Sometimes people say that water is removed from clothes in a spin dryer by centjl49tn0ms6n cq 7sh, d2dcnl:rifugal force throwing the water outward. What is jc2 htdn9sl046 7nd cqsnlm,:wrong with this statement?

Will the acceleration of a car be the same when the 7v 0b4)x6ger1n j*w 7qf ytg;ogd,vj tcar travels around a sharp curve at a constan)dj,be worqg *f4x ;t16vy7t0j vgn g7t 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. W+fio,l /d*w(lhc(m1x6qrvwn here 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 near the bottomq,ld h+/ vi(lxc1m*6o(w nfwr of a hill?

Describe all the forces acting on a child ri a*o*nr; lqkyw dmq ro/8,:*ybding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration oforq ad;,/wl*krmy*nq8b *o: y the child?

A bucket of water can be whirled in a vertical circle without thep,/pyue 8j1ac roa1cl5 z*l;u water spilling outupo; u8clzr plae y5j1*1a /c,, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your 8jn svg gzz zf0 j/,(dvq9li2ww4 m)hko(2r: fcar? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? W2swk zjqr 8w4(0f2,fnzdlzi(g/vv9 ):mohj ghat accelerations do they produce?

A child on a sled comes flying over the crest of ed g*/2v *t3dy0thazaa small hill, as shown in Fig. 5–31.0dd/aaz v3gh*2te *t y 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’s second law.

Why do bicycle riders lean inwat52 qadgtq )oay l 1803n2xlkurd when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle gwithu -pj8/+4 bfy2ot iven its speed and radius f/ up4 t8ji2tbow+-hy of the turn?

A girl is whirling a ball on a string al :)kys*tyw 5eround 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 thet)yl:wske5y * yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, xkx:h(t8u7n uhow large a force? Consider7uxnuk 8 x:(ht 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 orbit .1xqxns:qqg5bqg .ns: x1qq5xe different?

Which pulls harder gravitationally, the vz9jtn z w1r,z:1;ez zEarth on the Moon, or the Moon on the Earth? Which accele9;enzz zwzj,rt1 1vz:rates more?

The Sun's gravitational pull on the Earth is much : vnhs z*efm3d0n3(ur larger than the Moon's. Yet the Moon's is mainly respons z*udrsh(v3n: 0fnme3ible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh mw629 7b l0ckal0j8jwx etz p/hw7t0frore at the equator or at the poles? What two effects are at work? Do they tjc6w e9j 807w lp0tlf0a2x7zkrwh b/oppose each other?

The gravitational force on the Moon due to the Earth is only about half the forf3 jcd acg9x ibfks ;,lc,+-6qce on the Moon due to thexfg ccak;6il qf+db,93, sjc- Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger or smedzkw ksyjr2q: .w;p o *05ov)aller than the centripetal acceleration of thwopy)r:*k5 vkjs 02qowe z d;.e Earth?

Would it require less speed to launch a satel3 dn9a: 9spdnnlite (a) toward the east or (b) toward the west? C9sd nna9:dp n3onsider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a sc:it6 ts+ ybmhl; ue3;fale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) :ubm+y;h teitl3s6f ;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 coulmf q3(1chl /t 9 ugk7aqgsq8tb9rvm)-d 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 inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, a t)-b/1q( cumt lfq vqr9g7msga8hk93 nd (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weighhq 5x gro- e4:(am6)mhxigg/owwr . y2tlessness” between stepshxe5o.g/ g6ro )-rwhw4g(mx i:yqm2a .

The Earth moves faster in its orbit around the Sun in Januar2, ssv :bkkk4cy 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 producing c,sk4bkv :2skthe 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 untimfitpb7iqn 3373fxpad,8bi 4p acm6/l it was discovered to have a moon. Explain how this discovery enabled an estimate of Plutoqf7,p d3i7a4/ax ibp b3mmfcipn 86t3’s mass.

