Sometimes people say that water is removed from clothes in a spin dryer by ce3lha)ztre ft+d+kd9z3 ,a0 y j7fs;zpntrifugal force throwing the water outward. What is wrong with thir z t yl s3a +3kdp,f;h7tdea9+)fzj0zs statement?

Will the acceleration of a car be the same when the car trapz:c7a wdw,9ann a qrw(o (p(0vels around a sharp curve at a constant 60 km/h as when it travel,(7zqwc(n aowp9(a0nw dap:r s around a gentle curve at the same speed? Explain.

Suppose a car moves at consv 4w paa 2uf0n,zt-c-ztant speed along a hilly road. Where does the car exert the greatesta acuf-4-zwn0ptzv,2 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 a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round3 0pk/)fnng6+ /vtcf w; 6bv5msf*tyath7oug. Which of these forces provides the centripetagvghf+6/3 t6/nftn 0f *57k;o wpv)uas mbyctl acceleration of the child?

A bucket of water can be whirw4qrqnp7hn 4r25h u p,led in a vertical circle without the water spilling out,q4rn5 hp2rq4w 7nuh p, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three co)r0r ). cwhp9+ molns xv+b4hgntrols in the car whicbsvh lnrw.+pcx)m4 g 9or 0h)+h can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the cf pe5.x2/-owq kbsd)s rest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill.spqxo5fkw) -s .2ebd / Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when xe8hj;ms ;4j*rso/sq rounding a curve at high speed?

Why do airplanes bank when they turn? fu3 c)as6 z*r6q7icio How would you compute the banking angle given its speed and radius of the turif cq6*)z7rcas6i o3un?

A girl is whirling a ball on a string around her head in a horizontal planeqtt0m,1ds:9t y 5zp ky. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yardz0t:, m9t y51kqt pyds. When should she let go of the string?

Does an apple exert a gravitational force on the Earthd,quid r:uk q8/k 1j ),/ricwf? If so, how large a force?, duqw rkiuq,d/irk) 1/f 8j:c Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways woul ak:3*g3p sxoqd the Moon’s orbit sx3:q3o * akgpbe different?

Which pulls harder gravitationally, the Earth on titw wzomgs*1, 3co3+i he Moon, or the Moon on the Earth? Which accelerates mor1,w +go3osiwm3it*z c e?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yepmg5;pos 7y:ht the Moon's is mainly responsible for the tides. Explain. [Hint: Consider t o: h5p7msyg;phe difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poz+yj)mi s 4 7uxj9jdo)les? What two effects are at work? Do they jjdj4s))mo 9 i zxy+7uoppose each other?

The gravitational force on the Moon due to the Earth is on*99fbu1nlc 4sbt 0 jwzly about half the force on the1ulf9 tzcj *0nw4bsb9 Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Suqz s t/y)s,r2zl7 ,;kzf 6jcfon larger or smaller than the centripetal accj; )f lzs2ro6 /zz,,tk syq7cfeleration of the Earth?

Would it require less speed to launch a satelle p,o5g70s wyxite (a) toward the east or (b) toward the west? Consider the Earth5yso 7 xp,ewg0’s rotation direction.

When will your apparent weight be the greates-tuz/ aoq5: (pv t (-mmhoyx (sl+ay3mt, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (m(:y ta-yhomapo / v(t5(lxqs-m u+z3c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend londsd we mq/khdbn(*;5qt9 i n,0g periods in outer space could 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. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity yo/ d9;qb*kdndw s( neq 5,t0mihu can think of.

Explain how a runner experiences “free fall” or “apparent weightle) dg ;bojd3/yw. lkh3z8 qiwk8ssness” between hy3w8 )l bk.g/ z3;k iq8wodjdsteps.

The Earth moves faster ini ; 56iu(fh8);ffx y xj4xmgot its orbit around the Sun in January than in July. Is the Earth closer to the f;o()xiyu6t;h4 5 fi fxx gmj8Sun 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 it was discovered to havoq8r 1xvjb w9:f ,6jrve a moon. Explain how this discovery enabled an estimate of Pluto’v1qjb:,6wrv fr xo j89s mass.

