Sometimes people say that water is removed from ck 78 nxh3jbyy*lothes in a spin dryer by centrifugal force throwing the water outwaxjkhn*y 3 yb78rd. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp +o c+ otov2gn .z*wnc-curve at a constant 60 km/h as when it travels around a gentle curve at thcon zocot*v.-+ wg+2n e same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the c+a 1y5 j vfmr75b9mpukar exert the greatest and least fv1m7k u ajr pm+b595yforces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-socdjml5ft 7 .w 8h4a+go-round. Which of these forces tshd54.wmf +l7 o8jacprovides the centripetal acceleration of the child?

A bucket of water can be whirled if;u hs1rai-n+ n a vertical circle without the water spilling out, even at the top of the circle when the bucket is;1 u+hnia-s fr upside down. Explain.

How many “acceleratoip ,-noucjy6 6rs” do you have in your car? There are at least three controls in the car which can be used to cauion-py6cu 6,j se the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the cre)xj 4v zga0*gyst 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 normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’yg )*0g4jvz xas second law.

Why do bicycle riders lean inward when a09 ywkp;a4aa6cj p0vheqw ;/rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankine:p*uk)y vcm xtppda 9:*(j;yg angle given its speed *pxt :v e jy(;k :mpy9)pu*cdaand radius of the turn?

A girl is whirling a ball on a string around her head in a horizon2mg9vlg 6 tfz1nf9dmcs(p d81k vc+)btal plane. She wants to let go at precisely the right time so that the ball will vnt) lmm8 f+z1(g1 9dk6ccfd 2bgs9pvhit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gr.1,b h npousxyej;: )4wur; (z ribt:gavitational force on the Earth? If so, how large a force? Consider an ap; p(xu:h:gtj )sun1 .y;z , boerrb4iwple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whajonic)ij*j8(x 12k m ft ways would the Moon’s orbit be differo*mk2(xjc ijn) if j18ent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the E xlzn)ia8bx 0o-t. (jnarth? Which accelernn)xl0 tij8oz a- x(.bates more?

The Sun's gravitational pull on the Earth is much larger than the aguz. : tqwwh,-f0h3sMoon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one 0w3 : hsqf -uhw,gzat.side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What t*2 s k5l ex3ard)firys4si3- .mq ( ;,simntwgwo effects are at work? Do they opposeqle r) fg*2k4;rss.- i aiwniy3tx ,smd(m53 s each other?

The gravitational force on the Moon due to the Earth is only about half theb7va;f 2 yim*+sxhc3k force on the Moon due to the Sun. Why isn’t the Moon pulledm3hibk cv7s*;a f+xy2 away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or smy ezv* dkk/ a.4z:jgai)(uh7g aller than the centrz.uh:a4)ae dkyv kgi7 /z*g j(ipetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east lwbltm- +g5g1hp9z - s; slt3bor (b) toward the west? Consider the Earth’s rotat1p3-s lbh ggbt tzmsw;5-l+l9ion direction.

When will your apparent weight be the greatest, as measureci c+3xg0/dyf+jdy 6fd by a scale in a moving elevator: when the elevatorc0+iy3j /f6dcgxy d+f (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 4m/vm 0v dfl0gbe adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on 0l4 /dg0mfv vmthe inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences phq;b8 z/hc u1“free fall” or “apparent weightlessness” between stehucp /qb;1h8zps.

The Earth moves faster in its orbit around tkot4e)h/ z mnt1j5cy j2md r)9he Sun in January than in July. Is the Earth closer to thed m/y1o thrc4 enj m))k2z5j9t Sun in January, or in July? Explain. [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 knpdwle :d ;,1lp9h+quj own until it was discovered to have a moon. Explain how this discovery enabled and: h1,ej9;wduq+l lpp estimate of Pluto’s mass.

