Sometimes people say that water is removed from c6sxmtlnq/6z:c-8;up wb p +ehlothes in a spin dryer by centrifugal force throwing the water outward. What is wrong wil8mq/ ehp6n swzp- :b6ux+;ctth this statement?

Will the acceleration of a car be the same when the car trwye s/blpe /hj(c9oiw0+i-ir0d, ;keavels around a sharp curve at a constant 60 km/h as when wp/ic,e09 hd(y+-oewbie l j0i s/ ;krit travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant7 w2th (par::x6cexmewfvb 6- speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hil6ch2er pe x(wwt bmaf7:6v:x-ls, (c) on a level stretch near the bottom of a hill?

Describe all the forcg)ba2hxz li.sga:f (1k3b: iq jnz3 .wes acting on a child riding a horse on a merry-go-round. Which of these 3kw .1gxz)iabblghj.f:q2ia(nz3:sforces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water ssb-;4lbqod x-9u mu( f ybg0p1pilling out, even at the top of the circle when the bucket is upside down.9y(1f4- lbougd bmu ;q-bs0x p Explain.

How many “accelerators” do you have in you t6s0yy x+gf;lr car? There are at least three controls in the car which can be used to cau f;6tsygylx+ 0se the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill h0dwovg 21s l8sc;yb4, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal 0sv2y dwh b84gl 1cos;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 rxwf9l2 dx ;kfi 09eis*9mzru3ii-h /w(x3c vpounding a curve at high speed?

Why do airplanes bank when they turn? How would you compuiknx+d5f:p) -t:v ihxte the banking angle given its speed and r:ix i5:f+-t dphxnv )kadius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plfj q gqtg7j:x8eqs* -5ane. She wants to let go at precisely the right time so that the ball will hit a exq 5j*t - fsq7qg:jg8target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitationalbbe+ (d.fu +vm force on the Earth? If so, how large a force? Consider an e.bbvfmd(+ u+ apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were d+7ngi+c1cv:14 2,hu ye-xtzxsdlqjc (kfu/qouble what it is, in what ways would the Moon’s orbit /sjcl qfx1tyu4hkq17(eizcu v -+x,cn gd2+: be different?

Which pulls harder gravitationally, the Earth on the Moon, or the+ pu;nhi :y *mq:c4nqxxpb6h2 Moon on the Earth? Which acceleraqh yh:unp b p+xc m;*inq62x:4tes more?

The Sun's gravitational pull on the Earth is much largerloujdwz rn nis8/)tt;*iw 4q dw 9*v4; than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the d* ndutizw 9v8iwj4ql)/;dotw* n4 rs; ifference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more k zu h/mbm 8,:eo(:5mk)onjonat the equator or at the poles? What two effects are at work? Do they oppkm(km :,) meoo8on j5n h/zu:bose each other?

The gravitational forcy (x 5to(de (6jiyh 5sq)si*aje on the Moon due to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away fro5hy*ose)sjjxyt q (65( di a(im the Earth?

Is the centripetal acceleration of Mu; h0aeb+d2swars in its orbit around the Sun larger or smuhaed2s b+w 0;aller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellit8bo 0uvyy/1u2v4a qns7bydk /dg*.a ke (a) toward the east or (b) toward the west? Consider the Ey8v0/u1oya7kqn /g b d*bs a4k2uyd v.arth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a movow663yytqj8 ping elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In 3jow6qyt 8yp 6which 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 perif1j4txyha4o - zjz,( bods in outer space could be adversely affected by weightle14fy ,ztjh4z bo-j a(xssness. 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 you can think of.

Explain how a runner experiences “rl2wehb)h up;3fm2;g e)n j-lu s-l*gfree fall” or “apparent weightlessness” between sw)g);2uf*3euhb-rel;slh g n 2 lp-jmteps.

The Earth moves faster in its orbit aroqn ,ow3q .zf0wund the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its o qf3w.nz0q ow,rbit.]

