Sometimes people say that water is rem h:6ktcb)+oga/ox i7 goved from clothes in a spin dryer by centrk7hcoggb axo t+ )6i:/ifugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car traveihxz wlaj 87e a*);;7m;ok .rqtthy,qls around a sharp curve at a chqqjlaz.y* ;ak7xm )e, ;8;twtor ih7onstant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where d wgcw:.l);fzc:a c 8mz 6t5zmjx7+jgmoes 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, m maf 58 7lmtjzc+6z wj;wccxg:z:g).(c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on akl v3(naubo bn(*x95a merry-go-round. Which of these forces provides the centripetal acceleration of the chiknba uox avl(3 b5n*9(ld?

A bucket of water can be whirled in a vertical circle witcvrot yd 0lur -f1 y8g/ykg.;jl.v.p/hout the water spilling out, even at the top of the circle when the bucklky rcdo.f j0/ggrlu8yt ;1vyp ./-v.et is upside down. Explain.

How many “accelerators” do you af( 79u.t/ bk6 .wifoxjeq;vie ydt; ,have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. Whif7 teuby.xk. w6v(o/ a;d , tj;fi9eqat 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.ssz nwsa7 11;y 5–31. Hya;s 1s zn7w1sis 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 curve at high k355(q qimzi kspeed?

Why do airplanes bank when they turn? How wn3ush;je6. o rould you compute the banking angle given its speed and radius of thej.ne3ho6s; ur turn?

A girl is whirling a ball on a string around her pw*q-f pu 2ne7head in a horizontal plane. She wants to let go at precisely the right time so that the bq*u 7p-we2fpn all will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert afuvyjz6k hg6 v:.k *do3u w*4v gravitational force on the Earth? If so, how large a force? *vwdy6o6*f:. ujkzu 3hvk4v gConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways wohebc3q b-o,j4hg)0tqdz:t /* +smv .gpvu sn2uld the Moon’s orbit be vpbd2 , os.:4utmb-s /j +qve*z)30nchhtggqdifferent?

Which pulls harder gravitationally, the Earth on the Moon, q9t ;pt t/xw5uiu)/o6s kt1 kpor the Moon on the Earth? Which acce/k t u )wp91qkso/;x5tpt6tiulerates more?

The Sun's gravitational pull on the Earth is muc ,2 k- onx,pd.lg9aoceh larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consideo,cox-,dp.a2nle k g9r the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poleu4+e5oji/thm t 7.t6+eeg y yvs? What two effects are at work? 4uiy 5ty etjegomt+h.+v/ e6 7Do they oppose each other?

The gravitational for1 *b3dzz(t;kqi4s xtdce 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 from t3tqdsx *4d1kb; it zz(he Earth?

Is the centripetal acceleration of Mars e ;x,s8dj* kec blak-xw :3oo:3jp yg,in its orbit around the Sun larger or smaller than the centripetal acceleration of the8, lowe-kx xca:poyj ,sgj3: ;*dbk3e Earth?

Would it require less speed to launch 93ag5b 5rq2 knf4n pgj):n rpy/oqo5wa satellite (a) toward the east or (b) toward the w53pjg5g f5ao: )o49yqr pb wnrq/nk n2est? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by vbxw7j da2 w0me(7i0n a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d)xv7d2weni7j 00 (wba m moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected by1g(rja ,x,vpq b3 m/ho 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 (c) any other aspects of gravity you can think of/b rm(q , 1ovhp,gajx3.

Explain how a runner experiences “free fall” or “apparent weight3 q/nnz b-nqns b-9m:clessness” between stqs bnn3bm-qn 9-n:/zceps.

The Earth moves faster in it b9xielge81 p0s orbit around 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 ii9bl g xee81p0n 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 wa- u 61bujqj()9lzfriu s not known until it was discovered to have a moon. Explain how this discovery enabled an es u )(b r6ujl1zuqj9-fitimate of Pluto’s mass.

