Sometimes people say that water is removed from clothes in a spin dryew+jer9h49jen2 a0qhnu: o *b yr by centrifugal force throwing the water outward. What is wr+yuw9ho4j*beq e0ha :2n rj n9ong with this statement?

Will the acceleration of a car be the same when the car travels around t w(ddoh ny6ue7+ c8,da sharp curve at a constant8huy(don7wd6, cd+t e 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant:uynd .ydfi+) of+ -tp speed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch n dd. fonf i+)y+t-up:year the bottom of a hill?

Describe all the forces acting on ab0.8tpt m xvsdd f7v ppc82f7: child riding a horse on a merry-go-round. Wh7ttfs dpp8 vmd2:f7 0 vp.xc8bich of these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a ver fldzr,+9g 8f czc 7-(9oaufg+3lq zsyk 0aw9ttical circle without the water spilling out, even at the top of the cirdrfkzg 0 augff,l+ 9sq7toza- 98l9 +y3wc cz(cle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are aqzf. zjl o j08 xa9:h(k93zbuat least three controls in the car which can be h0kazf9qx lbo 9a3ju zj.8:(zused to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying ove)u7gw w2kml ls -dwa08r the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’sda 2)u w s80lgwkml-w7 second law.

Why do bicycle riders lean inward when rounding a curve at high s9; c ov)setj/7 r*6p wbwi*)cf3mhpil peed?

Why do airplanes bank wl wjdq ,8hja))hen they turn? How would you compute the banking angle given its ,h wl)jaqjd 8)speed and radius of the turn?

A girl is whirling a ball on a string around her head icu84qew(i c19 xw ugfo(c3ol9 n a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the str9o o8ef wi43(cwu9x1ucl (qgcing?

Does an apple exert a gravitational forc7 l4apvc5ll4w) rl k ,-q)uq/wvwnu2ce on the Earth? If so, how large a force? Consider an a745c qrk4)v-2/vwp lnqwl luc)a uwl,pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double + uxv+-mb +y34f ugqy8kozs j5what it is, in what ways would the Moon’s orbit be different5vyuf++qz- jk 4go sub83x+ym?

Which pulls harder gravitationally, the uzdj3 5cz;*mw Earth on the Moon, or the Moon on the Earth? Which acceleratd zw5;mj zcu3*es more?

The Sun's gravitational pull on the Earth is much larger t r4pmmt3+as jj dd+g r3.c12bchan the Moon's. Yet the Moon's .a d24 m3 rjrct13cjsd+bgp+mis mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh mo r3xf)vx2w uq,re at the equator or at the poles? What two effects are at work? Do they oppose each o 2xxwq)ruf,v3ther?

The gravitational force on the Moon due to the Earth i96xrvqq;f5wr p/3nzb0q werzy w* b42s only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from b/4 q0wvxpznz5q w*23e 6;qrrrwb9yf the Earth?

Is the centripetal acceleration of xj/f5t6mfg7hgoky-+ Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Eartg7yh gmtx6f/+5 -fk joh?

Would it require less speed to launch a satellite (a) toward the east or lal wj7:4pe(t (b) toward the west? Consider the Earth’s rot4e 7t:a llw(jpation direction.

When will your apparent weight be the )blwa hwmz,qlgnf-:gm u41i j* mk8m/(yy;x6 greatest, as measured by a scale in a moving elevator: 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 grounlmujk(m, g qf l;xbh4n6z/8g:iyyaw-w )mm1 *d?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversel zzxb iabd*z2s.(8b.ly 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 z 28*bxb . (aldbzsz.iobjects 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” betwcet n,-c2a lazsz0h q2+v,y2 seen cl2t haa-22 z,e0 cv,qzn+ ysssteps.

The Earth moves faster in its orbit around the Sun in January than in July.8zm0n0ovih5 vk:qc j9-vyvc(+ 2wh cj Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s a0:+hyjvq5hvj0n(98wmci cz-c2 v v k oxis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon. Explai:abzep x+ e.-wmm+5k rn how this discovery enabled an estimate of Pluto’s maxe+b5z +.-:kw me mprass.

