Sometimes people say that water is removed from clothes in a spin dryer by centr o:vl aj/hrdyg5l4iw t+ ) 7xw.l.i4arifugal force throwing the water outward. W4ra4w: 7lh/a)j l. 5vg.txr +ldo yiiwhat is wrong with this statement?

Will the acceleration of a ;nxw07cg n0/hw r (nyecar be the same when the car travels around a sharp curve ay wnw(7nh ne 0gcr;x/0t a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at const0fk+m3hx a,i tpfe.4.nrf *u bant speed along a hilly road. Where does the car exert the gre,ux*+4.makf hn0r pet3b ff .iatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting2 bgitv p)j12i- q ,.yce2oosg on a child riding a horse on a merry-go-round. Which of these forces provides thegj ,b2v o2ic .-gp tqo)ie2s1y centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circlek q7poi3vnurb tt 7,:lr6.n*mx q. 8oe without the water spilling out, even at the top of the circle when the bu t* ru7. erbqo mi,n6vqot 7pn3k.8lx:cket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three contrjbc/y9wjm. ,hfgt q 8 eefp8;)ols in the car which can be used to cause tj/8; bcmjg .w)ee8 ffqpt,hy 9he 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, as shown in Fig.9i.o hayg(ny (1c 2oott vqz+3yjk 8n6 5–31. His yvono+2z( 1 gt3jaykt(.69qoc nihy8 sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curs1 *jjo/ m4x- zz:qymlve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle ueep3 2n)bj -zgiven its speed and radiup en)eub-2z3j s of the turn?

A girl is whirling a ball on a string around her head in a horizonta g 4i5c2wlftiu 7y33wel plane. She wants to let go at preciselyi yufw3 itg c2537le4w the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitvlz :s :ieb *8i/nu/ s2ef9xgeational force on the Earth? If so, how large a force? Consider an appl:2lv/in :sg 9/eif*exes 8bzue
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wajv1 j4qg vz( keee-,lwc2 g1j5ys would the Moon’s orbit bee-(gvj v1 2c5g,lqjw ek14jez different?

Which pulls harder gravitationally, the Earth on the Moon, or dkc4:88 2j2f,i sn px xb+fmnxthe Moon on the Earth? Which accelerates mo 2bdfxxnnk:2i,c8pf+84jxs m re?

The Sun's gravitational pull on thex bs:wnkj 01;vi jnn58 Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explainijn bn:k;18wj v0sxn5 . [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator orq:dd )6;adgqh3u sa3q at the poles? What two effects are at work? Do they oppose each other;:gqd3 )as3qaq uddh6 ?

The gravitational force on theiua.t u2keqqt6 ,*j5e 9zlr/k Moon due to the Earth is only about half the force on th* qt.k 9kraj5ue,6uze l /tq2ie Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit aroun vr 34 i9qc9*ga3gw id;mnrs1t;qh do/d the Sun larger or smaller than the centripetal acceleration of thg4 ov3g/;9d nr9*1drqw csqham;i 3tie Earth?

Would it require less spe -fsq q*tfq( 7ewvq9.l,- neo p0febq3ed to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation direction ewe p0f* b9s-tq3qo,(leqn- 7qq fvf..

When will your apparent weight be the n 0n :5y8;+ hlcqmxug*pktx3x ,rxcx)greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downup 8;0q*k+ lx)h5m gx 3:rx,cxt cnnxyward, (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 oxg d0. u pr(kcts4q,1b8mn)uiuter space could be adversely affected by weightlessness. One way to simulate gravity is to sha0np x.t mq8)u4,bcgi s rd(uk1pe 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 exufucx 0d.td ,woff0(;6o4dnmperiences “free fall” or “apparent weightlessness” between uf,df mxd4 (dw;0 c tofo6un.0steps.

The Earth moves faster in its orbit around the S7 /:u*lv oso*/wdq oygun in January than in July. Is the Earth closer to the Sun in January, or in July?/7 /**uvogylqo: sw do Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have (7u+p- g.h5 olyqo4nb spwgn/a moon. Explain how this discovery enabled an estimate of Plo-+gnp.ly w (oqp54g u/sh 7nbuto’s mass.

  The Sun's gravitational pull on the Em bf rozkebym ;603.7o(7l unqarth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from tm zoob3lq6ry077 e.n(f k;mub he 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 198h0bavl2 b1 io hy 2d8v*bx0da2:ipvw-0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 u0 w )np7p8ff5f/re 9nm,noziaround the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's pu8z )efo5nw in0r m7f n/,fp9orbit 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. (olxhn93uxly 2s3w0c0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the ( ux3xlhncyos l3 92w0discus.   