The mass of Pluto was not known until it was disco p:k.s3l i,xv e((gq(/gfykmtvered to have a moon. Explain how this discoyx3:k(k(g ,mgql/.vpif s e( tvery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is mucq.-sa w5h* b8kmm.fl sh 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 a hk.8m* .m 5bawlssfq- 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 travelinlbcmmyb,l8f+ *-j8 8fcq 1a tvg 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 o9o*ekv/wrm ej 5p 61irf the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on wp6 /r5ojkv 9ei *1emrthe 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 a2lgj5o9w2rsq xlh8( tg dad1 j 5o68xv 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’slj62x g58 xvtjq9aohr2o5l 8g(s1ddw length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from v8 s)rd0ze4ejx 3 5avzthe Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express yours53rvdz8ezx vaj)e 40 answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accenu ;ejcwe7-2zleration of a speck of clay on the edge of a potter’s wheel turning at wzc-e7;j uen2 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string irt5m;b8;-i y -kvc )jlbhv4hha cas 0(s revolved at a uniform rate in a vertical circle of radius 72.0 cm , as sbrvt-4 ;)bklhh;-y sca5ivjh0m8c a( hown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can round a turn of rad6l+apnm2s, wv ius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result indepe6a,lnvp2+msw ndent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and t+yn :z t4w(n;dm /qe qvkbmxdv6o2;n.he road if a car is to round a level curve of radius 85 m at a spee +e6d /y(mtdk;m.4vnq:;z vxqwnon2b d of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed k*q ;tm8*zs e3wxb7 g k6,z2g*w lt/ofcumf6eto rotate a trainee in a horizontal cir*esc x,b owmm2*kk 6ffq/*l8 ;e3tuzg6twgz 7cle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she 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 up6( 3z(+ get,ulf qfqof a rotating turntable of 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 the coin slides off. What is the coefficient of static friction between the +q(zu,u (l gptq63ffecoin and the turntable?   

  At what minimum speed must a roller coaster be traveling when uo3lq :.9j/gqasxzi17xl i f 5rifp0v3 pside down at the top of a circq iil1z3fs/vx57o 39 a0g . qifr:jpxlle
(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 (includhl 6 15zk)*m/z03 bpz bnhnkwsing the driver) crosses the rounded top zzb10lk3 n/zkbmhp* n)5s h w6of a hill (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 a 15-m-diamete81+o h1zghy0k/k tzber Ferris wheel need to make for the passengers to feel “weightless” at the topmostk1bgh+ h8ye zokz1t/0 point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At thn7v9 n9hvbh6 oe lnvhb9hv o7 n69owest point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate i*(, v0 gu8hau ye8tr9b-f axra)ww ka 3nsg-0vf a particle 9.00 cm from the axis of rotation is to expe( 08v s3wahk0a8 fbt-)vegx rn,ar ua*g9uy-wrience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carj/ tt)6mwk y35w(peohnival, people are rotated in a cylindrically walled "room." )m5ytj3/ 6wept (owhk(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 ihj egrea 720zt*ywh rram8, qh.85g:zn a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central ho,2z: h8a rhe.0yq hg785ewgatrzrj *mle as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weight of the baq,5/yx.v)cnei8 m mibll which revolves on a string 0.600 m long. In particular, find the magnitude of 5bymc8m)/qi.,xi v n e$\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 banke-vil:76 er )k pqnm4nwd 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 massei1ca02wesc7 3 3cki vcs $ 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 sqzq 0w7 j3.nwdiving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal compon 4a,zp drc -kowgl 4/y:ac3 .eoy,h3wkents of the net force exerted on the car (by the ground) in Example 5-8 when itslkw3or : ck-dcy azg4,a,wypoeh 43./ speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianap8z(lrm5nanp z *iq1zv o)+qu8 olis 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is 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 t vqinap5)8zq(zz*n1r m8lu+o ires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particuls+ *0m tha1uhi ssftae./ t3e9ar instant, its acceleration is 1.05 tm*u teeh1a /.0ifsts93 has+$\mathrm{~m} / \mathrm{s}^{2}$ , 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 12,800 km (2 Ear76q 80lwtvauk hanz wi3g/ r-/th radii) abo0tn/6 vagulrwhz/87qk3aw i -ve the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, ftg,4l-0hzk w the gravitational acceleration g has a magnitu-f0zkhwgtl4 , de of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's ra6 jzxrhnw/8el nyev j1.2u,4ddius is 1.72nny wdj1z, 84veruj6.x he/l4 $\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 E dzfe5:z f52z. 3)4bkqi k,. ilbgrpqqwu/ 3qdarth, but has the same mass. What is the acceleration z:q)z .l /kqbfp3bq uk4 5g2ri,wq3dd zef5i.due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius.hav6a yq/k9,xde033xr; nk 8 gkf5tqv What is g near it3a, qh vdkefk n8/ 3ry;6a9q xkxv5tg0s surface?   