  The Sun's gravitational pull on the Earth is much larger than t pa2fp y-+ovqt ,0)/yf:u wafrhe Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider tf t)oy-+yq 0va pw,pr 2u:a/ffhe 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 1920rfnmogo6nauzb , 8 (80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 th* od) rp ,vl9(t olttmhu,md( *l(/ikge Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume thatrt,lh to,( go)u*dilv/(pkl 9m d(mt* the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as i piy p(umxcj,96jkz7hj7; yj:t rotates uniformly in a horizontal cirj9c,;mz k7 76iyp(j:hjyujx p cle (at 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 Earth'8(pj5br-x oj ws surface, and circles the Earth about once every 90 mioxw8-bj( 5 pjrnutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the ed dz el*u+(ebtbk;g2b, ge of a potter’s wheel tur, ;+ebbl2de tzg*bk u(ning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform ratd ;1wpjor m+8re in a vertical circle of radius 72.0 cm , as shown in ojmrp 1;d 8+wrFig. 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 round a turn of radius n0ku j4bo-rz3lo7 iw*o43js k77 m on a flat road if the coefficient r*s4k7wk-n3j 30 bju 4oiool zof static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and the r yw; dfiom,y:0oad if a car is to rounddw f;0,oy iym: a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet figh ppr+3gwa m iq:r688enter 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 h6iaqppg +wnr 3mre:88er own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating w mjkso8v4 mn1:f,ju4 turntable of variable speed. When the speed of the turntable is slowly increased, the coin r4,wou 48mksmj: jvf1n emains 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 roller coaster bee2ep/j7 dz o*v traveling when upside down at the top of ao2e *pe/zvj7d 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) crossesf+ l(8 operg*y the rounded top of a hilfp+g*8eyol(r l (radius =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 whc+sgp 74tfy5 aq1u*would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” hsctyg*57 q+p1 4a ufwat the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertxtqe68pbn ) i7ical circle of radius 1.10 m. At the lowest point of its motion the tension in 8nq bxie6 )7ptthe 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 9.00 cm r8 oojhe+1 p(+rqzn;k /20wfb q8eq myfrom the axis of rotati zqq8y o8;+bpfrk+o0jeqr/w(m1hn e2 on is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyliros;1(e 5adgj ndrically walled "room." (See Fig. 5-odj;a 1e5 g(rs35.)
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 fric j (arly)g2m4dtionless air-hockey tabletop, and is held in this orbit by a light cord connected to a danglin maj)2dry g(4lg 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 ig7(- uha ms:ttgq7r)e a y7iw cqaw3d+1noring the weight of the ball which revolves on a stri( e:wi3 aah q)tq1ugctrm d-ws7y+7a 7ng 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked 2sb;zm2l rq7m for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

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

Two blocks, of masses tl(8 zwg(u2h 8i dxw 0w,7bzlg$ 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 atvr2ru.d ; ))to4mzeotj vs2gjqv(3,yic.hc: 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net force exerte jl1f39oas*rhd on the car (by the groundsh9 r1lj*3 afo) 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 ape0x/xmc 5okcz)xsz31 vop)d*ijd:6 ccelerates uniformly from the pit area, going from rest to 320km/h in kxv:d) *sc 3 p6m)iooxd pcj1x5zz0 e/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 . At a partic m)vng z*cbtgs*-r0b-p 80usnular instant, its acceleration is u8b* t ncng svz)-rps-0bg0*m 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 Ezkdc:qdby -ti2,p i4zm7*bzx4ut l 33arth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface ikx 3b l-dzm3pq:z2tdtyi*4buzi47,c f its mass is 1350 kg.   

  At the surface of a certajc39lylt ) c9kin planet, the gravitational acceleration g has a magnitude 9kt3)jcyllc9 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.q.lga)u x )qx9shyy +u(b8t3h The Moon's radius is 1.74xu8)ql( b 9qyxhu a.+ 3)tsygh $\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 same mabrt-8 ;,kajedss. What is the acceleration due to-8a;detr,jbk gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radiusfxnsj -8* a 423r1drlqaso6x z;5pfia. What is g near it8;p 1-azsf4x 5dixq2la6*oajs nr r f3s surface?   

