Sometimes people say t pg*.x.yy*(cu njthx3 hat water is removed from clothes in a spin dryer by centrifugal force throwing thecjt(h.. nx*y*3 p ugxy water outward. What is wrong with this statement?

Will the acceleration of *,c0igs/ hsu(oxye g8es7i1ga car be 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 speed? Explain01i hc /x*g(go eu yse7i8ss,g.

Suppose a car moves at constant spev db4q 6g dz-m nk0dn7j9p*t2.i+vk zbed 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 stretchbdpzg 9q6vv+ b7j 2-dtk0 *z inm.d4nk near the bottom of a hill?

Describe all the forces acting oh;.ru q2pvfg+ n a child riding a horse on a merry-go-round. Whiqr;2g.v uph f+ch of these forces provides the centripetal acceleration of the child?

A bucket of water can be whir:tl *s0y7gqo; bhcngr) vm n4,led in a vertical circle without the water spilling out, even at t074,mvo)tbghsn ng clyr:;q *he top of the circle when the bucket is upside down. Explain.

How many “acceleratortvh 4 u+cl(u lkl;1aqi9iv) u8sh:li3 s” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acce: 4h viq uill31;u iutlkscv98a)(+ hllerations do they produce?

A child on a sled comes flying ove 60wv+1c7 jj/usakeap/demtx3o 6 ci. +dv* ppr the crest of a small hill, as shown in Fig. 5–31. His sled does no3pd0apc1+awdve6 6j iejs/k 7/tovu.pxmc+ * t 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 decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hig kxs 67r2;zhbdh speed?

Why do airplanes bank when they turn? How would you computespjf*z o3rl/tk *ft;; the banking angle given its speed and rptks;f*tl/* jof; 3z radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plane. x jt5)8puvf isr6hv43 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. When should she68v ) tfu5rh 4sijpvx3 let go of the string?

Does an apple exert a gravitational forceyqa n.v9+-tot v( 6 izc+j7fta on the Earth? If so, how large a force? Consider an9 y tz+.nc6aajv tof+iq7(vt - apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublexxi6h5ghp 2 yg. xslj0 5bbu 9jnq4+m; what it is, in what ways would the Moon’s orbit be differen u5sjbgn9yqhjl2i6m gp + 4b 0;x5hx.xt?

Which pulls harder graa5kmg51ms h x3vitationally, the Earth on the Moon, or the Moon on the Earth? Which acceleramms5 5 g3ahxk1tes more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet; *eujx9 o8zixx7g;3zay1 lxz the Moon's is mainly responsible for the tides ge7;a xiuxzz1z8j xyx ;ol3*9. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects are agy , c2iq84ew3*a7nwzih5 w.oxbzc 3st i4xi.2bscz * zgwyqca,n 7w83h 5 3woework? Do they oppose each other?

The gravitational force on the Moon due to the Earthcz;8h1+oh9s u(tjq az is only about half the force on the Moon due to the Sun. Why isn’t thez8;t9oauh+ sz(1c hqj Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or sm g2y jncbm y /zdx:2vy*tl+x(5/ ytxbl( 2dvgy:yxzm2+ 5c *jnaller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satelkfour(.tmy2h47 +vlrlite (a) toward the east or (b) toward the west? Consider the Earth’s rotatil+k m2f. 7r(trov4uyhon direction.

When will your apparent weight5ffxq2.vgyk 2 be the greatest, as measured by a scale in a moving elevator: whyffk x2gv25q. en 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 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 coubsu s-1h )khx*ld be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylin sb -1)hsku*hxdrical 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 you can think of.

Explain how a runner experiences “free fall” or “apparent weigg f*pbuki9;y2; 3lpy dhtlessness” between step23ldy yf* k;p9ip bg;us.

The Earth moves faster in its orbit around the Sun in21(yz /cucuh ep.jc u0 January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not muchcp0( c2h zy1/u .jcueu 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 itftn ka0;e)vzxgh+5- ktr+8q n was discovered to have a moon. Explain how this discovery enabled an estix gnkztt +v-;n0h rq8k+ f5a)emate of Pluto’s mass.