  The Sun's gravitational pullrd2n .v6(x3l(2n4yde tbzj au on the Earth 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 othern v(rxd( zbe232.6 4dljn atuy.]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 travelin9er h w9dnd,nbw0(,dms ens4 *g 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 accelervf)q3 cu39stu cz;+ tgation of the Earth in its orbit around the Sun, and t 3fv;)+ 3uuccqtgsz9the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 Nd- :44fizm e:wpmzdd2pf w2w-p;:qid is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m.4 pf; -zzq:2efd:wdm:wid-w p md42pi Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's sudq fgat; xbn;jdp:+68rface, 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 a6pxqat: +8ndd fg j;b;cceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a sr20-2lhgyvr 3 d9 uk9.po egvct(yf)p peck of clay on the edge of a potter’s wheel turning at 4 gv).09f e-3y9u2vlr2g rcdkhtpyp (o5 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a stringld i *b5:m4pjaq;frrt(5/8 drm*w xtt is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown d:r(8 5x*wlpij t;/*da tmt 45qrrb fmin 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 rbc-4oxaiv740 ed nlx9w xh5d.,2mycround a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result y,hv4. a5dbxc x9oi 0rx-w4ln27emcdindependent of the mass of the car?   

  How large must the coefficient of static fribh3rh1 gs2ln - h+ ylgl0ee:t) 6;tdpbction be between the tires and the road if a car is to round a level curve of0r: -d;2h)glg1ltht nhy 6le3bb +sep radius 85 m at a speed of 95km/h ?   

  A device for training astronauti -5 lqzze-mp(k+p iv*a7exyh1ju87ste 1 cz7s and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her ownlm 7jvzec(k-15i px7yh 1-t uzp8*seazi e7q+ 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 opho k3 1*agchemb9d8pkwb)h6q5c hhs- )27acf 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 c 7d3cc5bkw1 hhq p29ab)o8hghas c *kpe)6m-hoin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rolle/h 3 m:nysmif 6dg+5iir coaster be traveling when upside down at the top hs5mg36:y+f ndiiim/ 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 (including the driver) crosses the rounded:hvp.lak5+v;8 yo iz:pz*iv/ qyk0qw top of a hill (radius .ovyl 0 w*vai5 pvqkzy+ kp q:8z;:/hi =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-diameter rcqo ..gs;qd+ Ferris wheel need to make for the passengers to feel “weightless” ato. cqsr;gq+d . the topmost point?    rpm

  A bucket of mass 2.00 kg is whirle 0e+rdzw 08w33hgw-m bd3dbhi d in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is d0 3greb+3bd-0 dhwiw38hz wm 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 /e rx .,aa5pkrrotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 11e ,par5xk a/.r5,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricalj 8-bka o-o,gu0its, rly walled "room." (See Fig. 5-35.) r,js0b-g o -akui8,to
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 frictionlesr62w /6g3o cutksmv sjp44c,vs air-hockey tabletop, and is held in thi3p6k2vctv/u g, c4so6rm4 js ws orbit by a light cord 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 weyx f.hf.cu:zxg)c6ie s383 iiight of the ball which revolves on a string 0.600 m long. In part:fi.z3ecfu 8ishy) i 3x cx.6gicular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car travefr2 uwj18fl-i 9b):kq +h igkvling 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 4mn 4r v wmgrhte,8-/yce0o9q$ 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 evasivv-aw ,l *c1 zmhdyx-gao5s8 5ve maneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangenti75 almzn4omu5 al and centripetal components of the net force exerted on the car (by the gr 4u5an57mmozl ound) 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 accelerat( jgp+t uppz4zj4u3/frp m9(des 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 su9/z ftp4mdrj( zu+ 4ppp(j3 gtatic 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 pfe 7 5/ n3wfiyu)x ;7ypzkb f3-.lmpfinstant, its accebfz7ppp)w/ if;. 5 lkymfyxu3f73e n-leration 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 1 ue7b9,j f7lpu2,800 km (2 Earth radii) above the Earth’s surface if its mass 7befp,j79ul uis 1350 kg.   

  At the surface of a certain sk8sd 0z 9 wq-prs l.7m,vakj9planet, the gravitational acceleration g has a magnitude of 12 w-9vl 9 p0ss zqjs78kdk, mra.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 tqx184buv bh o1o gravity on the Moon. The Moon's radius is 1.714x1b v qbo8hu4 $\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 the sh:(zw cfq8i7 94lpgqgame mass. What gl:zg(chqif 4p7qw89 is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the q2t,m+th oux,1 ae3pv same radius. What isoq,3xe hm2+upt t,1av g near its surface?   

