Sometimes people say that water is removed from clothes in a spin dryer by cent 2ekrm1nljj;2n c f9g+rifugal force throwing the wa+fj1l cnk n;je9 r2g2mter outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp cca i-fngdgd c0z( /)/eurgi0 -a)g/f/d( d nzeccve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car+5 4pppa9 6sn0aoo1h dcs odx+ exert the greatest and least forces on the road: (a) at thxdo6do0+onp9ha4 p sp1 sa+c5e 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-go-rouiib)*njo ( 1zrnd. Which of these forces provides the centripetal acceleration of the chzn iro*j(1)ibild?

A bucket of water can be whirled in a vertical circle without the watyjt3 b 9rrv /+pm6qwk7er spilling out, even at the topqv9m y7wrj6bk t r3p+/ of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three contr5hyy(/hcc5* x s ) wmvs;87ur.diafghols in the car which can be used to cause the car to accelerate. What are they? What accelerations do they p y u8.vm fh5 ;s)c/7c(ia5dxwrh*hysgroduce?

A child on a sled comes flying over the crest of a small hill, as s)ji 62crqd5su7 l6da uhown in Fig. 5–31. His sled does not leave the ground (he does not achieve “a2d rju 665lud)7csiqair”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rou( +5i +1cgueut ggc/bbnding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bank vk2uc 7tbk vr2r,j;v6ing angle given its speed and radius of the turnvvbku2c kt 6;jr 27,vr?

A girl is whirling a ball on a string around her head in a y 4uczyppg6a4xy gra4 4 cv/)1horizontal plane. She wants to let go at precisely the right time so that the ball will hit a t4au1c4rp pg4y /y ) z4ycag6xvarget on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, ,+ myc;q n0zbjl :.uuer2 nt;rhow large a force? Consider +0 erzjm:q lb ty.,2;r;nucunan apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ii5w .)cv 9fanm4inq2ways would the Moon’s orbit be diffe594)i mfiqivna .w2ncrent?

Which pulls harder gragvlp7 u,)6/bolac p(q vitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates m vau6/pq b ll,p(og7)core?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet th42x+vm1j r;1to lajjc.h gl/oe Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in joo at;g 14 j.rh+1l mcl/jv2xgravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? Whatm 97e7x)mckd u s7.y+ tkea/qm two effects are at work? Do they oppom9 + cqsdt7um/77yemka) .kxese each other?

The gravitational force on the Moon due to the Earth is only about half the forc05 tz gv5u78h;qfqk(u) kivvx e on the Moon due to the Sun. Why isn’t the M v( q0z5fk;5t)vuixkhv7u 8gq oon pulled away from the Earth?

Is the centripetal accelb c:f+wycg2 fy 64-qxjeration of Mars in its orbit around the Sun larger or smaller than the centr+jyff6cy4q wc2x -g b:ipetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (5-pn 6-gm.n lxe wj,tk w)p0ktb) toward the west? Consider the E gjmpk pl)xent wn-kw0.t 65-,arth’s rotation direction.

When will your apparent weight be the gu+fin()u-u kl4h3*i cg1 rm2ciuu ah 2reatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in freeu4luic(*nu1 +i uugh i-22a) 3rcmh fk 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 zl kq*5 *vaq/jc)mp1 wcould be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside suczkj*q al* v)w5q1/mprface (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 “free fall” or “ap90xa0kd ,lvwh0v kxv0zlha7)parent weightlessness” between steps.xah0,9 dlhav0) klzw v0v07k x

The Earth moves faster in its orbit around the Sun in ) eqxy.,zbih-6 nlnq2January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis rbn. h6,zyxi)2qne lq-elative to the plane of its orbit.]

