Sometimes people say ,+lgv3su e y5m**dt *gzunk;mthat water is removed from clothes in a spin dryer by centrifugal forcete +u gdl*3mu gzsvmk;n,y 5** throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a h7.in r7d;z- tgdeh hf540bmqsharp curve at a constant 60 km/h as when ie i;z74dqhg5nfdtb-0hm7 h r. t travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speyst9(qnq;ezh6hig i-6 xbt7. ed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, ( 6n.g qh-9yibt7;ehzqi6 x(t sb) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-aqm o (iy1yzo8elyq j2s27 *8tgo-round. Which of these forces provides the centripetal acceleration oqyylm s1 ia8oqz82*eo2 j (t7yf the child?

A bucket of water can be whirled in a vertical circle without the water spill qu w*k4gm*3f3d0eztwing out, even at the top of the cdk*fwt4*m03zeg u 3qwircle when the bucket is upside down. Explain.

How many “accelerators” do you have (84q eyh*kj dxe luio8c)60; hcmubg:in your car? There are at least three controls in tlc;b x4:kiquhe*cy ohguje md) 0886(he car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fe,9nmnyf1g o9 ig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force betweenef, 9nm1ny9 go 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 aghdh iv: g).s p; e: 6x0voath4zct*1rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compugfuvw m )h1t9+te the banking angle given its speed and radius ofv twum1g9+ )hf the turn?

A girl is whirling aozxx 5vot((0zic4s ,q ball on a string around her head in 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 shov(o(q5c4 z,txxoiz 0suld she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how largb t;n 2y+l;2 (y etptse:)z7f bsxb*swe a force? Consider an7x ; ;stpe :)bbtb el ystzn(f2*y+ws2 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 oz z/z0p1.3rh+.b+tr na ui-nzovrzp9rbit be 9a .unn-rb0+zp zp3rtz zhv i+o/rz.1 different?

Which pulls harder gravitationally, the Earth on xl o) jlvkf3 k1ufp*30the Moon, or the Moon on the Earth? jlf kxo1ukf0p* 3lv3)Which accelerates more?

The Sun's gravitation m.z8 wedk78 u8y*flesal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the 8*myus8kdfezle .8 w7 other.]

Will an object weigh more at the equator or at the (g4cik 3*zbr(-cnts xpoles? What two effects are at work? Do they oppose eachg( rc*(xsi4 tz3-k bcn other?

The gravitational force on the Moon due to the Earth is only about hapsgak91velq6 -2 w iq7hpr1*bln 6gd;lf the force on the Moon due to the Sun. Why isn’t the Moon pulled6qwaend9gsvkbq;g2 -p*61i 1l p 7hlr away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or vdx q lq0efr72+v-u*z smaller than the centri*q drzq 0l+vue2-v7fx petal acceleration of the Earth?

Would it require less speed to launch a sate*0z,h rgxm a.cp;/j anllite (a) toward the east or (b) toward the west? Consider the Earz.ah/pc an,gj0x *;rmth’s rotation direction.

When will your apparent weight be the greatest, as measut:pq y :jrf2m 1ha3rt)red 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 the2yaprr:) tf q1t:mj3h same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend lgj-*3i3r p,wgiuv v(oong periods in outer space could be 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 invwg*(jro,- uvg33i p iside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiesh-1ytvay/0 ob 5 -yzances “free fall” or “apparent weightlessness” between step th/bv osa0y15-ayz y-s.

The Earth moves faster in itg27h.duu a:jjapae(+ s orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in prouaj ad +pehu 27(aj.:gducing 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 a moon. yk6o72vm.d(:k1 n( innhks6vl,cc rpExplain how this discovery enabled an estimate of n.l(r myk k(1h ,i6cskovcnv7d np 62:Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet 4k:.qsh:1dgp l -tm obthe 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-round moves with a speed of 1.4k:h. t- opb:l1dq smg25 $\mathrm{~m} / \mathrm{s}$ . 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 ljsb4 *pnc1ns6zhw8*/y ft/b 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 arounq(f4q cc5 0b4mupnr9bd the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.rqfnq c594cubb0 p(4 m50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 21z8 0 l8jln j+q3:ekih ;t7ztsi0 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at ar3+kiqj7 itl h 8e 08jzt;lnsz:m’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's surface, anpdat : jg/i,r8d circles the Earth aboujrt/g pad ,8i:t once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelerationmbnr,n5 je k0ez*:1n a of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheeam5b n 0,z:1nk*eerjn l’s diameter is 32 cm?   