  The Sun's gravitational pull on the Ea t/rb ae2xas) 7zlsa3*rth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull fro3r)z* ta 2s abl7ea/sxm 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 1e,22lsa .5xf hyqc st3q:i:rb980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Ei-ie6(w yb/jty :b (hharth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the( h:bywbje -ih(t /6iy 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 o .qb mx+bqhh,huqh,bcx t(- .v2:g2fgn a 2.0-kg discus as it rotates uniformly in a horizontal cir+q2m , qhbghb x xguhf(h:v-2c q.,.btcle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orb4,lf ocm+g cziipph ;,9ea,+git 400 km from the Earth's surface, and circles the Earth about once eve ,f+4ame ,,h9ccigpo;iz gpl+ry 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay oh *nip9ai2 (rin the edge of a po iair9h2 *(niptter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical cir: 2se5 va(*c mwr3pgsxh8i5 mucle of radius 72.0 cm , as shown in Fig. 5-33 m5x*rvgsc 2:5u8mhw3( sapei. 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 /sg+t(w zxr/q(t xk5tround a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? t/k(z/ 5stgrxqt+x (w Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be betwevl(e b,y7a6v ken the tires and the road if a car is to round a le 7,b(aey6vvl kvel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts +qkchykz4 y2a2q- ki; and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.h;k qkziq42+a yc-k2 y85 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 ()t 6cyfqpp1q53j dznl4ub 1s a rotating 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 c 41(n yb)fpdl61tu sq 5q3zjpreached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rol;7p s1p ;+ 7wfo4iknhh km/jlaler coaster be traveling when upside down at the top of a circl p;7kk /+7fosm4ihnlw j;hp1ae
(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) croszz 90:m)gon*sl s1a+4ik fjm bses the rounded top of j+09s k *zmfgnzms:o 1)lb4 aia hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need5nfx98/ q gisd to make for s5 gidqn8 x/f9the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg h te/uc;oh uioe 51-ahtt+m8-is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in tht-huuco t+h 8m/15ote e-;aihe 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) musa;0tinm .n31 0b9z piv w0pnhot a centrifuge rotate if a particle 9.00 cm from the axis of rotation is p;n0 ht30n 1 mivnwb9 z0aio.pto experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a c15 qg+e2a ma/ 3n.rfi e-ray7 ilr67rw :ljdkcarnival, people are rotated in a cylindrically walled "room." (See Fi qyf 7d:lkw-.laecn321miija/a6g+r5e r7 rrg. 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-hockey + fq(p:gfs5xmtabletop, and is held in this orbiqfps :xgf 5(+mt 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 , precisely this time, by not ir19(.el vrkxr zq24rm c xc ;n,kimf;0gnoring the weight of the ball which revolveckxcrlzr0k12 4mfv nq.(,rr ;i e;9m xs 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 ba+k:4rmh; w: caok e8drnked 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 massegsk5u7dx ,k8c5z ac0;n+; tav* mkkpns $ 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 man v;u6ib o:p)zpeuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net for6(0m a5s1a1l 4 jbcaf ipo3aoice exerted on the car (by the 4a0p65 1 a3j i( 1aoosafimbclground) 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 area, going froozt +lqvwj x f(ox+w8 f-5,5jfm 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 coefficienwwf+tx(zf55+xf v8q-, jol j ot 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 horiza .h2zbz gk;9e*(e my1ff c)urot89fiontal circle of radius 2.90 m . At a particular instant, its acceler8y; afrg9ef oi2h mc9zt1euzb*.(kf )ation 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 spacecraftjjbaeyn73yv :cfvi er5h1 a 3*7eq2z2 12,800 km (2 Earth radii) abov2 e 53ec v7ia *2bn j:yj3yearhf7zvq1e the Earth’s surface if its mass is 1350 kg.   

  At the surface of a cert i,g*7pzgk89; ftvyczgb g( i,ain planet, the gravitational acceleration g has a magnitude of 1gfgbtk;i7 9pc ,8(gyv*, gzzi 2 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. They an04;lf khwh19x m:mf-)t h ce*dt/e Moon's radius is 1.74fxh mt h/k- 4lfa;hncme9w:)d01yt e* $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 t klz+ 7 dabmhd s19sfb4ho,.h0sb(wy3imes that of Earth, but has the same mass. What is the acceleration due to1mhsb7f, lb9d h (.zwsbs a 0hokd43y+ gravity near its surface?   

  A hypothetical planet has a mass 1.66 times tha01gw u3sm(bwgyk3, in t of Earth, but the same radius. What is g w1kiwu 3 3gynb0(s gm,near its surface?   

