Sometimes people say that water is removed from c;w+ k/gt0 qcuq7cri8ig0 4lbelothes in a spin dryer by centrifugal force throce lr0qik8c0 7/i +btguq;gw4wing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels a 0buun4j0. gqhji-1 qpround a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speepb0quqj 0g.1u-i njh4d? Explain.

Suppose a car moves at constant speedp5,*d;oihug nj 3 pn1+u dnpw. along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bw3;nud o1hp,j5d*un ipnp .g+ ottom of a hill?

Describe all the forces acting on a child riding w * *72fy5mzvkb,ve qha horse on a merry-go-round. Which of these force,zk2bvmf5 w *q*7 yvhes provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withop0oj6dymad :3c/ - nzl;tdq :tut the water spillingdoctqj p:ln 3 ;t /zd60admy:- out, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do yo qrf)q dpp4 56czp)x(ou have in your car? There are at least three controls in the car which can be used to cause thqp() r46qp xpfdcz)o5 e car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crypqj1g:i )/6 3hb qjqaest 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 betwee 3) 6: hqqjjgb/qy1pain 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 high spvhkms;d0h s*slkl0 -7)esk 56q u*qaveed?

Why do airplanes bank when they turn? How wouda)au:+nah4hl t/rz .ld you compute the banking angle given its speed and radius of theu:n+dr/ ).ahl4aazht turn?

A girl is whirling a bao5; e,3g24d:/5fsuoozsb8 rv oulni all on a string around her head in a horizontal plane. 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 ss 4/8z3f55oavdb,eg2 u:;rouonlo i she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, 1.c x ixlh4jw)how large a force? Consider an 1.)lxcj x iwh4apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s okijbk+5: qrq6 6x8fvtrbit be differeqq: vfj6ikt86bkx+ 5rnt?

Which pulls harder gravitationally, the Earth 5 en,z,(d/vi(sjmvro 4j b:ngon the Moon, or the Moon on the Earth? Which accel ovn nv /5d,jgebr((j:,m4i szerates more?

The Sun's gravitational pull on the Earth is much larger than the Moeb q8hjx;wj+ 3o)l5i*z lcldo;3py v(on'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 j qo zdv(3w)jb+cll; 3pox* 5e8ih; ylthe other.]

Will an object weigh more at the i, 44l4ztq shiequator or at the poles? What two effects are at work? Do t4q,4tlhis iz4 hey oppose each other?

The gravitational force on the Moon due to theihjq 9 44s7hjk4 ccw05o:klpd Earth is only about half the force on the Moon due to the Sun. Whykk474d 4j j5clho wip90sh:cq isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of M;8jx udclsk0 pc153qaars in its orbit around the Sun larger or smaller than the centripetal acceleration ofa3q kxcljd;c58 p1s0u the Earth?

Would it require less speedem5lut/ /68va 8exav oh-*z yo to launch a satellite (a) toward the east or (b) toward thote h vo8/va e8mzyul 6x/-5*ae west? Consider the Earth’s rotation direction.

When will your appareney m1pd-+q-yo;a do*+u 4ebglt weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in freq -a+oem4dd 1ul pb+oyg-;ey*e 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* 8d/5nydtadvdc5 n 9r space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (5ar5* ct8ddd vn9ny/ dc) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betwee:z c8 x(ud l1 q4sp 6j:kj*c6pmmdxi)tn stepj (14lkpddmc8*):ism6 ptz uxc6: jx qs.

The Earth moves faster in its orbit around the Sun in January t*,aia* 8 m9ppn)e6 jjyi d/vxrhan 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 relat, 6ji j9n)/x**a mieprdypv8aive to the plane of its orbit.]