  Suppose the space shuttle is in orbit 400 km from thea o.d/fnbp5h; Earth's surface, and circles the Earth a 5ahnop;/dfb. bout once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edg oo, h8)+di7fmlow 4tie of a potter’s wheel turning at 45 rpm (revol47ldw8i io of+h)m ,toutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical ci;w dz 4mqcpz4nxvci. 7:9sts2 rcle of radius 72.0 cm , as shown in Fig. 5-33. nz vc zixs :2q.4p4scw m;d97tIf 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 vxauj(ad h0 f 53e-cm3with which a 1050-kg car can round a turn of radius 77 m on a flat road if t 3c(mfvh0uxa53ajde -he coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and /bjl fb v9h87othe road if a car is to round a level curve of radius 85 m at a spej87bhfob9l / ved of 95km/h ?   

  A device for training astronauts and jet fighter pilots:nlm 9wwwc1p ojs)c 1+ is designed to rotate a trainee in a horizontal circle of radius 12.0 m . wnp w:lmws) j1c1c +9oIf 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 turntablv5-e2i bmuz 6g/q bql0e 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 f5qi- 2bev6m0gub /ql zriction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down *o60lfyptix ;at the top of a circl6yop;fixtl* 0e
(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 (incljd2c:ww+9vgn: -)yrx,1;mqhmbyjm bu c1 / uiuding the driver) crosses the rounded top of a hill (radius =951nr;2vucx/y9,+ u j1wm w-byim:b:mh)gdcjq $ \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-diametmqbbr 6(z9)t her Ferris wheel need to make fot(h)m9zbq b 6rr the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a verticajgsrtcw,z31, n o2 ymt6 uu0/il circle of radius 1.10 m. At the lowest point of its motion the tension in the rope ,6 ,3uzuj y21wo/cingtsr0mt 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 p7 bjt4)ptun b:jb;)7 h6xxkoif a particle 9.00 cm from the axis of rotation is to experien7pbj6b; xxhbjt7nt:k)o )up4 ce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled ")+y h 6-r1awtfruvx(jroom." (Sr-v(h ) y jxrfuw+a6t1ee 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 circux sno677w u3oi8eli.0llzb a . +x-(w3 voferle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord lwn8ufzuoo7s07l.bawx3iil 3e.r (v x6 o- e+connected to 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 this time, by not ignoring the weighv nm/j9tyj. efcu. l8;t of the ball wh.m8;cv .u9nejfy/t j lich revolves on a string 0.600 m long. 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 perfeu2q hs)l rh9*)l0 wgi25ne4oi -w lngmctly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massesxt h- kq37i8 (6i3qdelkujmjd7dl 22l $ 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 div fp4l4 aq+ 6;riif1wefing 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 components of the net force e j7c mzzr)oa;zu6t xd: r-/i8axerted on the car (by the ground) in Example 5-8 when its;7-:jd/mzr8r6u iao)ztxzc a 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, goinr+t-;6;dc ktn z kn9sbg from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or s;6;-k tcd+ntz9 bsnkrkidding? $\approx$   

  A particle revolves in a horizonkjpus -5e;p 6vcds-wj(i 7) qatal circle of radius 2.90 m . At a particular instijj;pqe u 6 v5wac7)spds(--k ant, its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth rw0c nmwk,o g,m5k) e7e vbr/7uadii) above the Earth’s surface i) 5mukbwgnercmv,7/ 0 kew7 o,f its mass is 1350 kg.   

  At the surface of a ce0+ ;6 ealheomuxow q9.rtain planet, the gravitational acceleration g has a magnit+ ;9 w.0x emq6uheloaoude 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 gravityog j1hcj k.q;6 on the Moon. The Moon's radius is 1.746q jhcj .o1gk; $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet u/k:5)enpg 8z81kq j ckjoa6phas a radius 1.5 times that of Earth, but has the same mass. What is the acceleratic gpko k5eu kqj)j1z6p/8:a8non due to gravity near its surface?   

  A hypothetical planes87znygud(t+4 qs /oai v:6ybt has a mass 1.66 times that of Earth, but the same radius. What is g near its tso7y 8g4bnad/q(sui: v 6z+ysurface?   

