 .ll0)xz atohe tires and the road if a car is to round a level curve of rah l.t0a3ozl )xdius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to r1d(z :e)lg krc *awyw1/10gc :eqi qupotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her bacrywi0z/pcgaw()1ku1 : qde: g q*1elc k 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 r.tl lxzx 6him/l6 d:q9p(j lf(otating 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 the coin slz.i(txdhjq6l f9 ll:xm(p/l6ides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed mute8+/+m8ccajhmimuph q/+ u2st a roller coaster be traveling when upside down at the top of a circle /uhcpaituc8 e+mm+ j+8 mh /q2
(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 (inn0ek* u/zbu hj09 +rdscluding the driver) crosses the rounded top ouh/k*0s9z+b r0une d jf 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 ned.m+ gb y1cq,ded to make for the passengers to feel “weightless” at thbq,g+cy.dd m1e topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a km-wig0z( er; zz2r9y vertical circle of radius 1.10 m. At the lowest point of its motio zr9 rikwy0z; 2-mz(gen the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate i ctka62lq1, pif a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,000 kapi1tcl2 , 6q$\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at4 xi9op (bps;d.s z.og9 44y/chyctmy a carnival, people are rotated in a cylindrically walled "room. om444ydg9oy s9 bt(ipchz; s.xy/cp ." (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 rota1a+)h0ayu(z0u.tgi ;)nidrgd2r c zated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central holetzy(a0.iuu agc1)2+ zdn;0d rg a)rhi 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 tr sbrlgoq4s 2z 8.a4bd2 kmde:7ae;a+ he weight of the ball which revoa 4e bd2lg4 ;7eq28o.rambs krzs+d a:lves 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 for,ljc2oy69j) fhtomn+ eksn49 a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses ddplp83w uu61 $ 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 iy xka/g(f1-l 7xs ov;$\mathrm{~m} / \mathrm{s}$ . 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 force exertutpwe glzz2g 8g(,r2s qi 68,xed on the car (by the grw6 gq, e8s8rig (zlt2xz,2ugpound) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pi /po s,9t.6tawb1u0lpb8 vqf.bukk3j4 qd 7qwt 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, 4l3qdb68b9 ,q w.ptfv0ujk waoq/p1.uk bt7s 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 m . At ;t2y rz q-7/a6d1 eqx) xsfxo l0v2b8uobfi c3a particular instant, its accel2ie yq3xaoqlvdt;ur1ob6b 0x s28c/- fz7 f x)eration 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 Eard2w 9-0 l)e9awee wjsqth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg. jqwsl e-wa w2)e9d0e9   

  At the surface of a certain planet, the gravitational acceleration g has a mabit,,u. /1bbnsjhb 3 2wkg b9bgnitude of, ,n/ t.321uskgbjihbbbbw9b 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 acceleratioshvbb2/d; on:n due to gravity on the Moon. The Moon's radius is 1.7;/nbbh 2o :vsd4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, z.ezxxs;r s:hz6c p; i+ 27ulsbut has the same mass. What is t ;+s 2rcz7i;l.sex6 zuxshzp:he acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiushb4ssn t9 +,;k0o sfgc. What +stfk ;ghco40ns ,b9 sis g near its surface?   

  Two objects attract each other gravitationally w0-uu m y8yyl.yki0c t/ith 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 accelerati w1. tzy(ni j vfhbz46q1*.tsgon of gravity, at (a) 3200 mnfyw16z(qz jv. tsght*i14 b.    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Ea3z ya+2+ox +th7xn g96epbanwrth where thegravitational acceleration due to the En 9abe2 pxo7h x+6a+nygtw3z+arth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed in* .bq4x u0tc po)0rvyxto a sphere about 10 km in radi0brou)vtx*cy . xpq4 0us. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was anvc xdekbituq.z.6xecea14 * .)8b4 id average star like our Sun but is now in the last stage of its evolution, is the size of 1bi)8tdze4bu.ek4c *.v xi d6a. excqour Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining wh cw/qe mc6-kfar/0f5 (zz*ez jy 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 acceleration of gravity 250 km above the Earth’s surface inwz(z *cra/f5/ekjfqz m 0-ce6 terms of g.   