  A ball on the end of a string is revolved at cpm6mog*)j zmgc-m )pk+x 5ljpd / r-0a uniform rate in a vertical circle of radius 72.0 cm*/kom)z dmj-c0 5+mpl-g xc 6p jp)mgr , as shown 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 rzjlw2)tat t ps9 rt)j,3ci84 with which a 1050-kg car can round a turn of radius 77 m on ir zr a3t4wp2 )c)jt8l ts,tj9a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficie1 2j vzsgw rsv.9 klh+al/*+nqnt of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 1hnk9 ws+/. zr*v+ sj2lvgla q95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rog:vesi)+ t c,at* )xh47mom tqtate 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*htx+tvq o :ice,)4m)at7gsm 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 turnof8q4o6xriju :jr/ 9ntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is :i8foro/q u46n9rxjj the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be t6vhoe :dcd j,8raveling when upside down at the top of a circl 8doj6d,vh ec:e
(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 toq.i phv+b1raex,d i,, p of a hill (radius =9a,h1dq,e,+iv ri .p bx5$ \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 kl -1fvny9,- kzq(ydyneed to make for the passengers to feel “weightless” at the topmo 9z1vqfkydyy(-l -,kn st point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. Awlgb wmnc5 yuo58x0).t the lowest point of its motion the tension in the rope ) 0by8wu .onl w5c5mgxsupporting 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 u9gl3z rzypdg+l 6g+ut +ox,/the axis of rotation9/z3l+g z 6rp ygoxgt,l+uud + is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "rj1va /qj2d- ev,jwoo (oom." j (ao-vwe v,2/ j1qdjo(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 ) : j .:xlgb7*rogsatbj(o o)o.is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a o.oxt bj srg*()a:. :b7jolgocentral hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignoring the weightr9jzq4exhj 131oyd8h of the ball which revolves od hro 8ze3xqh 1yj94j1n a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked fo-+y hxbt sff6+r 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 m+ii198kt k 9)0j0zjohmf iib $ 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 div7kgw1om u- at(gfb3;ving 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 tangentiwjyk+qn 3rl*sf9 )1g gal and centripetal components of the net force exerted on the car (by y *j3r9kwn lf sg+q)1gthe 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 ug3,qra kqx)ee3si 2g( r.m+zd niformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this accer)xg q2ri g+(3.z sqkd3,meaeleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a u,fh/uc*a- g-emekya+ v dq2n4u3s9x particular instant, its acceleration i -vud qe-ahf*mkyen3u2 c sa9xg 4+,/us 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 0s0)t4 zm de fuw77xycjr7ji7gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if iy0 )xe7i7u0wmtj 7d47zjcr fsts mass is 1350 kg.   

  At the surface of a certain planet, the gravit ms/bnln-pr.e+ (b1zpational acceleration g has a magnitude 1-z+pnm es(nbbrp.l/ 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 radiu3xxj(+d:lz 8e/qnyoq s is 1.74yx l eq3o8q :dz+/n(xj $\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 of6mdx u5.tv)5fqix c)b Earth, but has the same mass. What is t5 iut6 x).v bd)x5mfcqhe acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, yi54t,4gshsli7 ox1 yuhsf)ero.q2 6but the same radius. What is gh6x1y,4o sir.f )s qit4 eul7shyog52 near its surface?   

  Two objects attract each other gravitationally with a f/.+.jqao 0clcin-ec norce 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 gravit ov .yszoj8 1ov3q*ff2y, at (a) 3200 mov o*q1vf jfy2.3o s8z    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earthyg )npeurs* . 0di5,no where thegravitationae.ryi, dupn os) g5*0nl acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times thy jbu4c+ung.7+ ir/ oxe mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity or4u+ ngxboi .u +j/cy7n this monster.    $\times10^12$

  A typical white-dwarf star, which once was an av;1kvip r ud5 6:nizxp(xl-* eqerage star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass x p1v6 erdn:izk5lpi u x;q-*(of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless n3wgz-: k 5f8 2jz2k4xey0ii ovb e7riwhile orbiting in the space shuttfenbgj4 i0v -:7ye x83zriwz2 25ikokle. 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 Earth’s surface in terms of g.   

