Sometimes people say that water is removed from clothes in a spin dryer by cenxgfyps9ijb*u(akhzn s2w ,:;, o9zu4trifugal force throwing the water outward. What is wrong with this statemen9f9 z,i2ho(k;ag u4 p,zsbn:su yj*wxt?

Will the acceleration of a car be the same when the car trav./dm(oriuu4pzt (se +els around a sharp curve at a constant 60 km/h as when it travels around a gentle curve a/ (zrtpedmus4.o( ui+t the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the g)8 hu-da/2rpoh+gdvpj0ytz m:3,z v car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip betweetg3d /rgup0 javzohd2v8y-,zm: p+ )hn two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a hors8uad 28 6 irw-tnarm+wsc7 v+de on a merry-go-round. Which of thesi d 7+2trnsmv 68+ a-uwrwadc8e forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circa e0 , dp.ymvu4n86iolle without the water spilling out, even at the top of the circle when va 8lu4 .dy6mn,ioe0pthe bucket is upside down. Explain.

How many “accelerators” dogbg5my0x bu9 s3b5uputxq c)9bf t(+) you have in your car? There are at least three controls in the carxbg3y tbc5s)q( ubbutg+fp0 u95m9) x which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying ovew sb.gp/:p1y tr the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feelb1/ :.gspwyt ps 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 inward when rounding a curve at high sei2 s7qu*z4iq( 8zvtwpeed?

Why do airplanes bank when i60u vgxhb9 27nm1l slthey turn? How would you compute the banking angle giv0g2xl lu7i hv61sm9n ben its speed and radius of the turn?

A girl is whirling a ball on a string ae30rm 6mv9pvok *xwv2round her head in a horizontal plane. She wants to let go at precisely *x 39kmevwr0v 2vp6om 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 forcdhzrptc+gsr9 ds 0.bw( m)j4v i*6 k9de on the Earth? If so, how large a forceg(w s9p.tihrdv6dz9 cjb4d0 mk s*)+r? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, hj xk0(ry*p e.23vaso(nda4;iuk vmnl.5-zgin what ways would the Moon’s orbit be difvjk2y;5 (na.g* mk o-hxi0sz( v4le.p3 undra ferent?

Which pulls harder gravitationally, the ; sn7-vdt sbiefp-d 80Earth on the Moon, or the Moon on the Earth? Ws7n-te psbv;0-8 dfi dhich accelerates more?

The Sun's gravitational pull on the Earth is much0cymfg+-baec-h;zsr:c1k +oma c 4;h 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 E;azkfmy4 ga-m+ cch +-0 :hc 1secbor;arth to the other.]

Will an object weigh more at the equator or at the poles? Whbq6)juqb,7 u 88m3j7ee b8*lw io pgmbat two effects are at work? Do they * 7bu8pm)b8lujieoweb,73q8 6gmjbq oppose each other?

The gravitational force on the Mtuo+xx8-l;6 mrl/x*y6rbn yeoon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t thouxln*r- x ;yx yer68+l/b6tme Moon pulled away from the Earth?

Is the centripetal accele.d c8f g,bb6mho ,cc9u4ncm8 sration of Mars in its orbit around the Sun larger or smaller than the centripetal9,uc8 .,cnfb6cbo 8scdg m4mh acceleration of the Earth?

Would it require less speed to launch a satellite (a) + 6ul-gbvji 7fv gf,-stoward the east or (b) toward the we gjblgf-vfs ,u6+ i-v7st? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest,urhe6dir qmg;7ytn0 6:gq* *x.vbg8j as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) am gitxg 6 b*:uh8yn*;dqrj7e6rq0 gv.ccelerates 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 adversely affected by )c8,ld c**dv mf1v.+nwqmzlnweightlessness. 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,mf)nmlvwn +qz1 l.8*c cdv *d on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessngzq+ - m0qvro,gn)-5o)1o e ulnl9umiess” between 9g oignuounmv5 l) q-zer+1l)0,-qom steps.

The Earth moves faster in its orbit around the Sunexdd-j6v)/t vvx82(tut: g u g in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is jvuextg8 )vt d xdg t6:v(u2-/not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to u(5w4 zvnms :w 2vja d;y2q)zkhave a moon. Explain how this discovery enabled an estimate of Pluto’s y(qu vn:wz;w)5 vs4zm2j adk2mass.

