Sometimes people say that water is removed from clothe3cz/l+g oj 7/sx(cr zvs in a spin dryer by centrifugal force /+gczj lszo3 rvc(7x/ throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a s .riz:tp1q (qoharp curve at a constant 60 km/h as when it travels around a gentle curve otq z1:.pi(rq at the same speed? Explain.

Suppose a car moves p l wij7)txs;6at constant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the tot x;p l)w6ij7sp 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-round. W 5a,2q /qh.sl0 vnmhyihich of these forces provides the, q./nyl qi5 0ahhm2vs centripetal acceleration of the child?

A bucket of water can be whirled in a ve .8zlrn ) m85eqj,friartical circle without the water spilling out, even at the top of the circle rer.,8)8 mj5z anfliq when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three conq;r frl**pw/ r69gp awp bf;3ctrols in the car which can be used to cause the car to accelerate. What are they? What accelerati*bpw6g; *a rl rf3qpfpr/cw9;ons do they produce?

A child on a sled comes flying over the crest o :dbyd;,r*f,n) 3 hcb+vsswzkf a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but z y +hddnws):ck,3;*b sb,frv 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 inw)fa +cm4jzehjpath* j k78 31card when rounding a curve at high speed?

Why do airplanes bank when they )2dn 8s2hwmex24qx*g t i8p(i d mpfc3*mnvn4 turn? How would you compute the banking angle given its speed andnqs42)(cm3wtddepn 24 *g xih2 *xp8 fn imvm8 radius of the turn?

A girl is whirling a ball on a string around her+gn jb n(8fhh5 head in a horizontal plane. She wants to let go at preciselyjg+85nh n h(bf the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a grqccu b() s/:hqavitational force on the Earth? If so, how large a force? Consider an q)hbqu :(s/cc apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublwy3 yve)zb0q5 e what it is, in what ways would the Moon’s orbit be differq wy3vyb5e) z0ent?

Which pulls harder gravitationally, the Earth on the Moon, oryr7 pu/9m 4nht the Moon on the Earth? Which acceleh m7putr/y 49nrates more?

The Sun's gravitatio. y -x6bf j3s 0p0s2omuvsa((qqf5qxasn2 x l+nal pull on 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 gravib p msya( 5xx +qsnsfs2 q0j3(.lv0 q6fuo2a-xtational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effectsr/enp:-xii k: are at work? Do they oppose each otr :-nx/ i:ekpiher?

The gravitational force on the Moonlkfdq:, t,r2t imt2:o due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled awad,il:ttm,fr2 ko t q2:y from the Earth?

Is the centripetal acceleration wn-.ghq6l3r jir30 tkof Mars in its orbit around the Sun larger or smallerq j n3wt.r6hg3- kl0ir than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east 03 96rfs;or /vxh yapjor (b) toward the west? Consideav;y jr6xr/ p 39o0hsfr the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a sc2:d+ycz 6pwjl ale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In wj +p2z 6ly:dcwhich case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected 0s 1svq+ +9)ahqwn +3ktdq sbkby 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 ks s vqah 01qt+bq+k)3wd9+snforce we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betweeakg p5qm9,nkv2h3 c0ow6slc9n steps.q592v gn,lk39w kp ch 6somac0

The Earth moves faster in its orbit around the Sun in January than in Juyqj/vgb1- to)ly. Is the Eartby1v og)qt/ j-h 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 relative to the plane of its orbit.]

The mass of Pluto was not known until iyr)hpr4ui 0o-gh g 3p+h(ngr :t was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto+ 4g(i0ghp 3grhryn )pu ho:-r’s mass.

  The Sun's gravitational pull on t,rci 5sgq+wig ni1-f)he Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in grsi1r)ici fnwgq+g- ,5avitational pull 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 r1rm-ohvk- u :um8t*,fpt q l31980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 fo : e34ma8dgcf-tya+ orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that toa 3y+4ad: fg-8e tmfche 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: p ea:bi+pv6 xgp3gyoht1l +-.0-kg discus as it rotates uniformly in a horizontal circle (o aehv-pp:l:xp 6gi+1+bgy3t at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 .s/fgs n: n(3rlnlymqi4s l f58i7 wx6km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbrs:8myx(i 5s.lfs3fn6 7ng/n li4l qwit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude o0x cs1li up272vp q2uhf the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minl 2uu17xsq c2ip0p2hvute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in aq,p, )fh:iz;u1r e mgx vertical circle of radius 72.0 cm , as shown p, q zef1r, h;x:igmu)in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of radius 7.znl.1m( bqf,l+t3j lckra ( i7 m on a flat road if the coefficient of static friction betweenl(bma.k c3,lzi+q nrjft (l.1 tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of sws 5;f3ix g)wotatic friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speew)igw5xf;3 os d of 95km/h ?   