  Two objects attract each other gravitationally with a force of 2.5o5ltb )u.ejf u 3kz3s5$ \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 effectu8dkks4 5ox2/ qxgim + gv-mz;ive value of g , the acceleration of gravity, at (a) 3200 m48k;kdv gm2/+i5soguxq x-zm    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside tzfikvvl)2 /vcd;9hz 1he Earth where thegrav9zh2fv;d v)1zv/kicl itational acceleration 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 massu+;drw8u7btgy z( -rp of our Sun packed into a sphere about 10 km in radius. Estimate the surfazgt;yb8(+wru ru7d -p ce gravity on this monster.    $\times10^12$

  A typical white-dwarf ste58qyi *8 f 3zplgfwe.ar, 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 mas f.e8*3yeg pq5lz8fwis of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spx h-tqref-y wbo+8;yry 5 6v.kace shuttle. Your friends respond that they thought wt-+yvyq-b e5rkr 8 y 6o.h;fxgravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a squargle x3)as,wamjo23o9 e of side 0.60 m. Calculate the magnitude and direction of theo 32gw)lsma,a 93oejx 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 the mns juxv-e62q5j r7h,e .0j buSun. Calculate the totajvehuemj.5b r jq 762sxn0 -u,l force on the Earth due to Venus, Jupiter, 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 4+(j v sh 1efyp(kfioj(.qt4y.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mk(p vf.y1itjjfeqs o4+(4h (yass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known *vr:rzhd0y 3uqs8ow twd7*pj.. cnx,value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s lawv 8*wsj u .woq7n drct3zp0y.* hd:rx,s, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit aiglp2qv 0v+ /tbout the Earth at a height of 3600tvl2/+ivq0p g km.    $\times 10^3$

  The space shuttle releases a satel/yn6xf/ ;vir klite into a circular orbit 650 km above the Earth. How fast must the shuttlenirk/v 6;y f/x be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindricap0bk hxsua 5;jd5- n)gdtb(a7l spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 g xah7d(;as 5 0butb-)dpj 5nkm, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite tqial6kuw (t;sy;w n 12o 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 the Earth. Does your result depend on the ma;(tw 62ywk 1lniaqs;u ss of the satellite?    s ~    min

  At what horizontal velocitnhm: lk ,orly/bm rwu7btj 818-g30wny would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Ea:,l387u/m mnto w8bkw01 bh jgnrl yr-rth?   

  During an Apollo lunar landing mission, the com3z/ wi-4c3pll e0p vynb8 fskdj*+u6 s ;sma(wmand module continued to orbit the Moon at an ajcw;lmwdueiksbl +pv(0/-4fa6*y8sz 3 3np s ltitude 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+j(/u w(8zulnsd/ uqy planet. The inner radius of th/ uuwn u/8((sl jqz+yde 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 onnj6p+. *a:off lpxn )0cpatw0 ce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight na nwf60xap.) fltpc: * opj+0(a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of th2vta::uncjnkf mv;2 7e Earth's Moon in a space vehicle (a) mcun::vv72j ;mknaf2t oving 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 st;j83j9 wwrd e)(d cjuniif 8niw 07z+tars of equal mass. They are observed to be separatwf0wj)7; n8 riijt9dw8zeicn3 (+jd u ed 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 scalcu7+ *on,b .fu 5zcvi8h5orp he read for the weight of a 55-kg woman in an elevator that mov.nco p ,f uu z+br5*5hivo7c8hes
(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 jy6(7zeh f))hlq +w wjcord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevato+h)w)zl e7h(wj 6yqf jr’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very ne.v.n m ,.engpmar the surface of a planet with period T , the density (mass/volume) of the planet is ,n. vgmm.pne.$\rho=m / V=3 \pi / G T^{2}$ .
(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 Moew i(nsi) )x:9a-tcoyon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s s)i) n-(9o :eysctaixw urface.    s

  The asteroid Icarus, though only a few hunda:xa ls5 qhvxno,, z33red meters across, orbits the Sun like the plo3 qvz,asn5l :x h,a3xanets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distav.18 if8+s *odn hekdynce 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 49mn*q4je w7d2ll/ j bg3szxfonce every 76 years. It comes very close to the surface of the Sun on its closest appjw/zg4*q9l mxn3dj7bsf l2e 4roach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxy buygw8846aghleoo.y k ua*40$\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, av s,w0geeg84oqfmpa;l 8*u e +nd mean distance for the four largest moons of Jupiter (m8efqe,*s 4gw8o;l+ ap vge 0uthose 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 periodr:b hcs-i o/,zi6i3ef and distance of the Moon. fzi3:,seh boc/ i-ri6    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, uss9q7pd v:s /yn 3zcnm7fg5u)bing Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compp)3ym9 7:d /gcfqsvb 5 sn7nzuare 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 bef1n 2sj.)+pfbaii07ew1kfx kiu *95v b:zx hgtween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that onjf9f)52vbfx.e+ * 1wuiknki0 1hp7i:xg azbs ce orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form o tuzz ,gh ).d2;,v wrdtdd*7bmf 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 ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolutidtbmzud; dt rh.2 vg)w7, *,zdon, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hs)p-h m1+aj/l yfi:q yanging 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 ihay)s +imly-pqf1/: j s 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of grzz6g bg8s4y; z4 z*3dpastw s1avity be half what it is on the surb6s*z3tg148;as zz4s gyzpwd face?    $\times 10^6$