The mass of Pluto was not know7n5c 15svt/mjgdi t4u n until it was discovered to have a moon. Explain how this discovery/ c7u4tdgn mjt155isv enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larpd; n.0,hvmz tger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sittingp;z.n0hdtm, v 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 cu4c3opc z2* :obj 0qr 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the /be:fn h8rwh7 Sun, and the net force exerted on the Earth. What exerts thishrh w/: b8nfe7 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 fhnt3j :h,h:xoib )4d as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Cal nt 3d4)xhiho:h:j,fbculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth'3rl5f+ joj gjzs k93cq tki),)s surface, and circles the Earth akf3j)5 sj +ri c9zol) kgjq3t,bout once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration m0k92byr.(koer un7 n of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if t 2b( orye.krnk9um70 nhe wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circlpp wfuwh28g+cc a86m)e of radius 72.0 cm , as shown in a8pu6mw +g28c h)fwc pFig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a turn of radiu8d,v) xjrvf1xxvu i )bvq/,g05o5zcas 77 m on a flat road if thei gq,d0)b,xv)v/ur 8c o xj5f1vazx v5 coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficie2rxzb1kbw4mq6hg;q 1 nt of static friction be between the tires and the road if a car is to round xkw qq1;g zrbhbm1 246a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astrony: ,f ;wcp3qlcauts 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 isf p:3lywcc,q ; 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 z(ps/r, u lvb9axis of 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 reached and the coin slides off. What is the ,(9upsbzrvl/coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when ui q)9pmz5. rahu8j ca70 oix.wpside down at the top of a circl)7j9.aicrawh05 . 8izmu xpqo e
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the:v5sf4)iroh)d ll 1zz rounded top of a hill (ra )o) 15dzllh i4vz:srfdius =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 need to make/-yehk246l nlv4 crmvxn o8w2 for the passengers to feel “weightlesshm46 o2 2r/c4-vw elkxnn8yl v” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a ver4 il+c. *muvdatical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting tu*cva+4. mldi he 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 axis sj3gx5f9a ms2of rotatio3m xajgss5f29n is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carniva) it;a9n2 4ww yhixfo.l, people are rotated in a cylindrically walled "room." (S2f ;tiyx9ai.w4)w ho nee 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-1;kc m(vf*5p 7mgv ude/jl8up6fiz k4hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a cent4(7 zgup vji5 * mf1 6lckvfkemp/u;8dral hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weight of tajf32uegq4kf, d9,x c he ball which revolves on a string 0.600 m 32kfx,gu, 9d je4fqcalong. 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 travelb,gd hcd8q t0;ing 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 masselyd:-fqz 4j q)s $ 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 verticalu48nmz 3d4e ddly 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 force exertev-n2ehc mup/)tn xn-4f 8y mzz+hr/)l,7qpmf d on the car (by rhcp2/n)z -ux 4n,nfv+m- mq 7tf8ml/ p)yzhethe 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 Indianapolis 500 accelerates unif ipg4rs k8i7*formly 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 ther7k i8*gif 4ps car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of9on/w: dm8 pz ta*5gl5jnzqz ; radius 2.90 m . At a particular instant, its accelerzzg/jz;:q9tpm n* a 5nl5od8wation 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 m6kevpzgsa./ 6 +vj07qatsc (of Earth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if i7ja z6t + akge/.(ssvc 60vqpmts mass is 1350 kg.   

  At the surface of a certain planet, the g enjxp9m.; v8gravitational acceleration g has a magnitudem8v. j gx;e9np of 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 gravity on the Moon. The Moon's radius is 12pat1 ip)g ac3,l 7wvv.7pt 7 ap,lv )g3c1a2vwi4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a r6.ppgxf mqioo;5z w-; adius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its suro;-65 gioqxzw.p ;fpmface?   

  A hypothetical planet has a mass 1.66 times that of Earth, butbn4wpwj 9bd wg).s96vh gla38 the same radius. What is g near its surfah)8 .s93ja gdgbv4w9lbnwwp6 ce?   

  Two objects attract each other gravitationalv6l0mm3cctu-t+z 1f62 z sft mly 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 acceleration e+1iw3,ar zohn6r-a;up 5eqw of gravity, at (a) 3200 m +zwa6i5h;ee u3qo pnr awr, -1   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance zc) 65oj( c8yh0dmfxp3.z h uqfrom the Earth’s center to a point outside the Earth where thegravitational acceleration due to tdf)c z z5xq0hmp63hy8 u (cjo.he Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of ou ) fce7+h1za rwvx ,mj-s* ik-0euyl/ar Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this )-eesur+ lcah1 70 -vizyxa/f *j m,kwmonster.    $\times10^12$