  Four 9.5-kg spheres ackzde m473u2 dre located at the corners of a square of side 0.60 m. Calculate the m 2m7z kd4ucde3agnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on thsyfu4 -0xf () 7*akmjl7qtu boe same side of the Sun. C7 uytka*msb)7foujf(0l-x 4 qalculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 50fbgbzc/co5 of what it is on Earth, and that Mars’ radiucc 5 b0fo5gbz/s is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of th2)lsr d(b g1que Sun using the known value for the period of the Earth and its distance from the Sun.d1 2 q)bur(gsl [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 circular orbit abou9kje0x h e+0hrt the Earth at a height of 3600 +jxer0khh90 e km.    $\times 10^3$

  The space shuttle releases a satellite into6/;m wd wc2rq(q )f( z1biamdb a circular orbit 650 km above the Earth. How fast must the shuzqf d1a(w im/d26mb;cwrq) b (ttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if d r b(51mjmt3moccupants are to experience simulated gravity of 0.60 g? Assume tm5b3 d1 tmj(rmhe spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit thed209xbm-g xtth-qt e 5 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. Dt0 ttm 2xqhe--9d5bxgoes your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be laun +p0pxqo :3zo oymh4u46d;tt bched from the top of Mt. Everest to be placed in a circular orbit around the 0y p4ttd q;h4 o3zxpomo6+bu:Earth?   

  During an Apollo lunar landing mission, the co.y*jbe h 7v3gaz*y mu h:foq(:mmand module continued to orbit the Moon at an altitude of about 100 km. How zjo7y(m:3v hf.y*uq *eh:b a glong did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit h5p+6upaqhn1p qf-w/ the planet. The inner radius of the6q5 fp+wua p1qhhnp- / 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 kw( b-)d;fy6bo eo;jtm in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’k) oydbe-tbojf; (;w6s 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 the center of *4meefhfupht (2a0 1gthe Earth02ef g etp*a(mf1 huh4's 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 consists of two stars of equal mass. They q 1 hjh5uy,5dgdcq 68r*qp7h jare observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway betwee ,r56dju 1y 8hc7qhq*hjgdp5qn them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator thg vq09 w,mu+/l0 )dqb8b reoqmv 7jr4pat mo/v0luq q879e,qm jvbgd p+b) 4m0owrrves
(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 w+5y+vf6w e9 ox)cfvs an elevator. The cord can withstand a tension of 220ofvcxvw+e6s5 + )fw 9y 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 windw x5g.2k6h jth period T , the density (mass/volume) ok6 n.hxw gd52jf 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 tqy;+7h -u* bz pej/p)elwo5.pr 1qtovhe Moon (27.4 d) to determine the period of an artificial satellite orbiting verqvo;e*j/wur.ty+p1)blo eph pqz -57 y near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits tc 3rlws)hoc4kdhkg3*zy:l vl y1 8/b/he Sun like the planets. Its period is 410 d. Wh3/8dhl y/bskk3c4hr1wl y o*l:zv)g cat is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averagv()*;m xiqc.al sw (gue distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. Itez6 jujms9z s-8,r gu kk*e/d. comes very close to the surface of the Sun-*jzke szue6/8 dg.skj ur,9m 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? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxyr g2jedx45d/;w g;dln $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moons og w*8xyrt8aw: -wd yb4f Jupiter (those discr-yy*wabwt:4wg88 dxovered 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 ac-kadd608ucniyq2 3z nd distance of the Moon. kacd0-u y82id zn6c 3q   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s m)hopp o4jqtg44-cz: zoons, using Kepler’s third law. Use the distaz4 ohjzot: pc)g4-q4pnce 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 cng*c )8dlzpczge 3 7+Jupiter consists of many fragments (which some space scientists think came from a planet that once orpge +ncczc38l gz)7*dbited 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 band co 7(qqlyg.,ftic i2 l7 fnkdm; 5:10atcw;aqmhmpletely en(1qt:7awff cth ;.c0;l,5 q2md kn7miq lyag icircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc flupbqj(*i5; jrom a hanging vine (Fig. 5–41). If his auiq(jbj 5l; p*rms 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 m long.   

