Sometimes people say that water is removed from clothes in a spin dry5r/ s.uk1uno-qtv(6 w-kr i)pde mt) ier by centrifugal force throw6i.1ei t(rqunvdp-5 rw uos-ktk/) m)ing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp 1s:3pmf+xrx f curve at a constant 60 km/h as when it travels around a gents f:3fm+rpx1xle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Wher5m 4pj6t + u.cn mjxb29lvkf7pe 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 hillst9l 6pxcfmvb jp.2+74 unm jk5, (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. Wha h7/y; 0 e)q cjepauq9fy-mb8ich of these forces provides the centripetal acceleratyucm7e- )q08ap;9ef b/y h qjaion of the child?

A bucket of water can be whirljb(rt-4p7,byl i 9wg hed in a vertical circle without the water spilling out, even at the top of blhip(y-7 jwtrg 4,9bthe circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are ato)jjbqw)24 ma least three controls in the car which can be used to cjq)a4) bmj 2owause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over t;i w;jg kl lzts,a a7i(/v ,bezh71jb2he crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decreasevba; ,i(ae t jiz zlb7g,172wljk /hs; using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high n;2f-ba z4 kshspeed?

Why do airplanes bank when they turn? How would you compute-(reb+gkk5 dl the banking angle given its speed and ralbd+kge r (-k5dius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plae c i.ek(.bmr2ne. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. Wh bek..iem2(rc en should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, hoh8. 32.je. 7gdxetp6emgegorw large a forcego6x3me2j. e.d8gretph7eg. ? Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doubaol2v+jyr 0ou3lrd 7 aai:8*vle what it is, in what ways would the Moon’s orbit be difiojr8* l3alva v 0od:y+r ua27ferent?

Which pulls harder gravitationally, the Earth on the Moonr s57xc d7/3 bv4jgt unhr8b(g, or the Moon on the Earth? Which accelerates moru4b7 jhd3/csbnx 7rg8( 5vrgte?

The Sun's gravitational pull on the Earth is much larger trzzh(k2v9*j7nj1 g vthan the Moon's. Yet the Moo9jz*kv 2z7 vt(jg1 nrhn's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh mors:jlror(k; :f 2g;, cm 8osqwoe at the equator or at the poles? What two effects are at work? Do they oppose eacc: ;qk(gsjw8o :rr ,fslm; 2ooh other?

The gravitational force on the Moon due to the Earth is only about half the fo gn;ww8 0x,tzqrce on0 x qw,;gwz8tn the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit a rsb:(0 jn,sgua 5qqw*round the Sun larger or smaller than the centripetal ac,0sq*r q : (ajw5ungsbceleration of the Earth?

Would it require less*98n gko p;c.daaci) n speed to launch a satellite (a) toward the east or (b) toward the west? Consider the Eartp .gnci9)8 ;a*noadkch’s rotation direction.

When will your apparent weight be the greatest, as measured by a sc 5d 2*ks4arjfv 8vkt1eale 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 which case would your weight be the least? When would it be td81vk akt4evs* fj2 5rhe same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long6jt*,f4c ec8 yun2tmv 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 c4cjm,6vt en*u8yft 2on 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 you can think of.

Explain how a runner experien 1jsnwt1)tdi .ces “free fall” or “apparent weightlessness” between s.sntt jd w1)1iteps.

The Earth moves faster in its orbit around the Sun in 6ek 8 i+1fs3efdepo1uw9 y,k uJanuary than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factify68 uu1 pkodsk,ew1ef+39 eor 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 w w,c.80nuedt,g,g7zq-ji a r to have a moon. Explain how this dig.08wu ,z ieg n,a,rtqjcw7d-scovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than thx7wvzd( kzkktz9ryq(io j. l .v)c,*4 e 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.tkvx(9 kzo d (wklq,4y.vi*j7 c)z rz.]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 19)xqwx 95r5z k /*wsmlo80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 thu;6 m+mqq-rnaspsm,;e Earth in its orbit around the Sun, and the nqmsm -6+ np;u,rs;mqa et force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates uniformlr t);,celyy6w:hwf l+q 19)s6 ynmnt zy in a horizontal circle (at arm’s length) of radi):y;qw+9zercltywhfy6 l6,m1n snt) us 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 kyjbba 8,pah/9m from the Earth's surface, and circles the Earaahypb98j/ , bth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge oh8 gg )pm0y-ulf a potter’s wheel turning at 45 rpm (rggh8m0)ypl u-evolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a strinyu blbc637bmhkkg:1k o -41idg is revolved at a uniform rate in a vertical circle odbklk3 cbg1bu hoiyk -:17 64mf radius 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 which a 1050-kg car can ro60 un bx 7ank3ky2rvm;7 ;chsyund a turn of radius 77 m on a flat road if the coefficient of static friction between tires and rosvy;uy23x; mk hak77bcrnn6 0ad is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficit brn7cpy4gh(5x262-ai az beent of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speedp5tb2ar zn(i-eha46g7cx 2b y of 95km/h ?   

