Sometimes people say that water is removed from clothes in a spin dryer j 5u,r;6 spgucby centrifugal force throwing the water outward. What is wrong with this stau cr6g ,jp;us5tement?

Will the acceleration of a car be the8zxj45j,zmf . yub7j/dca hc4 same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Ej4acu/ 7zb8j y,.ch54 dz mfxjxplain.

Suppose a car moves at k u 79oqs-vw qaya.91uconstant speed along a hilly road. Where does the car exert the greatest and least forces on the roadvk9 o-.9wua1 yqqa7s u: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child ridingjyxg1r x)r// m a horse on a merry-go-round. Which of these forces r/1yx rm/)gxjprovides the centripetal acceleration of the child?

A bucket of water can be whirled in a verezvcfhdc5o0ls09 ,wibv 0 w9+tical circle without the water spilling out, even at the top of the circle w 9+vwc0z00,oidvhcs 59 lefwbhen the bucket is upside down. Explain.

How many “accelerators” do you have in your ca ee6 iy:3xmjx7x) s+vir? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations djiyx3 6mvex7ise: +x)o they produce?

A child on a sled comes flying over the crest of a small hill, as shown ine+ y tr8 80tdp/7gsnbd Fig. 5–31. His sled does not leave+r8 b0te gyn7ts8dd/p the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean ac*i5z(h 7+ yn3q5ak sbw/xibinward when rounding a curve at high speed?

Why do airplanes banxac22)zgc 0 clk when they turn? How would you compute the banking angle given its speed and rad2ac20)cx zc glius of the turn?

A girl is whirling a ball on a stri w1hnvo3c e/,hng around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the str ,hehnw/ vo13cing?

Does an apple exert a gravitational forced)lrvhk64y6 k on the Earth? If so, how large a force? Considelkky 66hdr4)vr an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the2gb 2rqk38nxq*s4q ok Moon’s orbit be 32b 824*x sqkr qqgkondifferent?

Which pulls harder gravitationally, 2q1d n:ojk5-fnaae3i 9 p :ytothe Earth on the Moon, or the Moon on the Earth? Which accelerykf3- 1j:oan5dn te:q 9i2oapates more?

The Sun's gravitational pull on the Earth is much 0id mzxh ,gj-hg-5-gvlarger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational m 0 dvg -hz5ih--xg,jgpull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Wkvb7nh11,ifw i2aw u 5hat two effects are at work? Do they oppose each ovwka1 uibh7f,15 inw2ther?

The gravitational force on the Moon due to the Earth is only about hakielm yb4w+5xh/w/*+eri t g;lf the force on the Moon due to kwgit4/rl5iewb y;m*ex/+ +h the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around gv:1zwk,9x zuxm, r w8the Sun larger or smaller than the centripetal acce1: ,guxkwx vzmr wz,89leration of the Earth?

Would it require less speed to lau uwgev72w c:+knch a satellite (a) toward the east or (b) toward the west? Consider 7k+ew:vc u2wg the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a itj (,)p8ne vab:*/wybmmew( moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which cjw)wy*n/vtp (, :ae( e8mibmbase 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 period/hy( p5nr90d.phgv)bo9 niwj s in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on o opn )jyv99nrw pg /.b(d05ihhur feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparu qlv/z.8ifq-l yb9 *zzkl0vqh e8.z.ent weightlessness” between q . 8ei0q zflzv9qkb.z/ y*hv-8l.uzlsteps.

The Earth moves faster in its orbit around the Sun in January thgqm9;89aov jzwc6qjr 84;nl wan in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tw9zmo;6 nrj;cv49 g8qjl8 waqilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discoverem-fj mt 4 cl5uyg. s,84sb.ichd to have a moon. Explain how this discovery enabled h 8.b4,.sc mliusgy5-f m4tjc an estimate of Pluto’s mass.

  The Sun's gravitational pull on (, zx u1,qhz+so/iocj 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 pull from one side of the Earth to to hzix/o,u jq,c1s(+ zhe 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 19)l p.8-l)2zeps ybw )/vlmo zq80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 arounw/9n1upbi 8kj d the Sun, and w18j9i/bnp u kthe net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 21l .k9s4,w5 c eywepv*e0 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. Calculatsw*pyevl.kw 4 ,9e c5ee the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's siqvrxul0*dykzd bz+v 379 /u7urface, and circles the Eartzdr yiq bu/kz 03x9uvvdl77+*h about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edgei1wyr i6(b +.pfd9oju of a potter’s wheel turning at 45 rpm (revolutions per minute) if p(w yi+uo.if6j rb1 d9the wheel’s diameter is 32 cm?   

