Sometimes people say that water is removed from clothes t: 7aoejaf n;hhdc7d2dxhosq169j 18 in a spin dryer by centrifugal force throwing the water outward. What is wrong with thdf2aj98 xaqh167ted;s: 7jcnhoh o1dis statement?

Will the acceleration of a car be the same when the car travels around a sha2iyat.0w 7 x n+b(hlh6-h cifod t4pd9rp curve at a constant 60 km/h as when it travels around a gentc7i4yh whl 2 oha(td96ntdbxp- i0f.+le curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the car exepwp i-g)qlxtb. si.7hk90j )x:xk3 pi kr3u d)rt 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 les i733b)g0i puk w)t.k r) .9xxp-h:iqjkldxpvel stretch near the bottom of a hill?

Describe all the forces acting ono+ w)35albgyn a child riding a horse on a merry-go-round. Which of these fla)y3+w5 bgonorces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circm:7u3dafh 3 *yf cjky5le without the water spilling : f*5yudj7ah3mcy3f kout, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There ah.,ss32v t vmd b1ozqhpc.2)vre at least three controls in the car which can bsch.qhv m)vp .31bs 2z 2vdto,e used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying oveo4bpj bn,(c)gr the crest of a small hill, as shown in Fig. 5–31. jb np( ),g4obcHis 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 rou3 *:cesckkg1j nding a curve at high speed?

Why do airplanes bank when they turn? How woul4ou-nl+f6 j1+x wwds ed you compute the banking angle given its speed ande djfn1xw +wsl-ou+6 4 radius of the turn?

A girl is whirling a ball-dn q li231 st:yst;rc on a string around her head in a horizontal plane. She wants to let go at precisely the right time so tha1tris-yc dt ;q2 lsn3:t 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 gravi.,i w -snqj*bu.ne2 2, yqfryytational force on the Earth? If so, how large a force? Conyj2q., wysri.nq2-y*b ,n feusider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would m9ox0juiz s93the Moon’s orbit be differez0ux39 o9isjmnt?

Which pulls harder gravitationally, the Earth on the Moes52 5,fgjunew 1*fhlon, or the Moon on the Earth? Which accu5n5 1w lg*hj2, effseelerates more?

The Sun's gravitationy+s -nt/i:e;w dhvp0sal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tidev0 s:;ihne /wd- spty+s. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or a cf8/ )xz3usudt the poles? What two effects are at work? Do thuc x83uzd /sf)ey oppose each other?

The gravitational force on the Moon due to the Earth is only about hal u 0ximbxoi7o .a,o2n1f the force on the Moon due to the Sun. Why isn’t the Moon pulled away from th1.muoo 0n2oa,i 7xxbie Earth?

Is the centripetal acceleration of Marn,8* ss dw7yuos in its orbit around the Sun larger or smallersd7oswy ,n*8u than the centripetal acceleration of the Earth?

Would it require less speed twnby+q46a3q uo launch a satellite (a) toward the east or (b) toward the west? Considy3+aqu 6qb4w ner the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a sm,; yj z ei 8j,kawg4v00ivrw4cale in a moving elevator0vvk 0; ey,ij4 majzww, r8gi4: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affecutuid6 255pdgted 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. 5–325tud6du p 5i2g). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betpl(ou. rh57yve2xvpjp t66 /sween st ops6.r6/2t h lv(7pvxj5yp eueps.

The Earth moves faster in its orbit around the Sun in January .z )t sy*ymm)dy *7vvpthan in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much)s7t p zyym*mdy )v*v. 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 /2vng)5t ug 6kd-etoza moon. Explain how this discoverygvu ezog6)2nk -dt 5t/ enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is mu89e/q5y vj ndich larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-roundy qi59d/8jvn e 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 traveling7 t9q/sy v)egy3 //do vnfrnd6 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around thescsb*ce)h363k kzs j. Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a c3hs bj* 3e k)ckszc6.sircle 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 iso0f ;gb0c 4rgs exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Cal004bs;cgfg orculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from thep4m fl kmyjp j4-hm*.0 Earth's surface, and circles the jmp4mk*jy- lfhp0 4m. 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 Earth's surface. $\approx$    g

  What is the magnitudesq7*,7hr tsqi6 qp1mj of the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per q7 j1qtrsmpi,h67*sqminute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verth0b6xjh4g0g7ffe 7d pe(x : cuical circle of radius 72.0 cm , as shown in Fig. 5-33. 7gu0efpe4jbd h 0g7x6(:x c hfIf 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 rounb+h bgpit) j2u -c;oja3qb7 -ed a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80?qbio2t;a 7 jc-3ubjb) -g ph+e Is this result independent of the mass of the car?   