  A device for training astronauts and jet figh rkiw b1n,a0t*ter 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 7.85 times her own weight, how fast is she rwt i 1an,k0br*otating?    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 x-4lpufzabkcf: lr6p4 l7,w -00 pluirotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixxfaul,fblp-zkilr0 4:4 7upw0lp -c6ed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed mu eqqc9vq245onf(n sn0g-mk5m st a roller coaster be traveling when upside down at the top of a circqeg 2 n -nsf vo5nk5mq0c9(4qmle
(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 da7vwnp +ux2 h10p-t8sc.jsp ;iio b:criver) crosses the rounded top of a h o2ts nsi71c 8h.wijb pva;-u 0pcx:p+ill (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 p5.x dt/chz- r*oje;m t/hah3.v- bufder minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the .chuvf--*t/ oemhtadh3 5j xbd.r; /ztopmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle cw 0 gvy;tpy7z 6zmbau 1+ +nq)kc+6cwof radius 1.10 m. At the lowest point of its motion the tension in the rowm+ncayzutv; )+7bz w10c 6pg6+ kqcype supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm fro .8bk85oo)f6v dhw- o, ziguilm the axis of rotatiozg8 kf8l) vdou hwio-i.o6,5 bn is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylinqlm597 t4y 3ojnzg7hgdrically walled "room.ny7jo379glq mg 54z ht" (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockep9u oiiqw 0 w4m.h4nf,y tabletop, and is held 4pu09w hiqom.4niwf, 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 , precisely this time, by not adc q hsn,6z0*ignoring the weight of the ball which revolve6sqaz n*ch 0,ds 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 ofy8s:2uzg9r kv 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses c5vn (pbt zvz 5cmy6ff n9+,0d$ 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 /sd(jnf( )n g impd.z7rn5xb:evasive maneuver 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 com/d wi03v i6xvcponents of the net force exerted on the car (by the ground) in Example 3iidx0w6 v c/v 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 Indianapoli+qnd/ nw 4(hxhe,e y.mgq gak/08 x1eys 500 accelerates uniformly from the pit area, going from rest to 320km/h in a e8n 0egaw, +1 xq k(.4xm//dhhqnygeysemicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizonta3 )osoh(nfytjv7kq9 0l circle of radius 2.90 m . At a particular instant, its7 kqyv tf )0ojshn9(o3 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 gr4b 9w,ehqde5 * dkw6ofbby(k0 avity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface b0 (wod95kkqed ,ehb w6* 4fybif its mass is 1350 kg.   

  At the surface of a certain planet, the gravb: yk5y1b3(uwl noh ,eitational acceleration g has a magnitu3nlew y51hbkyo, :bu (de 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 piciiv 69lq 8gai.aol t9*rh1.4 ug1q on the Moon. The Moon's radius is 1.74 1u 6or qila99 ii.tcgpq*.lga4 iv 1h8$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tih-1vpl9wrwa hj(n ,: a-6 slabmes that of Earth, but has the same mass. What is alljh-w -a ,whs:a61(p brvn9 the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Eartho /xgmy eki0(/, but the same radius. What is g near its surfacom(/kyexi/g0 e?   