  A device for training astronauts and jet fighter cionm 7a/pc0scqs6+)txiz; 9pilots is designed to rotate a trainee in a horizontal circle of radiusx9nc+ciq m tzo0/;isc as 7)6p 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 cm from the axis of a rotating turges(ga8l8w3i)kb1x tlk ;z;dntable of variable speed. When the speed of the turntable is slowly increased, the coin gg(;1l t walkkxs);dib3 z8e 8remains 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 zdz 1q/t)vi2u traveling when upside down at the top o2z/ 1t)dvquzif a circle
(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 t0 uc3k qd3/1 mof1xy/ ba3qaumhe driver) crosses the rounded top of a hill (radius =95ab0a m//cm3 xk13o3du 1yquf q$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need to make 1u c; /kbac+j5dw:g9ommgv9vforgm 9mgou1 ckvc5+:/av;j b9 wd the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle ofonszuv9 zo:)s 5 15vwo radius 1.10 m. At the lowest point of its motion the tension in the rope supporzo5ssoz n:)v u915wovting 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 from the axis oj gz9: bl +f4us./(vzwcom kn4f rotation is to expeo(4lc b.j 4gzzmw+ n/:ufvks9rience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a camnzf(vsw/ m z6k1przq:k(3 6 hrnival, people are rotated in a cylindrically walled "room." (See Fi /n:rz kphz(w3mzqm v6fs6 1(kg. 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-hocof 4u;; 3jiwte; xx3xokey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown4 ;wo;3j;e3x ioxxut f 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 ignori4cx(geeh fgo07k nyhr98 4u ucwj+f:.ng the weight of the ball which revolves on a string 0.600 m lo+ o c04g nuwuk h.8rc7y9:jf(g4hxfe eng. 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 rad/e0n1 tslb:jz/h4j coius of 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 o o)khv(p19zy$ 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 ev9ffhttekc7q) u(6n 8jasive 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 fx3x7i5)f *sbtuktc:da vq lp6-ikihn7 (+ -bcentripetal components of the net force exerted on the car (by the ground) in Examp bki7dqf +)3( n h xla- sxki7v:fti*5ub-6tcple 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit a cck 9m nx enj4ez wl9-d(mmb866e(h/.* xcdtwrea, 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 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 e-989w.je6(xdbz 4d/lcnc kthxe 6cmw *mmn (slipping or skidding? $\approx$   

  A particle revolves in a horizontal cirvndigp2 ob1:ni i(+y. cle of radius 2.90 m . At a particular instan21gi.b nvdi(+:y op nit, its 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’sd1c q2u0u 2r-* zclcqe;pm1q 4v 4jbke gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1 cuq4d22 pj0bl*m1 qe 1; zu-crveqck4350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magnr+b 5vb00vtu5z4zlr6izv zc3 itude of6vvrrivub zzt 03c0z+4 bl z55 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon.(yt m nu2wh-:1nmxy 37mz3;(jceb txx The Moon's radius is 1.74ym u2(jtmnthx3:e;c- 17ymxw( n3x zb $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a rafo1/w h +vd4 .d-lxek0x hupy:uwl/r7dius 1.5 times that of Earth, but has the same mas.4 dd-r7u vl kf/:h1 u0lxx y+w/powhes. What is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, lq,: b5)xno2ed0i xiabut the same radius. What is g near i) q,2ei0l5dn o:abxxits surface?   

