Sometimes people say that water is +s s70e lazcspun9c )4removed from clothes in a spin dryer by centrifugal force throwing the wateranszsp+479l 0)sue cc outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car trav3bshk) 9 k7vr swzj wmbl.)d67els around a sharp curve at a constant 60 km36)kmwdsblkjvb797. z)hwrs/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wd+c43pos;z tu here does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between u 4 os+3dpt;zctwo hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a mercqc(/bil4-q5p x *v ssry-go-round. Which of these forcbv -cc/pss i4x q5(lq*es provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle dxpk3 n6r45as64 tpsfwithout the water spilling out, even astp5nspkda 66r4 34 fxt the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car69c4re nze) th? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?he)n9 rtze6c 4

A child on a sled comes flying over the crest of a svcc3s,: dhpzkf /u 64jmall 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 slep3v/jcdzfcs 46:uk ,h d decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders leanj,0zbkibbhh:;s) c )o :nw c3 j66hxcu inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankin* ezpg57kl*)7sf i0dyirr4p jg angle given its speed and r sde*57 if0 kplrprz)* j74ygiadius of the turn?

A girl is whirling a ball on a string around her head inlm ,i.73guoi 9/dic xs a horizontal plane. She wants to let go at precisely the right time so that the ball w.mui,lxi d 79i3/gsc oill 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 d8i/s/ lt*;:dqei y emo3hco0a force? Consid/iq3 8*dyet :0elc;s d/mi ohoer an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moohegnkd al2w7n(3as 87 n’s orbit bedgn8l (h7s ak2ean3 7w different?

Which pulls harder gravitationally, the Earth on )h( cp uyb8j,48nhamithe Moon, or the Moon on the Earth? Which accelerates mou8ynji( m bha)c p8,4hre?

The Sun's gravitational pull on the Earth is s.)e7oms x+dtmuch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in.m +osd tsx)7e gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at ta l1r (p raavu+j)ke+*ut/1w yhe poles? What two effects are at wo* 1kr(u1wl) +yrujva +a/pate rk? Do they oppose each other?

The gravitational fo rs-+aw8bati4rce on the Moon due to the Earth is only about half the force on sr4 it-8awba+the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleratio m3 ( hn3/h wk,qlgbt(i+gm;omn of Mars in its orbit around the Sun larger or smaller than the c m;+obn itwm k,3mq (h3gh/lg(entripetal acceleration of the Earth?

Would it require less speed to launch a satellite (aqlizbhl q5-vtobte/i:7 44t() toward the east or (b) toward the west? Consider the Earth’s rotationhi/lbi 4ov e7:ttqbt5l 4-zq( direction.

When will your apparent wee3 ki/kynm5miey ):4 bight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) acki3) y m: 45nyikeem/bcelerates 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 ou.eu+u xa /rxr0ter space could be adversely affected by weightlessness. One way to simulate gravity is to shape t.0rxx +eaur/u he spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “appa h(sndxd.x 73lrent weightlessness” between d3 nd(hxx.7s lsteps.

The Earth moves faster in its i c1:etyy3( +8c ( vasjxpcxe+orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main: jpsc+i x vcy8y cx+te((3a1e 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 )m gj8rf(feo +u.vx,b3wy hu(+nt, futo have a moon. Explain how this discovery enabled anrw3n fofu te 8,hg).u x(+v ,(bjfmy+u estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much lar*ui sb.0 aqw)*sdi*sx o/kr7g ger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider wsssqka* gixob.) /i0 *7r*udthe 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 1980knu), 8 .su(jclgxulwo xi6+/ $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 aromf g) ;g9x/*ox/oe etlund the Sun, and the net force exerted on the Earth. What exerts this force on thee o)x/og9gl* ex;/fm t 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 214gl6 5t3lqbid u:) awx0 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. Calc g6dqibaw 5llux t34):ulate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circf+p9 e ti43rb2j ss/xhles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer inp23 tf+s /eb9xsrj4 ih terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the azv 0odid)71j6ir uhm )(6psc2 jaja,lcceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per6mh1j7a0iz,iorva( u2d6dc)) l sj pj minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a strmc,av qj6n.*k ing is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.0m .kan*c6q,vj0 $\mathrm{~m} / \mathrm{s}$ 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 obv b.q4qr /od+bxv wp r7(b,1wmf 85xzf radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this resu,x/ xzf.8w47( +5d1vpqvbbwobqrrbm lt independent of the mass of the car?   