  A ball on the end of a string is re/0 /cy7xy0r3qksu h s6su p8ge4(paufvolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If iq/(3yp sa078scf4 u0 uprk6s x/ue hgyts 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 0.9sz jt8qgex round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car? 8g09xejst z. q  

  How large must the coefficient of static friction q(vn7 e1kjx (:nwu7gebe between the tires and the road if a car is to round a level curve of radius 85 m 7 vq:x1(uekgwn7 j(ne at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotat;qarq: rs be;551 t weclbi-x3e a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.8brr :weq1;a ;5bc qi3-sxtel55 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 turntable of variabbpf+/ sgz,d+hx0kh 2/ hly lu8le 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 slides off. What is the coefficient of static friction between the coin ands/ p/h +lf8bu0+glx,hzkyh2d the turntable?   

  At what minimum spee 1u5v*w t(gaqpd must a roller coaster be traveling when upside down at the tvu 5*tgp1wqa (op of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driverh7( ( *n 5ztbxztbn0vs) crosses the rounded top ofb(n7vs x*t th(zb50 zn 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 n c8w0 in6x0wnwheel need to make for the passengers to feel “weightless” at the tiw0x0w n6ncn8 opmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a jnls.2 3z/qrq v dp7vjm:sjsf e/ jd sk6;93l(vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N. 6ql/fj;3n ss/7jqd.:mdk(rssj3lz p2 v e 9vj
(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 particle 9.00 cm from the x/q 2eoey( j1maxis of rotation is to experience an accelerat/x1 em2y(joqe ion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled/ ,0/*gpmw p6jbvdn yc "room." (See Fig. 5, cb pp6jw dmvg/0ny/*-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 rpklj-jsl,4sp6g/1 c-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) tkcsl6 p,1p-rg s jl4j/hrough 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 the weight of the bal b2v+8pkhrbh zrest fx6-7:y9l which revolves on a string 0.600 m long. In particular, find the magnitude2 b9:+r x yf6khhvpet-8b7zsr 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 m3t:farv /nla 3 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 masses. 565srnstwft $ 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 jatgbl67 +,dzk to77cby diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripet0rmb +6vm;h hq9i4 yvaal components of the net force exerted on the car (by the ground) in Example +h 9b 64rvvaym;mqhi0 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 area, going f 7nh,mht mu .s)vy,mx9rom 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 the road to provide this acceleration with no slipping or skiddinh snmmhtu7,yv9,.x ) mg? $\approx$   

  A particle revolves in a horizontal circle of radius 2k nbvm6-g 6f9y 7)yukf.90 m . At a particular instay976f6y mn ) kvfugk-bnt, 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 E9effropz0pmzi8a.n . *dr z 83arth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 ar*f.p3nz dfrop i8zm.8ze 09kg.   

  At the surface of a certain planet, the gravitational accelera3:bi) x0 rj jxf7 f27ljgfsms52 0fftntion g has a magnitude of 12 m/s jf 3gn2jiff)b0sfr msj7xx2tl:50 7f $^2$ 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 acceler 6*kncyc6e ;ri qnwr78ation due to gravity on the Moon. The Moon's radius is 1.74 c7qk6r 6r*inw nec;y8$\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 ggobj ;6n dj6n;94ejeas the same mass. What is the acceleration due jbn e;6d 6g94j;nogje to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Eag +,k 8gvihd:. mxoio4tgpl++ rth, but the same radius. Wha,+x p8do gihot:g++mg4kv.il t is g near its surface?   