  How large must the coeffic3vm91u3els 7wwlv tyz r7 -0hhient of static friction be between the tires and the road if a car is to round a level curve of radius 85 mlw7m 7y1hlzs3thw 39e- r0vvu at a speed of 95km/h ?   

  A device for training astronauttlajyj:p.n u(q:e: 9bl2) j+ngf3 gr gs 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 own weight, how:g:e gb 9jqnl 3 t:+yfj2lupr(.an)j g fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable 8 6nxs2xt3gwu (fy;dr 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 xr g8n2wd(x u;6 f3sytcoin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upsidt. bxwo9p4n w6 d3v4r6yut2gse down at the top of a3d 644oxv.6 wswtbryut2p g9n 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 theqs zk+ h+bt / jfr xv2il79wx-2vh2rt- driver) crosses the rounded top of a hill (radius =95b-tjvrv27 /il+sxhtx9f w -2+2q zhrk$ \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 mim3d)6c ye u(kmnute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at t(emu3) cy6mkd he topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radixjx6g k8;)u 8h y9d: cghwm5ayhocm,0us 1.10 m. At the lowest point of its motion the tension in the rope s x5mcucawh8xgo,80gh)6 myj:k y h9;dupporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 cm from tho0g2ar0xl .c ob-3 kkze axis of rotation is to experience an acceleration of 11 az2k -krcgl0 3.0xobo5,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are roc n5m.cdk ;ox(tated in a cylindrically walled "room." (See Fig. 5-35.) d(kc com .5xn;
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 frictionlessi 10ph; ytgjna;6fmoh x;j4l4 air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central;4hft4j6;y;h1ligjx pn0 oma 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 iia*hj*s:w m o*gnoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the mai* j:h*owm*sa gnitude 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 travim*o ig1ytb4 20v4 5q,rnkebj eling 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 masseg8qdedz: fts2 j.l4j -s $ 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 vertically at 31)1c llqy bdd 7;ryxw910 $\mathrm{~m} / \mathrm{s}$ . 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 tangentialco v5mikqnt d,8l1/jlj -+9nqx6ln*o )u k1o x and centripetal components of the net force exerted on the car (by the grnnqqkjn*i l jto ,l89 1kd/v l-x5+6oxucm)1oound) 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 accelerao(sa+obbql 2 4eth); ztes 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, ass hbal+(ebsot4) ; oz2quming 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 civk.m n)i ejou lag+ r/j*;,p+xk3s 6cdrcle of radius 2.90 m . At a particular inmp; xc)sa3*riku.j6enjo + g/d ,kvl+stant, 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,ng0wak oli1 4q-;lsm .800 km (2 Earth radii) above the Earth’s surface if its mass iiog041 .kla wls-m qn;s 1350 kg.   

  At the surface of a certain planetu+ s t.xl3br8fo bsg:2, the gravitational acceleration g has a magnitu3sxtls8.or2+:fgu bb de of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is g1 jc: gsbfdxkf.u*p h:(8ei ;nv68yc1.74 *c18:i;nef. ghdby6fjskup vxc8( : g$\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 samy lh ekwpm1:gv)(s81hx55x,f +sjr nhe mass. What is the acceleration due to gravity1 svx +1jmhhkpyh 5xn5)s(gw8 ef,l :r near its surface?   

  A hypothetical planet has a mass 1.66 times that of Eax/,0 / kfj(c2p/ g a tjblcjfxeu3(k.rrth, but the same radius. What is g a,0/ u f k3xrfcpbg cl( /j2extk(.j/jnear its surface?   