  Two objects attract each other gravitationk)4w-e gi1sv*b jna g+ally 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 acceleration of gravity, atwz, jy6(o0 ew;fh uypdr5o7 s- (a) 3200 m roeohz;y 6jwdwuy(,f0- 7s p5   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cent)ia1osq7 s)dw, qxf/ he:o7 swer to a point outside the Earth where thegravitational acceleration due to the Earth isq )7i)xwo hfd:w/1 s,se osaq7 $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packedgr qzbggs.-xr r-k; (d4; 9qbm into a sphere about 10 km irgkb x-gr4dq bgm; s.r(-q9z ;n radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avehse68-ct f3h qrage 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 hcqft e3s-6h8 our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitru+-pt)q ogn2pskk9xqz( 2k8 ing in the space shuttle. Your friends respondqrs82-tp2 +uqpgk9) x(n okz k that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square oix.kvbrrk d8nh(.+ i9f side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one spher8 (r.9ivrxkh id+. knbe by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yearsoyky1lx 8h6o;e+y1--r;la kdmq m o)p most of the planets line up on 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 (Fig. 5-38). The mass6koy dpr 8 oheo1ym -xyl-;+a;1qlm k)es 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 -e/7xgsikvyf:wzd ;* of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 34 ef;*yzvdw g k7-i:/sx00 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period .rn3 08q4s2wgpv8kmwr7r3n wfjl9pm * c l5ifof the Earth 3p48 *r rmm.krsn 5l2j f0wwq9fw vcn7 gi8l3pand its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable 5tl as/x .as7b4 :j jc94ulzqgcircular orbit about the Earth at a height of 3600 k.b:97lzqjata/ ss l5juc x44gm.    $\times 10^3$

  The space shuttle rele;z re ,s4+iuefases a satellite into a circular orbit 650 km above the Earth. How;ez,4f ru i+es fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupa2: zkul q v*7u(oiyo0o 9xvx(mnts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time neezokv:( uo( uxml7o0 viyqx*92ded for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circd8 zj;d mfgh7,56vxe pular “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 yourh8;d ,j5xe zvd6pg 7fm result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity wouldba;f)o g4 lmy:wa r09;6kena i a satellite have to be launched from the top of Mt. Evwn4gm)krf o;aa;b6e ly : 0i9aerest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orqy, qj67 ( nx2fnev1jtbit the M,xy26n vjj1nfqe7q (toon at 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 chue iga8a-skc( 6hvmk5.nks of ice that orbit the planet. The inner radv5k aih.-acgm8 e6sk( ius 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 dy o 5 8g zrs8l3(shvwuj3;zl.diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight t8 33 8o(h .5rwj;lzgyuzssdlvo 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 the cent *ru)8+2aago sg z v*mueum.c5er of the Earth's*+2c*mveum a8 zs5) o ugga.ur Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consisthu/fb(ey+- 8syga,kb2 6 aytms of two stars of equal mass. They are observed to be separated by 360 mily m(skhbfua be2 y+y-,68g/talion 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 r;x 80b9gfm)x j4mkyfyead for the weight of a 55-kg woman in an elevator that moy4fxf09 j km)bxmg8y; ves
(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 t9z odsh aqf,0 mp6uqcmnrr8 3-;m1 :iahe ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimupcfqi,mhaomnq1z 0u a6s-:9drr 3 m8;m acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a p bee52nj)age 83v,odi q6p+ oblanet with period T , th)bd6eigo,eb vja3oqn e5 p2+ 8e density (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 perihnd451k 0f rlsod of the Moon (27.4 d) to determine the period of an arti r 5ds14k0nhlfficial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters accqdwbfi q/(b*a4 p5k1ross, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from q/af1b(4dck*ib5q wp the Sun?    $\times 10^{11}$

  Neptune is an average distaj,vgbyh m.n1 (nce of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughlyp u*na6hhf*i1 once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there?au*h*16hf n pi [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 cenc: ,e8xo sxn vim:jml8 9ea,-nter 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 dis c-,c iyjxh7zi3x. 4ratance for the four largest moons of Jupite 3jhi .4,-xy rzcx7iacr (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the kno3 u6ldctd4)vjkb( ug5x ltv07wn period and distance of the Moon. dkctd3 07u)(v l6v5 ugxt 4jlb   $\times 10^{24}$

  Determine the mean diskz p3k -/b hwdeop (4if8oo-b+tance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare twpo8eo kzbpbh-3 fko(4i+d- /o 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 awrd;r, yv w2g6nd Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but wav; rr6wgy, d2ws 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 artif9hy ;bic97d3eaqx7n k icial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). 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 9d xq 73i;hac7eny9kbthe climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in 9 3 e2dqjnms eeolkl23h1 +mn/mt98hcau;pc .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 lowest point of his swing? His mass is 80 kg, and the vine is 5.5 mpe2/ 98 mqu 1cmj 9;.lncnh el+3oa de3hstkm2 long.   

