Sometimes people say that water is removed from clothes in a spin dryer by cenaaf:hna2y6zws5 d p8*trifugal force throwing the water outward. What is wrong with this statemenwadha6 2f8p:s 5any*zt?

Will the acceleration of a car be );7h6idvzywv the same when the car travels around a sharp curve at a constan hz w)vdiv6;7yt 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alon o 908bo 3v.kimbe+nitg a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of m98e bt+ibkno i0.v3oa 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 ridi4v y.alya.gk1ng a horse on a merry-go-round. Which of these forces provides the centrl4gv 1.yakay. ipetal acceleration of the child?

A bucket of water can be whirsb8,0n2+z waxgc vsf0)l z 4qzled in a vertical circle without the water spilling out, even at the top of the circle whefv ,400zz8lzsac)snx +w gbq 2n the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three xczol)yw;25+d a c.:auft d9w /sv kh+controls il v/yo+5 +9:z.da xa;)ccsfwt k2hduwn the car 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 over the crest of a small hill, as shown in Fiyq3fn.3s. w ibg. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled desw3q3.yi.nbf crease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders l 6z n3q /y cj6r1us.so8qqjsc,ean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankii:*h. rub(oet )6l q qlr r:g3poc2j,z43 uodxng angle given its speed and radius h lo q)p3: tbor*:ru(x63jle.zd qc4,o2 igurof the turn?

A girl is whirling a ball on a string around her headtxymakr-; 1xce65 j.2cn 0pgu in a horizontal plane. She wants to let go at precisely the right time so tcx.e0 cym ung25;kjxt6ap- 1rhat 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 gravitat8:vq y(f:yb+ t gml5kaional force on the Earth? If so, how large a force? Consider akt :yfg 8m qbv:+5l(yan apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublu t24+ fya4wrhe what it is, in what ways would the Moon’s orbit be d 4 wt2y+r4aufhifferent?

Which pulls harder gravitationally, tgk*zse bc o96fj) s7)khe Earth on the Moon, or the Moon on the Earth? Which accelerates mozf)ob kskeg c679j*s)re?

The Sun's gravitational pull on the Earth is much larger than 0mq.fe7i;.arsla p,e the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the diffe p lsiq,;e a07amf.e.rrence in gravitational pull from one side of the Earth to the other.]

Will an object weigh bhnnxs:-r. +9zr .zy smore at the equator or at the poles? What two effects are at work? Do they opzrs +nrhbz:9. .xnsy -pose each other?

The gravitational force on the Moon due to the Earth is onyjvi:8qu 9wb2xw+cr0 zt.edtc r/j 93 ly about half the force on the Moon due to the Sce/ tjb.0v9+8crr2y z: iwjdxwtu9q3un. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in irvi ui6s nc +j*;d4 a(*ege0rkts orbit around the Sun larger or smaller t4*d(+ us 0g*race kievi rn6j;han the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (aqf1*s(k i s,i qy2ujd o9vs66a) toward the east or (b) toward the west? Consider the kq6 ,odui6fasqvi*s(s12 j y9 Earth’s rotation direction.

When will your apparent weight be the greatest, twe jxp5 jy35vh/2 i0mas measured by a scale in a moving elpi5h x y /w0vj32e5jmtevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affect th-m tve7p+k/(g3;y ppa c9sied 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 our feet, angpm/t7t h9 3 si(y+ ;papec-vkd (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or ykzahc86g v *2“apparent weightlessness” betwee2c *6ghvka8 yzn steps.

The Earth moves faster in its orbit around the Sun in January than in July17a.n.y(tl -y ,b ylv(vuc exv. Is the Earth closer to the Sun in January, or in July? Explain.ey(x(,.v ubyavtv.1n c- 7l ly [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 until it was discovered to have a moon. Explair n5-d5fit m2jn how this dis5 mr5-jdt2fnicovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull ox3*a-nqk0 i;qu2x ib tn 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 pul3nqxqx-ubka i 2*;t0i l from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling )smxk2 hmcg*km +*t/h1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleratg.pgdnbe5s8 3ko-8 s yz3lc,qion of the Earth in its orbit around the Sun, and the net forced en8ks qs y b3l3p85g.co,zg- 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 210 N is exerted on a 2.0-kg discus as it rotates unireiq5yd:b4y7r, dp i -formly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the dri :r edbp7iyd4q-5 ,yiscus.   

