Sometimes people say tha lq+ 0ar1sogn(hr4v 3vt water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this stls30(1o g4av+n q rrhvatement?

Will the acceleration of 5grxsl 4;l,tzwcfm1 jerq kje-d , 3:(a car be the same when the car travels around a sharp curve at a constant 60 km/h as when it cd lkjg-;:z r1, e(s jrl,tmeqf5 4wx3travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alw6:+t a+dhj-q pl2 bkkong a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip kjl kbq+p62d-wa :h+tbetween two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a ch2e uurygx+pu.sh p)9+cf e2ot x)t;s)ild riding a horse on a merry-go-round. Which of these forces provides the. ueg)h; +syse px) )9pcrtu+tf2o2ux centripetal acceleration of the child?

A bucket of water can be whirled in a verticakk+6// lxpp*3) l jk*klhpfjvl circle without the water spilling out, even at the top of the circle when the b lh*/fj3kp/p+p*k6 ljxkv )lkucket is upside down. Explain.

How many “accelerators” do you have in your car? There are ai q t981 b)rt 4cytaw,+mvkt2rt least three controls in the car which can be used to cause the car to accelerate. What 2brt i1tv tm8wy9,+ )taqck4r are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as b s hcjvm7x*14shown in Fig. 5–31. His sled does not leave the gro 7j*m4csh bv1xund (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 w*qw sove 7,fc3hen rounding a curve at high speed?

Why do airplanes bank when they turn? How wouc;d3p5gka3gk4c bv: lld you compute the banking angle given its speed cav 3g p5k lbgdk34:;cand radius of the turn?

A girl is whirling a ball on a string ar 5gjh* ,v); mp 9gemfb3inl5vround her head in a horizontal plane. She wants to let go at precisely the right time so that the ball willi5;3fg*h v mmvj5egbr n,pl9 ) hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitationk dj pm( j:09(1vyysescwan/dzm,()dal force on the Earth? If so, how large a force? Co ,: zd 0)epc(ssm nyam(wj/jky1 9vdd(nsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s q x;wb5p gbtt(2lzm9sew f8eh3/3* qgorbit be diffeg 8fp2 tbz3hs9ww5(q *m lqet3 ;bxe/grent?

Which pulls harder gravitationally, the Earth on the Moon+ gqm)1:y 6nagx3byz ;i8xm;rf t*dt k, or the Moon on the Eaz+6y my;gbi *at;dn1x qrx 38gtk):mfrth? Which accelerates more?

The Sun's gravitational pull on the Earth i d.3ylmc1(s2o f4sj vcs much larger than the Moon's. Yet the Moon's is mainly responsible for cc j1 yld s(o.m24fvs3the tides. 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 at the poles? What two effect iss8kw2 /1rt gft z-9m;6z/c+ncuqqts are at work? Do they oppo;91 fk 2nizc/-z/+qmt t8 wgtssqu6rcse each other?

The gravitational for.84wrcoi 5 ;4.st6awnnkrc w zce on the Moon due to the Earth is only about half the force on the Moon due wwk cw z.i8na 6c44no ;r.s5trto the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration ahz)c)iy 4ju+ of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Eijz yuh)c+4a) arth?

Would it require less speed to launch a satellite (a) toward- wd9te dh-n/5a4vjd- pxn 4im the east or (b) towardjdxv- n4d tpimn/ ae -dwh94-5 the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in z87 9phb+ ryfca moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fafp7hc89+ ryz bll, (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 bmypxg)y:h1rt teh 5*t2i k8 fq+ j,c(ze adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fij1 :2)*ctmrg thqhk, t8+x(zy5eyp 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 falhx,u(lm6nf/gys4z cw5 77doz l” or “apparent weightlessness” between stepo6s,zw(ly4nghm5 c/xu7z7fd s.