  The Sun's gravitational pullhb5 ,65f a(mr 8pgd 1vcr:pnwb 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 other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.2a (5pcbprv1ngd8 f6 r :b5m,wh5 $\mathrm{~m} / \mathrm{s}$ . 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 travelingliy8g g.dg+ yb*3/jyr 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 orbibtoht ze1:7*ft around the Sun, and the net force exerted zt tfb1e7h *o:on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg.v, 0x,yqddk-fymp4 z discus as it rotates uniformly in a horizonzpq, - mxydyk.f 0v,4dtal circle (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's surface, and circ uwhgkqj;4t,* * bky0bles the Earth about once every 90 minutes. Find the centripetal acceleration of the spaceb**ybg0 hwkq,j k ;ut4 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 accelerati*7dphg k.ytko :gydk8 vy66 ec,oo):bon of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (6bkg,7toyo*cd:)ge dkyyo p hk. 6 v8:revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of 5cv)rf*eh ge +a string is revolved at a uniform rate in a vertical circle of radius 7rhg*e e)cf5+v 2.0 cm , 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 with whi0;2.l66mzzi jxtyw otch a 1050-kg car can round a turn of radius 77 m omx 0jt66z.zwy ti;l2on a 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 coefficient of staticys k,k wijk*7, l53jyo 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 95km/kik,yw73 , loy*jsjk5 h ?   

  A device for training astrof)1p957npzn(nghe s t-n c*r knauts and jet fighter pilots is designed to rotate a trainee in a*znp( e gp-tk nf 19s57nch)rn horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of variable s9fwyxlc:; sh)us2 zyf9bpi/ 6 4yhyh8peed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reachex9hp 9slyf 82y /z;6wuicy)4h :bhyfsd 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 be traveling when upside down at the5f6k5q l/b msqeo m;/j top q5oefs/k6l;q5mj m b/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) crossesot o :rq4.uz4.v-itv(zc)1s2p x s os-wgl(rr the rounded top ozgz :u2ilxv)ov4.tw rsrt-o1(o qsr(. s-cp 4 f a hill (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 ps2 d,xl ij9 b6k(oeo/zer minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost xo92/s(oil,kd j6b z epoint?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 4nv7bl i2ylr p f0d6p6m. At the lowest point of its m0 d piy47 6nbfl26vrplotion the tension in the 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 frokru6l vok2/a7m the axis of /r k 7lak26uvorotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically3zzptr:6np v 5 walled "room." (See Fig. z nptr3 6p5:vz5-35.)
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 airwm ; mr3:-7fotvcd)3wg xg k hat;t3*n-hockey tabletop, and is held in this orbit by a light cord connected to a dan37ao:wt*x t-mf)mdt;nhw; v3gk 3 crggling 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 thu c jz9badm0.1is time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the mazbc9a0u. d m1jgnitude 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 bmdw+*rb*m )y of 88 m is perfectly banked 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 massejha*l+3qzqt uyru 18 .6f/onu50sgpjs $ 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 maneemkvw) (urb0d0c. i/.8llwnn4j))e0lw f m rvuver 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 compone0qn3p/ 8vm z6envxe s4nts of the net force exerted on the car (by the gr34e 8n6 n/vmzsqevp0 xound) 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 unif:j 0jtfhd74.eeszu* z ormly 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 t zs :7.*0hd4zejtfeju ires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a h*2l.j h2hyr1g ,nvk twbcqz3 7orizontal circle of radius 2.90 m . At a particular instant, its t zcb v3g*wjh27 2y,rl1 hk.qnacceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of d0m s;q.t/y dkEarth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s d .t 0d/yqmks;surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accelera9jvspnupg20o4h5j9 xtion g has a magnituuj0g 4 jp xson9259hpvde 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 accelerationwk jlj38 3feqyr6qpumq)1q2. due to gravity on the Moon. The Moon's radius is 1.7lfe8 q3k.1 2jmpquw6jrq yq3) 4 $\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 samqaz7mj ,x ,2dme mass. What is the acceleration due to gravidx j72 m,qza,mty near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same kjp-qg*c .s1e i)w (yo-l:ax uradius. What is g near o.:gsu*(jayxwc -p 1kl-q)ie its surface?   