  A typical white-dwarf star, which oncea;(ab-zwn2q e.8eyi a 4wzg) x 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 gravity on w)wni-a 8q;y e.4gxzb 2(zaaethis star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbit v)mid j+.9l(e1huqlz ing in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’tlzd)v.mhu j ( +ieql91 so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are lj/ j cy ikn+/:kxj;q+cocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction y +; x:c/+jkjqjkn/ciof 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 up on the saad 9/y 6c vwoy-ex;zs-me 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. 5-38). The masses a9 ow--e xs 6;dcvy/zyare $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 gravi zb1,zwe. v:v-jjon s*ty at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of b1zj:sjvwnz .- voe,*Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period ofp/hkpn78l ah6 the Earth and its distance from the Sun. [Note: Compare your answer to hn/7ah k p8lp6that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit aboutk*/9xln ix; qj the Earth atiq *x/xj9 kl;n a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 wl/e:p1ygx+j5akl 9l km above the Earth. How fast must t/l 5 e1g+y9 apjlklw:xhe shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindricamsp;nlnj 7.,a me8/v1 zqoj7yl spaceship rotate if occupants are to experience sin/q8l;my7pj sv7ejna.o z,m1 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 satellit7bo uxw13/8up kqjn e6e to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a hen 8o1j 3/kb6xuupq ew7ight 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 velocits9i d2kkx )2 txy*o81mmjw7mfy would a satellite have to be launched from the top of Mt. Everek212 o7)sxwtj*ky fdi x m98mmst to be placed in a circular orbit around the Earth?   

  During an Apollo lunar llonfteep5) .5 sm*(is anding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How l seef(o*)tn lspim.55 ong did it take to go around the Moon once?    s

  The rings of Saturn are composf yamgcj, +aubfv o9hjk6+5;x3z:+ hred of chunks of ice that orbit the planet. The inner radius of the ringsgf m:9yrucao 6j35 +jh ++ fxb,a;kzhv 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).4)o g)q-stes v What is the r)q)tsev- gs4o atio 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 astronaut qlbf-wt :vw+d ngq*k0y*t0mx4v, fi 8 2 x2irw4200 km from the center of the Earth's Moon in a space vehicle (a) moving at*4tlk2mi0qnfvqx*d0r-, w:tw ib+ vy8 gwf2x 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 sl7 n9*)h.1xh q5pcf hfc7n dvitars of equal 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 the mafci 7 hcl5hqn 1d*p7f.)hn vx9ss of each?    $\times 10^{29}$

  What will a spring scale read for tw4nngw)w,c 8kry*np9 he weight of a 55-kg woman in an elevator that moves ,ngwcpnwn8 rkyw49*)
(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 w qrw)k y q0do2ja+ krsc-7m;*rm5oo-v5 lz0ifrom a cord suspended from the ceiling of an elevator. The cord can withstand a tension ofj0 -m5lwq;zoyar7ko)im+cs * k5v do qw0r-r2 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 (d x q9f rd.b7nv7o-fwof a planet with period T , the density (mass/d- bqn(od .wx977r vffvolume) 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 d) to determine theeapco4qmmbi r4r 70bt. .4+i(zhlq 4r period of an artql(ri4+.44pb4ih r bem7ozrctaq0 .m ificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acro,cxe)cs7k.hu0m qa 9 w*+e tmoss, orbits the Sun like the planets. Its period is 410 d. What is its uece*m) x7 qw.,s+kmht a9oc0 mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanceskt;bl+ 7m z:wpg 4dm1 of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very yi e:t 4s* y: ftz4k ud:canp,/x/oin;close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The meanp yka4/t: fn,inz4 cyu;td:*xo : /sei 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 Galaxy tug6 il-0x)ka7 n2x it$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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-x u0;c)/xlnyb ih5 af largest moons of Jupiter (those discovered-5abixc 0hf) lxyn/u; 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 periodv0 yzxwi (9ui 8:v2agb and distance of the Moon. : 9giiu 0wbx(z vavy82   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using.d - v9uv+teup Kepler’s third law. Use the distance of Io and the periodutd9p.e -uv+vs given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter cxevynf o 56k/+onsists of many fragments (which some space scientists think came from a planet that once orbited the Sun but waenvxky6f5 +o/ s 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 artchsbxo. xl:-, ificial "planet" 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 is the same as the Earth-Sun distance (to make the c hox.:bx l,-cslimate 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 pw,fg.tmf+f dfue2lox f k9-n8;n(/j by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of hiseg/f8-kf pfwf29f( l mon+t;un ,d jx. swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surf27qf177qyq fih,jp h:e mwsa3ace will the acceleration of gravity be half what it is on f137pf jqyqhq2 e:iw7h7a, msthe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and sf . re5ughcw ifxsyzm1z 4e:0a 1l*)m:pin in a mutual circle once every 2.5 s. If we assume their arms are each fr1a:u. 4yl1sfe: hg mwm)e50zix z*c0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotate(gikz:o (mv) fs 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 of this effect. What fraction of g iv(mo f:gkz) (is this?    $\times 10^{-1}$