  How large must the coecbn7zfwp+y4 9,jdk-qfficient of static friction be between the tires and the road if a cw-9npf z,bj q7+cd k4yar is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronau 3hj:/ xjrm0wuts and jet fighter pilots is designed 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.m/:w u0hjrx3j 85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntabcmp;rlkqvv:)nv.st2 :m o-b3le 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 slid b:m;s.v- n vk)v3rp qct:ml2oes off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaste4lq.jip0 7s+am-aivo r be traveling when upside down at the top of a +lm.aqv-o j740i apsi 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) crosse u-t mtq.rvz b0dv,74ns the rounded top of a hill zu4qdt .vm ,v -n07btr(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-ditsd :9i9o1yz iameter Ferris wheel need to make for the passengers to feel “weightless” at the 99d: itzyso1itopmost point?    rpm

  A bucket of mass 2.00 kg is .4-onpf(f r)*m wcymz whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in rzc 4nypf )m( .wof-m*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 if a part.uy cl4f(rs 1mtj3 m/ux(.rvsd :0auficle 9.00 cm from the axis of rotation is to experience an3x(4u1fmlu (u a0v:s.sdrr.m cyj/tf acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people ar5dw:nos b g1n5e rotated in a cylindrically walled "room." (See Fig. 5-35.)5sngb dn wo51:
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 fri f/ k- s qs:un,qao-brrw3:2ipctionless air-hockey tabletop, and is held in this orbit by a light cord connected to a qfbusqn/aw:o- 3k:2r ,si r-pdangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , pi x9 gocdabk7/xjtb*.li1 ;,t igt-9krecisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long1 kkg. cbt/l t;jxbg7i9a9diix o, t-*. 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 gqt(hvp67 cn ;is perfectly banked for 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 massefa5flf r/j 45;s5/iwx8 lumrk 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 evasive maneuver by diving verticallyp3+3gndl()jku pd;qv uhr; y6 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 force p(8x 9.ui w 4ya:zwdu 7uqc9p8 8ewphvexerted on the car (by the ground) .pp4we8 z(i8vyqc 7udh9 w98wp :uuax 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 pit 1 ejuhz sz;:yz ii)a56ne x5z0area, 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 coeff6izey)hn 0iz ;1sa:ez5zjx5 u icient 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 horizz8x)oz :j-c,ta7 pbi.ra- jfdontal circle of radius 2.90 m . At a particular insta dox -azt b8czp 7:jfj-.)ira,nt, its 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 spacecra3mx5fyx pksr)k;wauu )p/i m.vv7/p 9ft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg. k3w7 p/y xfxm)5u ;a )pv/9vkmiur.ps  

  At the surface of a certain planet, the gravitational ac kot+fnu4 jg47celeration g has a magnitud gt+o7knf4u4je 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 dueg 6l +6e2-w 30fvdvzho zb(gxx to gravity on the Moon. The Moon's radius is 1.74 0g6dbwl+zx3gfhz-eo (6v 2 vx$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but h*a5dq 1o/3e0cel o wfwas the same mass. What is the acceleration due to gravity near its surfac0/wf35 oaoeqcw ld1*ee?   

  A hypothetical planet has a mass 1.66 ti vnk*p:*+e-ww hwktc*60kzmr; jh6o omes that of Earth, but the same radius. What is g near-mw ;0* owwh6rkk*tp +ej :6 kcnoh*zv its surface?   