  Two objects attract each oth g7ic b2x,*lvmer 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 acceleration of gravity, at (a07))fqva vz ftv 8i7d-yb y*cs) 3200 m -d)yvqv*z8ya7 sb t fci) v70f   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from thehyoj .5r x0x.07brt7m py6mnd Earth’s center to a point outside the Earth where thegravitational accelerab0y.m hnmx7r. j07 x56rdptyotion due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass oit.9yf0t o69 pyq g9yzf our Sun packed into a sphere about 10 km in. qy fz0p9gi9o6ttyy9 radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, w+0 aqqrn xo4hsq2k7x9hich once was an average star like our Sun but is now in the last stage of its72rqs0+q nh qxka x4o9 evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel we8.bhu6 3gh bpxightless while orbiting in the space shuttle. Your friends respond bh3xu6g b8.ph 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 ouy9a )fgoy8+ +ahfc r4iu)m/ rf side 0.60 m. Calcu +f haufa/go)myy+ 9u4i8c r)rlate the magnitude 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 mowg0 o, eg2 ptb7ek2v2ast of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter,e b72,wtga2pk gv0e o2 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 accele.baim -twnld3ei(41 i ration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determilinib d1-i3ea.( 4 mtwne the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period7i, jt*rmcq i0 of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.,0qc7mi*r jt i]    $\times 10^{30}$

  Calculate the speed of a satellit()r. fuvdo4v yk9oja+;.lm l se moving in a stable circular orbit about the Ear.fj dy 9v rv(m.o)oul+l s4;kath at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abq0s mouk atm4the(c:0fho. :2ove the Earth. How fast must the shuttle be moving (relative to Earth) when the rec q amtuf4oe(k2t ms0:h.:ho0lease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupant9hja7.0gozw5d jp1p v s are to experience simulated gravity of 0.60 g? Assume the spaceship’s diao5wh p17zdjp9gv aj .0meter 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 satelyxgoz*d5q.i /ys 42 xalite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbixoiy5* y4g/za. x d2sqt is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have yy u;n ;zkfnpny76l; :to be launched from the top of Mt. Everest to be placed in a c yuz ;p7f6;y:kl; nynnircular orbit around the Earth?   

  During an Apollo lunar landing missi+id;3;-gl z 0wyzqph( 8l 1ucrrtxu*aon, the command module continued to orbit the Moon at an altitude of aboutiuwdzyzrcu ;;3x l*gtap(8qh+1 0-l r 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The inn+6j ; fj+uc4fsuzr9q aer radi ujrqa +9uz sfj64f+c;us 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 diameter rotates once every 15.fa 7kcn9+9jyhyx 4v2u5 s (see Fig. 5–9). What is the ratio of a person’s appare+vyk xhc94 a2f9u7n jynt 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 astronauthvpe85q zt x+qqw+*2 v 4200 km from the center of the Earth's Moon in a space vehicle (a) moving ae+pv 2 hvt5q*+8xqwzq t 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 ofz7(h3m0 ngd sto7kt, t equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass73stmttho, z0 (7gnkd of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg wom148p qyvn9x f5u fp:vfan in an elevator that movev4 :nquxfyppf15f9 v 8s
(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 frvn bw/ej :y/;iom a cord suspended from the ceiling of an elevator. The cord can withst;bw/ y nvjei:/and a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a p kp- qzzgz;it*l29u3tlanet with period T , the density (massiz zltu3gp k-t 2q;z9*/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period zn+:.3 a aupf xh5yczc9xmy39of the Moon (27.4 d) to determine the period of an artificial satelli h:cxymu+cpzaax.9z9n yf53 3te orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbitst6hm+vl8-mis the Sun like the planets. 8+mhv6i m- lstIts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average diet9 -kz.9c e jirk73yustance 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./v6. o4u. zb8ey3 f* npkxh/kbjuwz -v 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 upx/3. v/j .ykezowbnhv fk4uzb8*6 -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 sd9. *g)pwc9 y,snivkthe 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 dist 0cuio5 s8mu2yance for the four largest moons of Jupiter (those discovereusyui8 52cmo0 d 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 apx7z(8*nci nthe known period and distance of the Moon. n 8n7c xza*i(p   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Ju*fwf+iwi ;.l3scx0depiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare tie.ci; +wx f3w0 ldf*so 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 Jupite) f:yb6ykmmxurzs a n5*q48i7o;pv6 lr consists of many fragments (which some space scientists think cak qb aui4p5)866mo*syvmnr7 lfx ;zy:me from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "4u,t rakk ;vg/n3rp5ske :oi)planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside4enk/r p:, aosu 3vrk ;)igk5t 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 a5w-8zdf i4 ter8sa7mnn arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine,sr-4 zam idfwne7 58t8 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 +fepb-jgi(+a2 hdz06a /nwbi gravity be half what it is on the surfacej pb(zn/aa+2f6-ghdiw e0+ib ?    $\times 10^6$