The mass of Pluto was not known unt 3a2s53utjpv1q qm7 nf+ni b2gil it was discovered to have a moon. Explain how this discovery 1squij f+q37pn5vn2m23 tbagenabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than thh3o5qpybbw4-i gg .*s e Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the bp goq5y-.s*wgh b3i4difference in gravitational 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 1rz hdsv29ji;7/a ex0o980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Earj8 jy-k0*e4soqwj )0+ gmkwrzth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this zsjkw wq*m-e 4)8jy jr+gok00force 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 rcuyq r9tk5ixy 07* 7zdiscus as it rotates uniformly in a horizontcitrz09u77 *r 5yxyqk al circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle w 5 )j qxfuyhu4 q,vz82b;ia1dis in orbit 400 km from the Earth's surface, and circles the Earth 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 Eartj)bfxau q24z w5 dvy,8 hqui;1h's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of l mc y9uybp.7:clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minutep. m9ucly 7by:) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a unif 33r*irka t;qnorm rate in a vertical circle of radius 72.0 cm , as shown in Fi*q ;rna3 trk3ig. 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 10 :6e1l:p:lbz gd jnzk250-kg car can round a turn of radius 77 m on a flat road if the coefficient of static frictio:d6j:2pn:kglzz le1 bn between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient ed(t,g32 - gm8roj2pmovo1p8 cs 0iizof static friction be between the tires and the road if a caro2o(12s rc,8vp0 ojz g-g3ei8mdtpim is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet figh4ufq is978fkwter pilots is designed to rotate a trk s97f8 qwu4fiainee in a horizontal circle 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 of a rotating turntab/(rum.(v myuid4 su sfl,k.m+ le 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 frictv .udsmu(iu/,f4(k yl+ smr .mion between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsi(iu5)72e bz(eypw zy ode down at the top7)i2 (pyee (5zouwyz b of 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 (includin8jdk:ybh 4lhl*6b9f wg the driver) crosses the rounded top of a hill (radius: hbfbl h *6d9lk48ywj =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 z- 2j gh9mf/svper minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost point?sg2-vzfmj /h9    rpm

  A bucket of mass 2.00 kg is whirled u(nzjvqb)pjd/, jxze3;4ov. in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the(xo 4n;e/3z.jvb)qv uj j,zdp 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 r c3f3hb 9vddj. eletc*4t ebbp,6im06 otate if a particle 9.00 cm from the axis of rotation is f*bv eed .9m4t 6e 6jh cb0,lpbcd3t3ito experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wallef8n21)vn be si(m6mz*4lvgsxd "room." (Sesg xfs8)bmm 24l6z e1nv( nvi*e Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey sii 324xjg-jutabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a centrai g3jsju-i 42xl 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 , prec6ml,q8 :q59kp) a sdqpfyv.xsh6*ly ercn27wisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magc)6a.fqrv8 lw h:d7mxye q ps5n,s6k yq2p*l9nitude 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 tr p28f a8 qqpm+.nh4eieaveling 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 a). (yk -zazvy :y,wen11vzyr$ 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 vertafov5+6g b hgtwp/*8dically 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 na 3dzdzu-lr bg y h5ab,1s;;/net force exerted on the car (by the grh-uz3a1 d 5y,l bsd/n;gz b;raound) in Example 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 area, going frd 5nv,1./n gfud5 grsdom rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and r.ggfn d5d5un d1/,rsvadial 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 circle of radius 2.90 m . At a particular rq 9(kvo* +/i1b9sm6ygatsiv instant, its accel* /mosgkiv6q+rav i9b1ts( 9yeration 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 gra *qmq4 e.p ;8ly2kauq ykjl0;vvity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surfpkv8.yy l*q42;ae0 quj; qklmace if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has av2*h*.yfvrsicj.eg +etdh-/ magnitsr*c /fey+2 hiht.-e*v.vj gdude 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 Moo9j n0ca :d h/r7n97ms)l zbsmcn. The Moon's radius is 1.79 a0m9c r nznmc bs/7:7lhjd)s4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has the897 u5,rrt;wuh elev qz8nvt2 same mass. What is thez u,w952rt8er7l e8 ;vunhqvt acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same raiqi2p- (:nzinqxmx bp6:( ht /dius. What is g near its surface? 2iimn (hxz6q:-txi bnqpp(:/  