  How far above the Earth’s surface will the acceleration of gravity yj8(2sk-; h*c3qe:mxkb3bfx1ex v vube half what it is ovbxj1(- qxfehmk:83c;3vsy 2kb uex*n the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grak6cs mzcv.q8) b hands and spin in a mutual 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 they pulling on )s6mq8z. c kvcone another?    $\times 10^2$

  Because the Earth rotates once u+sn1nut)*u) yka2kv;f mc u j3e/bm/ per day, the apparent acceleration of gravity at the equator is slightly less than it would be if t jku mscu/ /kmn);y*2ube3 uva)nt+1fhe Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling dir) hpd36 dgh n+ixis8x4ectly from the Earth to the Moon experience zero net force because )sd83 +higin hx 4d6pxthe 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 bathroom scale in+0rovy2 cs x;a an elevator, it says your mass is 82 kg. What is the acceleration of the elevayo v+2ax0rsc;tor, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circularwfuiq2i-w,sm y)- wu. tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formedw uy-u w2-fs.q i),miw 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 aircraft in a vertical loop (Fig. b)gzjn0 r uwhs3-aq8-5–43).
(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 ohjk/d iq -d: /-8o;zkz pnz.tr, the acceleration . ozd;k zoi/:-ntjdhqp8k /z- due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a stringmx:4zv 1b /htiitya4 () is deflected from the vertical by an xv( ab /ztt41:iy4mhiangle $\theta$ 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 coefficien j z8aigx y*s6.9x/xvbt of static friction is 0.30 (wet pavement), at what ranisxy8vbax69z j */.gx ge of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast thatbu m-lnb8l t 304c ,j-ghbewv v(87ih(h ltv6f objects at the equator were apparent, wl-lmj63n 8it7cb(8 vf(gh4hb vbtve u0-hlly weightless?    $\times 10^3$s

  Two equal-mass stars maintain a cb w) ulsp7f;hi 8+fko79iwtl )onstant 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 roundswun ecsp:3516r- +2 d frnqgdu a curve of radius 235 m. A lamp suspended from the ceiling swings out to an angle cu6 we-f31dg2pq5nu +:snrd r of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as th 2wz53ko4iqjg q7aoe4e Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on q4 74 q wi3ejg5okoza2a 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 Hubble Space Telescope deduced the presence of an extremetud b2evb bv-)*4a, (8nwmb skly 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 measur,)u4 8b2 * amk (nbdeb-wvsbtving the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valdq m+s-49, kjjems nct:20klzley 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 losing contactemjk,sn 4: cz29+k0 jmsld q-t with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group o9.azht 6 suw-v8q0l1vuo cm: 9h 16ckg3anippf 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the96v9h sc6 .1n:h8 uc ua3 gaitm l1vopqw0k-pz 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 (NEA98m(o :khfar dR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Efm( :ro d9ahk8ros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite ij x* vp i +cho92gw/b f:/bq)ed8av;min need of repair. You are in a circular orbitvfeb/9px*ga mdb:h2)i/8 ov w+ j;qci of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean dista+q)a qqxn8) xd1 .u9li ye-sxw8g 0wmance from tm+y qaq8s.)ln xa-081w 9eiwqxd )g uxhe 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 b fou4n(. li6uee if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like F fn6ol u4 i(ue.$\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Ga cwr;1yo2kq)pj9e1vv laxy (Fig. 5-46) at a distance of about 30,000 light-years; r2pcv191qyewo)k jv 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 square 0r sjksj46; zd9.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom s 4z;sj6rj kds9ide of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg osb; 5ohqo7m1 erbits 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 expepvv9i/1;ux1v3f e zrt rienced by the tip of the 1.5-cm-long sweep second hand on your wrixvepu/1v;zi 3vf1tr 9st watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a1( u(6ju9im* l4 0li hqgmkwtv circle below you on a 0.25-m piece of fishing line. The weiuk(hvgu 4w(l6 1mii *mljt09q ght makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new 6m4iyb9 it/nz4 -: vooxoam ,nhighway is designed so that a car traveling at 6:nx4to omv/ oi,49 yzmban -ispeed $ 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 cars7vfujk l27-l3ao5 ipq when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acoj37ap 72qkfl vl u-i5ela 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.$\approx$    $\times 10^2$