Sometimes people say that water is removed frw)hupea fv8 x,0ynl5 +om clothes in a spin dryer by centrifugal force throwing the wefpu+ 5,lw8) hn xv0ayater outward. What is wrong with this statement?

Will the acceleration of a car be:p7qtaw49dq g the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed9 7gwqt 4q:pad? Explain.

Suppose a car moves at constk vq-*yssr y)rmj4g9* ant speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of ms9)4r-k *yrs*y qvg ja hill?

Describe all the forces acting on a child rbiay k8tjkoo2 ii -5*3iding a horse on a merry-go-round. Which of these forces provides the centripetal acceleiki3 yijt abo5 2*-ko8ration of the child?

A bucket of water can be whirled in a vertical circle without the wa* (c )sk9kj)ciqqlr;i ter spilling out, even at the top of the circle when the bucket iskc(kj)qlis cq* ;9 )ir upside down. Explain.

How many “accelerators” do you have in your car? There are at least three c)r6t ra-6 k)z,pv jdatontrols in the car which can be used to cause the car to accelerate. What are they? What accelerations do th j6tap- trdv, kazr6))ey produce?

A child on a sled comes flying over the crd hcrcq -mhjs1 3 df,g0;r.(upest 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 th1ddjr0csqgmpu; ,(. r -ch3hfe sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a d4rbl8x4u29e/zjjrdd95cfs 5 kv ;f c curve at high speed?

Why do airplanes bank when they turn? How would you compute the ba0v fecqb; 5wi+nking angle given its sp w 0f;cv+qeb5ieed and radius of the turn?

A girl is whirling a ball on uml0:f v)zga t0fn6n7 a string around her head in a horizontal plane. She wants t7)f ztu6ann0m0fg :l vo let go at precisely 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 gravitational force on t;:mk/6gn d;kv.wxhb the Earth? If so, how large a force? Consider an applk;/gtx n.hmw6:d;vb ke
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’ns;;0 a-r qc7-jmevbw,) koyds orbit be diff;ne w-kqdrmb- ,0ys;j)oav c7 erent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon ,ju +pbrx /cn2on the Earth? Which accelepxrcun j2+/,brates more?

The Sun's gravitational pull on the Earth is much larger than the Moc7n /fjx o65hybtk-)kon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in jc-nkft7 / 5o h6kbxy)gravitational pull from one side of the Earth to the other.]

Will an object weigh more at t4c0y1b7ujqd)ve8qj dhe equator or at the poles? What two effects are at work? u8 jd 17)vbyj4e qcq0dDo they oppose each other?

The gravitational forcw),( lqqrw atv 0y(:5ozk e:s)gtzey::rpe 6ze on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the El(qse0 : r:zq:rzy ev(t,6 )oa):5twy p wezkgarth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger obi(p xr) 4(uua.(k,j i*nv cohr smaller than the centripetnhr. ixpvu(u4aoic(* (, jk b)al acceleration of the Earth?

Would it require less speed to launch ai6s-ch67bd/ l lnqx2 a satellite (a) toward the east or (b) toward the west? Consider th67l/b2in- h6qsdax lce Earth’s rotation direction.

When will your apparent wfkpj+z3 d9 mk /y5yd0height be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant spjd0kp9mh3 k /yd+yf5z eed? 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 couldvu0// j 5c7rddh f;2 )uv2s6bm,vh2o riotmso 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 surface (Fig. 5–32). Explain how this simulates gravity. Cvdv2o 2 h/m),/;0so h7turfcjom6br v2d s5iuonsider (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 “freup:/56k-udiv *7a7ztzd qm-.o) boc( fyeipf e fall” or “apparent weightlessness” between steps.: obop7- iu)i/-*zqu fa emvtk6ypz5.c(7 dfd

The Earth moves faster in its o h16rx -bf*w )daeme2urbit around the Sun in January 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 seauxe *-dm wbe)26hra1fsons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered tlyz ek8 rio0;tvlz4mpd+6- /go have a moon. Explain how this discovery enabled an estimate of Pluto’s mass. km4lr0v dlpy+teg;o6iz 8-/z