  Four 9.5-kg spheres are located at the corners of a fxn82+ g ez;8ng9rod xff.qn9 square of side 0.60 m. Calculate the magnitude and direction of the total gravitatifz ngfn r29qn8 8ox;xfge9 .d+onal force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the pl xz (9spgfn ehbi5*b 5jmql03*anets line up on the same side of the Sun. Calculate the tota 5*s9qpmizf j h5nb3* e(xgb0ll force on the Earth 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 acceleration(mnwp+nl 4 xezy 53i:f of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is (:+we43f5 np mzxniyl 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of thejsf+zfm+ u hvnge3.j02al7qzy fk0* 3 Earth and +zks73gyf0*e3j zum2h nqfva +f.lj 0 its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abour4fkcs s95hzn;;pyy, t the Earth at a,n ch9szfyy; r;5p4 sk height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 kwh2,h4h01 z dw,lihf2 rlg7z ym above the Earth. How fast must the shuttle bezgl h i h7 yh021zdw42rw,l,fh moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occ 8gc;emm o fgk7(sy)+lupants are to experience simulated gm(ke8+gm 7cy l)s;gof ravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to (razc5on yz30 1k8m :m2uwnugorbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height anougu3z0am1: 2nmry w(c8 zk 5bove the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite hbjw8o4 xd3qrq1 tx*h;ave to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth? r4*xq;tox 8qwhd3b j1   

  During an Apollo lunar landing mission, the command module continued to orbit tei :z;r dk8un1he Moon at an altitudnd8 re;k z:i1ue of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. T(mdzsvq5; jm,0j4h zbwirw 4 7he inner radius of the r i;m wvs0bd(zw7m4,zhr jj45qings 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 ht:miu2y ;1zpycv50s 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 y0uz; 5itvh2:sympc1the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center oft5xc- va5h 8 :ymwyt 1ea73 hkhe5f+co the Earth1oy 3t5av h e +8f5hcykh:xcm7ae-5tw's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-si 63m.hi phct2tar system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to 32m6iic pth h.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 wo s69yi1yviiob)t8 8l.k.w; tx5vfl ynman in an elevator that myx8l.o1ksyl;6 yt5f) .nvibwt8ii 9 voves
(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 ceilingloln19 8,nz 5x7mf a)*opuwzl of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What waom751 loxl8,u p l)*nznazw9f s the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with p,d-)xetm4ua 8c4vliks z6q4c eriod T , the density (mass/volume) ic v xmk,zu4ce4ad tl)q-6s8 4of the 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/ untf,h)5 aun-n8n7ky; pqcd) to determine the period of an artificial satellite orbitin8)ny5;c-ak uf7qp,nq n nht/ug very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits th7n4fhlyfhu3 :e Sun like the planets. Its period is 410 d. What is in h4y uh:fl3f7ts mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average disu+h93zvar-gy w j:5y cx. g)kpu6 rm)itance 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 +v0pir,sqdt0 vqs2 3p5 e;ba5*e fzd honce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest5+3erpd qt 0vq*p5 ;h0vzis, edsba2f distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the G aw2hi qgp8+3v42qmqsalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, au5t w34y b jr0b e0x(1vait3ewnd mean distance for the four largest moons of Jupiter (those discovered by Galileo in 16at v53 xybtb3 0uie1w4jew( 0r09).
(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 periosxtt8zuth3; ic 5f0v m6ujvcey29q , 3d and distance of the Moon. c3tv;3equs vyx6tif8h0u9z,jt2 c5m    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiterag a+49 8xyvjo’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table. aja4xv+go9y 8
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (whipc cc2-hg)p* ich some space scientists gpc*p )chci-2 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 deswif1 /i( *fo;p1vkrun cribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagiwp(uok;1 iif /r1*nvf ne 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 a hanging vine (Fig. 5–to6(o 7nftntw2gt 3-v4xbeu /snx +x.41). If his arms are capable of exerting a forco t4fnsxn(vo6 wbxn7xtge ut+2 .t/-3e 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 acceleration of gravjy9t q1a+)mixt z4k8uity be half what it is)k+184ti zyamq jt9ux on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab ha fonyi6cg , 7a16ullu7nds and spin in a mutual circle once every 2.5 s. If we assume their arms are ea7aygl 1fui 76nu,o cl6ch 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once n -(hz,rafl/4/avn zz ,od ,rmcg60r0kg1 tld per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate hr fz/l4(rd,caga-, 0md1lz r6nog ,/0kzvtn the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling direy)kc)ye 3ri q5ctly from the Earth to the Moon experience)yk3qi) e 5yrc zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 6i (plc65c7ld e46hvv6-vc bb(i+pv ud 5 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of thevicv uedc- db7p5cv6p (lh4l6v+6( ib elevator, and in which direction?     ----待选择----upwartddown 