The Earth moves faster in its orbit around the unj 0r9;d5v g2 3uod)idkr9eiy3k ss, Sun in January than in July. Is the Earth closer to the Sun in January, or in July?v edjdr2kr ,u;gs5i)0siynd9k 9ou 33 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 noc bh:uo*/br+ytq;s8f hcgujc ik76i3u -0b.st known until it was discovered to have a moon. Explain how this discovery ena+hbtj6 yb ;uf-o usb08c.ic7hrc :qu/3gk si*bled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much la md8vs/nqy56c rger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Cons5qdy8vc/mn s 6ider 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-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 198lt1msb cufxp+77 *i:t0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 arol2(0krts00xr (z bdq h5h6otlund the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit ir2lrsb(5dkxt6 hzq0 l0oth0 ( s a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rp9h yg:kjk3fkqisv -x(k, h8* otates uniformly in a horizontal circle (akk8j py* k-hf9v(gk,hqi 3x:st arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earcq oe)fs0jz 0p- zgajd7ap: y2 hg+5z4th's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g pjazoq2z0 5ed0 h gp-+c:zjysf)47a 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 edge of: g d-gbe dwo+c9nmk79 a potter’s wheel turning at 45 rpm (revolutionm:gc7bgwodek+ d9 9n-s per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a stringzu)grue/hbx )3gz4b qb 7mt)+wst-q0 is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as sho4w xqse0t)zt )um3u/ -qhr bbg7b )z+gwn in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a vy5ubds cs, ; *a. 3f:xx5hdab1050-kg car can round a turn of radius 77 m on a flat road if the coefficient .bsb:*v d s 5f,x5xda3cyhua;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 thehebywgy;n5.groq :s pj67)2d tires and the road if a car is to round a level curve of radius 85 mgj;y5 q )p6b ghw.d7r seo:y2n at a speed of 95km/h ?   

  A device for training astronautxg1v 7sr j-, +mo:(3fp sfrxfbs and jet fighter pilots is designed to rotate a trainee in a horizontalffx7-r,b+o s1rsmfg :v(j3xp circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a flp5g)wd5umtt-+c q-3 bbz75xjw - xk rotating turntable of variable speedt -5j-c-tq wwg bx p35dz7mbf5u)+kxl. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rolle4 mo.0 hq hos4eg4jlgvl(5qu7r coaster be traveling when upside down at the(v5o h4ql 4gme 04s qohj.7gul top 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 toqp:vg 0uju/8yp of a hill (rad0 p/8jyuvg:q uius =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 Ferris wheel need to make :hci e); e.1*h ,dhkcxm jn6xyfor the passengers to feel “weightless” at the topmost e* x ym.xncc:j)eh6,idhhk;1point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of / d;;qb.)fenc i2zzre radius 1.10 m. At the lowest point of its motion the tension in t zez;ce)2;dqi.rfb /n he rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9-jp e q,t:5rdwd5ue p8.00 cm from the axis of rota5qetw-:d r5pjup d8, etion is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylind mv1- eel:oaah3 tak3dhq1b5ot 4b 9l,rically walled "r1htoe3lk ebvmt:a-1,od5 b4 39ahl aqoom." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockeyi7l8kf8. xmk. bgch2 k2f:tle tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as .28gt8e c: xim.fkhblkf2 k l7shown 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 , pd5 ,5beszpd+1 o gtp9precisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m l9b dp e5 ppo5+,sgzd1tong. 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 perfectly banked fo 1 6c7evm(fg0udm:0ehsy gdg3co :x -er 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 masses.h rth i::hom 7j)yio/ $ 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 evasp: ;vt;iph :ubive 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 tangential and centripetal com fcgel /7*ne5aponents of the net force exerted on a 75fcg*el/ enthe car (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly frt,:fzrbi4kze8h 2e + mom the pit area, going from resi z+rekb2f4h8 z,emt :t 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 skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . Asz;yo* 5q6z7k a7bjwkt a particular instant, its acceleration is 1.7k 6 57o;zbk yjzs*aqw05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 * e(alsvjb -xotgj.,* km (2 Earth radii) abovx*- ejtsv,l j b*g.(aoe the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratio *du cha(y7dn2n g has a magnitude of 12*2dn(7ch ud ay 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 Moon878q hn, cwco3qlzj i/. The Moon's radius is 1.73nc,ci w87jo8/q lh qz4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiu;k s2bb z6xah;s 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surfac xba6bkh2; ;sze?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sambnp;o3tsn v0 5e radius. What is g near its surf tpb30;onv s5nace?   