  Two objects attract each other gravitationally with a force of 2g d3,l t knm/oi(6i1 -pz73l kmfrnz:c.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of graq4b ooe/ ymzpe ( 6*qzfa(+i(kvity, at (a) 3200 m ( /qyze (q ei *a6op4+(fbmkoz   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsi 7g3-hqzaa4xi: u 6djjde the Earth where thegravitadh6jg aa4q-ij u37:zxtional 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 the mass wtn1z/sg*x- tc( 1z, nyxpd)dw- b0p t,fdhy.of our Sun packed into a sphere about 10 km in radius. Estimate th0zxw/(fn-tdbpg t1y h n ,pdx -*1ctz.d)y, wse surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like oubgd+ r+8; thpzyvn3l)r Sun but is now in the last stage of its evolution, is the size of our Moon buthr3+ bgvd)ly+;n 8 pzt 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 i;v9,i d ek(hythe space shuttle. Your friends respond that th;ih,kyd(9i veey thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square ov9yes4nr5l 8rf side 0.60 m. Calculate the magnitude and direction of the tl9 n8rrs5ey v4otal gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most op w11ma sm/gco :npe/5f the planets 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-gc 1m5o 1pn:esp/ awm/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 thp zf0*;yf gt/ee surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 340t *g/ yez0ff;p0 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of tha8lys0/ x o*,(q cdhyee Sun using the known value for the period of the Earth and its distanceslay/ e8hoqc0 xd*y ,( from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abou:pm d+iwm4f(,u6yqvo5r4 mf b t the Earth at a height of 365i b +y4p v(odrqmfu fm,w46m:00 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit mg d1-we:k)st1jc1 sw650 km above the Earth. How fast must the shutt g-) wj1wckes1td :1smle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to9wi90dz suo r12f5 aqu experience simulated gravity of 0.60 g? Assume the9 z5s2q1r 9udaoi0wuf 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 sa5:lg *f vy96rb w ood9a1q+yoytellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” 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 ofq* 9r1oywfya 5 yd:vo b9olg6+ the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the zdx cwt0x;ku8)y80 fi (oy) cstop of Mt. Everest to be placed in a cirzu;woxdy0)s fi)k8t0c (y cx8cular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continue8jg g,vqv4:g 5ta8s6iyvqy/pd to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon on8,v8 pjv4yq/gs tqvig ag6y: 5ce?    s

  The rings of Saturn are composed of c5r5ewk;c ti j:v-nwh,z4tk(do0 6t s ohunks of ice that orbit the planet. The inner radius of the rings is 7ozh tttsk4nw ,r5w(oc0;5 k i:j6ve -d3,000 $\mathrm{~km}$ , 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 e6**xp h n;9wg, sr) vppvos+ahvery 15.5 s (see Fig. 5–9). What is the ratio of s9*w,nv )hh*xars;6g+p ppvo 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 75-4w ec7 s1l ya-86u-dtnmow3apkg astronaut 4200 km from the center of the Earth's Moon in a space vehitdlc p6-ymao3-ae u wn8s174 wcle (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 equal mg;o (pb 2fs;mw/whu+ rass. They are observed to be separated by 360 u2 +o w;sm p(bhf;rwg/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 thehwvsv.n orq ,i n(w3/+ weight of a 55-kg woman in an elevator that3 qihnw svov+n(wr., / moves
(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 ,3 fvjg+-+ndwi gvj0q elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accel-v0+j+g w, 3 gfinqvjderation (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of 6upnl p:05bxz ikhj/. sp-j/qa planet with period T , the dens hl5i/ j0bzp: s/.pnq ukp-jx6ity (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 tjk. 5oyvf8 o/1mbgj0nhe Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earj nky18gm/f.j5 0v booth’s surface.    s