  Two objects attract each other gravitationally 51;hwt.n av lk/,rni1y j(q9fu ccdh2with 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 acceleration of gravity, at :f7 tx-/xx mtdrmmr..(a) 3200 mtrx/:fx dxmt.rm m7-.    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point out t./r c7rx,+vsc,p)lx:v dy4v ts3 zsgside the Earth where thegravitational acceleratsc+r3tv:lzr,sd) x,vyx47 gp s /ct.v ion due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun pagd:b7 ey jh nay2-eg1dro i6*5cked into a sphere about 10 km in r redg7 oy:eb*iyh5j6d12g -anadius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which92mqc s:qk/xav9r 4 7h d,,ki lcfevd) once was an average star like our Sun but is now in the last stage of its evolution, is tlkhd rqc q,a9 i/s7mx9f4c k:v2v) ,dehe size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless 0sotiddkm bs- m414t7while orbiting in the space shuttle. Yomtd o-mbk70id s441t sur 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 in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calcuqn/* x13cwfwn late the magnitude and direction of the t3n*1 qcwn fwx/otal gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of4o6 nmwclhjuc.0/kp 3 the Sun. Calculate the total fo n/mpcw j06h3lco4 k.urce 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 of gravity at the surface oee7:l65y ovvzvi4 l(mapd9l 6s3dd e3 f Mars is 0.38 of what it is on Earth, anpead9l(svyd 4z v3: o vil6ee57ld3 6md that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the per.5j0ira08,ro:,gbfx4i upp.s(w viwze-aw eiod of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Examp wagzpf0ij ra. w 4evsp(rxuo0w,8ii5 b,-.e:le 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving inp+ okxo0 o,dmhw8wr(2 a stable circular orbit about the Earth at a height of dx0k8,+( 2phow orwom3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circultu,foq+k(y lso4 s. f;ar orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release o.yuol ksst4(f ;+ o,qfccurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants0hhe5hf bwxk 8d e/4bm)b- e0y are to experience sme/ hhhekbdyb400 )e fbx-5w8imulated 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.)   

  Determine the time it takes for a smzk/yqx8 gx6y +atet3ap2 (g. atellite to orbit the Earth in 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 tpa 6ma8/yz(gxt3+xkt2e qyg.he satellite?    s ~    min

  At what horizontal velociy1h4 cmpvs. j/ty would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit aro /j1hpcs 4vym.und the Earth?   

  During an Apollo lunar landing mission, the command module continued to j: fu lp+a *vppbx/.2gorbit the Moon at an altitude of about 100 km. How long did it take bguav+pl*pp.fj 2 : /xto go around the Moon once?    s

  The rings of Saturn are compz r g7ohv)9on7osed of chunks of ice that orbit the planet. The inner radius of the rings is 7hov9r 77z gn)o3,000 $\mathrm{~km}$ , 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 yh5g*-zsf 7p1+ lhkgmdiameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a pers *gh+f 7yh1-5p mklsgzon’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg azvqn 1zt- w0(lak+5xcstronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) - lk01w tx(v5+nczqaz 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 ok:3d-j66fv4nv g :vw koc 3ljrf equal mass. They are observed to be separated by 360 minwf:36c d6k jv jv-gov:4lk 3rllion km and take 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 scn3y 2 oss 802lop9 (medr+2-i omvznseale read for the weight of a 55-kg woman in an elevator that 22 e+ 8-dimonls nms3o2zvy0por(9esmoves
(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 susfuk37fd- n68q/k ,nh c 3xqm dx,mgzs,pended from the ceiling of an elevator. The cord cankx,c /-3fhm,un fn8sx d7 6mk 3zg,qdq withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellit 0n5-s;ngnypbk dq30 le orbits very near the surface of a planet with period T , the density (ln3n 5-kq d bgs;n0yp0mass/volume) of 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 d) to determine the perezs7sr3wpg 2 9iod of an artificial satellite orbitingsrs7g239zew p very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred metezgozlqm), 72 brs across, orbits the Sun like the planets. Its period is 410 d. What is its mean distz7 lqo,z )g2bmance from the Sun?    $\times 10^{11}$

  Neptune is an average dw7zhn x0i7 xvk6z 8g2distance 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 til/qf , 9:l6rym y-34 suzdpikhe Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fi9pi/ iz u4r y mly-6,dsklf:3qg. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the c ;.qtx 4w,dm1( kxky8jkw(jf Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and m0ldyx1t9/ 5vvlm) tacl:22hi dv3en0 pvd/ab ean distance for the four largest moons of Jupiter (those discovered by 2vm0xdtb09ll/e vv y 5pld: /a)dacvh 23in1tGalileo 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 h wo60fdx,l n7the known period and distance of the Moon. 7dox6,wnhl0f    $\times 10^{24}$