  The Sun's gravitational pull on the Earth is much larger tyc ,vlu 1af:q)han 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.q1 lfvy:a)uc, ]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 1980k(26(: ) *q(w h:.4w h xhfkmyjy klog*xiylto $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orb s x9dry7, 7lgerd7vv3it around the Sun, and the net force exerted on the Earth. What exerts this force on t x79gr s3rvdv7,lyd7ehe Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it r2h*glig)r1gn*, f xdjotates uniformly in a horizontal circle (at arm’s length) of radius g*r n *)g1gfh2dxji,l 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and circldhkh)km+-nnb yh8 6d1 es the Earth about once every 90 minutes. Find then bny8 d1khk)dh-+mh6 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 on):wri dari v(a2 ;gs3s the edge of a potter’s wheel turning at 45 rpm (revolutionsa sgi i2):rd3sar(wv; per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a .;z0xlv+4w9da)dzn7 i u7lxudo q n v6string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , a;. x7lxdznuavv6 ldn4qu i 7ow09z +)ds shown 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 k((p(xrdh3hui olt 9 1turn of radius 77 m on a flat road if the coefficient of stathpdox r1ui(9l((3 hk tic friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be betwe6tt , cg;4y+rjtqnk2oen the tires and the road if a car is to round a level curve of radius 85 m at a speed of 956g o4ktr+c,n y2;tqjt km/h ?   

  A device for training astronauts a( e7e+efnwdnx+ +y) fwnd jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainefdn+nefe+y7 w)+ xw(ee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from 3f,jtka 4ze/cx71/e+icdlmo;gtz v4 the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turkz/xfe4cotze +,7tc1ag 4m /;ivl j3dntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsideznb. /*1pxcs 1 a3hutd down at the top of a cad s1t3 ub/x*pnh c1z.ircle
(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 rounded to 9sfgxhzwy( yjk204js4;iu m4 p of a hill (radius jwyz; s j2f4k4g 9hyx0us(m 4i=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 pwhen3)dp g)d/acyr g;p*n-: Ferris wheel need to make for the passeyph/;-)*:wrcdgadneg ) p 3npngers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kgpo;h;uz0e hh1t72 w aecqfc 65 is whirled in a vertical circle of radius 1.10 m. At the lowest point of fh2 q;1650woc7z ehec puth;aits motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm*pfv5g ya4x(hft+ y z* from the axis of rotatio5zhtg* v f(xp+4 yayf*n is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wwgexd+zwb 1 56 qg *bx6j:5duialled "room." qug: d65xe1bg* 5w6dbz +wj xi(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 ) iqe box( z82,bns rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig on8(bzx,beq2 . 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 ign xa22 s5xsfhu;sp:.mnoring the weight of the ball which revolves on a string 0.600 m long. In particular, find m;as.:s5su2ph fnx2x 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 8hiqsx-cpjp :lsi)9nani*7 0/8 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 etj pvjgh-gms; f63 x0p+*ri)$ 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 evajha2f) c 3vhohb.+h e7sive 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 components /az)xhapr 7f1 of the net force exerted on the car (by the ground) in Example 5-8 war xhf)1/azp 7hen 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 unifors, zd9qra7f0f., cpi smly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfwayzr fsdcp79 a ,0,qsfi. 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 of radius 2.90 m . At a partigk w7 g.9)kfmjcular instant, its acceleration gkk.w9fmj7)g 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 Earthq2(li( m(0mv - 5 chp3 xkbvo6fpqe*uf)hdxe0’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kg.*v2exf dxch p iboufm(0 (vqpl5)3(-qm 0ke h6   

  At the surface of a certain p0au 5c6+*quakel ;5o4rcaa dslanet, the gravitational acceleration g has a magnitude of 12 msckqaarael; 6d *o4a0 c 5+u5u/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 radiuhs4tiin 8s1f, p2x:d us is 1.741itui8 n: s p42hfxds, $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planel5i 9o -tgng0znw8e7ypf- o/ ot has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near oi9-f-yno t7g 8we g oplz/n50its surface?   

  A hypothetical planet has a mass 1.66 8 rf) 9zht+srsew:vv),t 1lw2jjro;ctimes that of Earth, but the same radius. What is g near it w:hczs2)ev osr91,rvt )tjf8j +lw; rs surface?   