  Two objects attract *ivvrmg(r /(meach other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the ynwwl+ an6qc(;a2txo, n4 d5tacceleration of gravity, at (a) 3200 m l(;nwn 2+46w,5ctxnoaydt aq    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsid,zjsttz-. w/ u82njp ;kqk id6e the Earth where thegravitational acceleration due ui p z,dj8nj6;sk.-2wkt/qzt 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 packy6cg)v q9 -zz5v;ma zned into a sphere about 10 km in radius. Estimate the surface gravity on this monvz5- ;6zycm)9zgn q vaster.    $\times10^12$

  A typical white-dwar 3-wb gov,ja) w35fsa22cwyvh f star, which once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the massw )5,cvgfwy2h2w3 jav-ba3os of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless 6nnf 3/ls ss2cwhile 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 calculating the acceleration of gravity 250 km above thel f/6sncs3ns2 Earth’s surface in terms of g.   

  Four 9.5-kg spheres are lo:l i 8kwlos,3qcated at the corners of a square of side 0.60 m. Calculate the magnitude and dirksw,8:liq lo3ection 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 the same side of to j5qf fc/pi05ik9ecj8o 3xd+ w)7ae xhe Sun. Calculate the total force on the Earth due to Venus, Jupa9o8e3d wfxx0joj)e+7cic qip5/ f5kiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of what itl*5 /e( uetw os6 9ejv(b1fqxg is on Earth, and that Mars’ radius is /q5(o tfes*lj9w(6 e vx g1bue3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usf bkts:e 0t+(ving the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answerfbv+kt s t:(e0 to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit abzot/pf2/9k3za2 ahq01 bln j dout the Earth at a height of 3609z ftpnako2h3a/j2d1q bl0z/0 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 *gf00aa /sa r2 72(:rw nodzh hoky0mk)qdh*ckm above the Earth. How fast must the shur am*:rwagd*qh0yo0d o)n f kc kh 2/0sz(ah72ttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupa/jd,*c pfunu6 nts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answerf,6 /unu*pcdj as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth inwcv3 9 m.fhj/a a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the raawf93v / h.mjcdius 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 from t8phu gwzsr 0oppq5m 6a5c s-4qzn 67c7he top of Mt. Everest to be placed in a circular orbit around th0z m5chquo6zps- 4 q87n g6w5apscr p7e Earth?   

  During an Apollo lunar landing mission, the command module con 99qg00su vna i)xicoma9m+h *tinued to orbit the Moon at an alt0+u 9)igv*cmq h0xmoas 9ia9nitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The innct ,+,sl5s l9n5sjjyfer radius of the,5ly+sj,9tcj s fs5l n rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (si6vc 00reog9t;kh*x wobb +6uee Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the0iwb66e 9voc0ru bkt*og;xh + top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 42qgg (clhn5ey ,-.+tvh 00 km from the center of the Earth's Moon in a space vehicle (a) moving at conn t5-g.hcg,ey vqh(+l stant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star sy+vlotm;x 97ccn,s 4gmstem consists of two stars of equal mass. They are observed to be separated b;7c+x vnsoglc t94m m,y 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a r*tl:(b szir tv 3pp -o*mx,tl6*x9gb55-kg woman in an elevator that,pr **3(tp:gx6t-*mlvt isb xbzr 9ol moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an ljbo+(iv56 9h6icc kxelevator. The cord can withsta vi5bjki9 xlc+c66ho( nd a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet wit5;dz q* eo 1iksj hw(he09ntfkmw*p1+h period T , the density (mass/volume) of the plan pq5we*+f tki0j1 ed khmzs9o;(w1*h net 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 periq2tz+wo 3 g6l a1kxpx4od of an artificial satelq l1 gop+x2tkxw4za36lite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across,g cg9pd8g mi.w d.,ujg x1fm1wa8 j3-r orbits the Sun like the planets. Its period is 410 d. What is its mean dista983pm dg1 i,xugm 8g .-.wjdjrwafcg1nce from the Sun?    $\times 10^{11}$