  Two objects attract eacai4ket,0dc i3m be7h ,h other gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the accr:5ncu ihn /s7eleration of gravity, at (a) 3200 mcr5h7/snnu : i    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance fros-rn1(8zuepz2wai7jvw q7 )hm the Earth’s center to a point outside the Earth where thegravitational acceleration due to the Earth)ia7 znvj swwuze(7-1 rq p8h2 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 pacb6sov1u7k-b;uh h5w k3 i .s ,hshoj3uked into a sphere about 10 km in radius. Estimate the surface gravit1s33 ubi ush,5 ovok6ku7-;jbh hswh .y on this monster.    $\times10^12$

  A typical white-dwarf star, whufustlgp 5 84*ich 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 mass of our Sun. What is the surface gravity on this star?8uts p*5l4 guf    $\times 10^7$

  You are explaining why astronau/(+o3p2jqtl1ah 3 feqf0wnqots feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up t f(hoqj/3owl 3tp qa1fq 02+enhere. 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 square i 5u:xo8 jlon g,*k2fkof side 0.60 m. Calculate the magnitude and direction of the total gravitationol8j n25g*k ,k i:fuxoal 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 saip f( :vdp)bw+me side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and p+v:b dwpf) i(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 gravig5 xsb5jjo/9fd ) 8jsctb+o(xty at the surface of Mars is 0.38 of what it is on Earth, and d jgtxs5cos( )fjj/+9bxbo58 that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using th xdd+fz: y2 t5sp2lv5ve known value for the period of the Earth and its distance from the Sun. [Note: z 5+dvtpvsy:2dlf x25Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satwtx h3-a(khj5ellite moving in a stable circular orbit about the Earth at a height of 3600h5 x3w- a(kjth km.    $\times 10^3$

  The space shuttle releases a satellite i 7cspx0zpo:0tnto a circular orbit 650 km above the Earth. How fast must p ps0t7xocz 0:the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate hs5txxvzkmya / +):a)if occupants are to experience simulated gravity of 0.60 g? Assume the spacesx yv mz)aas: ht/x+5k)hip’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 takes for a sas/f*jtq ps4i+erslrdm 4, 0 wtmfc4: ;tellite 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 the Earth. Does your result d 4fj 0mmp cs/i,;tr ed*4+t:srfls4 qwepend on the mass of the satellite?    s ~    min

  At what horizontal velo02333 9u2ozp v ryfwwvuww(vg city would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit a3fwvw wuv 30w( 2p3gyv2zou9rround the Earth?   