  Two objects attract each other grakcl , ye5tyrj6w2w+2 xvitationally 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 acceleratiom dur4x*s7ha i )xz+wc.-.eiu u,p)eun of gravity, at (a) 3200 m xieu4))r u -xpsediawmh z..* uu,+7c   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whe.06 bmvx2bibbhskv17m* bk j*re t6 bkb.b2vx ij*kh*m7mv bbs 01hegravitational acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five time(. h ttia:wv wm.5gk/qydyg *+s the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monstag w5k.*y(qym/i+vg w. ttd:her.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun bu64v khg3b 0vvct is now in the last stage of its evolution, is the size of our Moon but hash4k3g 0cvvbv 6 the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while o e 5o3o1:pcd+8dthnko iut /s)rbiting 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’t so by calculating the acceleration of gravouo d1+tn):8ced3kp/o t 5ihsity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at tpiwo:g d+0h9khe corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the ip+g9d:koh0wother three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the S m-vadd *9z+lfq3 i72nnvntn3 un. Calculate the total force z*nv tdm33qnfn -92n+ la idv7on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of whmc r64teziy;(o *n) ecat it is on Earth, and that Mars’ radius is 3400 km, determine the mass( *6r4nome; ciety)cz of Mars.    $\times 10^{23}$

  Determine the mass of the9llw*7zi s/l b Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.] 7llswil 9z b/*   $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit about the 7q0ai0ir xk4g mnh zl4v*97klEartlq7nm4 0l09aiik4kvg*hz rx 7h at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into axt7c ct*tw /,w circular orbit 650 km above the Earth. How fa7 tw xw*,tct/cst must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rot5qi+gsew.k ,i ate 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. gqi.ik +5 we,s(See Question 21, Fig 5–32.)   

  Determine the time it takea 8p s.w*bce2js for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a heightcpbw. sja* 82e 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 satellcr tv6kpqs0 d 62hbv 4-1s*myiite have to be launched from the top of Mt. Everest to be is6q 0mp64kv d1yt-rs hvb*c2placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command modu-z4jvxsdno8su5/u fv6t*35dy cwiy3 le continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moo dv3sj5y8 yfi -cu/ sx6zn5o* dw3vu4tn once?    s

  The rings of Saturn are composed of chunks ofueho5hm4z2o * ice that orbit the planet. The inner radiu hh*4m2e u5oozs of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fig. c2uqk:0 wfny25–9). What is the ratio of 2 ck0yfwnq:2ua person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weighua q; 4q+d6zoccjlf4-t of a 75-kg astronaut 4200 km from the center of the Earth-6jzlc;ocqauq44 df + 's Moon 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-s*5jeg hdmxx(; tar system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth yearsg(m*dhe xx5 ;j 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-kg womahg v/r6:+l4y qfq/yc(7ehsh sn in an elevator that moves yh4 r6 vfh ://sqe(qch7s g+yl
(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 anut5a5l;v+n t rm:nlq8q*p u1m elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What v* :5n5llaq1 rmtp8u un ;+qtmwas the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits vertv h,5*r06pu lcg js4zy near the surface of a planet with period T , the density (mass/volume) of tjvlcg r56ztu ,0p* 4hshe 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 deteeu x)otp *oak/ji.2 7.e v2xtormine the period of an artificial satellite 7 j* xok2e)evaopi2ut..x/ otorbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred mido/ydj w x4;)eters across, orbits the Sun like the planets. Its period is do;xy4wj/id) 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5t :9zpvtn70x2zq ij 75rm1blv $\times 10^{9} \mathrm{~km}$ 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 yearsyk d8 ;n:uc,ei. 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 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 th dn,e8 ycik;u:e nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about thedcg:(1 txi9iq center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four la/tv(s:q q1vqorgest moons of Jupq vt: v1sqo/q(iter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distancm.7qls 8vux a5.vjya2e of the Moon. .vya2s m5v.7uaq j8lx   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of l2mr ai i+d(iqk w6+1lJupiter’s moons, using Kepler’s third law. Use thel(wk1m++26 airq idli 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 Mars andx0n pyq5w;uk0p u61in ei8 du(g2utz8 Jupiter consists of many fragments (which some space scientists think came from a planet thau pki( g0u;850nqwuyu 6 eid pt8xz1n2t 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 artificvj.4rbapud7 a(*sy 1bial "planet" in the form of a band completely encir.r1 7ad(*y4u p bjsvabcling 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 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 swinns5)nz x;e ha02v5ggvging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerta) h02g ;5gnzn5sxveving 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 acceleration of gravity-snwe kzc6af9sl+zi35n 9oa6 be half what it i5a +9fzlzn3-koi6 aes9c6 nsw s on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab h-:3l/f z/ opq;wq(klr 3eg dfoands 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,(l r3p /fkodo/ ql3:ezw-;gqf how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelerbo3 bm83dbe-ration of gravity at the equator is slightly less than -3r 8e3bdb obmit would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from tdtb)k b;meq,v8ci hl y9- p7b8he Earth will a spacecraft traveling directly from the Earth to the Moon experiev)pb, 8cmdtehy kbb7q;8 i 9-lnce 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 scale in a-st) kth( :;9 a(addfyyvjma5n elevator, it says your mass is 82 kg. W(dt:t ava (m5kaydh9-j s)f ;yhat is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists otc vu6/y(rp6y)p ,dshf a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle f 6spyh),v 6c/ud trpy(ormed 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 aircrw8tsj2 farftm9:+8 cghb:tz .aft in 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 the mass of a blp 8 ixp:l(a-wj1r3 *)yhido planet in terms of its radius r, the acceleration 83piid-*1lwhr(j )yo bapxl:due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical b(o 3e(9;vgo r5xzaijx y an anglvo(ia gxo(j;3e9 5zxre $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefibd*l)) r/asrficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?ir)) bslad*/r