  Two objects attract each other gravitationa*c9e jn;ltmbr r92pd c1deyhxf 9*2eb 10l /qully with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the (31ioi 1gbxbl acceleration of gravity, at (a) 3200 m ibi1o1lbx 3g (   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s h4s4i7dqdyrn hrr ,d61/er;a center to a point outside the Earth where thegravi;sr arrdh q1dridh4n4e,6y 7/ tational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times 2dx5sf iyp1 +othe mass of our Sun packed into a sphere about 10 km in radius. Estimays 5+ o2i1dpfxte the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which ontrwwlzy;b7t,tu9 2h*ce was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface wwl*ut tz 7bh2y9rt,; gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the (* r08swd fvv ac;:cshx yj/m9mz*on: 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 x:fr9za*s 8jhocmmwd vv;:*/n(s y c0by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square omd ftc azc.x1gbe 84h.qq3v68f side 0.60 m. Calculatebd.8gfq83xzq ct .e14 acv mh6 the magnitude and direction 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 planibmvsow*h+6qr90 5zu.yp+ u tzhkn8 6ets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-3sthw z bvu5z6hum.*6r +k09oyq 8nip+8). 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 acceleratioy0 7kw4js5x( c,j fsbon of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the w50 4jsbo7 yfsjxck( ,mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun us4 bcnm/z j(mxs81vrg* ing the known value for the period of the Earth and its distance from the Sun. [Note: Compare yourmc4*j8v r z m1bg/n(sx answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a 3 gnl :zg3lx-dsatellite moving in a stable circular orbit about the Earth at a height of 3600 km3lz d -xgl3g:n.    $\times 10^3$

  The space shuttle releases a ve. f;qbiov : yh.50n ph0lm0msatellite into a circular orbit 650 km above the Earth. How f0;fb :heyv n..o0iv qpm5mh0last must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship 5lo2o sf(2t ejrotate if occupants are to 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 2o5fj l(s2toe, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earthy r5p-ov49efu in a circular “near-Earth” orbit. A “near-Earthry ve9pfo45- u” 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 a satelxx z/jq9zj7tbu37a,/ x vaq :plite have to be launched from the top of Mt. E73zqt /ja /bz:xp v qux,jx97averest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the commkoo0;ph49 9au w is)k; atdwe(and module continued to orbit the Moon at an altitude of about 100 km. How lon49;o(aw it oahk)pd kw 0su;e9g did it take to go around the Moon once?    s

  The rings of Saturn are co8g 3 vyw6btmj ;q7evj24 u8wggmposed of chunks of ice that orbit the planet. The inner radius of the rings is v j8t mgj8eg;432b6qvg7uw yw 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 everyml 84/z:8 bg2-mqlekua9x cps 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at thcgm z2 a/bp kx8:84meuls9l -qe bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fg l4 9 1w f3z0/qofzubmk2e,jjrom the center of the Earth's Moonw3z4 0,eg 2qbmf1jz/f oukjl9 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-bw8i 8 bw be../yqgf2cqwle3-star system consists of two stars of equal mass. They are obwb38fw.e w.bq/ i qy 2cg-l8beserved 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 55-tl(hv90ww/vml1/fx qy:f :qq kg woman in an elevator that moves vwxl 1(q//9fhqvf:wy:mltq 0
(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 fr0bdfjcvy q:n.s9 c:/ aom a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was thes/: n.aj0dq yfc :c9vb elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near3z8:bky(cje y6c4r+i defr b 9 the surface of a planet with period T , the density (mass/volume) of the planed68cf b9ceiby :jyr(k+ z4e3rt 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 plry )v*ff 8,lqeriod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very nvy8*f,lql )rf ear the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred mete+,as pm5;2e ginvm0c-px1 tlcrs across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fg5-icln, ps+12eva;mtp m cx0rom the Sun?    $\times 10^{11}$

  Neptune is an average distance +lv/hn03we2t(nfh ueh 6,cbdof 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once pz*0zt jp 4yg4mhzde -2ux 8:nevery 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 comet from the Sun. Is it still “in” the Solar System? What p2gx0t4ez uhy j mp :d4n8z-*zplanet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the 6 ,wvtub*m/vd2d).bn g+k-r1bx ak deGalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, ands( gb)3cc/ ft wzlq3gam/ 0jd7 mean distance for the four largest moons of Jupiter (those disc7dsgc q (/zj cw3/ a0bgltm)f3overed 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 / rt93w.w7uxiah * b,6ugr c2sl jzt(speriod and distance of the Moon. a czl9bwsu3t/wrgr,2 i.u 6h* tx (j7s   $\times 10^{24}$