  The Sun's gravitational pull on thllzm) te(;v:6:s 1 qeydomw- +bl si:pe Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitaly6 o v)(t+w;zdlib -e m1s ::sepqm:ltional pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling n0(wdf)jzw i9 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around the Suy5h um,i j o,4tqx8s5sn, and the net force exerted on the Ear t4,jqm5,oh8sus5yx i th. 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 ao:c4h5,gp7j cdfl ;hh 2.0-kg discus as it rotates uniformly in a horic :jl og7,5 ;hd4fcphhzontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 2 uf3 8j+ky-cs9p +jqiw t*ipf400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal accelerap9k3++ q-s cijufpy wf2tj i8*tion 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 s6gq*x9plve d. s4 cpg(p.b/ithe edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s 64vpp9l .qs/b(xed . gc *gpisdiameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform raxs dm3m*,st nb-*5qupte in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4 s-s ubdmmxp3 5qtn*,*.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 whic9j n +v;nzs1 3mid6dsg bu3wm06uiuu/h 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 resu3suu/9s +zjdumm 1g0 v66dn;wn i3 biult independent of the mass of the car?   

  How large must the coefficient of static friction be b 9j) ,a*4vz lazauiim owj*.m 8dfz05retween the tires and the road if a car is to round a level curve of radius 85 m at a j,lf vz9m0)r z ai*zuw4.aimd8*5o ja speed of 95km/h ?   

  A device for training astronauts and jet fighter piu80ckdj th* v7lots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . *80uctkhj7vd 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 turntable of , u*i;iu cbw+j2vjhl/ variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and wjiu,+2 u/ hcbj*vl;ithe 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 trav60 ,44flrx.atagu r fuwcg;, meling when upside down at the top of a c;4a 6,0t rx l4gcm uuagr,ffw.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 roundesv;6djl 24ltysa. vm .7gtf7b s.xy2wd top of a hill ( ssj6s .tgy7mv..lavxdtwb24y; 7 l2f 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 minute would 6jqhoqbec5vo ,2g-y) a 15-m-diameter Ferris wheel need to make for the passengers to feel “wei)evcqohy,6q o5 -g bj2ghtless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. mzcl9jb7 n,gd(0g,ir:)drrh csp-*z At the lowest point of its motion the tension in the rope supp -, sb:)izz ,pd dgjnhrc *cml9rg(r07orting 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 fro8 xnu8s-/nk d;xfza6hm the axis of rotation is to experience an acceleration of 115xa;f886 sdkh/uznn- x,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people arek+ r 2hzu6v+u. 8cj8zrna a+jr rotated in a cylindrically walled "room." (See Fig. 5-35.) rcvjur.8+jzn r+z u8a62ak+h
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-hc:z2fgi ye 0/dockey tabletop, and is held in this orbit by a light cord connected toc0i2gyd:f/ e z a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely d3+9 vby: warythis time, by not ignoring the weight of the ball which revolves on a string 0.600 m long.+ db:yw9 vy3ar In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling7h)d+occ :zen f fyji(h/-y8 q 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 :hq q i5 kn 5efo5t6r:ai2/cpx$ 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 ve*uv614/ k)h0ga,sx2yvrye utfp f y6y rtically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerted gl1g 17 , 4bkox(ysnwekv ney3 s8h(,bon the car (by the ground) in Example 5-8 when its spe1bkbyh(xvs,7geksow4( 3 ,g n 1l ne8yed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis b7u ,jz(4 evt8ys 9kkx500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m4j 8e,7b kzyxv k(9tus. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal -xik/ rpl tl8( 1cl/opcircle of radius 2.90 m . At a particular instant, itt lpk/ix8/or 1lpl-c (s 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 gravity on a spacecraft 12nwhz)fe nr8ft. u+iy./ )sv: j,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350 kgw.i) stfznv h y+:rnjf).ue8/ .   

  At the surface of a certain planet, the gravitational acceleration g has a mhteblr v+r z 9h)g8x,7agnitude of 12h) 9br t7+ ,hxle8vrzg m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is su;/l/pfz6 jj(ot /0,zltt suxn1n(f1.74 /upn/o0l6tzl/su , j1t; nfz( fx(sjt$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a xk2d 8 p9k/mg,ufwsv2 r ye,o(radius 1.5 times that of Earth, but has the same mass. What is the accelera,xg,ewf8u vyd9ko22r kp s/m( tion due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, b 8t2 ry-*ay7nwz )zrumut the same radius. What i8y*ranmtuy7z zw-2) rs g near its surface?   