  The Sun's gravitational pull on the Earth is much 4npg s4,b 0hzxlarger 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 o4,xnp z h4gs0bf 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 ffb9uje:j39ggq d8*z1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 thi233ovx r7gdd e Earth in its orbit around the Sun, and the net force exerrgi3d3d7xo v2ted 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 210 N is exerted on a 2.0-kg discus as it rotates uniforchf1 4yphby s -z+zc6nk*ff5b ;3dul (mly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.-( 4cuy; * c3d5klfzfz 1bsn+hbf6phy   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, an i:u2r1, eysknw(i*rq j :y)eu85juta d circles the Earth about once every 90 minutes. Find the centripetalsejiae (kj 5r8:1)wy*i2:yqu , n rtuu 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 edge orq 6/u- gzshrhtuktg/) 0p-k: f a potter’s wheel turning at 45 rpm (revolutions per minute) if the w6 s-prz/khhtuq0)gt :/ukg- r heel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate i-jru*k/rv6zekssr 0l.; a7 wcn a vertical circle of radius 72.0 cm , as shor s7c.j;ku/ -la *vkrsz0 6erwwn in Fig. 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 round a turn ofb2d*y z 8zzaj+e2ra3n radius 77 m on a flat road i*adyr2jb+z z82n3e a zf 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 stat0;q6zi.bzuy an 8v3wmo,s p0 wd: j5qlic friction be between the tires and the road if a car is to round a l,nl0s. a w0d5v jqyizbwpu z63om :q;8evel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots iz gh9irf:3pw0m a .1oqw-/ vmfh .3txls designed to rotate a trainee in a horizontal circle of radius 12.0 m . If thexww g 0o.r1ah f3l tfzvm.mh9/p:3qi- force felt by the trainee on her back 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 xyr ku4f4g7:t6n) nx frotating 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 slides off. What is the coefficient of static friction betweet rk 4x7:ygnx)ff nu46n the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upspop0sk3/ +-ziutd(u xide down at the top of a circlezit0(-3k s xdp+p/ouu
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rouht+u zkf9ih3jes6w)mzw -2 j)nded top of a hill (ra )j hjshz-ziw 9e3wtk 6+mfu2)dius =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 whe :i9j aie/ns(mns to-(el need to make for the passengersmnn sai(oij-(:tes/9 to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circevh4rnsd yng;0hjvk l)94q ,0le of radius 1.10 m. At th rdj l0s4envghqh49)0y; nvk ,e lowest point of its motion 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 if a particle 9yl()lynvbm l6tv5 7i z6y3c6m.00 cm from the axis of rotation is to experily6z tylm(7 vmb 6l3c 56nyi)vence an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at 0rrltjt q()r/a carnival, people are rotated in a cylindrically walled "room.rt/ rrt)0 jl(q" (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hov(i5b-ka:vbo-qoh m vf-z6ip: 0 emc7ckey tabletop, and is held in this orbit by a light cord connected to a da-m o(a5 mvb cfvi0b: qh:6-eik7opv z-ngling 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 , precisely this time, by not igx e6ym1dgd/x) noring the weight of the ball which revxmdd 1ey xg)6/olves 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 a car traveling 7sds er4h s,xu4 :jo+k8*:byea;j4jli 5 $\mathrm{~km} / \mathrm{h}$ , 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:izd:6p/*s (g 5de3mlcjf wku $ 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 di t4u6t+)pafmbving 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 ce 4u./s k(xx+kwnt a09xutnc1 untripetal components of the net force exerted on the car (by the ground)uxsxa/kn( c u tuw0t 4+1n.9kx 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 a .eh7a71-; jptqqfos)eyvm.qrea, going from rest to 320km/h in a semicircular arc with a radius of 220 .a; 7qjtqm- f)7vo.qpheey1s 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 skidding? $\approx$   

  A particle revolves in a horizontal cguw)ech*pdyh * wr36 8ircle of radius 2.90 m . At a particular instant, its acc *dh*6)w3wc8 pe yghureleration 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’ v)(ib7kg++yo + twz/w0nd bols gravity on a spacecraft 12,800 km (2 Earth radii) above theb ln) wo+y dt/7ov(b +gkz+i0w Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g ha.i 5d,ycei+ans a magnitude of 12.da, eci5 iny+ m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radif9g.mu hpc sy1e w (+uwn8) xa2kmnj8,7p :xjyus is 1.74 9yj)xpu2. +w,: hmjn p(uwx fsce8g1amn k87y $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a ra 1o qyq0dlh p8-:o0.qby1 ;o llqdo2uzdius 1.5 times that of Earth, but has the same mass. What is the accelerati d1o:q2yb 0d zqoq ;.yu1-qllh8lo0poon due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times tr) fss7qir/zp 9l4vg7hat of Earth, but the same radius. What is g n v qsz4)7f/l7g9prri sear its surface?   