  Two objects attract each other gravitationally with a force of xc0or volv9n6y131 b-p7jiqi 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 , thew74,keggyok 9a3wf9c u6rp. f acceleration of gravity, at (a) 3200 m w r ,k3.c9oufwf9y4p 7g6kega   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s centv* zvc/yq6v y,c*oxss1o1 o7ger to a point outside the Earth where thegravitational acceleration due to the Earth i1v **y vo 7voyc1 6cxzqo,g/sss $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mau 5gs)/r.*aqs+ :hj1c 2y7vnwoq hp qxss of our Sun packed into a sphere ab+.w2asg s */ny1qv7u)hoxr5 ph qjqc:out 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star likd9sub,.gg/tb) i0wvs e our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of o.u 0d)sv, /tigswg 9bbur Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless dfk/v pe-te( :3gh qo5while 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 isn’t so by calcuq:e3fd(g -opv5/ht eklating 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 squ v2j89yab8ci4e*tunw are of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the othwb8vyan92 t 8ie*u 4cjer three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side b lcv)0gvl(:p j/ah 2c0 8zhcuof the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a 8gup(h b02)avlcc:h /0lzjcv 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 gravity8firdly*y)g,w6l qizoy3 jj c 1fv;85 at the surface of Mars is 0.38 of what it is on E38il8vyj6,yy of);l*jf w rzd1g 5q ciarth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value fo;xe*y w q(s1vfr the period of the Earth and its distance from (;wxef *sy1vqthe Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed kqu s: i+r,5nja)qahs6/y j*nof a satellite moving in a stable circular orbit about the Earth at a height r/ sq :sny *aqai5+k)h,6njujof 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circot4( blcbx)(y ular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occu)((xcobl y b4trs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate i x.gs:v n77l3eqcy)2tqux2 rif occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 217 y)xqqvx: inl22u3r.ecs7 gt, Fig 5–32.)   

  Determine the time it tak3b rlxiyr :vef(m7k 46es for a satellite 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 vyve7f4 m3 ki:rl6(b rxery 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 afuh5;n)kz l2lb./.d iom l4 kh satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth? b 54kfo2z)il k;.h/ulnm.dhl   

  During an Apollo lunar landing(,w+rh)puq i1 s 5wxcg mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go a(h,+g)usw5rq i pc 1wxround the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. 1fskx *2xc5 fgThe inner radius of the rings is 73,000fsxxf kg25c*1 $\mathrm{~km}$ , 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;da qw/pp(gbmv +mnu -w:f, f. in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (gm,uw- nbv/af(;q:w d+. fpmpa) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 h8lii* owd/w zud /dkl:ws2* 8km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocih2/od/l*8 u:wws8wd*l iikdzty,     ----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 eqsf , k *6:whgi g/-yv.w+xlszkual mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mwhsz fg,-i/:v +6gs.*xkykw lass of each?    $\times 10^{29}$

  What will a spring scale read* b ed uaqy5s7w4g,5cd for the weight of a 55-kg woman in an elevator that moves 7equ5w dygb* 5 cd,4as
(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 elevato)c6eb6 f:njtiqozec ()8 qgd 1r. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimu ojng8b1e)(fe )qqci c6d6t:z m acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very; m8va k 3z+vl rnyf21gjs7t)ie y*k6c near the surface of a planet with period T , the density 8vt j3s7c + vgmk)*zf 2rin6y1ya;e lk(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 the Moon (27f,,w dd3r4jp zaa08bm .4 d) to determine the period of an artificial satellite orbiting very near the Earthawa,4b dp zr3jm0,df8’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orb zw dei(e72c(qits the Sun like the planets. Its period is 410 dedq 7zi(e2w( c. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance ofyp 2j6:, x)mvmz: txw7zjp; ptgp.1 jj 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once evep4rzzs ik 48p;yb ke0z2 +je7ery 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hinze yz0pbs8j e4p kr +7e;4ikz2t: 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 ce31ki mm5vmke. nter 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 mea;gk fpv-m4cq48*l (gndx c l.qn distance for the four largest moons of Jupiter (those discovered by Galileo in 1609)cd nq* 4qmgc .pg;f(4v-l8kx l.
(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 anvmjx:s zda.5hp2w )cjy:k90(c1jn jh d distance of the Moon. djpjx01:ny(ws) v9 j.:cz5 hcjhkma 2    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s62dccpx 0uvo 0 moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values inc 0c 60vxopdu2 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 consists1 ypit 6)o6.isw 7rz6/c cqyrz of many fragments (which some space scientists think came 6 c1i)w6.zrctq z7i6sypory/ from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" delpz ep3hi,:;/ qrtb (1l q.bin the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Su1 z,;epdlq:3qeript.hblb( /n 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 hangi 7t1vbk5ybd8s46u fn xng 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 kgs ktu41b n5b7xvy6 fd8, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half w/- sjbln xtyg8si542u a/qb8ew+ i7p fhat it is n2-/x w ys+s8aqipelb48ti 5/gfj7u bon the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hars;, hsya(u 9,37rlaiibclhmm5 k 4g ,nds and spin in a mutual circle once every 2.9ii hgh rkm (;b,lya3,mlsu574cr ,sa5 s. If we assume 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 o/rh ;kplm.:1byk k e o;hnd8n0nce per day, the apparent acceleration of gravity at the equator is slightly less than it w.hnbh 8;lpe;:r kyk01m dn ok/ould 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 the Earth will a spacecraft travelinoxc03z4ob*b:sqv)vg;o5ulxgna1 t ; g directly from the Earth to the Moon experien5 o ; );nbv4tv1lo gzbo0uc*gas3:xqx ce zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, 8ltd .04e;bp 3kxyp,z zure*u but when you stand on a bathroom scale in an elevator, it says your massx8 ;uz*duppzt3 keyle ,0rb.4 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 p:l5q1 e82iyvbz,0wm. zl 7cfspj )qktube 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 gravity at the surface of the Earth (1.0 8:e kzpzq).1cj7l,qsb 0fipmy lvw25g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical lfm d7-v4,8hi u jobyh0oop (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 i8x w 9h7u *xpeeaem+;a planet in terms of its radius r, the acceleration due to gravity at its surface and the gravitational constanew huxe;+xe9a8 pi* m7t G.