  A projected space statocdai (y; ntxs*p; u7f(r3v 8bion consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. Whaux3 fip*dn(oc ;v7bsa 8( yt;rt 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 (Figi*51hu+viiv b . 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 o j5-y acumr)nm/b68nl f its radius r, the acceleration due to g5 j/ 8malun)rmn-bcy 6ravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the verticalc36k+/xdba fgc75bo*6hm 0 b4rgqet i by an anbogt b 6bc6+h4g dfx3e5mqar7k/c *0igle $\theta$ 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 sperjqjj8nyj(7/5 x+ hxau ;ze64*cpplmed of If the coefficient of static friction is 0.30 (wet8(lhjq p;ceymj+*n47px5 j z6ua jx/r pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were bf0,uqxlym cv175ab 0rotating so fast that objects at the equator we 0b17u faxm0 b,l5ycvqre apparently weightless?    $\times 10^3$s

  Two equal-mass starsj-8ot q+8j/ec* oaokb4 as, ih maintain a 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 speed rounds a curve of radius 235 m. A lamp)6ipl.u1vm enq 125jkxu wwa+ suspended 62 vea il.w1u p+ujq5kx1 )wnmfrom the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has j/ay cr w*(cpkn7.)mq 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 pcnyqrcj( ma./w*k7 ) =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 Te:ckkj:(uk+c- rniq* mbw q1+alescope deduced the presence of an extremel+jw1 uk+ :(cn*akc-qqbr: ikmy 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 of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and ydc4u, f6xbu8 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 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 rox,fu84cuby6 dad at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 vze y cs5 3756cjh9 ann4+ -alaq;nhabsatellites orbiting the Earth. Using “triangulation” and signals transmitted by these satel l9y-z+a 7he55s 6 cacjnab v4;qhnn3alites, 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 /g1mkl : lr.di2hfqzbnh1,p8 meant to orbit the2f ih qg :rmnh.ldk81b,1/ zpl asteroid 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 4do d0dd+.1 f0x1ikhxfoi of/ need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 kf0xid41fikxdho +0d/f doo . 1m 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 pe lel14qj:rjy -t12wzpwb2on,riod of 3000 years. (a) What is its mean distance from tly1n pz1 bjjqt-2 ,elwwo 2:r4he 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 of5mq.e,) ubc kp G would need to be if you could actually "feel" yourself ck,b m5 .e)uqpgravitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the ce k(9dfraz6n+ kf4-;.iw lm zqc m3n(hlnter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from thmnh3l6fnz+9a4. fdkr(q k(-l; ciz mwe 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 of a squarzo, uodh 883doe 0.50 m on each side. Find the magnitude and direction of thz3o 8 u8dodo,he gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass ( oybh9 k,6 y;nuucpj so1w5n45500 kg 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 the tip of the 1.5-cmyi cjfm7;z vt*s j b6*7sg7bj;-long sweep second hand ;**zvjyj 7ts7 b;gj fsb6 7imcon your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored annu4nl,7 rhq 0rw.qq(rpz 0v 2rd start 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 s7wr ( nqhlzu0 q2,rrqvn40.rp. 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 newf4s4nmg. b ,2 pappkq,i7/vfooy. /nr highway is designed so that a car travelin4nk,i,fbso /n47 aqp/ r mppovgy .f2.g at 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 th):m54yx1huz flzu* js2wul+ 2kbt lv4e cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 624w+)u5:4xkjluh yvz zm2tu f 12b*lls0 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.$\approx$    $\times 10^2$