  Determine the mean distance from Jupiter ffn9ysk y) 8.lz imk()bor each of Jupiter’s moons, using Kepler’s third la.ky(bn sf9l)8 ik) yzmw. 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(57 z)sagqv;kv *zvev Mars and Jupiter consists of many fragments (which some space scientists thkve;v a(*)zv5vgs7q zink 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 t1wn)cq ufm l22he 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 rotcn2lf2 u1q )mwates 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 swi(kol-d-f j9gwnging in an arc from a hanging vine (Fig. 5–41)l wfjkd --g(9o. If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accelera*uu +epw3o7(/ i;sm9saa fslvtion of gravity be half what it is on thwi a /svlf(e9+o3* apmsu;7us e surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass graqgxgloei/8hv/ ipl( gd:0n56 b hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pullingn l/e(g65pioih 0lg/dgv8 :xq on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of5 roy1z- dwq4v gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this efv-zy4qo drw51fect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveli7nvz56mtkr92 s/vu )ir8hnudng directly from the Earth to the Momtv vkr hn9d8)/2zi75 n ru6suon 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 scz.0j shgmv*cci-*w4+v 3blpfale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direcvcb3.jp c+gv* s0w-hi* lm4fztion?     ----待选择----upwartddown 

  A projected space station cowx;5ac qmnq4m /m3,k*lco l3o nsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube hnc 4 c/x*l,3;3mawlkm oq5m qoas 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 aircraft in a vertical loop (Fig. 5–43)kefure -7e8(y.
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in termx/7 -vda(m zmhc l65e .vxx9grizl 8k7cmi s72s of its radius r, the acceleration due to5x7d r9llk/g-c. z 72 (ix8zimex67svcma mh v gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a strin uyc*wh m lf(b)h0e:37hgv+ slg) is deflected from the vertical by an amhes( *7 b+):uv0yhwlf3gl hcngle $\theta$ 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 arwtp zmeh(g8chx 3(.eb4 ()8oeuj6 my design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speemcxtp)j6h(r34g(yez.e e h 8(8mwbuods can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at the e;ptz;ml g/onb*;i6auy( rl k 9quator were apzn6/im r gp(u a*ltl ;;o9kb;yparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a ckn( hsm+,5/ojjhaf3ionstant 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 constant speed rounds a curve of radius 235 m. A lar)xfh: f1vsg)yyy(w), xr 3h mmp suspended from the ,yy)f:s1h r) 3mrwx )vg hxfy(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 ;mj/;oy*i15 upl2pf xr9re *zis) elvos( y*w 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 would experience at the equator of such a planet. User f9 luj* s/(mzip5xleepoy r ;*1*;)o 2wsvyi 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 thew r;3yb;y uh iq;dx2,dimr44f Hubble Space Telescope deduced the presence of an extremely massive core in i yf4y2; ;xqb4w3drdur ,m;hithe distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shown ijacbma10. 3k frpw8x0n Fig. 5–45. Both the hill and valley have a radius of curvature R. 1a bkcaw3r mj008 .fxp(a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (Gwa sf*8f2)p lko +) ,(a:+mk0;kgzhmi bxhqbuPS) 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 orbalo)mf28+kksk:+gx bpq0afi*z b(wu;hhm) ,it at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is m itzxl c3 8,ufsu-2wg0eant to orbit the asteroid Eros at a height of about 15 km . - l ct0w8xg 2,fzuu3isEros 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 sh gq ,x3n.t +b-pczmgb+uttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (40-+ tn ,bp.m+ggxzqcb30 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-mssoq,5b,a9 ;ldxp3gy ju8f4q+rn n distance from t3q nyl ,x jsmu8g,5adnf q+4-sorp;b 9he 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 va4poi80xxxwo( ),fghjlue of G would need to be if you could actually "feel" yourse0xiw x),po4hjxf (8o glf gravitationally attracted to 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 z )k -:iy0erorcf 180ra8wrvudistance of about 30,000 light-yeaz uko i:vy08r)fe0-c ar8rw1 rrs from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each side. 9363x fnb r0seq dssk7Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of txb6ks s7 r9eqn3fd03she bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earz:7x p: )qrcsqth $ \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 x 6vdts i17os *7uy)esexperienced by the tip of the 1.5-cm-long sweep second hand on your wrist w d)xv6s71ye*t u7soisatch?    $\times 10^{-4}$

  While fishing, you get bored and start to* *r* koen76bucr/tq r swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight /renr k**o7br 6 uqtc*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;ra7 4 1vsmhhs in a new highway is designed so that a car traveling at speed rs4h1a; mvh7s$ 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 negotiatinncosola8uc n;43i c da2.u akp+9 ch7,g 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 forcoskcc;9nid+7aoh 8u 3.4 a uancc, pl2e 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.$\approx$    $\times 10^2$