  Two objects attract each oth0h*xhx7xs21rdy + (unouu;toer gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g pl/lux0m: :d) jvi5ol, the acceleration of gravity, at (a) 3200 mpou:lvx:i5) d /ll0jm    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earthi wm9suqik6*d: y5) wj r/,6hort,olo where thegravitational acceleration due to the Earth is o j:l9*d,swqwum 5y6/,r koo t)hii6r$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the masbdb;tr;)vvwfp t+9lv .9ir ge3 e9,ans of our Sun packed into a sphere about 10 km in radius. Estimate th9;w+vr9rl nbb 9aep3 ;,g.ittdef ) vve surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun buti +cbmfx4)uxk x6j* /t is now in the last stage of its evolution, is the s xx*4t f/+6icukmxbj)ize of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while b:th 8px7gl)rc+ .4-rgb4t jii h6fdnorbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Ear4) xj7thli ggfhd4+6:i r8-bp.t brc nth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the co*0ygid;(1 rqx0ng 3 4jy slaforners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravify3s1*4rqjd0xgg;( 0nol ia ytational 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 xor :x/ag)(;qlei5 ly the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line l)oiq 5( ;yg:elr/xx a(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 surgeb 2x2elp*l)s)i )kjface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mas )2 eie*kjxp)2l)lbg ss of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earthp v54f3-durve5kj iq7e:e c2u and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler: r25ce7dkuee pv5ifv-u j3 q4’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite movinqgn(uie8 ,tk2eh ob )1g in a stable circular orbit about the Earth at a height of 3600) b oen,gt1k( eiuh82q km.    $\times 10^3$

  The space shuttle releases a satellity7-km0ak+a goe into a circular orbit 650 km above the Earth. How fast must the shuttle be+k goy -mka07a moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spac*ew)rgs ai*3e.+y axj eship 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 needed for one rev3*ig x*e.wsaa+yre) jolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellit2 hc :qe9,8rvaem2,vy u8eseke 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 sv,v9e r2eek8y2 , s:qhema u8cmall compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellicfu k7nol6 (e:v z7*aocn1dt 8te have to be launched from the top of Mt. Everest to be placed in a circul1 cd7* afo8zkoet c6(nu7:nvlar orbit around the Earth?   

  During an Apollo lunar landing missionf-odb nco 9( 7 (splcf-ld96en, the command module continued to orbit the Moon at(9c f pb(lcn fd7ln -6-9sdeoo an altitude 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 planes u9jb/ pcc ffz69,0cpt. The inner radius of the/ uc,c 0c pfzb9fs9pj6 rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fiv tm 1jgd9w,)hg. 5–9). Whatt)9 hwd1,jmgv is 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 astronaut 4200 km from t3(+ rewsemdg1he center of the Earth's Moon in a spa3e1(r +wge sdmce 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-sl,2y6 . xf11 rzwwm ,p(xkrvtktar system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a p( ,r6 2lpmvt,wkxxr11k yw .zfoint midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-ktyi6 rq 2hu4::/irq izg woman in an elevator thaqrtr i6/:iq2 4hu yiz:t moves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. bw2+dk ij3( ;x 16b5bxgc hq(xky/ldcThe cord can withsbdbkhdx qx36c+wx 1(l2 kyc5gi bj;( /tand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with perio i* mxzb:4hufesei/w z9t; -o4d T , the density (9xi zb:ztusm 4-f*ewo i; he4/mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (6 inil:i /eer*27.4 d) to determine the period of an artificial satellite oe:l r ie6nii*/rbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orb;x3q1 t;v5y;k ib oqupits the Sun like the plan1xt3k qvqp; yu;bio;5ets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.zk,d xr 6j5/ed5 $\times 10^{9} \mathrm{~km}$ 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 ondy8 bc25b7y,tyxmri.5 +zb sice 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?2z dxbbm8+y7ysc, bi.5ti5 ry 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 t /3gru..d:krpe tr- iahe Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the 9x1s2v2 w4y9rgvf0n4vqsz i wke+ b/u four largest moons of Jupiter (those dvs9w0 bk9qsi4g2veru x4 +1fvy/ n2 wziscovered 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 kno ;fvelf;7/kg)dy wnz0wn period and distance of the Moon. ekwly;;) 0 zg/dvffn7   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of: ml3kiuvj3qi*3os3f Jupiter’s moons, using Kepler’s third law. Use the distanoj3ifmi*3q 3l: vu s3kce of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of ej.iq3qn,e,k18-cgm u i:q;rts xu8u many fragments (which some space scientists think came from a planet that once orbited the Sun buuq t8- 3mj r ;xsiqqink ceg:8,.u,ue1t 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 ar5em mhsvw46c/tp udu8;s+x, wtificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabita ds m5;+/68t pcvs4ewx,hwuumnts 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 revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swi0sqm zuk51: fxnging 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 tolerate at the lk :xq5mf1s0 zuowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surfa*pay la vxq.:9ce will the acceleration of gravity be half what it is on the surfac.v*xa :a qpy9le?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutui.gf n: mg:d2zal circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are tnm g .z2igf:d:hey pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of nk ,o yw;lbqbi11mnz+r v2;s- gravity at the equator is slightly less than it would be if the Earth didn’t rota 1s vyibmb-lq+kowzr;1 n,n2 ;te. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will ,ir 4m+ xp4el: ,innqka spacecraft traveling directly from the Earth to the Moon experience zero n irqx,: 4k+lp,n4iemnet 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 aduwj +t+lel +wqr d*s)foa l-90kk7*s bathroom scale in an elevator, it says your mass trw *)sea*+d 0+-7l fjlk9w +ldqsokuis 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 ce i+ih/rf (j6frk/r *that will rotate about its cent j6rii /*rfkh (/+rcefer (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 felt?$\approx$    $\times 10^3$

