Sometimes people say that water is removed from clothes i usnvr ,4:bdco7eg.6 vml73hw n a spin dryer by centrifugal fvsoldwu : 7g.reb63vm 74,nc horce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around b2+e+ fbp / 9mkwxxcv+a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speex b+/b2xp mfw cv9++ekd? Explain.

Suppose a car moves at constant speed along a hilly road. Where does : p jmvh4chr3+arlil 2:i.a 1pthe car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level vl+4rpal.ahi: 1:jr h c2ipm3stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse o:flf.t5 fv04vw q);hx j/9x y easeyx9n a merry-go-round. Which of these forces provides the centripv;law :fyq)f sjx 49vx. ef9e0hyx /t5etal acceleration of the child?

A bucket of water can be whirled in a vertical circle w4xao: wkgig2)v9 g6 tlithout the water spilling out, even at the top of the circle when the bucket is upgta4)ko9gl2 wx6: i vgside down. Explain.

How many “accelerators6id/b2; a5 i5 d enk)a;pyzspa” do you have in your car? There are at least three controls in the car which case;i) d5b pdz/k2pi5a n ya;6an be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the cresta m-c-i6vmix cam 81:1f yi+chv: txs, of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normali,acaxiv:8yiv6mfc 1c 1mm-tx -: +hs 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 areg8; mk2,ajz 7+kz uhigh speed?

Why do airplanes bank when they turn? How would you5boq cdif 6)dnc6gu-3 compute the banking angle given its sdb5c fu6oqi36cn d)-g peed and radius of the turn?

A girl is whirling a ball on a zq9za52/dbl; f6nogq string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a q;a5d ngl6ozf /92 zbqtarget on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitatiz 6a 20va:r ,vvddm:fchb1i3sonal force on the Earth? If so, how large a force? Consav13fv: sd:rm2 zva6 ,dci bh0ider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doub ;q7ck, eaqgh;le what it is, in what ways would the Moon’s orbit be diffeah cqg;7q,ek ;rent?

Which pulls harder gravitationally, the Earth *o f 9.fm8-p hvmepcr2on the Moon, or the Moon on the Earth? Whiph-*8 efpcvm r.9fom 2ch accelerates more?

The Sun's gravitational p8l bthfdb4.9dull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsid4 f9htdbbl8. ble for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects akxsx t 0st8l70v 68shyre at work? Do they oppose each0kthtv06xs xlsys87 8 other?

The gravitational force on the Moon due to the Earth is only t +fxffj(6xq7zxwbioum1j7p:z71 0p about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from thezm(xx1 z7p q:fx0pu7w1+f ift 6ojjb7 Earth?

Is the centripetal acceleration of Mars in its yk -8zv)dye;4k bhl0l orbit around the Sun larger or smaller than the centripetallbe8 0ly4)zykd-; khv acceleration of the Earth?

Would it require less speed v-ifr4jf r2 5s2spks 7*x ix(dto launch a satellite (a) toward the east or (b) toward x*rsx2 fpk7is 5djs4r-( f2vithe west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, -f c8n0 2t1v(pdn-n6 j1ghd. ggzkucf as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (pg n-cn12f g(kfg8zdvnut0h - j. 1c6db) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affectn. 1yu3e,mrd,;h8 ccd oucw:llu 5rd *ed 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 (81 ,dyd:cm,wu5cn dlecru;hu.3 or *l 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 exp.;o by c(n5mninh(y8 keriences “free fall” or “apparent weightlessness” between stibhmy5ck ;8y n.(n o(neps.