  On an ice rink, two skaters hus f1cr( k;o,/.x: xzgvyr3a of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are eachza v. o: k1(u3gy ,hrrx;/fxsc 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 acceleration of gravizh: y s bz4 t0,6(ey8e,tobi1jw2tp inty at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraeeb1yn h wb :t26(4,osttii8p, jz0yzction of g is this?    $\times 10^{-1}$

  At what distance from the Ear/3w0bs pqe +xsth will a spacecraft traveling directly from the Earth to the Moon experience zero net force becpss3e q0wbx+ /ause 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 ba wla..n 4w.5 ni)eglbsthroom scale in an elevator, it says your mass is 82 kg. What .iae). .bw ns w54ngllis the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tin 5p +vhh8c; ko53lhdube that will 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 equal to gravity at5k+cl85nh;dv hh3 opi the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his ah7:k i *wx9epty-i1ke ircraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, tg)u9 y0up/m*xpg (ngw0ir0czhe acceleration due to gravity at its surface and u 0prxz9gi*cy n0( ugwm0g/)pthe gravitational constant G.

A plumb bob (a mass m hanging on a string) is defw;1:pk46b7mn jrm xh+mjp(x qlected from the vertical by anp41(m kmp+ mjj:6 h;qnxwr7xb 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 spenko (;tebf7m (ed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?nbfoe( ;m (k7t

  How long would a day be if the Earth were rotatin;0+qvqlhiu o5 g so fast that objects at the equator were apparently weightll q+ov0qu5ih; ess?    $\times 10^3$s

  Two equal-mass stars maintain a cogj-0 4k x,0 oypfqo5fcnstant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 23,zd ijpr m0y t:e(fy+-5 m. A lamp suspended from the ce(+ im-epdtf: zry0j,y iling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 time; *he j57j-enpx26 *vqnzeb1 4zcgok1f+a ppjs as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g z j nqpcpoxefv1bj6zj4* a125 *ehkp -;e7n+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 extreme-rpu+ - bk/waily massive core in the distant galaxy M87, so dense that it could be a black hole (from which no/urakb+ - ipw- 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 constant speed as it traverses the hill and valley suo2sgv;8s* heoua ;ukolq3 j9t9:a1w hown 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 c hglsuukw:3e ;v9so aa9t u2;oo81q*j an the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 21 vlnr5,v0n93mvhq pn4 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four snvv ,mh9npr503ql1 nv atellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion kmu3x3b6vdy ,bb , is meant 33udy 6,bv bbxto orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a sea() px(ddj q:atellite in need of repair. You are in a circular orbit of the same radius as the sateljx ep)((q:addlite (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 perstpvy*zl 06xsqna4 uy(+plxg 4 o+e/9 iod of 3000 years. (a) What is its mean distance frol/ yaozs9pstu+y 0 g v4(enp*6qx4+l xm the 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 o;z / py 7zxpm-gx8nb qc)fs4.need to be if you could actually "feel" yourself gravitationally attracted to someone near you. p)x zo. x 84;cq-/zgyfmnbps7Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the s1w rs(0:vsm3*qrycpkpyio )+i1v2a center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-1+( 02i 3pvypircrass1ky m:ov)sqw *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 square 0.50 m on each side.-s qbd)-ttt 5l Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed att5t-- dstbq )l the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orb z,3b; s rdo.jfl.ql7qits 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 1 *yuukehs .k:6g 4kbzthe tip of the 1.5-cm-long sweep second hand 1es 4zy6kg .k:khub u*on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker6tz 2pu1o4zu j yl)tn/9kh*e o 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 that2 61t upojo*l yzkuen9 4z/ht) the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius qnl mwh0w jv7sr/f (f1g(mkb4)r 99xh R in a new highway is designed so that a car traveling a m/jwmvb(rqgh)9 94(fsrn17h fxwk0lt speed $ 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 whenju1i(za0 a7fr 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, th71 aria0(jzuf us 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.$\approx$    $\times 10^2$