  A jet pilot takes his ai5 uua)kzpr8k.9+f mhhrcraft 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 o3b91qat1ktwik-zrtiba 9 v8ecz,8w3map4m ,f a planet in terms of its radius r, the acceleration due to grav z-1,ri ,btacqtz3emi 984tpba1 a39 kmww8kv ity at its surface and the gravitational constant G.

A plumb bob (a mass m h:ot+w)krq0geg-k13jd;c ad 8p:wf/t w sxm,ianging on a string) is deflected from the vertical by anf:xa)1 :0kd; jwir/eptq,8cwm+sowg3td -g k 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 spe4r1xf/wp8b: bsh gc b8b2pox 7ed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car b2b x8f x7r8gb4cpw1o/h :pbssafely handle the curve?

  How long would a day be if the Earth wm uk;gwvyg 2q+ )z*1xd/zji8eere rotating so fast that objects at the equator were apparently weightl d w2e*8;k+yqvum/gi 1x z)gzjess?    $\times 10^3$s

  Two equal-mass stars maw7;zt wk n90dpintain a constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp / ;xpx3ihzz.l usnfk-bfdf1j++5* nv suspendedls-xf1h+vf+xp*n k.b 3;zf /n zui5j d from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive8kdp13i6of.y bvfejz9 5h4 kc as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't surviv9o68 fpb4ifhc3z ykj 1vk.d5ee 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 deduced the presmikxcwsxs,loa,z qe+h8o5 6lm ;+4d1ence 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,laow4hx ,sqd8eoms5c+ 6zmxl + 1 k;i 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 pxf+uhqyqm-1ze+qgu ro7 500: lo)or 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 do the normal forces actinu m+fro q 0x+-hlqegp: 10) ro5zuo7yqg on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellit)ysu,x+n2v3 f lmbx 3nbu(r1 ges orbiting the Earth. Using “triangulation” and signals transmitted by these sa +3nlms 1(,v x3 bxbr)yufug2ntellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billioiz9*ufvxf *44( /q (ff9prb wv.ymkdzn km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40f (fb9/vp miwx4zu ff.(ry *dzv49*qk $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . 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 x8kkv jq2 /8pnthe space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km qkkv /2j88pxn 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 pdwz7w fv c:06z8/0mps utt/pof 3000 years. (a) What is its mean distance from thfsv/dp t 8wz /t6cu0zp07mp:we Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" yo()ca,s:12eem b -4jaw2k zp: rzem4czti sko ,urself gravitationally attracted to someone near you. Make reasonable assuez, 1ce :-,s2:e2ts4krmp)ba(cwjzo kmi 4azmptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of dbl 48 rki +3g6oncf;hthe Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the ck n3c dfi4l;b6+ohr8genter $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the cornerszg5i r(o 9f4:h d5 n/pnvhd pexz3g8m4 of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fipnfh on(r54h /deg vxp3 i5 8zmz9:d4gfth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits theb ; b3 jgk u:7jsm zh6zmcb+4gf)mm8/w 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 tip of the 1.5-cm-lon2p+l3f kn:tulg sweep second hand on yo:nkl+t2l uf3 pur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to7 5o1h4pcppm5 vag*os swing a sinker weight around in a circle below you on a 0.25-mp*7p4g m51 cshaov p5o piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radiubng.-pp .hp1cf6tm 1n s R in a new highway is designed so that a car traveling at sthp ng nm1b1pc..-fp6peed $ 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*+5affrab c9kting curves. The angle oa*b5r9a fk +fcf 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 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.$\approx$    $\times 10^2$