  Suppose the space shuttle is in orbib(g;g(mry*n upo(k* e t 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration atop(g( b gmne*u( k;y*r the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the m;px33(cgezlib j+*m edge of a potter’s wheel turning at 45 rpm (revolutions per mi cx;e(lmj gbm3*3pi+ znute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a stringoxub:*pi4::buw r qs 6 is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4br4ibsqo6w:p:*: uxu .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 10,vi*nyk.8kuz 8 ayv2w50-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tireiawvyk zk*.,nu28y 8vs and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction *a t7qbpwka60w)obm 2be between the tires and the road if a car is to round a level curve of radius 85 m at a a0q6 )*p bmowwb7tak2speed of 95km/h ?   

  A device for training astronauts and jet figh;2)+9hantvw puld) *iet q xm7ter pilots is designed to rotate a trainee in a horizontal circle of ))xh+*we;mtpaqdu9 ltv 72i nradius 12.0 m . If the 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 rotatingnh;ff31,oxp(+ kld sy 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 between the coin and the turntableo13d,f( ln xkh+spy;f ?   

  At what minimum speed must -ne-wt c .imn(a roller coaster be traveling when upside down at the top of a circle t-cwe m-n(in.
(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 950z ijadpre hq9*b4 ,5i()7 yxqw kg (including the driver) crosses the rounded top of a hill (radqa(i7dy4 j 9,p *rqibz5 )wehxius =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+w+i:icl mz+ z;rcx3t0r6 pkw minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the top +lpkrc 6+ w+;0zi:rxtwi cz3mmost point?    rpm

  A bucket of mass 2.00 kg is whirled in zos8 sdi1a:p/ a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope support8ia sp dzs:1/oing 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 9.00 cm from the axih iow24 o2lzy5y:nzdmf0 20dss of rotation is to expeho2420yl iyzd0:z odnwsf 5m2rience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are wk)t ga.nf 37p6fnqxh(+p5 uorotated in a cylindrically walled "rog6 no3(5pp qwf+7hk fanux)t .om." (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 fric)vz;tihay 9r:tionless air-hockey tabletop, aa v;)i: z9rythnd is held in this orbit by a light cord connected to a dangling 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 , preciselydse(fo:8 w3j2d.lsp.w4r 7mgoxx v(x this time, by not ignoring the weight of the ball which revolves on a string 0.600 m lon(f7sl8x.4v geo pdsxx2: 3. (dm wowrjg. 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 travelin1 0fl)e2uaf8w csc;wx lyd*o*g 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.r hl-6a she5fy f0ue/ $ 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 verg)q jq gk: yu9;gm vg) lp+x5w2f/h9nmtically 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 tangend967euu0wsb 0rnkzk8 tial and centripetal components of the net force exerted on the can0s 8buw kr90dzk7eu 6r (by the ground) 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 Indianap6o56gf+mbyxi t;fn54 2nxq cb olis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would th b2o xnfym5nx6fig;t +4bc5q6e coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of rahm u(2zr 70p zgicb l44b3kmu9dius 2.90 m . At a particular in( 3umlgzib4kpz ub4h9rm 20c7stant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraftt/(exw 07ef;yr rik+g 12,800 km (2 Earth radii) /ri+f weyge t0xk7( ;rabove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the grz1:klpa u 4xj:avitational acceleration g has a magnitude o1:jzakxpu :4l f 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 /q7 bamj*4 ,2hvx yw4omr:jxj due to gravity on the Moon. The Moon's radius is 1.74 boj4a*wv:hqm/,x 47 yx jm 2jr$\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, b,vxp) p1r9.+i url9z.dnume l ut has the same mass. What is the acceleration due to gravity near its surface?.p uu n.piv)r z9 xrdle+9,1ml   

  A hypothetical planet has a mass 1.66 times that of Earth, but the s:i06j8jxrik2s t ng*,oez ub 0ame radius. What is g near its surfbun t0iokz6,0:i 2serj jx8g*ace?   