  Two objects attract each other gravitationally with a force of 20i mb7pw ,io mly(8ch7o-0 sxt.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 va5dagt ,8:mssn tkz7qe - qa+;ylue of g , the acceleration of gravity, at (a) 3200 md+ 8,5:zgqkya asns- tqte7m;    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a poinnksz-4 x( 4hijt outside the Earth where thegravitational ac sxn ji(4z-kh4celeration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed ix8yb-n.t(+-a9 ta pirk5uyufhxx*oe . e)p2xnto a sphere about 10 km in radius. Estimate the suretu9pyb i u*x.ahkxo- f -)2e5r(t+.8panx x yface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star.phe d 5z+wy(w like our Sun but is now in the last stage owwhzd 5(.ep+ yf its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining w msk djvxynh5frq/+83 / 2w0cahy astronauts feel weightless while orbiting in the space shuttle2mxhy+5s/va3nwc fjrq d /k08 . 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 gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calcwu2l iwxb97t :ulate the magnitude and direction of the total gravitation ww x:bt7uli92al force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of chc-ujcw c:7 8the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planju chc7c:-w8c ets 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 th )dj *9ye4q-mwr)v xvxe surface of Mars is 0.38 of what it is on Earth, dvj4)x)xvq em9*y r -wand that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earqrlyr +i.+ uu9th and its distance from the Sun. [Note: Cor+quy i.u lr9+mpare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of ag ze w*a.is..f satellite moving in a stable circular orbit about the Eartg.fzie *. asw.h at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite inx*b7fz6 tln b3to a circular orbit 650 km above the Earth. How fast must the shuttle be x 6z7f3*nlbb tmoving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to expe(zk84:,n-c rx)e 0nkcxraix lrience simulated gravity of 0.60 g? Ass-4cl08i(rxre,kzxacx : nn k)ume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takei-dx0yo1;cav fk-l cq s n1a+t4w:0w cs 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 very small compared to4+:c0c -dn;ywxa tqf1vco l 1k-si0a w the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocitywkmv++16i s*hr t fwe5 would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit av *56++rwht1 esimfkwround the Earth?   

  During an Apollo lunar landing (7mm jkyz ubq0f0 tv92mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take tt 2fbz9m ykj0(vqm0u7o go around the Moon once?    s

  The rings of Saturn are composed of chunkqa.g t)kgo.d)i,jsonu w1uqts63a0 is98 c5ts of ice that orbit the planet. The inner radius o,qi d.w as6n.tktgutqu o9) a)5ssc13j8g 0oif 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 h ttpc36wt7jq/zlvofh 0 +x+ 4d*7itgin diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real j f+07q*vdx+ topg4ltht/ 3it7wh 6c zweight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 kmhlb05 jntd;vxi 7fpj ;9 (6zlj from the center of the Earth's Moon in a space vehicvjd7t56 ;pnhjfb z;(9ij llx0 le (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-c ,e(gkzyw7yu4xo (v.nn5kz 1star system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. We.k u4xn7y(zo(,ck5vg wn1yzhat is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-7 5aer.5mw gt2vdkmubw k.- x6kg woman in an elevator that moveska-5k xwd6v 2gw.5e.rt ummb7
(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 2z /k 0oi ys /mi7axq.2fnfqy*the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates.s i0m2yf*xz2/n/oqi ka.fyq 7 What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near t9n.de/e1;ddluco l p4he surface of a planet with period Tn /le9pe41dcldd .ou; , the density (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 (27.4 d) to determine the hura qv7i, 6 +sphrrt(b4zaxkn;be:b m9)8r. period of an artificial satellite orbiting vern6b:(kb8rr9t. i+,aps;req)h 4 a bu 7zxvhmr y near the Earth’s surface.    s

  The asteroid Icarus, though onlya ja.3*epm d0e a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fr3* 0aeaj.dpmeom the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5m fvnv7ci5wu.. 8nj 6k $\times 10^{9} \mathrm{~km}$ 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 yeayeurg s+-ze;+4)bh k u( gd7zkrs. It comes very close to the surface of the Sun on its closed;+gzheyubs(r7ge+ )-uk z 4kst 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 the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates abou/.npuda nu3vopy01g (t the 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 distanc3j,8 q fw,paczi3,gmce for the four largest moons of Jupiter (mw3z3j ,ic a8fc,pq,gthose 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 di/o j ufqnk )dey(4:wk7stance of the Moon. uj(dq:e4ok7y /f n)kw   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’uk mbebf ( qkt4 i6t(u9nmc96;s moons, using Kepler’s third law. Use the distance of Io ab qnt 6 4m(me9u(fi9kkbctu;6nd 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 and Jupiter consists of many fragments (which cq ka2m3 ypce2s 38-ijsome space scientists think came from a planet that once orbited the Sun but wac 2 im8yj3pc3aqs k-e2s 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 descru 9py3g ;sb*tv..dcku*a1 tb qibes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that th3av ku cbd 9tuty**.qbgps1 ;.e distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a h(8tuhzyi vy:)anging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vinet zu(8)vyyi :h, 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 surfacy/.w6g7*vpmel.)ak,sb nayw e will the acceleration of gravity be half what it is on the surface? ./enwa,sa wyb6k)glp*mv 7. y    $\times 10^6$