The Earth moves faster in its orbit around 4mwb/69d*lne:lzam b the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Expl49*lz6nl :/b a mmebwdain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known vjz5hn(*q geylj0 3gd302fdauntil it was discovered to have a moon. Explain how this discovery enab 3hnj5* vy(zg2 ljd00qed3afg led an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yu;d(ro7gtj233vpp j qi; hrq5et 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 childo7g u( qp5d vjrtpjqr 3hi;3;2 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 5jmz41drmt h8w r 9my71980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 theq3eie+py1-dwjte/yu7 :x4 9 dx vx o/j Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts tox d+ye w/y4i9jt v7dxuep13:- /qje xhis 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 rotategdwv-irf3p 7*s uniformly in a horizontal circle (at arm*grw7-pfvdi 3’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earthhv. xgp)*fl,t 's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the spacetxg v, p)fh*l. 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 edgroyq-hj1s 3k9o*k 7awi5rx3d e of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diamet51sdawo7xi3o9r3 -*y q hkj krer is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a 2 svf( f7;v*1gvx hagovertical circle of radius 72.0 cm , as 2sf;(vvv7f1g h agx*oshown 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 1050fqy ;7yr.u(.zsb n4fq-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires an.zsnryby.q 7f(u4 fq; d road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tire+enf.:x k2nw mz .qbb(s and the road if a car is to round a .ke2zwfbn .b:+mxq (nlevel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to ct4ovtuf/2bxt zk353v ae+ 6yqzn0c,rotate a trainee in a horizontal circle of radius 12.0 m . If the force0z qf4ob3653ntue / ayct,cvz2t+v xk 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 rotating turntable of variable spe -5)cyfd 86hpfvg ewf3sm8+/vt7 xrkmed.+m /85fvvrf )eyms3p 67f kgxdtc8 -hw 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 and the turntable?   

  At what minimum speed must a roller ;:rgo-ay0 hww6l z as*coaster be traveling when upside down at the top of a cw;r ygzao- 6a lwh:*s0ircle
(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 thep ej5+vxoev a.i6;2 te:c kkt. driver) crosses the rounded top of a hill (radius =95ke6kepixc:evt.o v;ta52+j .$ \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 per7f(6 g1e39asbkb ow x4bqo 9fy minute would a 15-m-diameter Ferris wheel need to make for the passengers to feeo4f9 k3g96eys1 7 xqb(wobabfl “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle cmgk1 6rh0ai9 of radius 1.10 m. At the lowest point of its motion the tension in the 619mkrag0hc i 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 partii 9hz d6dw8 5pocr/s); mfmpr;cle 9.00 cm from the axis of rotation is to experien5d wp) 6c9zfm/;rsoim8pr ;d hce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wallxjb. buparsr;;6, qq l*b5t 2led "room." (Seerlaqprbbsj;. x;6*b, t q25 lu 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-hockeye9qwyp s:b8 u6 tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in 9 86:qyw pebusFig. 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 n:8m( v4uimkjb zr*xey/j1 i/yot ignoring the weight of the ball which revolves on a string 0.600 m long. In particular*kx mv b4ejyj/ z8i1r/y(im:u, 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 perfzu4fr0xsz +s 0o*wph5ectly 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 xeyyho d/6(p:v8 y(ke $ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at ngqq39b:73h jt9tjr h o:e lrxt/(r;z310 $\mathrm{~m} / \mathrm{s}$ . 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 centripetaldbed/b3y7p -kd , drfy 9)8ypq components of the net force exerted on the car (by the ground) in Example 5-8 when its dpbqb 3epk) 8dyy9fr,/7y -dd 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,e 1ttlt46 gols6*8zk yk j(y.kyiq7c. going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration wit gq6jt1kk stl6y*y7ct 8(o.ze. yl4kih no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circlei (s6e2r pb06tjjj i8u of radius 2.90 m . At a particular instant, its accj08sj( 6e b ipru6ji2teleration 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 spacecraft gw r1g 6e,4gdy12,800 km (2 Earth radii) above the Earth’s dg6ry,4w1e ggsurface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a td /5ks;f6xrgmagnitude ofsxt dr f;k/6g5 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 due to dlbx6om:z+s 6lx u-h;+r) ri hgravity on the Moon. The Moon's radius is 1.74 hdm ;:+ bhs6ri+ 6lxu-xzro)l$\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 has the s7oe/2hzuu3x n ame mass. What is the accelerau z2uno7ex/3h tion due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that ojv/ ;qgni32 auf Earth, but the same radius. What is g near its sv/g 2 a;nqu3jiurface?   