  How long would a day be if the Earth were rotating so fa(o (qi2g6l rjkst that objects at the equator were appare 6(i2gjk (roqlntly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance14rqcle0o5 ue 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 2z9 hpi0ak)- yb/daw4spoh :da constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling sz k0y:/do9h24pwha-)dspa ib wings 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 the Earth. Tcb;8 o,q 8mg );jrk7 oyy2jynehus, it has been claimed that a person would be crushed by the force ob2ocqkgr oy78nm;)e y y j,8j;f 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. 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 extremel)vk w iq8yd1n-*k6 ymzy massive core in the distant galaxy M87, so dense that it could be a black hole (from81-y q k yi6zvnwkm)d* 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 constant6 qkt j+krk9x1 ,efgt8 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 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 aq+k1g j6t,trk fe xk89t A?

  The Navstar Global Positioning System (GPS) u7 u *)pnmvksc.rhp(ymbo+ f):tilizes 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 tv)o puymch7m)+(.:rnk f sp*bo within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, / pv5 6t yg 5tknqlh1 wru(cj1pc84kx9is meant to orbit the asteroid Eros at a height of about 15 km . Eros is 5j6pgq9tux4vrwyn k/ck(1t1hcl 85 proughly 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 repair;av,+.b5nk kjbpld ca: nt4*qq(yi q1. You are in a circular orbit of the sl5kq( .:j 4 va+ntbyp*cbkqqn , 1;daiame radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has jh o: ,v7o1mira period of 3000 years. (a) What is its mean distance from the Su:7ovomh,ji r1 n?   
(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 woulnk3g 513 k(al zslt.qgd need to be if you could actually "feel" yourself gravitationally attracted to someone near you1t .s l zkqg5ga3n(3kl. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (F n6kyv x1x(z73w2ey e2 8patswig. 5-46) at a distance of avspnt8e3e x y7z1 xw62 2wak(ybout 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are locatehfzj9gd b e p* o1(v+m;psm:n:d 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 mip*+zfob jv :(n g9 :1hdm;spemdpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ea-czq u tk;j;mtq i;m/-rth $ \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 ;ag:egyo9y z9kj :frtm2 (c5spj fc,2by the tip of the 1.5-cm-long sweep second hand on your wrist watcjy;pfyg: refc t smc9jk2oa5 gz ,:92(h?    $\times 10^{-4}$

  While fishing, you get bored and start to swingh. hdtx8s92;0lh sl.gd w chq6 a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a cow2s 80;s9clg .dlhx hq6hdht.mplete 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 designed so that a cuig)wa etyu; v8, kl68*8t gmqar traveling at speed gi ytl*)88t 6u8kv;m,a wq ueg$ 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, uein( + bf-v1djk-uy y:tilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more 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-d+u k1n(:fejib v-y y 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.$\approx$    $\times 10^2$