  Two objects attract each other gravitationally with a foxrw )av/:,jj hrce 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 acceleration of gravity,7*kr psma ,q,8ztd9ch*g*uqa at (a) 3200 mat9*k, * qhc8 ru,gmqadpz*7s    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whl4u)c-xxp/ pi2r /nul ere thegravitational accelerati clu-i/ n2)lpux/x4r pon 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 into a sphere r)xkfq5hlc6q ;1xr k1 about 10 km in radius. Estimate the surfx)rq65kc rh11qk flx ;ace gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average s,2 2rpwn1nt w3w +4w 6hgonvdgziq) 8ttar like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sh)2326i r 8wwnq1wntt4o+n z pgdv,wgun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting iuau 59d0ow4 rvn the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourselfa9v 5rud4ouw 0 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 loc -iy.r qtct(7ajhcz4 5ated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one spherat 7ity (4qcc-5 hj.zre by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of thec (p/0x8sqycy9ul d;v planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, 9p cqvxucdys(/ 0y;8lJupiter, 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 acceleratigu: x 4s4:kh8 (cdh,nqt-wtyaon of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determihws4yt4, :8:d( ucx g-t nqahkne the mass of Mars.    $\times 10^{23}$

  Determine the mass of thexz/o,dz 1g*bvj8 rr3cz * w7rt Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s la r*g8rxt j/3dr1zw bzoc* zv,7ws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a dwk*o/ /x; q)jayxk0r stable circular orbit about the Earth at aowyx/qj x;/d*kak)0 r height of 3600 km.    $\times 10^3$

  The space shuttle releasxh* a(c9/1w .gaotv +b,0rnc6po rytves a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) wrc*tg /nhoboyvtp.6,x 09wa+c (a1v rhen the release occurs?    $\times 10^3$

  At what rate must a cylindrical spqyujxfjc; ,wf n 9c9 ,2th jbodfp8.52aceship rotate if occupants are to experience simulated gravity of 0.60j5f.,phq x8w2 bjo2c nc 99jytf;fdu, g? Assume 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 takftg4wby-- y l8)hs.yx es 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 to the radius of thesy) gb.xtw8-ylhfy 4 - Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would an hw;8 o jx8-sr .bsyp;hmkg9+ satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit arounxr hg pkwbno8j s.9-h y8;m+;sd the Earth?   

  During an Apollo lunar lan+lm hp-7ibsot h ja(,89b1im wding mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did -m1p,9 i7b8(wh btmjh +sol aiit take to go around the Moon once?    s