  Two objects attract each other gravitationally with a force or a/p.9(b .blbmcaf2g79tei cf 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 accelervpe2s ab4hc /+617lj0baszeoh, wfa+ ation of gravity, at (a) 3200 mz2,vhj csa +h47sop6fe b+a 0alb/e1w    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wheme1peb (+dot( re thegravitational acceleratit e(oe+bp( m1don 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 mas 9+d. *-xbn+qsi;u0t 7tlqnqogs*fke s of our Sun packed into a sphere about 10 km in radius. Ess9 k q+7sufx+q g*.lq;e*0tboi-td nntimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avenyj6dlsu- hd)c:3bi 8rage star like our Sun but is now in the last stage of its evolutybs-:j nc8 ihudd 3l)6ion, 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 weightless while orbiting in the spac -vaozu2h56huvzg/:je shuttle. Your friends respond that they t2: v6zz-ho/auhj5 vg uhought 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 lo d58lyo g7a6rucated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the totaly5adol87g6ur gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sup4ccdakp 49(m n. Calculate the total force on the Earth due to Venus,a c4 pdmkc(94p 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 e f):(pb)yazes5kre5 the surface of Mars is 0.38 of what it is on Ea:ye a(b sf)5z )5prekerth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using ts 3 z74qnekk0uhe known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Exampsu 74 3ez0knqkle 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stabljwfu5 afau4bt25 /j4me circular orbit about the Earth at a heiutmuwfj4455j a fa/2bght of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite intol.pn- y dj 1u mmg-h/u37giwm)y, exh6 a circular orbit 650 km above the Earth. How /gmuj-3.-phd emgi6wl )mxy ,u17n hyfast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to;)co 1is/fb- n0in cat experience simulated 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 ni0c)n1it-caos /;fb.)   

  Determine the time it takes for a satvmk ; .*bi ue8dd(uw;wellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the swmidduu (*;evwb ; 8k.urface 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 gbc 04e, y4bg)wvzgoq: *we ,kwould a satellite have to be launched from the top of Mt. Everest to be placed in a c gw,ok0e*vw4c4 b):zyegbqg ,ircular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to v3a;j xg jq+nbnq /z*wq 1f6l:orbit the Moon at an altitude of about 100 km. How lon6 gnq f1lavqj;:nxbj +3z q*/wg did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice th0vmdguw2no2)( pk e)tat orbit the planet. The inner radius wdm 20o(tke) gpuv2)nof 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 rotat:nby9efl8aa +f6 io n-es once every 15.5 s (see Fig. 5–9). What is ta69 :fab-yi fel nn+8ohe ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astz1km wil5l/3va6ge bgc 5, 7rrronaut 4200 km from the center of the Earth's Moon in a spavw5/671 il k amzrr3g gce5bl,ce 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 consists of two stars of equa7apbfy92 ,vlx2 zi4url mass. They 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 the9l4i2r, byvfx7 a2zup mass of each?    $\times 10^{29}$

  What will a spring scale read fou l.bg/6lh 1x dt qydyv,:67zdr the weight of a 55-kg woman in an elevator that moves uqdv6dl yg/dzbt x1 , yh:7.l6
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. T2mgu;j2x 43kw ulam3whe cord ca23kg3 4u ;maulm wwj2xn 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 surface of6ks/7jy4 zqps n4q0qm a planet with period T , the densit4qs/pnq 0z746smkq j yy (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 dxm 7zpj+igqunc 2:e4:) to determine the period of an ar4 e zqn+xp:j:cugi2 7mtificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbq8: m 8.ertan6mywj:awud*; gits the Sun like the planets. Its period is 410 d. What is its mean distance frm.m:w*:;ry6 qwt88 jgndeauaom the Sun?    $\times 10^{11}$

  Neptune is an average dv-w 8 ocyo+i4histance 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 oncewhsy;- /b,y)y9b u xlu0 pib :4qpw3bq 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 comety p)yuhqqi;ww0b,4b3/l-s9x by : upb 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 abouto ea u/6dj1gb/ the 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 f pu:n)/e .h6no)cdx txour largest moons of Jupiter (thosexcht6) ox/nd.npu):e 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 the known period 476 pt urqmi 9bq85umr,yhwg/and distance of the Moon. /mbgwur,7u6phtr 4qq 859 im y   $\times 10^{24}$