  Two objects attract each other gravitationally with a force of1lh x1c/kkzf 3 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 acceler ( dqwz:t52qw/vk*6 cb t4c dxy0p0-cjq d3vzsation of gravity, at (a) 3200 m5dctp2 k t q-xdqq* 6(4j/ wvd:bz0cy0wzvs3c    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fr wya,j9gz9p s9v7o) ooom the Earth’s center to a point outside the Earth where thegravitational acceleraw,7 9aosyg9 oj z9v)option 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 packed into a spbv* )p uqpdo 35fq9jb2here about 10 km in radius. Estimate the surface gravip35uq*2b d)bpv9jfoqty on this monster.    $\times10^12$

  A typical white-dwarf starr/u6, oe pn2 git+/wia, which once was an average star like our Sun but is now in the last sta6gt n/+owaip, ur2e/ ige of its evolution, 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 feela,dn,03tnb5s(z j dhla8 kd, b weightless while orbiting in the space shuttle. Your friends respond thaaaz 08sbd b3 d, nd,(jnklth,5t 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 sqk)-/ .2 vf jpocj7hjotuare of side 0.60 m. Calculate the magnitude and direction-2/c v kfhpj jo)t.oj7 of the total 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 u nt jq4y9m5+yj e-hzs8p on the same side of the Sun. Calculate the total force on 9 j4 +ynqehymst-8zj5the 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 0.38j r/ w:)3pkfrc of what it is on Earth, and that Mar rj3fpr/w ck:)s’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the f86-lpix89q /+za(o( bzc hmxxfi9nwEarth and its distance from the Sun. [Note: Compare your answer to that obtained using xalff8(i h(-6x9w x+bpz/n qmi89z ocKepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbiz o82.:kps xdcqmwu o/4i.fm)t about the Earth ao)ikmf. d:p8x .wusoz42/qmct a height of 3600 km.    $\times 10^3$

  The space shuttle releases a oi* zk5h7sufj m/i 7s9satellite into a circular orbit 650 km above the Earth. How fast must9zuishm7j*s f/i5k 7o the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotatef/ .crns0g147cuf +ez ln3im l if occupants are to experience sinf e+imcgzsl.r 30c1u47n f l/mulated 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 Earth vl83p krbuqy:1ywl83in a circular “near-Earth” orbit. A “near-Ear v: 38rlk1plqyw3bu8yth” 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 would 7wggkqq;xvqfd -k- x 554(wld a satellite have to be launched from the top of Mt. Everest to be placed in a circular or5g(k; x5l wqfgv-w4d dx7kq q-bit around the Earth?   

  During an Apollo lunar landing mi )5j1wtabuv4xssion, the command module continued to orbit the Moon at an altitude of about 100 kjvw51b) t4uax m. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. xk jq;gwf:-c :8j/gwyigj/(5oa4 bx yThe inner radius of the rings - c5b xqog4f/g8 gy i kawxjy;/jw(j::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 Fig. 5–9 xg )1gea3sx3b). What is the ratio of a person’s apparent3x 3x1eabs )gg 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 astronaut 4200 km from the center of th- ;+aficj1qj re Earth's Moon inf1jaj+ -qri ;c 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-star system:)jde(wdz 0 vl tms)c3 consists of two stars of equal mass. They are observ)0e( djcs3l): wmzdv ted 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 each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55hx aq w3/8/ddc-kg woman in an elevator that /3qw8c a h/dxdmoves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from5k -y1:h vpxi:cq biu. the ceiling of an elevator. The cord can withstand a tension1puc i v:.-b5qkih :yx 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 surface of a planet with perioiqy4o91v+r qxd T , the density (mass/volume) of the pyqq1+ xri9o 4vlanet 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 xck 43kh-fa q5o .x:bod) to determine the period of an artificial satellite orbiting very near the Earth’s s:kx boq3. h-oafx4k 5curface.    s

  The asteroid Icarus, though onlyt8xvf -c, e;2xwn,j+ bkrwfs6 a few hundred meters across, orbits the Sun like the planets2c8,s+xn;wvw- kbetf 6, fxr j. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averager670x6 k /w3t8ab j jqsstiz *c(6hlmb distance 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 roug2 e;w5mtzhi f,hly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the co2iftm ,ew5z ;hmet 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 tssm+ zr4d*vy,3katc2u 1, zbfhe center of the 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 mean distance for the four largest moon(hwv7e )u+ mhbs of Jupiter (those d +e7bwhh vu()miscovered 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 vh;i** o vnjs-from the known period and distance of the Moon. nh* ov -s;*ijv   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons,+aj 8hack tp )5j*/zfvto7 ch* using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Ta v8*o)ath /k cpj5hjc7zt *f+able.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt betweeaa*.f k o9l+us emhr:.n Mars and Jupiter consists of many fragments (which some space scientists think cama f9a*kehl.ro us:.+me 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 "pt09kdjw(j;/ft283o y qjjidb)z )ab ulanet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band zjjtwoj ju09 yb/)2fa dbkdi83(q); tis 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 arlomjb q e(to 5.hzwz-8 48;atkc 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 tj m kh- 54aze8 o.owzl;t(b8tqhe lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s wn wh1;7(plbr0z2iib surface will the acceleration of gravity be half what it is on the 2p;rn7wbiwz1 h(ib0l surface?    $\times 10^6$