  Two objects attract each other gravitationally with a force of td*rh8s )re 4:kgij tr)e9( k+rr-sm4(djwdb 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 (a) 3200 qotpbz:plr, g,ep lqt/m,9 i4b4 7ld5m bm,rlp4t7 e bqop dtqi:,l95zg/l,p 4    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the hpy 0 f/k+; 3pe2u6/bfc(zmmqwpq gxr42ee l3Earth where thegravitational accelerkb2+30cuyql2pfr6(3/ ;/h xgeqzp emf 4 epmwation 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 Sundqflhm6c w* winmy(),u725jn packed into a sphere about 10 km in radius. Estimate tw)j ywh7qnui5,*n( m lfcd2m6 he surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like oums(ehipf 41e1tj u1j- r Sun but is now in the last stage of its evolu hjp11 fesmuj(4 1-tietion, is 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 weighz chc1jbw../0 egajr ;g1r3bs5k rm.qtless 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 calh5gwaqrjc bs1 .rrcgzm..k/03j; be1 culating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corn k-4p)dt3u f8tkxpgp 1ers of a square of side 0.60 m. Calculate the magnitude and directf- 3upd4pxt) gkp1k 8tion of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yearsp 6su- ;ccz5oxo1c0mzztj v3 (,ij zp) most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due)zpi0ozjcj xtmpsz uc1,; (v5oz-6 3c 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 0.38 of whswnt4sn30 rhp (07axqecej0 i ,t-f3oat it isxtohf 07a wq(i0spte,ne j nr0-c334s on Earth, and 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 th: mlv 1 eb6hck cqa,ux(u/dl2vk;3r i8e period of the Earth and its dea k, 2v ql v61ulu/ic kd;3:xcr(8bhmistance 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 about thc1c* z 4gy y )(hmnp7-2zlqxk6:lrez ae Earth at a hl- cl p*7hn y2(zyx6)gmrz:1qa4zce k eight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km so-5dz u9l.ctabove the Earth. How fast must the shuttle be moving (relative to Earth) when the release d zu9-c.t5 soloccurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to e g 167b1frsfmsdhya:nhe*n5 ;xperience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your a: * gn;1d7 5fs6mnasbhehfr 1ynswer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular.j o *ta*l e05prymlqt88q 7ox “near-Earth” orbit. A “near-Ea*oq 8m50et8l xa lqro ytp*j.7rth” 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 the satellite?    s ~    min

  At what horizontal velocity wowgzvm,n3xb l(o .;f 2itk4 lo*uld a satellite have to be launched from the top of Mt. Everesv3f*wb. ;i4 x(,klon ztml2og t to be placed in a circular orbit around the Earth?   

  During an Apollo lunar la 4s,cmfc:fg ,rqe1y/cpqg3dub4ok, n;ec2y-nding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon onccscyq4-u2ofqd1 meb :g3 ryc, e4kg/,f,n pc ;e?    s

  The rings of Saturn are composed ue :q2c)u4qu uqa,d+2fvhlk) of chunks of ice that orbit the planet. The inner radius of the rings iq )luu dc+aheqku2f4u q2,v :)s 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 Fig. 5–97ynso,f re)-pacs ckkf 6d r:71vm:f)). What is the ratio of a person’s apparent weight tcd fv::)7er7a- f kc) fkosm1nsr6 py,o her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 42n4p q9)z)d8 q c5e..nvhdp rz(m 2tdbo00 km from the center of the Earth's M8tebnqdp vocmzd pq94.h2(z )dr)5 n .oon 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-s wg6tsdd; 2-toqlg+m* tar system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years tdd;lqw2- 6o t*tsgm g+o 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 woman in an elev6g/bh hs- ct3)p3j kicator that movesh 3cgsc)iph b3-/ j6kt
(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 sus3xp 8ft j-tz8o,a1 fud7dx v/gpended from the ceiling of an elevator. The cord cxo8d8f u13vd/ptja7t ,fg xz-an 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 satellite orbits very near the d.(, yn0w mbzosurface of a planet with period T , the density (mass/volume) of tyo zdm(bw,.n0he 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 anh-z1low v;l 5 x33nbjad the period of the Moon (27.4 d) to determine the period of an artificial s lnavwoj1;3z5-xbh l3atellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred mete),m6al: qpe rxrs across, orbits the Sun like thm ar,:6)xqpele planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.jedrmm ( fus))* mw+)u5 $\times 10^{9} \mathrm{~km}$ 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. dis 94lznmr/u8t(m ge vm98g 9It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar 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 thez ugg/ 8l(tminrm9sm49v9ed 8 nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the G15 vbfv /5fwfwi2 sur;alaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 foaawi))gr ; )g 3k tr((ojblvq6r the four largest moons of Jupiter (qkb)gr(6tr3va w(a;) jol) ig those 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 Earth from tmkcq4r g+15ye0 dkh;w 5flwg ,he known period and distance of the Moon. mr gw 4,d55cewy0k1ql+fh kg;   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of yq5vp 1z6h 0eoJupiter’s moons, using Kepler’s third law. Use the distance of Io azvh o51pey6q 0nd 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 man4qjkyf: r9g-n s0 56b1c+rjz otssu)uy fragments (which some space sc+gy9c:ur4t jqj0s6o fn kbzrsu1 )s-5ientists 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 describes an artificial "planet" i1 v,mv8hup, jvd 3z/ban the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the u zh3vm,bjp/1ad,v8v period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorg e1k0t)r,gi)- nxe ylwe by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what 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 xn,1elwri gek))0 t-y m long.   