  Two objects attract each other gravitationally with a force of 2 yrleh(t/y28j.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 valusrcx *l p- ,h j,6l1ly05v:lnd(pvbcaf+)alxe of g , the acceleration of gravity, at (a) 3200 mx fl a:-cvsc*l vhd0,n1l,r6lbl p()ja xp5+y    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside tc .,)gc ewvpce2n+ e7dhe Earth where thegravitational acceleration due to the Eartc. +wev2 e,egccpn7d)h 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 into a spx2,cmcy 8 a1rqhere about 10 km in radius. Estimate thecry a 28q,cmx1 surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun butupk)1lm7 1yi m is now in the last stage of its evolution, m)l7ui1ym 1pkis the 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 while orbiting in the spac w/p y)sudd;b0z46iw+srd/ qde 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 kb zswdr+/ 0s/6p;udqdwdy4) im above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of ktjsfq zw.*1vy:t(vu* v e2lv17cgt6a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational t kq ts2v:(w1.*gz6t 7y*clevuv f1jvforce 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 ets(kx (4 q4cvof the Sun. Calculate the total forcetxs44v ((c kqe 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 of Mars is-0un 2ze v6 3d3worc/bl:bew gnuq45j 0.38 of what it 2ejr 4dgq3 u w60w z/ln:-3co5eu bnvbis on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using theqwuznb6 8vv5u1 ie.b6h/zy 1u known value for the period of the Earth and its distance from the Sun. [Note: Compavu zvub y /ezbwnu16i58 1.hq6re your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satef;8(a d;fqdqwc;e 3m :w o uo2suc9fz0llite moving in a stable circular orbit about the Eartha;uqoff;ed9 m8 :q0 c ;s2owwzucf3(d at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a cir1 ajtyvu w)b4l7.a rv/cular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when th/av74u)tlb .jv1r y awe release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceshipq53+or hwdv;i rotate if occupants are to experience si+ irqh3wd vo;5mulated 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 satellite to orbit the Enns3n/jad 5 e8arth 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 8en5n/ds a3njthe mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be l,n cyb sz6xq2ek /s f4l)(wy+launched from the top of Mt. Everest to be placed in a circkz,s4)nyqyl (xfwb+l es 6/c2ular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module cont); gkum)j 2c 4m7esz.gcn*gduuf 3x5jinued to orbit the Moon at an altitude of about 100 km. How long did itmj sdc. u5c)f3n*z;gu)kxu2egm7 jg4 take to go around the Moon once?    s

  The rings of Saturn are composed of x4 u pi5 axx3pgkcfi n5obh9/:+mm.7 wchunks of ice that orbit the planet. The inner wn ox.i p4g u5 xhx5/:mcb7mfi9ak +p3radius of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Ficdi i,4*xs.fgg. 5–9). What is the ratio of a person’s apparentsgcxd*f, .i4i weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight+.*vdfajke 1a07 ycgnshd;;g of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) movinggdgana0ch. sv;* def+1 y7;jk 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 equal mass. Theyfiue1uiz1rry69 5 k3f : fioc3 are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of ei 69f:ry c5if31 1eifour 3kuzach?    $\times 10^{29}$

  What will a spring scale read f :7fwi )l2-boz ij0(py ba(d(sqv e0xmor the weight of a 55-kg woman in an elevator that md0(iq0((oi )7e2bywx pjz -vl fsam:boves
(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 suspendedv)+ejna kv--:0hbkd x from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator acced vkxajh-v b)ek:+0n-lerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of53k 3yi xgkl/83xuh ke a planet with period T , the ihyl k xkk33ugxe/385density (mass/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 88flu g1dq4g 4oa b974uvyhhld) to determine the period of an artificial satellite orbiting very neaa8 lbu1hyvgoghfu8 944d l q74r the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred metep..e2/aweuu;7 azjova j58h77 ixnel rs across, orbits the Sun like the planets. Its period is 410 e j;p7/l8h.v an.wjxu5 oz7ei2 aae7u d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distaneml b5l5(hr1ia p*na;ce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes ved7d.12 fs cz7utq/ksxtx .k8o ry close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from tx sx.77fzk2st/8. oqc d1udkthe Sun.]    $\times 10^6$

  Our Sun rotates about the center of the 1nl k/h4 228dn bvcfr2fg smv9Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 moons om qdh*f0qn(ku (ur6w78 qwr7zf Jupiter (tho*f ndw (q8m7zk(60hurwqru7qse discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Ea/x):v ds+gjsk fshx7.v g-1re rth from the known period and distance of the Moon. f - ev7)jdss/h1g :v+.xk rxsg   $\times 10^{24}$