  On an ice rink, two skaters of equal magv/ )px)xjko)hd d q;*0xl-llss grab hands and spin in a mutual circle once every 2.5 s. Ih*x o);pll)d )g/x0xl -vjdkq f 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 accelerationpz+c/d a u cit1;)n -m;q9obci of gravity 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 g is +; -zp;i9/1oamqbcnci)tcu d this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from the Eay/izger7;3 fhnq;jume 4 z)c0rth to the 7 g/3j;)mycun;zi4zr0 efehq Moon experience 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 a bathroom scalel jz /ta c8 mh7o5 )tao-)6iqfvzlj:2x in an elevator, it says your mass is 82 kg. What is the acceleration of the5zjcvz72)/xlh- of8qi 6)tlmota a j: elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rot8b plfliswqdo:s;, e/(p 3,lvate 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 gravity at the surface of the Earth (1.0 g) iss,lv e,(3o8bs; pdpi:/lw qfl to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43). ;rhi*gyw /jd5w5i t z2
(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 enofaryi 3yq4( 6p *0hpoy3t+ the mass of a planet in terms of its radius r, the acceleration due to gro(p+ iyh* ra43y3p nyeto q6f0avity at its surface and the gravitational constant G.

A plumb bob (a mass m hanginf5k 4sur- wqmdr,k-6t6fq:uog on a string) is deflected from the vertical by an angle - 6t,od fu4qmfwksk5u- :6rq r$\theta$ 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 of 7mf0 v jetmo nt*/)mh0 If the coefficient of static friction is 0.30 (wet pavement), at what rangemm f7v0m otj/0t* ne)h of speeds can a car safely handle the curve?

  How long would a day b vsb/q-yb:w t8s.xa: se if the Earth were rotating so fast that objects at the equator weress 8x-w y/.a::sbtbqv apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distanc:qkwn /rca bnu, o*4b6e 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 afblpn lv6cuwxu81 83 9 constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to awvulub8n3 lfc8 91 p6xn 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 been claime xjyuimz -:yos1: ;tp8d that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calcuy u:x:sm zy ;po8tj-i1late 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 ab77v4j8uvpxy *,k uk presence of an extremely massive core in the distant galaxy M87, bvx,7 *kaku 4ypvju87 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 strg/lup jj 81;peed 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 would the driverjru;gl/ t8pj 1 feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24mc-/gcz x ij9s1bso1/ satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determinescg1oj1z i b- 9sxm//cd 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 billiogngg) 3l) wn;an km, is meant to orbit the astero);n 3alwgn)g gid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing q;bwd98m ee6za satellite in need of repair. You a ;em89ebqzwd6re 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 distance fr9fjf b15.boh,gj1wa sob9 .hg1aojb 1w,fs5jfm 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 could actually "*.p +db)zjn2fz fxr) afeel" yourself gravitationally attracted to.bfazfr+*pn2 dj)) x z someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of 2 qwqx8s 6bao/the Milky Way Galaxy (Fig. 5-46) at a distance of6o8s qx/w2bqa about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners h8(7tzfvimil, g2 h u,of a square 0.50 m on each side. Find the magnmvtlii,8zf2 ,h(g7hu itude 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 the Earth se:sq fdt/sm2w8g67d$ \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-long sty r:ls7x5q0 nweep second hand on your wn7 y q5rx0lst:rist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around inu5hv7 kg.w/x bn/ o9lk 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 the fisk gnk9uvh b/5 lo/7wx.hing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of rux 8hypxx;o qcr7b.2y lq :30qadius R in a new highway is designed so that a car traveling at speedoxp yqq lbx.xru;:yc 028qh37 $ 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 whepn6cwu jwl2g;9; epp yhf2c sl7+u;d-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 9f jpsywwlpehc ; cl2g-u;6 7;un2+p dcomfortable. 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.$\approx$    $\times 10^2$