  The Sun's gravitational pull on the Earthw5 j.y v(w )o0hhcokt) is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of cjt0yo) ( ) vowhk.wh5a 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 1 hidz(*)d(zt-iy( l:jy k my32meqs*g980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 k ui w qetm4wzkgut*)3e; 6c63the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is 4iewku3kq*;gc 63wt m6 zu t)ea circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates unifj t 52ys.*kclnormly in a horizontal circle (at arm’s lengtk2. tlsnc*y j5h) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttlv1v5:vip9* bd f22.xfhjl 6pjo r y9mee is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the cenl1 f iv 5v29ox*eh6vdp j:fy.jb 2mr9ptripetal 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 b*lx /zi1c:qw65bjlgqo-r8 uof clay on the edge of a potter’s wheel turning at 45 rgwbq/r- o6ux: 8 l*zci1l5jbqpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of ak.9jr8u su;( 5mb)rn 3k kxbrw string is revolved at a uniform rate in a vertical circle of radius5 kkw (nkub rb;smrjur9x)38 . 72.0 cm , as 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)at) ad4lkq8 z which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indez )qt)adl 48akpendent of the mass of the car?   

  How large must the coefficient of static fricti aok9h(7gkq)o on be between the tires and the road( 9)qagook 7kh if a car is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter gdht-5smzr 08 pilots is designed to rotate a trainee in a horizontal circle of radg8rdh ms50- ztius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 l ;eyymg9,fqi4r ;vde 9 rs-*hcm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increas*4srlyr, d mqihvee- y;9;f9 ged, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at tk 54u8lpcn:s nig yuq4 84-a,7op fjzghe top of a ciun4ju azkqf5 4, s8c8-gy:p g 4plin7orcle
(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) crosse7 fimik 1v ,e9v8v8ap3ad0qbos the rounded top of a hillaboi mqvpd9ev183,vaki8f 07 (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minut ym11+6g)dxnkr2bi 4aq s,gkhe would a 15-m-diameter Ferris wheel need to make for the passengers to h+ aiq46x1)gk dy1 2gsbnmkr ,feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirlcicj.( v.f7klee ( mtx*/pf;6b*kxr ied in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension i .ktlk67rbifeex j*c;* fx (c (vmp./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 pare cdmh;t;be ig* k:a/)ticle 9.00 cm from the axis of rotatmig* ; dcb:k)heae;t/ion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindr0z.f6q xv+ksx,3-ty w qh7fqkically walled "roo xqkhqszqk.f 7tx0w,+y v3- 6fm." (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 frictionler028q rda0 *;ggtiauass 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. 5-t0 ;rg 2d8a0iu*aq agr
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 ig3kd, -f(jv*.su kfp oinoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the k*kf.(ij v fops 3-,dumagnitude 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 peohd 95t2.pp 8gbje gx-rfectly 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 gz-.oww0pt-ay1dw *cl9kn d9 $ 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 vertically at 31tbhcdu1:j8difez6-(l uz1 l(0 $\mathrm{~m} / \mathrm{s}$ . 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 aohc;a7keywhz)(fs f 4h w,61atbrt di+ (( 1vand centripetal components of the net force exerted on the car (by the ground) in Exam bedf1ia4t(k(+)azh 6 ro tw1awv7hh(f,c ;syple 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from thpqp c9 r fkz41b99w2hnwgm*o)e 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 ca1ob npw k9)qcr4*9hz9pf2m g wr 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 of radius 2.90 m . At c5kmk ekb/dh3te9x,jm,w q9 ) a particular instant, itmkx39b,d5h)kj ,qk cm w9t/ees 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 gravitygp+3: t9s ;ycxtcf s-b on a spacecraft 12,800 km (2 Earth radii) abov+cb g:tf 9p;y-tsx 3cse the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a mag2 tg(6i ajd2ra9e,ltf by21cp+he ;ainitude of 12 m/y h, l 9 ae;it1ba2+ pdti2fg6je(r2acs$^2$ 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 cb,p ,o5.y:)5sq uclctot/;kcb (v togravity on the Moon. The Moon's radius is 1.74 obp vsk,5ct;5c/ (,o:lq .bu)c cotyt$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has t, khjgq/:l z-jhe same mass. What is the acceleration due to gravk/j ,jh-qzgl:ity near its surface?   

  A hypothetical planet has a mass 1.66 times jmm.rhb9fb6 i n) )g+qthat of Earth, but the same radius. What isn )b h+mj.)g6br9 fqim g near its surface?   