  Determine the mean distance from Jupiter foruu.o8x(kg f a*:xaka - each of Jupiter’s moons, using Kepler’s third law. Use the distance oouug.kxa-a8ax f *: (kf Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many frag)qj0 rzkfe() *lny d,yments (which some space scientists think came from a planet that once orbited the Sun but was nd,q k)yeljry(0z*)f 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 artific4j 6; .3alv*zxrjybg zial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface.azlz4 x3*r bjjv;g6y (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 hanging3*brneh2jizx/0 k+ig vine (Fig. 5–nb0i*i2/k+xz3g rehj41). If his 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 acceleration of grav/fr4nf ryqhw0; h ;.(.thdqdrity be half what it is on the f.hr(/0 rdtyq f 4h;wh.d;nrqsurface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circlewxyb9ulj.t:3 d4z7 hst j*oe4 once every 2.5 s. If we assume thei73lw4uty x.ebj9stj* h4 do:zr 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 appar jg)pz /k-(8g)filab rent acceleration of gravity at the equator is slightly lej8gg fz i(/l)- prkb)ass than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a h9 +2 o ewztg mhbokt)l:dt+ v8/spbz558s*kt spacecraft traveling directly from the Earth to the Moon experi9t zt +poht*kgsb/ls58mbkv8d z oe)w+5:h2 tence zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on auo+e2 3(0omicif bp-b bathroom scale in an elevator, it says your mass is 82 kg. What is the accep- ( 2+ueimoiof0cbb 3leration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will tkfm/d*1v50 :yjkllv-b. xs frotate about its center (like a tubular bicycle tid:tvf *ly/f.1k5bxjsmv0l k -re) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircn h,ph*6 o xhu*yvm-ijp4 78vdraft in a 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, the 5ms- rm eyh7 x)a5h1nnacceleration due to gravity at its surface )h7mnehs 1nr ma-y5 5xand the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflen9j b n/xe6ni2;i0tjbcted from the vertical by an xi 6b/jjn;9n2ib0nt e 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 banke92te,i ja,vr zd for a design speed of If the coefficient of static friction is 0.30 (wet pavem2 e,jazv 9rt,ient), 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 objec5hndvlds r:t4z . *(dnts at the equator were apparently weightless? dnz t5nd. sv rl*h:4d(   $\times 10^3$s

  Two equal-mass stars maintain a constant distance apartmy 0 3ed4j) 7l,hnmlsq 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 ra7u/yvu no gu.gl3*/radius 235 m. A lamp suspended from the ceiling swings out ga/y.rg*v/ ulo7uu3n 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 ,nt 8i7 neqhw+9t *d6yj2emsx)ypg0 bbeen claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't su8d 7qmxtiny)wnhgees2+yt j 0p6b9 * ,rvive 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 the presence 2z0 svgf5 a16ibdb(giof an extremely massive core in the distant5 bv6 fabdg0 i1(s2izg 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 traverset+r ) kot2g,ne0jck7ws the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? +kt,wrcg 7oet2k )n0jSmallest?) 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 Positim.wk ub3dxsx 3j0ka6j6 -i nx(oning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver onak6sd 6xm x. uji3xn-k30wbj( 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 k gx 13doios29hm, is meant to orbit the asteroid Eros at a height of abo13g9hxd2s o iout 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 w2pew m0f2uks19;u a vneed of repair. You are s9 uf pwv20u1;mk 2eawin 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 .*j/11;xy)/hlk - c j uzhvtjdsrcc6iis its mean distance from the Suj. t)c1ic/r j1-z;*h sx/ uyhlj6vkcdn?   
(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 a3bnsxwe-g (*v i oy15need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Ma1( ny-g* oxvsbwiea35ke reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a dist6 t;iur9qc -zyance of about 30,000 liir6 tzqu;cy-9 ght-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 corners of a square 0.5(3 hy5uzxz6tlcar(l. bxm38 3bjuh2- 0 sokil0 m on each side. Find thkb3zycza-3bthrlo 62i (3lu5s0x j hm8u. x(le magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits twjy qb/ v qvybl7;,25che 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-lxyz9k6n zr-q) ,cjo3fong sweep second hand oyk3f z)z6x,9j -oncqrn your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and starwdsrn6,*w * h) gikmk:t to swing a sinker weight around in a circle below ydrg*) siwk ,n6 wmk*h:ou on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of f1qlae n965py radius R in a new highway is designed so that a car travelf6 1yn5 apelq9ing 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 the cars when negot s*m3k4 lvau- f 0xky-ikitkj1bn62.liating curves. The angle of tilt is adjusted so that the main force exerted j* .0xa b3kvmisl1kfty 4ul k2k-6 i-non the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$