  Determine the mean distance f8-kc+urlcn l.cc6 rz 4rom Jupiter for each of Jupiter’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 Tclcc.kr8ru lzn -c46+able.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments jotmmtec/dns p-,l/-u;t+y v, c(o :f(which some space scientists think came ,evy,(o-/dm:m/+ lcnup t ;toj s-tcffrom a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of a d0+,j: teiy: h s6eik sp-cv,jband completely encircling a sun (Fig. 5-40). The:pts i,ckjy-hi6j v,d :s +0ee inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 5–m*5 s.2uv+u wr agut-b41). If his arms are capable of exerting a force of 1400 N uwvmsgrb5- ua+* tu2 .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 surfno v zb/x 0dq7ad.b*t*ace will the acceleration of gravity be half what i7*qd0 btad o.x*/bnzv t is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circlmla.m uih 9d:)jxz26re once eve2.ha 6rli x) udm:mz9jry 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 another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravqi dyzi6n:h jm;q;s*7 ity 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 gsd:*z6j; m; i7q hyqin is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directnlc5 +4d(z kruly from the Earth to the Moon experience zero net fod +5zln(cruk4 rce because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stanu bfdx6qnk(pa t 133q*g6k4d4b.mvtod on a bathroom scale in an elevator, it says your mass is 82 kg. What tm1bqdnp (.otfv g3a64*bkkq 4d3x6u is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circulara eoqk x19pb)ix 9m*e:fmex7; 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. What must be the rotation speed (revolutions per day) if an effect equal to grav :9p7 m)beq;if9 exx*oxk1 ameity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in ubk:tdxp6ezv w0;.ze5c4 o(gedy . +va vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, 0fi4bll p/wdr gbf6pektybr3w)6; *:the acceleration due to gr: 0/;p3b fktbl6bygi p6erw *4wfld )ravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) i2ji(u; v1m l l1ght)nls deflected from the vertical by an lh)im vlu11n tgl 2j;(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 banked for a design speed ov g(zs:m,i 2jtf If the coefficient of static friction is 0.30 (wet p(,stz i2g:jm vavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that cfwl78 ey/gg1 objects at the equato /cefwly81gg7r were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distancewqpsfks8s)v:+x(9k1sa 2zz z 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 ro o1ve ndg-p t3d,cex.+unds a curve of radius 235 m. A lamp suspended from the cec +,1- pgtd vod3en.exiling 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 h z,*ow e;,-fpgvkaoj, as 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 v;joe, g*,zao-,fw pk 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 d9vetay,zq*q 7 educed the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light esca,*9zv7e tqaqypes). 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 valley shown*k2fv/o6w lsfkb;1 rn 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 road at A?ff6on r1;bws * l2k/vk

  The Navstar Global Positioning System (Ge s :;ycc0psue8 j(q)zPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few s( czpejs:)qcey; u0 8centimeters. 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 (h omw2ysx )/4m,r+qb +jtqu,aNEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros i, +4,jy )qotxwm abqshm2r/ u+s 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 (i0v pz)o7szj) pryr2o7:t3myxi x7 fof repair. You x27ior 70)xjm:7iyrf )opy(z3sz ptvare in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean dista8)tcujd52 wj /tl-bb ;xofox(nce from the Sjx5/j -);8dtcwox bl (bfu o2tun?   
(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 7,rod xo+hgfmz14 cc5 if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like m1f7h5dcg+oz,xr c4o F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the cent*mg**xu:ucq1p vql 4cer of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 ligql*:cgm vc* q1 *4upxuht-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 located at the cornexfkp 6/rbzqg)ed 61o0/y juk8 rs of a square 0.50 m on each side. Find the magnitude and direkko)jx8rb6y/gd fp 6uz1q0/ ection of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg ynzln yhy2;2 r f asfxo;6*.8sorbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-lom; ywb3cy8- vfx el82yng sweep second hand on your wrist waty82e v8xc;mlbyw -yf3ch?    $\times 10^{-4}$

  While fishing, you get bortus1n, l 4s2tok.:6t dbl7 snvwjrx bs3n)t21ed and 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 s. What is the angle that ,nsl:tdrtb 7sstnkv1nj 2l4b13)o .2t ux6s wthe fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is desigwtsz j/ zs:03( p487 nhwdmkjaned so that a car traveling at spe8(:a3zs0d7 /4n w kwhzjstpjm ed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cyw )a5uge1 :caars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a spee1ae cw:yua) g5d 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.$\approx$    $\times 10^2$