  Two objects attract each other gravitationally wii7m/bjw8 /mz,t hq4:xs f,zrl th 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 , t t 9gx*m3yf+vxd0h(lihe acceleration of gravity, at (a) 3200 mdx lv y3*(+t9gfhim0x    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eartht(hqq 7 hg8f)w where thegravitational ac)tq whg7h8f( qceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star 0;o: qo*igil:ow op6we :cm;ohas five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity o:om::lc wq o;*iigewo p6o ;o0n this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star lot1 k8lf ycu5+ike our Sun but is now in the last stage of its evolution, is the size of o f8u+15cktl your Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightlqctew,/ ty 16iu3 hcdr.fko-5 ess while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it iy hktw1uqt if cd 6-o3c,.r5e/sn’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 loct +, :(nis5j ostryin/: x2hblated at the corners of a square of side 0.60 m. Calculat:s2/ sinnt 5j +r:x(bit,loh ye the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on th1xcf9tm:se;, ax8axp e same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, ass cp9t8x,a: ae 1;mxfxsuming 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 t(0e9oc b w7eithe surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the ma(eo tb9we ci70ss of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known valu*9 + xlqnhqa0ue for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example+*aqq l90hnxu 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit aboutqqojx k1 a5uivalk040( sl c**ez *zh* the Earth at a height of*qkca lo uh0v *e(*izsxa1lq*k05 4zj 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular ojj:3 :yaxgd *drbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when xj:*y:dg3daj the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if ocz(ucw *u 36fn7tzrx we1+ *ayjcupants 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 fjna1zetz fxrwy *w*7u6+u(c3 or one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “nez2q6um(e(qbac;g.fho 0 3grsar-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the ch(ba3qr 0 gge(2o z6m;q.s ufEarth 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 satellite have to be launched fc2y1g.e9h w+i pfzd;vrom the top of Mt. h1+.v cgde92 yi fwz;pEverest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing missionak *v .x+,-vf css8tm0sw9ly7 fl) nxs, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it0)lf-ssx . vtkc8 axs7y+swm vl9fn,* take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planeb6 c(2c ayx6sft. The inner radius of the rings is 7ycs26af x6bc (3,000 $\mathrm{~km}$ , 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). Whyk, (mddjv ;0v6zpmczn6, 4/encv v l-at is thezev;4,m dcm0dzk v(-,ny v6l v/cnpj 6 ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 7y 1f*b y q5wl)/,dxfip5-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant vpy)q5i*b 1 lyd/,fxwf elocity,     ----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 m n.vu.(sgkm y9ass. They are observed to be separated by 360 million k mu(n vsg.k9.ym 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 reada-rl ijzoj -8w8 :fyd- for the weight of a 55-kg woman in an elevator that movesj-ly- jz 88iaf-o:rd w
(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 frj*02sqaua(py 0xh zr4om the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What wa4z(ax asqypjru*0 2h0s the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite6//jtex e xb7bnl2hia .8nt1e orbits very near the surface of a planet with period T , the density (mass/volume) of the planet ise16jnt8 x ./xbthl2i en eb/a7 $\rho=m / V=3 \pi / G T^{2}$ .
(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.;vpfocf0 -* pv x48z)vr-o /mqsipp,l4 d) to determine the period of an artificial satellite orb )lpp4z0 c-;rqvf8 *xpopf-osv m/,iviting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred of no5st dvfj qye d: s(jt01/tb/74)kmeters across, orbits the Sun like the sj:onvt)5/d0t (/jf4k qbt ody 71 sefplanets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanceift/fkx+yts )q , *x,z 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 onceurx t 9xk(r/;b/ ;vpib every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of thrxx /;i k/ r;u(bvb9pte 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 the 38v x3n q0ycnxsnns( 5Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 lciq/6l f *wj;oargest moons of Jupiter (those discovereq ;w/6ljciof* d 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 knownq)y5jk(fdkc cc.,x t . period and distance of the Moon. txc ,.kf5dqy.ck c )j(   $\times 10^{24}$

  Determine the mean distauog:qk4fp l0 ip4 zg188yf;jance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the qo:z;8yg 4 pkj1g08fuai4flp 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 manyteet dk),9u ;. fo5csk fragments (which some space scientists think came from a planet that once orbited thect5s ) ,;otkue9dk.ef Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "plane 8p2bxfxo.mq:8 u;yawt" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (wher8b2m:xwa;p .x fyoq8 ue 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 seo spp2a ))j.vwinging 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 his swing? His mass is 80 kg, and the via2 p)so.)v pejne is 5.5 m long.   