  During an Apollo lunar land sogv0h,x;l;xf2 trmh- akihsl * 09f9ing mission, the command module continued to orbit the Moon at an altitude of2s9 *;m0 fas9txk-0ollvixh; f,hr gh 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+otbdjp*7xn + 6 io)dd orbit the planet. The inner rd+tdoi6)n+j 7px do b*adius of the 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 diameteax 56kko(aiq7r h+wq4- ulwp: r rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the p(hax7uq k4w5or6+iqal:k - wtop, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from thfyi;(nteuz r/.1*k 1 gms0nlie center of the Earth's Moon in a space vehicle (a) moving ay0 fr11 ;(sm eiiknz.u/g*tl nt 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 of3+z+g +mgfo98uyud cf two stars of equal mass. They are observed to bf3+z m+dy+ufc 9oggu8e 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 t8z0wzf -nx -jweight of a 55-kg woman in an elevator that mzzwf8nx-0j-t oves
(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. yd, rs2l*f.xg1vi 4duThe cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnituu rl,sg.yd42i d*1xfv de and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with periojsus4 pi.2j 9 acdm 9.hwzw- knx9;0ald T , the density (mass/volume) of th z.pdsx4jl9 h2m ckjuw 0a9snw;-.ai9e 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 (27.4 d) to determine the perienk+(- u;kva-lp8n 8e jd hdp(od of an artificial satellite orbiting very near the Elk(e kp+p(;vd-au jd- 8hne 8narth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orb;-pyt pm 7s8xpits the Sun like the planets. px ps;-7tym p8Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average diszu /w s7 .(p6f)sbw)b6ryk raytance 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 thkca g74tnp0nb79 v0lz e Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still t07 k7 pl9nbgcvn4z0a“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 cente6gtaql:2k3 vf)js)+ jsq )rb/gxks497bon a yr of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean u 7o pmk*yx:xl,,x t8jdistance for the four largest moons of Jupiter (thosu k,7jo m xxlt:y*8px,e discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Moot(. ai*41b yksl ed.d+c;hz qree-er8n. 1.req.eha; 8tby+-(c esiekl 4z*dd r   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’/sfd.(q9:8di szc 1s l ,erlcws moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the va,w q/9sl1li(cs8 dcfdes.rz:lues 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 fragments (which sr03ypje( n5 /qk zs)dpome space scientists think came from a planet that once orbze s (pjn3dry /kq0p5)ited 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 of a ban 1;ouxwxlh4tr0 ;hpcz. ddm1(tzz 6y 1d 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 perxoczm ;1 6p0ux;zlt1t r(1wd. zdh4yhiod of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge jg apjog ljqptv 0v99()9-mmik70 bt4by 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 maxi4vtpg(-)o9qpjgjlt09bikv0 j m7a9 m mum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half wh-lmssga5) v2pat it is on the 2s mglp5 a-sv)surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual cio3l w*l.l: vvvrcle once every 2.5 s. If we assume their arms3vvll:o .vw*l are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acbvq)( 6 d 7lszrm(c)r- ppug:cceleration of gravity at the equator is slightly less than it would be if thg(dc:rmsqzlc-(b)7 p6)u r p ve 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 travef4c x +q:amw,30xjvm p-uc h/lling directly from the Ear+f vcw q xc,xlj-am/4hu 0m:3pth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a apa 5qtgv3 l:(bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which directiqp5t: (vagal 3on?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotat1fo y8dldvmriy ,ql /pgxi ;1m;** t*le about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at tv,t1p 1 dg/y;xl ;f8mqiilyl*or * md*he surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in g 4(uo 5xbqu )pcuueklo9ziu9 )y8)m3a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, thjv y2pa7ev, ko vh q/14aewp1/e acceleration due to gravity at its surface and the grqvweej4y o, v21pkavh /p1/a7avitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical in 9ek+zw7 uw(j5dt8iby aiu n+jd5 tw7z( 8eiwk9n 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 coefficient of z4ea3ap ls4wk:xl2 5rmd5-k f static friction is 0.30 (wet pavement2 aef-4sxlmlpa 5 5k3zkr :d4w), 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 the e2sp5sn4 dqr00gz mi -og 4mr0zo2i0d5qnp-ssquator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maint0x87uvs dpxn ) ocig+,ain 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 csjwje 9/4n/j:7l1zrbtoi la- onstant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an anjltwjb snj49ar//1: e7lizo -gle 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 b xx xrnqfvzd4)d ,6:-b-p lys*7;dichas been claimed that a person would be crushed by the force of gravicp d-dn6;sx-x7yf4b d l v)zx*b :i,rqty on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubtvb*;5eks4 zv ble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). vzbv* 5 e;4tskThey 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 thege*.yhw9p(w 6f1nyijxy:zz(p, r h o, 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 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 69 .*w o: nh(x,g z1fpe,ywzyhirjpy( losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 saz 1wwoca.j*g 550rh jdtellites 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 sag *drjhc5jwwao 5.01ztellites 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 billion km, r 4j;nlr 1h6esklpy u)9g(a.yis meant to orbit the asteroid Eros at a height of about 15 kmp 6ge jl.yk1h)r9 4nas(uy;rl . 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 sa/1t hzeff,qf g; sdt1(q8j-kktellite in need of repair. You are in a circular orbit of the same radius fkfgkh;/(,tf tq11 -edszj8qas the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean d)n :wzxbvo c7n.d)h2qistance from the Suz)v n.2nx7owdh)cb:q n?   
(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 wotloi zi3:by- b;r: 9-tx5l 3-qc7gli9huftcmuld need to be if you could actually "feel" yourself gravitationally attracted to -m uh:;9 tli-5 7b933:o itzqbrgifc xlcly-tsomeone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the centers:b8hml cfrvo5 v hz (k+4h2n4 of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30 hkshr :zf 4o84bl+h52( cvnvm,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a squarwqjo8c4.ew (9gk yj-d e 0.50 m on each side. Find the magnitude( jckdyw8.w9jqoe g -4 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 k ig-cw83*xkkk/azp9o g orbits 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 tip of the 1.5-cm-long sweep sec g.d1+ojtf 6pl2a3khqond hand on your wh. j1dqoaktfpgl6 32+rist watch?    $\times 10^{-4}$

  While fishing, you get bore16kt:my6f w hpd and start to swing a sinker 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 the angle that the fishing line maket 6k yh:w16fmps with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new hqt z3nvj,;m52hw k4: n igrsl+ighway is designed so that a car traveling at speed+3w5mlkr n4zjqgvt,;ihn :s 2 $ 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 negotl dtx puguh:e5w8::2n0i1ri miating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt.58hp nm:u0:1ei2g:td iwur l x $\approx$    $\times 10^2$
(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.$\approx$    $\times 10^2$