  The rings of Saturn 6-*. ynjcifs gf)t c8iare composed of chunks of ice that orbit the planet. The inner radius of the rings is 7f *tcs-8)y6j.cif ing3,000 $\mathrm{~km}$ , 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.-eghy3a* vo:z 5 s (see Fig. 5–9). What :3a-v*z yoe ghis the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astraq * rw: mhp*3l4xg5hxonaut 4200 km from the center of the Earth's Mo 5 max**hwh rg4qlxp3:on in a space vehicle (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-star system consists of two star5s+ + zbx/da9hpb ohcs;o,)p v ufa:.ps of equal mass. They are observed to bhhz+9fs/xoba+cp;v.p 5 )ps ,ou a: dbe separated by 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 weightb0q*2 ge.kpk r of a 55-kg woman in an elevator that movp bk 0q*k2r.eges
(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 suspendek f0e hlb2pc7 /-rfz1emd oi k:4g/x-sd from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerkkz1 cf-7 ld:0 2ixmhbseg4ef//r-o pates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surfapuj(at. g47gxz (eqk0 699p gn dzzh5oce of a planet with period T , the densiu0x9tk65 gg e9o4pj dnghzq( z(7paz.ty (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 p/mmnxv;,6*f n(cqiq ;;bw iom19thmmeriod of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very nearfm*w( tm ;x 9h mbqni;oi6q; cvm/1,mn the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbitg-+.kamv8 r kds the Sun like the planets. Its period is 41 ma kg.vd8k+r-0 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distaigjr9a: 6u-sc mz0+btiz .rr6 nce 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 Sw9 .68;dbsxou,:-py fpa duvphs x+; eun 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 nea9,;uy fe:od8pxpwsh p;b u +dx-.6asvrest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Ga,2 bgm8w9gm wxff 83yhlaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest mooei8h l fvaz x.f4s-* ,b.bh8zfhyb 4n*ns of Jupiter (those discovered by Galileo in 1609 e . xzhvyzf84-bnhhfis, bl.**4ab8f).
(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 thns3 7.mqagtjn:v6ex * e Earth from the known period and distance of the Moon. a3. s *gnj6mvtx7n:e q   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using Kepl:*vrpv5 r2ne ker’s third law. Use the distance of Io and the periods gk nve*rp:52vriven 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 fra2) 6 exty6mlgggments (which some space scientists think came from a planet that once orbited the Sun b6le 2tymx 6)ggut was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form o5t1r+qlg9 lvgja8czr + 8xcx 9f a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (whavc+g59xl+ rx 1 gcl rq89jz8tere it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross bf7 wb+.azjlic;v 4 vp17el, ++enelqa gorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can to+zbnefv. +jl 71 ,4c+ wqe;a le7libvplerate 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 surface will the aced,p1li vxgx h,r2k/c+;c-wkceleration of gravity be half what it is on the surface2w i,cxdp+gr /ckkex;l -hv, 1?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hanzur8u.tvig tic p,i52 ,)k dv.ds and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their indivi2z,i)dv ktti 85upg,..riucvdual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration(nvj0yt,tyu. 23w u.(uwq kkn of gravity at the equator is sl (2(yj unnwkt3,uqtk.v.wu0yightly less than 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 from theoecnt5pd/:y 3 Earth to the Moon experience zero net force because the Edpnc :3 e/ot5yarth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand o6cx gwmfrzj*pso;ogtj;. )sg)v;b4 ,lp;xq 0n a bathroom scale in an elevator, it says your mass,psr)jpmlg0;sxob.;v o f;)wz4;tcxg6q g*j is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circula0fizyhgq/r-rm **) fd7zzc 1n r tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by td1 */rhz g*r fiq)y-fmncz70 zhe 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 ogcz2h),qg yr )9ix(h 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 termsakzx2wl- m68 3s; wmxn of its radius r, the acceleration due to gravity at its surw6z-m3 xan;ms 28xkwlface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from thek8niy nuw w wine8oxg,* .6d0( vertical by an angl i dnwkwix*eu 8no6y.(w08,nge $\theta$ 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 gl 0b hkebbwi/ks3+5*sign speed of If the coefficient of static fric0+b*hl3wkbi/eb g 5k stion is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were r rs*2e mhwrl*+q9,8pq2 yu zjqotating so fast that objects at the eqqw2p 2qr e*r8z+s m*huqlj,y 9uator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant (p/..snl a), bqbrnfj)akxwe, .ci oea/y 8+xdistance 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 roundsezj9ni;4;u x u a curve of radius 235 m. A lamp suspended from the ceiling swings out to ;9;uizujxe4n an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been clj+ ay8kuy *rs+4;bdaw aimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equab4+wakyrd+ ;sa*juy 8tor 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 (o9l6zh g+q, v -ntbmp1e nhn.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 ligmnhzn+e6g-vl n9otb p .1(,h qht 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 constant speed as it traverses the hip.v r oya:fm24 kf)3bswso7 p)ll and valley shown in Fig. 5–45. Both the hilla4 r) 7ypf2pwskbm.vs)f o:3o 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 without losing contact with the road at A?

  The Navstar Global Posipa4( tz*p0acuwh; 7 qc-i,wtxtioning System (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 f upatx c4;7c ( pt,-wwiza*q0hour 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 Renj3y6bd li j3+tdezvous (NEAR), after traveling 2.1 billion km, is meant to ojdlyj3 +6it b3rbit 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 the space shuttle pursuing a satellite in 0z: ds 1uv3iitgtyq mqn .9qi w7:z/u-need of repair. You are in a c- 3q0vwd:unm.ziu1t :iig7zsqq 9 t y/ircular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 yeaskog6;ab i6 *p cr5:x-knb1 roc ury(e5r0p a,rs. (a) What is its mean distance from 6b( y: oixpa06 oners-brc,1u*grp5c5 ;krakthe 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 actua8ychyz4-s wv.*naui)2 qlsa6 lly "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, likeah *zlc84uayv.s)-ns y26iqw F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centen 6 mfivn19ixr 1ic+k4r of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 lighv rii 1xn+ik 4nmf691ct-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 lo4hsb;geo ifam22 rc-,cated at the corners of a square 0.50 m on each side. Find o m;,2g 4herc 2aifbs-the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orb5):sby kr1qijits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tipqu q,jt 9392vz;d7romph; vxi of the 1.5-cm-long sweep second hand on your wriqpxv3u7;o;qm2zi , 9r tdh jv9st watch?    $\times 10^{-4}$

  While fishing, you get bored an l1x,eb3c0z w29-oos:pebvjj d start to swing a sinker weight around in a circle below you on a 0.25-m pew-3vbzlb0 s:xj 92 1p,coo jeiece 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 d*kz nd.4fjs, lir:yp0 h/uo,k esigned so that a car traveling at ,u /,lhkn kpsd40j oir y.:*zfspeed $ 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 negotia.8oa;fcq4 apn1 /)/xhw invmuzr;/q z ting curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal accelera;amq/r fn/4 z)n8 wu.i1c;qox/zvh p ation, 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.$\approx$    $\times 10^2$