  At what distance from the Earth 608d rvy(fefdw7if 6ywill a spacecraft traveling directly from the Earth to the Moon exper e8i0y 6ffv6ddry(7wfience 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 stne9 slwgb/ d61and on a bathroom scale in an elevator, it says your mass is 82e/b 69sg1 wlnd kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of aoyhhz.-lm cc(7 s bd2o *m,y;;zdtiv * circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle fbys,.d2(vl *ih-zhc;m t*;cyo zodm 7ormed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43).vk2 i jj-vp2weiyn 9xf15bfo3v:y24z
(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 jd s :emaov7r,gc1 5xaqu9m18of a planet in terms of its radius r, the acceleratude15ag9xq:c jo 8s,1 am rv7mion due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) t--nfdq a:)mim5 -bpfs-mjd7 is deflected from the vertical by an ang paj-f--7 5- i:dmqdnb)mtsfmle $\theta$ 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 k4m:( *zpqc/gy gq ct8a design speed of If the coefficient of static friction is 0.30 (wet p( kmgc:/8qy* 4zqctg pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Eartiej z *aiqyq/yaf86 /2h were rotating so fast that objects at the equator wereafyq q8z2/i * j/ai6ey apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apa*x(1e4zzsr gn*s*6bup ptij( rt 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 bu1asmgz -a8d(awu */:7h xd la constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle w:dma-xg1a* ulsa u hd8 7/zb(of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Tltm *f1;o0a 5ri)g2;9 shqa 3pi o(kemy4dfk uhus, 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 t0(;3uq1 f ytk9miom sp*k5il af); gro dh24aehan a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an ex/ry+otu3 ;t b,xru 4sutremely massive core in the di+4 urs3 ruyuoxt/, tb;stant 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 constx l;qgf3.j 8cpmyh)u (ant speed 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(.l my3jf;x8hqg u cp) 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 (GPS) utilizes a group of 2i-nnigb(i +s(4 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit niignb(+-i (sat 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 traveli9fl-c pa r9r:3ank-l hng 2.1 billion km, is meant to orbit the asteroid Eros at a height of aboutk rh:l 3 ca-99anp-frl 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of repairz u:srm13 /c,habtsd 59i;lpeh ,: eqs. You are in a circular orbit of the same ra,,z qb3t1;up/ s: 5 hassc:l9dhemeirdius 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 distancbltt4m::bpdo dwq2e* 27c nl (e from t:toed 2lb (2 :cndlw b*t4m7pqhe 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/p*ed1 f vfd*qjppa 56t(/drg:od:n z would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like F p1rq5do vfepdagd :d6 nf/(*t zj/*p:$\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arounh8xq vx9 .yc5td the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 lixvq89yt x5ch.ght-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a squo2zefb,purm 8w;+ k,:mtp 2mware 0.50 m on each side. Find thw 2pzt :;2mmbof+pu,wer k8m ,e magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbivq8ln7k9fwty .yr ;+y ts the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 16g.cmf7y:cj ii7r6f j.5-cm-long sweep second hand on yourji6:j cm 77yrf6i.gf c wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to smj5 gv5g wmt8jrg;/; p,a x9twwing a sinker weight around in a circle below you on a 0.25-m piece of fr;vtm,/a p m;w 5xjgg58j9tgwishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designexjwxrvqg8- * dn3d* -bd so that a car traveling a vdxw-8qjnb*-r* gd3x t speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when n-ss3wgnq6xk5fl/-h 5acul- 60w pk u0 +lsekiegotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of m5plss36ew6 kui-u0xan cq/k-5+ lfk0-wlh g s ass 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.$\approx$    $\times 10^2$