A plumb bob (a mass m hanging on a string) is deflected from the veskqk*m2+x zo;rtical by akx *k2qmosz; +n angle $\theta$ 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 +3/(,dadzdibcqy x;cfor a design speed of If the coefficient of static friction is 0.30 (wet pavement), at /;cd(qb,zy3xia c+d d what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that obju,hary,l:(h. v vp zai2o);wwects at the equator were apparently weighth2awa ), wz(:; uioy.rlhpv, vless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dis 4im6n-f/ysoytance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed ro98ndu, yk. culmx97e punds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle pmlx yu, ku.de89nc79of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the01ouz rm+ vm3xf7xc+ e Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: ma7e m3x xf+ vczrm1u+o0ss =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:pcywlww ,s--n+w/ 4 kngw;vg Hubble Space 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 light escapwv+-;y ww:wlkn gc,wg4np s/-es). 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 61xupr rc1g j9 snft78:,a jfa 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) r:ft,cj91un8p6 x7rg saa1fjWhere 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 orpcu2na:ty jp4(+, bof 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit j:op a ,yn+pt4cr(2buat 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 jf.g4 uw;3mx(dg6y 3lv1 vccd 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rlu(36 gcfv3m.d j1xvd4gcy;w oughly 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 sate*t-gro/l z z;jhg q*,n;m7nje)ktg9 hllite in need of repair. You are in a circular orbit /j 7),oegtr-tl;;jmqg9 h* *znnkhzg of the same 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 a period of 3000 years. (a) What is its mean distan 6kz nx7rq0mw;.ohj5 nce from the Suoh60x5kqzrn; mj .n w7n?   
(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 sfyg 7kg l5iw j+a(3)jto be if you could actually "feel" yourself gravitationally attracted to3 s5)jfwygjki +g7( al someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig ez1 aoqe*6ym6gl -zw). 5-46) at a distance of about 30,000 light-years from thyl aqzwm)-1ze66 oe* ge 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 ) ucbe(pm 4r3zof a square 0.50 m on each side. Find the magnitude and direction of the gravitre)zb 43pm(cu ational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 ph9mirc:sc;.3 5bwp rkg 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 experiel 23c x1gkez -xy dpsee;)(4hanced by the tip of the 1.5-cm-long sweep second hand on your wrzk (y1)34-xahdeg2;leexcp s ist watch?    $\times 10^{-4}$

  While fishing, you get bored ancis1ln .v- *h 8:gnvrnd start to swing a sinker weight around in a circle below you on a-lr1n.in *v8gsc :nhv 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 vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designe0-yb0i mkzpc6. io5yc;3 lq jid so that a car traveling at speedmklpi- 0c5 y;ij 3 czb0yq6.io $ 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 Acel9j4*f(u1hdd k. lqvp sa, 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 sp svl.1h( j *fpd9uk4dqeed 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.$\approx$    $\times 10^2$