  How far above the Earth’s surface will the acceleral :: tu2jk8ftwtion of gravity be half what itf8kjw: utl:2t is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutua hz 5i3.spm,cyl circle once every 2.5 s. If we assume their arms are eac m,.h sc3ipy5zh 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 acceleratio-8/ jx xsaw9e9vswz4r,4lppx n of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate th wpzr49jw 8 lsxpx,94e/svx- ae magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from :bx as/ y*6anethe Earth to the Moon expern:*a b6syexa/ience 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 yagc3 8 9y,s0ew5kemf xou stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which 0kcm8 we,y9s35xga fedirection?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about 1 ); mlqz,+ pmuo,gi7yo vte-t tc2hv7its center (like a tubular bicycle tire) (Fig. 5–42). The cvoo,t,z;)hce1up t7t7q mil vm+2 g- yircle 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 aircrafn2l fft2r3wg-t 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 of4i4ea. pnvlbtm9 h 9b1 a planet in terms of its radius r, the acceleration due to gravity at its surface 9b4evn 49p 1.abm ltih and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical :lhb.)r 4) y9a.h5b f sozdkvgby an :flk)45s9az dybohb r v.g.) hangle $\theta$ 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 des3e x25rw wepco1e0. ciy5s.ot ign speed of If the coefficient of static fr3 ip1r ex20ocwo tye5c5es..wiction is 0.30 (wet pavement), 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 objects au: cq ot):8joou*s+dw ,kbw+pt the equator were apparently bc +usuo wowd:qj+)pk 8:to*,weightless?    $\times 10^3$s

  Two equal-mass stars mnq9ox)k 0xr7/moju 9l aintain 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 conskj a9cg d/f)d8tant speed rounds a curve of radius 235 m. A lamp suspe89dcfdgj a/)k nded from 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 bee4, 8 zw ko(u:kts5sbilj;5vfrn claimed thakv55wi s8f,t r4;(s bkul:oz jt 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 =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 Hubbl 6*m9n(dkxzu4x*og d6np )mlm1 5zunve Space Telescope deduced the presence of an extremely massive core in the distant g nm z1 *4nmuulp95vx66nd (*z)modxkgalaxy 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 spekt +69 civ 9q afp:uep*t.+klved as it traverses 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? Smallest?) Explain. (b) Where wouldi+f*q kp+tk lat9.cue 9v: 6pv the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Sy6 ysj0xx,. w t;wjy2qwstem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within 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 approximatjw, y.6wjx t2xw;s y0qely 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 - ed8wth4a2ep1ai)*v/jz l aj(NEAR), after traveling 2.1 billion km, is meanthi1aelt e*a4)-/8jva d jzpw2 to orbit the 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 shutdu::du(avgwl96ic ,d iu 4g(c tle pursuing a satellite in need of repair. You are in a circulagiuc:v9 ail4u6( :dg(ucd,w dr 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 yh9 5f z .g(fscqhsr9yy2+2cshas a period of 3000 years. (a) What is its mean distance froms(y9+yf5 hqh22 cys.fgz9 rsc the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you(wrzb5(bzbjqw 7a; pmfyy: ex8 w)a:6 could actually "feel" yourself gravitationally attracted to someone b7wfz:pexyr;jy5m( w:(wa6 )ba8 zqb near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Mi;nqeb- yo-u i5qsu4e ta*-*jwlky Way Galaxy (Fig. 5-46) at a distance of about 30,000 lig-ej;is*y 4u5eqb-* twn aou -qht-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 gg ,5bk rvw4 ns b-7bpv 5em6hkqb,)a/square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the vw /a, g4b7,r)q- bkb5bp hk6mnge sv5square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earqsuh:3f65 (9m x,6g tslt xcuzth $ \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-l d:25cnyh xuh*ong sweep second hand oxn u hh:yc25*dn your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around iv+-xb(ln fe/r n a circle below you on a 0.25-m piece of fishing line. The wever-xbl nf/ (+ight 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 radius R in a new highcc:j qs lc1,+lway is designed so that a car traveling at jl c+1 lsq,:ccspeed $ 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 da (;q48*aacb(rohu n 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 speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked andar4c(q8(b*ha du;no a 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.$\approx$    $\times 10^2$