  On an ice rink, two skfjx( bbzr.l -p)vc8s3 aters of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0 .br(8z)jpv b- lxfs3c.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 rotatefi b k+n5qz06:6y euvj)afa 1y7t si,:8vqy bks once per day, the apparent acceleration of gravity at the equator is slightly vf6,i 8yjs:10 )n 6 ak:b5yqbiv7z k+uetaqfyless 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 travelink3. vf69n8r8ywpi/dem g)slo9;lmr kg directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposi ) r/ogwk9. vnmr dmpsei6ly fl89k3;8te forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale pjrsotu3e1nv.ml g62cyz/f69(o- o x in an elevatotruoyox6/v1 s( mo62c .f9zp 3-ljegnr, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate about itsh( y.d5e tsq2 q;z.oox center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What mustq q.2hz o (sodx.ety5; 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 aircraft in a vertical loop (Fig. 5–43).m d8ajto:x8p*
(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 of its radius r, the acxk ncc+8pa4x1( zl3jk2j dnu;celeration due ta cl(u kn84 jd;nc2 x1p+jz3kxo gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging o/yk s:) jy)arjn a string) is deflected from the vertical by arjk /jys))a y:n angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coeffgu 7f. 2s.jsmo( 5hfwqja-*it icient of s. g7fq5-t*w(ujh.s io2mfs ajtatic 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 the Earth were rotating so fast that objects at thkjhen c:d 7-a9yf(5blze;*ww9b oao* e equator were a cjooh9-b(nb*:* z7 wkweelfay9ad5;pparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dhm6 mqtnx 5:84rgxu -wlfmb/ ,istance 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 rounds a curve of radius 2- i+ t,t7pje nlcr4j3r35 m. A lamp suspended from the ceiling swings out to an angle of,ti3cne 7rl- jt jr+p4 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 hva:x-;1ta nnfas been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.-xnfa:v;1ta n9 $\times 10^{27} \mathrm{~kg}$ , 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 ;hiya m3ms . rfq11sw zbgr,5pw9y51ikq q w2,Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes).pbg9 ,wirzsrwq m1 y 15isawmq. 51yqk,2;fh3 They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and vall /kt+rcpo5* tvey shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car 5oc*k+ rv/tt pat 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 Systrrc5v7pv, l b:.hui/d g+a.8 pforq(nem (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 navigational “fixes.” The satellites orbit at an altitude of approximatel:v vrr.i5o/r+fn,g8lu dph7.a p(bcq y 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 (z4eiq6 h jfinmx edxi) 5+,1hRendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid E ix nxif+ ze(id4e6)mqhh5 1,jros 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 spae2u(0 eqv zi*gce shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it. e qe(u0 2vzgi*
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean distance am. qeeszu,u/o./f0jv kp9o+ e0gr5 xfrom th,spgu/. 0 o efv.xk0mj9rzq/e5 u+oaee 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 tomep 7b5- ze5 d qndrul4/9fv8q be if you could actually "feel" yourself gravitatizldd5eqn7 b r pve5 q8f-m/u49onally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig.4.bsxi:k1bsk 5-46) at a distance kikbs4x b1: .sof about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are lg2c8e69/.pq hyn a frqocated at the 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 bottom side 8/q.f2ryah pnec g q96of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits thfo 1*k/rw8fggs9/um n e 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 8/ nyi2fb o;s/ z/owpsby the tip of the 1.5-cm-long sweep second hand on yourpwofib;//8 2s oz/nys wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sidj ack co1n/ h(ered,7+ z+s-onker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is t +(-enc/odc7kjz,es o+a 1rdhhe angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radiyfjg5 ah ew;p1h+/o 7aus R in a new highway is designed so that a car traveling at sp ;/heoj wfh7 g+ya51apeed $ 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.tva 6 ,.uu*fwct e1ho cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passeng .a,ec. t6 f1wu*touhvers 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.$\approx$    $\times 10^2$