  Neptune is an average dii* 0mjd(v-k lwx*m tc(stance 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 once every 76 years. It comes v,svt,k-gd+0uwy ;- b7m omgipery close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The me -t-go yvsdm7,+w,0iuk;mb gpan 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 pqr7cqwx e,pf ()4rk (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 meafn z2q)cv q:(zy9q3nxt6e h/ln distance for the four largest moons of Jupiter (those discovenq/2xt:vqyqz (e3 c 9 )lfz6hnred 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 * (ga 2 tr08xgz mmq(cy+x-qoithe known period and distance of the Moon. ac8qxqm 2*xo grg+z (0y(mt -i   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of 8+nf ghxyoje r culnk :q,x;0*h0cc+ 1Jupiter’s moons, using Kepler’s ck xn *o n;1, +xrl:q0hheug0f8c ycj+third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists ocpeh0gq iw f7z1.j)1 tuj /*eof many fragments (which some space scientists think came from a planet that once orbited 0o.gcit q 1jj1 ) pu*z7h/weefthe 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 describec.b+d mse 7o 3,o-2g0kmpvkvz3)mv cns 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 the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring2 .-b, mnvsmv c3z+vmkoke )gp37ocd0 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 h2gyh 7xd .rp/tanging 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 isd x7tr2hg/ .py 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will ttezs q5 ( w(ttumcxdb7.u(0:zhe acceleration of gravity be half what it is on 7u(t0:zetsb5(mux d(cw qzt.the surface?    $\times 10^6$

  On an ice rink, two skatebca 1g d*9)toors of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their indivi9oda ) otgb1*cdual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day,zk; f u.pf(oz+yuh t,: the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of zfupt.,+uy:;o f zk(hg is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft trav6gzpl1 h* q dsql*2/pueling directly from the Earth to the Moon experience zero net force b* zqus 1g hdq/*p2pll6ecause the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 6. wpa:g(,orfqjk m.5eik *; gex9f v5q4b:pwi5 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of thkb59;m. :o g.,* xrq:pwefiij4 wge5f(pka qve elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube /0m5wcl/r /suto qg:r that will rotate about its center (like a tu5mt: cwq o/0/surgl r/bular 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 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his- my6sre4e8cyum / o*q aircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms rnaqo .-sjg d01gk./h:;pef20fkg 6k; qajlcof its radius r, the acceleration due to gravity at its s1f2g-ke.:a/ lpqk;g.jfcdqsa ;gjr 0 k0hon6urface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical0 ds,l-nq)fdv 93 rtlmi9 lw3b by an ang f tv,)s39wl9-db n dill0qrm3le $\theta$ 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 speedcbk0bgjqybs a m88xc ,;.a., h of If the coefficient of staticj.y8m , bscxgba;kac.8 bqh,0 friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if tbqg 7xz,9a-br)*fr j whe Earth were rotating so fast that objects at the equator were apparently weiq,xr z7b9jg*w )rbaf -ghtless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart: bdm 248q kqifw9ur/b 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 rx:6ttb lz:n;uc,xp) lounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle obx:nt txlp: ulz, );6cf 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, in ,7vp6yn+d mb34b tzrt 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 6ypntm7 z3d,brvn4 b+number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble,0fj3h:+ g kwwyaq lt) 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 la qj wgyk 3l,thf):0w+ight 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 consto)e s:eax z1d8l-d.wnant speed as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) H 8w-e)1szn.ol x:d adeow 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 :1g1l yi; jwojsatellites orbiting the Earth. Using “triangulatio1 j;wg1 y:jolin” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after6)m/ty4ls.d m fcuphr53 /ros traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 1)fymou6r.r s //l hsdptmc45 35 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 pdix6 7 ly49 upginkwv79g 7ut2ursuing a satellite in need of repair. You are in a circular orbit of the same rap69dg 794ik77nuxyul wigt2 vdius 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 yea.m0qvon dyal ca7d6 6.rs. (a) What is its mean distance frol 7cnqy6dvo.0 md.aa6 m the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually " ds-je:u3j g;5xsh+1 bznw,cgfeel" yourself gravitationally attracted to someone near you. Make reasonable ass,eg+ ;5us3x gnzh:djw1- bjscumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky 72l3uftnmti ;m)t,jmk*qj p (e59 gz ny04kehWay Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from tnhj 03zim(mg pm5eu9l 7kk2 qe*;t,jn f)ty4 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 loca+3trujtr e y6j ia+-s4ted at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational forcert-ruts ij+3y +4e6j a 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 kg orbits the E:kg;u xxph)k. arth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tidhe+8cfryy089 x 88u njdlwn0p of the 1.5-cm-long sweep second hand on your wrist watch9yu0hcj8x 8yl d f+ennw0 dr88?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a s+.ft6vkmez(p7 g1m jcircle below you on1(+s6evm mtgjp k.7zf 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 vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travelers oe90-wklyk05cavr5 4m * ning at spev9a*k-5k ns0wce r5erlyo0 4m ed $ 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, thep7fqwq d/pw46;(v8pe bh, a2t urs.gx 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 pro2 xf746w.wdug/ ;qqts herb(ppv8ap ,vide 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.$\approx$    $\times 10^2$