  How far above the Earth’s surfh+ te+upg 14q;eeed7 t)j* ofxace will the acceleration of gravity be half what ifoj 7e*eqt+g+ xt;4) u hepd1et is on the surface?    $\times 10^6$

  On an ice rink, two skaters of e84 zvi azq ut9m0ingxken59*+ qual mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.ti+vaex98qgzz* n94 50mkiun80 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 acceleration of gr3wd8;3--+xl9e yu vg)2r ijstcelx goavity at the equator is slightly less than it would be if the Earth didn’t rotate9g-y8 gse3)o+je; licxu2td3x l vw -r. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from gsn.+i3mndj,mle 0sp-4 o i9x the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal a3,pl- .se nx n ji+mmd4ig0so9nd opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you sw 0pu+qtz.xt:+qj9p rtand on a bathroom scale in an elevator, it sa tt 9 +jw.zp0urxq:qp+ys 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 wih45 fvbe +7u+ ztrj)kfll rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect eeh7ktf) brj 4v 5fzu++qual 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. 5–4307z y0 nlnt24 m3yp izi7xnnf+).
(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 kf4of6py q gz1+v* zk3oe *dik;( pfduog x+*,in terms of its radius r, the acceleratqifv zeoy d4 3xk*pf;z +fgok1dou ,(*+6pk*g ion due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging oy-mlai5i,w4faq x(3 xn a string) is deflected from the vertical by an angley ai w ,m(xxq4-fl53ai $\theta$ 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 - mv 8+vsjif,jbanked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a cf jsv-ivjm+,8 ar safely handle the curve?

  How long would a day be if the Earth were rotkr1m6 7tt d/qo4ox,k-qv iuy3ating so fast that objects at the eqmo61t ,7 43kr dovui -/xqqktyuator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apar 1u*rjeup2:5x8mn ksg t 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+;ws mmcd,g,2o awe t- rounds a curve of radius 235 m. A lamp suspended mw+cdao e,g, ws ;t-2mfrom 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 massive as the Earth. Thus, it han0cbqno pe 1s+yp8r6oav-) cp w cv(2-s 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 fo wpq)v0nc 6b-- n8operyc1 vp2ao (sc+r 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 presence of an jd 0 vz.9*emoiextremely massive core in the distomj z i9ve.0d*ant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core 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 const6wt6gpcpq9r6 ant speed 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 acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (r pt6qp w66g9cc) 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 satel7zr6.eg fu- q 0r)zwvglites 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 approximately 11,000 nautical miles [1 nautical ]. (a)qegr)r . u7vzfzw6-g 0 Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Renkvop0k f*c:v 7dezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughlyf:opv0k7v ck* 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 pursu97zwat3y5:pbow2c hh ing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above theph wobh9ta52: yc z7w3 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 mea x; fz 22f)ta;mrba*fjn distance from tf*fxaaz2fj mbr;t ;2)he 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 nee1tlafb7 84 tqkd to be if you could actually "feel" yourself gravitationally attracted to someone 18tf la7 kq4tbnear you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky*a9z- + wfl ;j4ndmfgs Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from th*gal nf;4 jm- z+sdf9we 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 square tc :33c+rzx) 6 trmcyq0.50 m on each side. Find the magnitudzr3t 3)yx6+ctc :rcq me and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ear;4fcd 0b-wvr)r s uo-/xxcfpqg 0vc,)th $ \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 tia3unf v5l:p )xud)a/xp of the 1.5-cm-long sweep second hand a/auv x3n)pl:fdu5) xon your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a 8 (x9zqq+ka3 j/xaav0r2dnprsinker 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 axa +r 0vadzqx pk (qj3982r/nline makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car traxfyx q5(dy: ttllz02+veling at spe( tyy05tql:+zxfdxl2ed $ 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 negot jd,ofmx-il7 6ln8 j:9p (wk7xe(yjuuiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal8llj jmydxif,u( 6j:x -e( nuwk7p9o7 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.$\approx$    $\times 10^2$