  On an ice rink, two skaters of equal mass grab ha njkezii)5vrtv29bf4b4h j2; nds 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 604k;bnif b9ve5 v)2z jt24ihj r.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of grav 9wto; )/ev1 1klfza(rryw t)vity at the equator is slightly less than it would be tlz r o) 19a wf/vv)weykr;1t(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 m9 / v hiw,bibiup7ken j+*)4zEarth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth ubi7k*94peim+bjn h)i/,wzv and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kdf6v wc7t0pu ov.*kp8fny76xyx2 x9mg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which fk7xty fn66 m8dxvc. wv7yx*u2o9 p0pdirection?     ----待选择----upwartddown 

  A projected space station consists of yn 3p.7fyu+( -a z mm27zyezyufmr 7 1-u6lwxna circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of abomex-77mp+6 umu-una zfy.l(y7 wz 1rnf2z y 3yut 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 aircragacniepwb(1;q qnyg au(47(; ft 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 d 9ikz zze )rzs)z)gk:pd4 *1oa planet in terms of its radius r, the acceleration due to gravitdz 4z)*zoz1: egzip9r))dksk y at its surface and the gravitational constant G.

A plumb bob (a mass cgb4js4gq/h-/dfl 1 rm hanging on a string) is deflected from the vertical by an an lg4/ qc-bd h1sr/gf4jgle $\theta$ 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 zm)nf3et 6pwr0a3rkrh4 ,r3t is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of30 pr,hrkz 4a6 etn3m )r3rwtf speeds can a car safely handle the curve?

  How long would a day yaf,y6y-c:l p be if the Earth were rotating so fast that objects at the equat yfy, -6:yapclor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maint (;zy 7nxwnxe-/;m owqain a constant distance 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 round0zjexybf j: 25s a curve of radius 235 m. A lamp suspended from the ceiling swings oue2zy 0jx5bj f:t 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.tqe20 weqk**fps ss4 ) 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 2e**s qp)wss0 tqfke4 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 Spacdr)hs.m) i;:fe:ug hhe 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 esef:idg)h h:u.h)r;ms capes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill at x cw5*wyp/6qnd 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 wi56cw/ pyx wqt*thout losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellitesn g j:g nw)h7j5+3*u negha7cd 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 saten 7nn:w5gh)d+ja he3gcj u*g 7llites 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 Asteroijvs8wd5 l)zsy- (lsu -d Rendezvous (NEAR), after traveling 2.1 billion km, is meant to(v )5w-j8l s z-sldsuy orbit the asteroid Eros at a 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 xpb xs x;/3vp))b)uivs0 p1 6dz6 ztdethe space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (40 vtp / pzx3)b)ix 1zv)esp6u0sxd6db; 0 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 pe5 9va;ww;qx njriod of 3000 years. (a) What is its mean distance from thw xna95q; v;jwe 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 b8z9.awv dz mx5e if you could actually "feel" yourself gravitationally attracted to someone ne.dam9 5zzx 8vwar you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galv01.i o enb4hzmj0x,gaxy (Fig. 5-46) at a distance of abouto0.0bnm ev1 , zijhxg4 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 located at the corners of a square 0.50 m o fbyez:u 39f y10xt(cyn each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mafuy ( 1yx:zb3y tce90fss placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eai3dr.7b t88yejo- bgsrth $ \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 by2t5u4vy/flb g the tip of the 1.5-cm-long sweep second hand on yo gy52lbv f4/tuur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sino ka 3k7v;usa1mbj9h9ker 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 fiso1 m ;ka79jhkvubas 93hing 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 tub:m5/8sbi/a f-xz s1xmbeoawp ) :, a car travelinx:fb:b1t zm)awm / esu-o85sx i,/abpg at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the f29hy ijbq lay:/9-ia bk/ ,xhAcela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force e2 ,/y9lfih:9a i/qabk bhjy x-xerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$