  Two objects attract each other gravitationalo/vq-jrtz16/e omj f3y3prn +ly 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 ,b2 3, tqj 9c+v0yovtw((ti bls the acceleration of gravity, at (a) 3200 m tvvs(b2 y0 ol +i w3bqj9,(ctt   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s ce ullunjdc(*(e3 1wwn8nter to a point outside the Earth where thegravitational acceleration due wlu u81ej(l c(d3w*n nto 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 p2rp62p :mp ryhysf: p)r cbvo.s76pb7 f no+6uacked into a sphere about 10 km in radius. Estimate the surface graviuocv72rfb :2 yspfn6:7ps6mo. +yh pb) rr6 ppty on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like 54k wb dap femtiy/og/h+024w our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of dp h2+4wb0yio 4ew gk/t m5f/aour Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spaceo;xfugq*(c- q1xr*jx 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 the Earth’s surfacx(qoxj u;x *-c1fgr*qe in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square ofj6gp(qh0 7wrht.q.6 - xxk 2)gcilq nc side 0.60 m. Calculate the magnitudwtgh(7p . x0n rhq6q-j.ciq6lck gx)2e and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on thyykzkt z(so9d4//c0w1dca e1e same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, andyez0(1 /w4tk zas ccd ykod/19 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 at6(0poth65ttoxa gy z ( the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine thetp5y(g toahxt(z6 06o mass of Mars.    $\times 10^{23}$

  Determine the mass of t,uqdy qib 2y vw40tirf 6l69g8he Sun using the known value for the period of the Earth and its distance fvy9q rd 0qb686gt u,li y2wfi4rom the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite movinxd ubr;8t/ .ovg in a stable circular orbit about the Earth at a v.ud/ 8xbr ;otheight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite*xt27 mi (yk 3/qfp9t .ctkoam into a circular orbit 650 km above the Earth. How fast must the shuttle be mo3c oqa2mky ( *im79/ktxttfp. ving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindricat9; r0(phmumec -y/0osq1qkv l spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time nemu;q-0cqrs k m1pvot0he9y/(eded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for j2bjy kf- ee 5-ku5/bxa 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 to the radiusbue5/jk x-eybf2j5-k of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite havybnyta1:6 6g+drf z 1qe to be launched from the top of Mt. Everest to be placed in a circular orbit1da gyyq 6 bzn+t6:f1r around the Earth?   