  How far above the Earth’s surface will the acceleratock4cld g -zs;*6yu f,ion of gravity be half what it iud,-l c ks ycog;46zf*s on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands nhui*vd7rac 1n)b n(1and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and n 1 c1bva(nd*r7un)hitheir individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravhee z,e63)frhmldeq9 dy(+d 0ity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect0+3(fmede e,q hl dy6 zr)9dhe. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth wil5alrgb8: v1tj5 e/kq1viit4el a spacecraft traveling directly from the Earth to thlg iait1vej4:8k1 5 qe5trv/be Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bu y5wx/ s-r*nljt when you stand on a bathroom scale in an elevator, itw /5r y-njlxs* says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about fjtod *+o it7v:(9kwvits center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube h i(7tjfok d*w9o+ :tvvas 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 (Fim0mjo3u p66 gag. 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 planet in teraiq2+8d cum s787tpz;0yyuw q ms of its radius r, the acceleration due to gravity at its surface and the gravitational c qp;uy7sq0tmizd 2wua+ yc 887onstant G.

A plumb bob (a mass m hanging on a s7x:0fdw b z60tdyvd4otring) is deflected from the vertical by an angf6yozv dd0xdtb0 47w: le $\theta$ 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 0 vq hjm0h)qq7 If the coefficient of static friction is 0.30 (wet pavement), at what range of q) h qjh0m07qvspeeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at tyn-6jc: ;ruvy1 yz-5htj mqv;he equator were a6y;u;hjz1 :- n tr5qy-vvymjcpparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart ogk(f)+u uqe9a f 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant d9 (xpdqbw./x +*zhjubr5ek( speed rounds a curve of radius 235 m. A lamp suspended from the cei wk(*jbz x/d(9x r5dupbeq+.hling 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 the Earth. Thus, it has /hb /totndnx 8u gzf 00yztc k*ql6k0kd93)*vbeen claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for0d/qt xf l*k)c ko y9z*830vht n6 /kg0dubntz 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 Sptbngok m9a 2iv:zf9.4 ace Telescope deduced the presence of an extremely42mn k9bo:ag9z.i fvt massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed 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 con7x.nu, wfez6o gyy3r/sqh ivjx91u+) 8oe3q gstant speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley havnsg/ j3yywf 8v9oox,equxhq 1 e)g3ri z.+67u e 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 at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites or9a(yj lkp j2jkk+/x;nbiting 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 altitu k2jxa(n9j lp/+;k yjkde 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 trajk (l-tplz.h; s2q:khveling 2.1 billion km, is meant to orbit the asteroid Eros at ks ;l.-:p(hjltzhq k2a height of about 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 needa5:*p3dqi hy7p zzvba* 6 xwy8 of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it. q*6db* pi5yvhwzaz:ap37 y8x
(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 yea+ (2dtgehqoo t +jv-y.i n-s0qrs. (a) What is its mean distance from t+ng q sd. tootei +jv-02(-qyhhe 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 to be if you could actci2j ohgg ;m5mxc,ihei-/ )m(*p g q.rxa4l2s ually "feel" yourself gravitationally attracted to someone near you. Make ri e ir*cpagmm/j-og x;x gh4sh2.,cm2)( i5qleasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5z5ibkq (p:72en 3 vjcj6te jf:-46) at a distance of about 30,000 6qj5zj p2 ibn: :ee7vk(tj3cflight-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 square 0.50 m on each siba 5jye.-iza /lo70 .oe.qympde. Find -a.. pil7oa.ez/y qoj5bmy e0the 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 5 3g+ 1c4nnmahb500 kg orbits 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 6 lks3y(zt2ee mr *bf wgcw*56j5bzj 2by the tip of the 1.5-cm-long sweep second hand on your elef 26mbcjg6 twyrz ws* z*3(b25k5 jwrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swi*uuztc*-n0 .v e aanl i))jqa/ng a sinker weight 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 that the fishing line makes with the ve) / njz*)vclantu-qu.ae 0ai*rtical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a c6(m5r7 -thktr*cru7 vz8og k:njv l /7fqat 8rar traveling at spzrrha( tlcmvu ktk6jo78r57rnf/ qt: v7-8g *eed $ 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, zgu;yz t*we 12the Acela, utilizes 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 the t*eyzt z12 gwu;rack 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.$\approx$    $\times 10^2$