  Determine the mean distance from Jupiter for each q qph+k 4.l+1 xv57ppvl/ tkckof Jupiter’s moons, using Kepler’s tlpc5k/ 4q+ pkhx+1v7q.t vklphird law. Use the distance of 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 Man;vo,oo0;q2aob t+4 cpz ) nvk. 3cbqars and Jupiter consists of many fragments (which some space scientists qozbq2ot ccbo;+ 4n. 3k ),pvna;0vaothink 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" in the form re1 0m(ctied. 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 rtd.em0c1ir ( eing rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vi m89 gstn) *qks,yb+dyne (Fig. 5–41). If his arms are capable of exerting a fymtss,y qk b+)9 gdn8*orce 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 gravity be m2*gv lggs 9j) uvse 7bl)hlot4,f)v 9half what it is on the sur lj)h4vbe f gvvs2)7 g*9m9slgltu),o face?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a m6sd- x(pm t5yz i9,mhmutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and theiympdm5 m,tz- (x9hi 6sr individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotatesulf58si +1/ltcg wzxg 13krz /q3vg:k once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude/1qkwlg :v/ trg8cslz +uk1 i35x zf3g of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from t de06wglf18asmmsejwogt-o / (fd70 /he Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force moew70t1 l8f /a f0j o-6g gsed/dmsw(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 a8zhowj+dh-i 6 4ry( /j3aco aon a bathroom scale in an elevator, it says your mass is 82 kg. What is w(- 6oo+rj a4 3jy/caad hi8zhthe acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about it)jqn-d9l+2 bld; -wi b toq6nhxwf -a:s center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has ;ll:q qd-ijwnb9 )2 df6+twa--bnx h oa 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 aircraft in a vertical loop (Fig. 5–436j4l zrk+6cfo ).
(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 pxsppv:):l9fidh0 ;ib lanet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational p)b x h9l p::0ifivd;sconstant G.

A plumb bob (a mass m hanging on a stringhk(mbt.ftil2m;y: , o ) is deflected from the vertical by an angle o;kt(iybt.fm,2 hl :m $\theta$ 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 If the coefficient of*ou0c,b,b)uk57bh7 pdtp)f hps, yd h sthy 57b,h))ofkd dp0pb*tsp uh7u,, c batic friction 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 at t-ety-zt )rbma0(-ntq he equator were apparenrt0ta -emy)nt( b-qz-tly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 deej. a + bp 2j/c1b4j1f 5 nhnnltm.3wrp;nr;$\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 e5 10wyy:ug9(b2) zw vkwdbkwspeed rounds a curve of radius 235 m. A lamp suspended from the ceilinvg dww (yzk0wy5 ) :buke29w1bg 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 massg90 g 2v)(nig trf c8abop24anive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person wg 8b4t(o0gaf2g ) cni2 v9nrpaould 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 Tv qv.*bpf 5b/telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed ofv*pqb vtbf ./5 gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses t kc+gv5; l m(:j4kiatkhe 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 driver feel heav;mgjv ai(5 4klckk t:+iest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Syjn2 7b ,e pyf8yg+c5vestem (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 abyyg, e jcn527fev p8+re 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 travd+ qx c-e8z00zc.von leling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 c.z0d8c+eoqz -0x vnl 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 shuttlev+xoh,2xvxxf ) d96kt pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abovehx)2 x6xvx ,+fo9vtkd 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 meanl7 ( .tzd;msocubbom :24st g0 distance from the Sun?4 7t: m;bgcomtd0uos2bl(.zs   
(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 pi kbeovjn:q)a ,w 5s/lth1+ 7"feel" yourself gravitationally attracted tot7jvlib+)koa ,w/nhq 1 pe:s 5 someone near you. Make 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 difnyw7 cvb0y18stance of abo7 nf10cyywbv 8ut 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 nadi)h+ki, k)yq.pgi5z4g qtd + i0:rthe corners of 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 ofn hzki a5g rg iq4p+y. )d:dt+kq,ii0) the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eakp.iz9.dh 4yblujc 28x3 3e bqrth $ \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 h9po vm+,f;0j+ocf m--4u zuda /x hprexperienced by the tip of the 1.5-cm-long sweep second handh -0+j9ur4 oxa+umfmho fpdc ;vp ,-z/ on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight aroundq9h9wju ** uo*)zeb kz in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]ew* k99h)bu z*o*zujq    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a4-yyk sdej6k3qfxf(9t 0 tx1r car travelingtyrqjd139 0sx 46yfxk(kt-fe 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, m3rq -ys:xc*g utilizes tilt of the cars when negotiating curves. The angle of tilt is -sxc:*3rq gmyadjusted 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 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.$\approx$    $\times 10^2$