  During an Apollo lunar landing mission, the comk +rns,szm:oe3o6y hel2-h7w:ssl /cak7h7 vmand module continued to orbit the Moon at a sezhl r /ywk n72-savc 3:oohms67s:,ek7h+ln altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are co +jm ypxoym1h.z le744mposed of chunks of ice that orbit the planet. The inner radius of 7 pxhmoy.1 +j mz4ley4the 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 dialkvo u2 yjc+r)p,:/ ivmeter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the botlvv)2 ijk:y+ ,/uocp rtom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from *arsb jptdg f hd1akb0(/-o9c*:lt) vthe center of the Earth's Moon in a space vehicle (alb(r f1d*/atvdk 0atps gho*9: bcj)-) 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-star system consists of two stars of equal mass. They are;m+mjf no7 tptc8+c6 h observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between mhcj;on+p 67ft+t8mc them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg womanubdoep3iyakrk i 28k),pzx+)1qwxm l1/2 u8 z in an elevator that mo +uprzd2 w381oyu1)zkmii8px kx k2a/qbe ,)lves
(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 elevator. 7,oy+4kn:,ywnwq x mvThe cord can withstand a tension of 220 N and breaks as the elevator wyv+qyx ,kn,7:o 4m nwaccelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the s,f 4rg2 dzp bvyq;9xw-r(/ tqvlzju*7urface of a planet with period T , the density (mass/volume) of the planet ir-9qt gvw2z x4pqvz*/lb(;df 7, yujrs $\rho=m / V=3 \pi / G T^{2}$ .
(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 determin3 qro75j xi4 q7xxfpu:e the period of an artificial satellite orbioq 3 4xxuxpfrj:7 57qiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred ve84f3 ;f ( sqa)bhaypmeters across, orbits the Sun like the pla 3f;8yb)pq4 e(asavfh nets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.dq,uc 0s*-:spdl sjb+gpn82 vfk1 i+i5 $\times 10^{9} \mathrm{~km}$ 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 thexd0 ( dbn dos)x(mj02u Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is neare(ddb(xumdox ns 02)j 0st when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of t ofb mke:sn:+,;h1avn+s9 tp)ui6w sche 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, periodz ;eza((df2sd, and mean distance for the four largest moons of d2;as zezfd((Jupiter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Moon. 1t0km yrje42, r) gwn -pr(bftf)j w2g4(te0ynbp , r1r- krmt   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, l+onnxb6k1r2h9* 7 nqvonqh/using Kepler’s third law. Use the distance of Io * rvl6nq2hh oonx7+9qbk 1 n/nand 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 fragmentsu)u ( 4e 3tp:(py7cb:npqniou (which some space scientists think came from a planet that once orbited the Sunptp:o4yei 3(uupbnnqu 7 :c() 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 "plan4 9p c)1mc)mi1axkq qoa/o;)qw*p92v ogcgj o et" 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). xop)ka1qp;cv 4oqi/o91c)c gwm2mo aq* gj)9Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an aey5;4gbi4(rri6s vwg rc from a hanging vine (Fig. 5–41). If his arms are cis54 e4gwirvgb;6 y (rapable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s sursgw,.n 5hxjb: 0uki geg2e5s 0face will the acceleration of gravity be half what it is on the surface?.gew u g5,j0igsnk 0: eb5h2xs    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual ci ef+ dcpy):n5ircle once every 2.5 s. If we assume theipy+5 )fde: ncir 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 once per day,:4 +sdfh /v jy:2jvmyjvue3b5 the apparent acceleration of gravity at the equator is slightly less thanf4hvbm uj:ejs+d v:/3 jyvy25 it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly //pvlwk d l71mfrom the Earth to the Moon experi7w/l dlp1/mkvence zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an v 8l(c6x(mo6 u ggdu nr 55xe,n1+oyxgelevator, it says your mass is 82 kg. What is the ac558clmg+vdn r,x6 u 1x 6ugn ((gxooeyceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station conmnklj2o9 11j it u1o*gsists of a 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 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 i1oo9g1j* 2t j knml1ufelt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5hnq ro z9xcz)8y*kmh v t3,/p4–43).
(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 plan) kuzmzck*/v3 p1rpk1et in terms of its radius r, the acceleration due to gravity at its surface and the1)czv1 r k/pzk*pkm3u gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical byv2euwji 39:qhw*x+ uz an angleijqu +wu xwe:h*v9z 23 $\theta$ 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 de.tc/1izx/sdjdd fkjx. 7+6wrm6pp9 psign speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a xftk 66x w p.9cdppj.1 +7/i/srjmdzdcar safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at thez3a4pr 1ja455f e lth uket,/ 8*mrmte equator weretkepaj/e*ra3f851, mt l hr454u mzte apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constadr*u om qy gkbuqt,k ,135kkw)8(u0ok nt 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( ,;kuwb hhh0j constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings ouh0j(huh bk ,w;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. Thus,j 9:ixzwg +u8w it has been claimed that a person would be crushed by the force of gwzji8+g uw :x9ravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope ded3rfg4 dk3pwt(cnwj,+uced 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 escapes). They did this by measuring the speed of gas clouds orbiting the core ( ,wnkpr4t wdjc+3 3gfto 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 speeda7qivs +ap yuh- m wcs:zs6a 0e67c+,z 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 do6 +sqhcsap6eu 7-z: +wc a,amsvyi07z 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 fe vr2muwa ps;a*0f36System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined 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 navi mpa ufrw;6f03*s2veagational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveli0t w o 35az-wofvj;pf3ng 2.1 billion km, is meant to orbit the astfva5jp fwo0;t-w33o zeroid 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 thegj h waa)x65yg: c/ok xi4(8si space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radiusxog8sg 6w:i5xi) /ja hakc 4(y 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 it72r ub9cf; ;r,xhg6 ryhquwl9 s mean distance from tu;;r7r fqu6gcwhh2 r9 lb,9yxhe 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 n 2wrr sw;wsn+2eed to be if you could actually "feel" yourself gravitationally attracted to someone near youw2s+ rwr2nws; . Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arouatrhd1t9n u.azkd*45n 4 j8j mnd the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,r1 d4j4.9a kujd ahn5tz*n8mt 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 thiki r2ch+ 2ee0e corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottomhkre0+e2 i2ic side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ear+fmnsn5k0pk; upgf/d 7p1y 3cth $ \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 acceleration8z0.hz2 doku g experienced by the tip of the 1.5-cm-long sweep second hand on your zu2g.k 0 hzd8owrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a ywgroq ga6pltsn/mrm /( (8 (6circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 sm w(gtr(gorm/l6qa(sp /6 y8n. 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 desigxnm 7er*8:9 q8tfuyccry 7ut( ned so that a car traveling at setfy8c: umt(7urc7*98yq n rx peed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars when negotiatixnrz8owf )(5s:;i ln zng curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on f (w nn :l58);srxoizza 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.$\approx$    $\times 10^2$