  The asteroid Icarus, though only a few hundred mj+ee).jwdgyt nnba*9 xkm,+1p)fme;eters across, orbits the Sun like the planets. Its period is 410 d. What e*.gnayjb)fx+)mw9kmj 1e t+ n ; ed,pis its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4. nhyx 98sjq*dkp* l0/p5 $\times 10^{9} \mathrm{~km}$ 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 .(iaheo 1a2mv.,qb lv the Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). 1o v,.ba(q lmhi2ae.vEstimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of kfvltj:st 5rt gp ir9zfq1)z5x6:h6l+ s9 ql)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 vb/v ffh,fs91fv246oa qp y z,mass, period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 16spvo1 vhf fz9a,b/ ,6f y2fv4q09).
(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 and r5 -qhck.qyfh5*pg/ca0 x(mh/ fuw5 ydistance of the Moon. my.uar(0w 5gc5 /c- fkhp/*y h5qxhqf    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usiokey(;-oun-y,o szc+; f xzq -x,d0 inng Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare tox -;0u;-zey(zci, o of, oyn+k xsqnd- the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (whzs )hbgb90-mv ich some space scientists think came-ghmbsv) b9 z0 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 demffjg+9 d r77o*kr-8 4nel k1soax o-uscribes an artificial "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 thek kuj8r f 4malxsngoe*-d7+o1-7fo9r distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fimb- l(bm*f9(ofj n0ugg. 5–41). If his arms are capable of exerting a force of 1400 N goml-u9 (*jm bn(0ffbon 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 wil9z5ryrz zc13xb ,bp m)l the acceleration of gravity be half what it is on the surzycr)rx53 pb, 1bzm9z face?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in ava08 p,n qnnsahb1-app)tz( . mutual circle once every 2.5 s. If we assumepa-,8p0ztb aan pn qvns. 1h)( their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the4bjn -yor, t2nxm m )nya-q8f+ 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 fract)f aojyyn-,mx8rn4n bm 2-qt+ion of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft trad.f62e 0 9+z gh,qamwsjp 2o(qdw0speveling directly from the Earth to the Moon exped szpgj69w+.aqohfpm2e,e0sq2 ( 0wd rience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kf/ssxtv1,j.r g, but when you stand on a bathroom scale in an elevator, it 1 ts.jfvx/,srsays your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space stas9sshq)ahh g6ar1x5 lhb;r)2 tion consists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to grar)hhr)q 6h15;2sslx gb aa hs9vity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft ick(amz,t nkel(qxrhwe o h cln,114c s(6.k;* n a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for th(b8)v ip:p hn1) 2zpttl 6fbdf saw 3iu)9z(lue mass of a planet in terms of its radius r, the acceleration due to gravity at its surface anw)zit)h(d 3 bnf(utsal 2:i pp 8f6p1zv9l)u bd the gravitational constant G.

A plumb bob (a mass m hanging on a 92l csk0et, 1q,hvqlxstring) is deflected from the vertical by an q,e2hx,1ql9sl k t0 cvangle $\theta$ 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 k.mjrer.3 p7z speed of If the coefficient of static friction is 0.30 z7e.3j mrpk r.(wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rota r4.dumbj0xi:i +zqf *ting so fast that objects at the equator were apparently wei+r ixfjibq0*d .:4umz ghtless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.0 2z .jt-uk f-sn$\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 radibpdch lepd09 (4m2 ,xrus 235 m. A lamp suspend,b9p lmdch(p e2x0r4 ded from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as*unc+gmm5 tk2b h +o1s the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on ah5+cg*1butmn 2oskm+ planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble S hy;2c +jlcra4pace 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 l cacy+lhr4;2jight 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 vaqty4:a5hcdc q ( kt0f/lley 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 heq th a:fd4tcq k/(c05yaviest? 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 24 satell, vu z-+rz-ivmites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satez u-ri v+,zvm-llite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 bimb(+ qawycd9)h1lx:v d - ;iwtllion km, is meant to orbit the asteroid Eros at a height of about 15 kma)y(hbv mcl;dw+w :1 t-9dqix . 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 cvv+ u8j4 arpbzxc+z48 q 9p1pg4bj)grepair. You are in a circular orbit of the same radius as the satellite (400 km above txbgj4rp8 4gca1+j)c+b 4 9zq p8pz uvvhe 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 i t*dlf.9ijs , q4zwc,rs its mean distance frtq.s4*,j, 9 rdzlci fwom the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need oymtt8 jf4:-1tru0r3tes q7d to be if you could actually "feel" yourself gravitationally attraoru3rty0t1s- et84d qtf :mj7 cted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of yd idl46kw ;*.dtv ca*k9wd7xthe Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years fr t7ai9d4cwwdvykk*ddl6 x ;.*om 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 locate6jfjsee);f f+0:lo t 5:m/vh 5 tqyvlcd at the 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 t65h5;:otv e +fft)fyjvq/j e0l lc ms:he bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits1a 5)nsz 7cwpyi*wel8 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 t9wa,wt kh 5+yl(kk8pj6hg1b fhe tip of the 1.5-cm-long sweep second hwt5ahgh kjk9,p8+ l 1 bkwy6(fand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weih9-s -rcvuth )daj z9;wrjk*,ght around 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 t-,c s-r jhd )a 99trhv;uz*kwjhat the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car tre; c-iu 2 tl9io:kwy6c6w32.oi celnjaveling at speedoe;e3iun2o6:jckcww 6 yt ilc2.-l9i $ 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 15nc i6a-ueo6x/dk15 dc 23 huxfycdm when negotiating curves. The angle o a6du c5di-5 ux1m e31h/6d yc2fxkcnof tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked 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.$\approx$    $\times 10^2$