Sometimes people say that water is removed from clothes in a spin dryer by 3; ,/ly(:vd+ eufhomh0 w tcxdcentrifugal force throwing the water outward. What is wrong m 3,o/ u ;x(hwe:c0fdyvd+lth with this statement?

Will the acceleration of a car be the same when the car trz8,oa:ts - q-nb ok+bqavels around a sharp cur,+bbko8 aq-zsq :nto- ve at a constant 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 hilu9b7xctd 1ty;ke5fye2 ky qr fl(p.0- ly 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) bp;- r.e0tyxl9fyq (dtk7k2 u1e cf5y on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on j/ge+/n , hh2cbpwd ,w(smau8a merry-go-round. Which of these forces provides the centripetal acceleration of(sund 8h+jb//wc,phe ,wa 2 gm the child?

A bucket of water can be whirled in a vertical circle without the water spillirhix exzc;/cm9 n2.s)ng out, even at the top of the circle when the bucket is upsxi/ xms hcr9e2zn.c);ide down. Explain.

How many “accelerators” do you have in your car? Thi.y-ta hi)h, cere are at least three controls in the car which can be used to cause the car to accelerate. What are they? What acceleration-tih i,ahyc). s do they produce?

A child on a sled comes flying over the crest of a small hilldk-t :dzc,/ j2bunvx, , as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal forcedz:j v2,,x c-nkdu/bt between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when ra13 f4c 2v*fbaa:o,ex)zs4sm:-yvhl;s va tmounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute qbfm z n 0io-f6m47f(q6g y,jcthe banking angle giveqgfy6q0mm 46 ,oz(if- cnf7jbn its speed and radius of the turn?

A girl is whirling a ball on a string around her heaetp b2,jqtoje0efrm4 6- 3t3cd 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. Whenrbeoe0 3 p6tqtfm-3,ct e2j4j should she let go of the string?

Does an apple exert a gravitational force on the 4ps eoryf.amkmk.6k1 mdb1 ::Earth? If so, how large a force? Consider arb: komy6 mdkp:e.sam1f1k4 . n apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what itcs noiv hh:1-, is, in what ways would the Moon’s orbit be differ1,s-c:nho vhi ent?

Which pulls harder gravitationally, thouiv3 e0re. 9 2zgidd6e Earth on the Moon, or the Moon on the Earth? Which accelerates mo6u2idi 0eed gr 93.ozvre?

The Sun's gravitational pull o mzu11fbsw/d ( ki0zm(n the Earth is much larger than the Moon's. Yet the Moon'sf01 1zbsd k/iw(mu (zm is 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 more at8c1yl)ff 4xael :z/k h the equator or at the poles? What two effects are at work? Do they op84/ecxf:l al)h yzkf 1pose each other?

The gravitational force on the Moon due to the Earth is only about half the ef+r s vf9k--zforce onf-r vsf- 9ek+z the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Marsga kg swe 5-*hry3ce88dh8ee2 in its orbit around the Sun larger or smaller than the cenyhws-deka*h8e2e c r8 538 gegtripetal acceleration of the Earth?

Would it require less speed to la3bh 3s umwj/4ounch a satellite (a) toward the east or (b) toward the west? Conside3us/mj 4hbo3 wr the Earth’s rotation direction.

When will your apparent weight be the grd vn( )yi4zo5beatest, 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 yod4n) zibo(vy5 u are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adver 7 gqf c;iqgr )w*qag3i09.cuxsely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking i0) rg3qqiqu 9c xg*f.w ga7;con the inside 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 experiences “free fall” or “apparent weig/a)e +rlwg f*khtlessness” between akwrf)*/l+g esteps.

The Earth moves faster in its orbit around the hri59)c 5eqcvSun in January than in July. Is the Earth closer to the Sun i5icvh cq)5r9 en 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 axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have po7lw ,06zkm ta moon. Explain how this discovery enabled an estimate of Pluto’s mao w6mtk,p07 lzss.

  The Sun's gravitational pull on the Earth is muc 8jns-7 wt7*.li; ygsxa,im bsh 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 mej;m b 8y.xi,wg77-nst isla*srry-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 19yduc 1r ms9:6:-t(x+ovktq og80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 i/;mxsm5,ptig v2v( u nn its orbit around the Sun, and the net force exerted on the Earthmg/,mv 5s (tuv2p x;in. 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 dihzvg4;v q/c 9cscus as it rotates uniformly in a horizqghzc; 4cv /9vontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orb6*t2h sfadm qo 6)pld8it 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. 6ptmo8fsdd6 )h2la*qFind 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 edge of a y,a2ib)oep.n.8 +:w b hfwasapotter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s oeh:)snf2wb+aw p. .,a 8ayib diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a ve1j (p pyt,1zb rip6cf 7)9ykvmrtical circle of radius 72.0 cmpczv97 (y )b1i,6jtpr 1 mpfyk , 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 which a 105pr wm,d3cisv7xq-5 ;o0-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independentov; rpswd x5qm7c3i,- of the mass of the car?   

  How large must the coefficient of static fribmh- p21uwg4vdtiu/4 ction be between the tires and the road if a car is to round a level curve of radius 85 m at-gvh4w1buid/ 2 pu4tm a speed of 95km/h ?   

  A device for training astronauts and jet fighterh 15nf e/m2gq(piqe0v pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on higpe qe f(2 5nqvhm0/1er 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 variabl:b e r-v2vy1sae 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 -es:2vyar bv1 and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed mustn rnp*b-)js8l a roller coaster be traveling when upside down at the top of a circlebn-n * lj)rps8
(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 roundek,g( r hv3jz5,dyy9) pfty qg9d top of 3,q fd(kvj t r99,gg z)h5yyypa 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 per minute would r+g kprs)rz, 9a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at theg)rz+rk r9sp, topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle o,3ho a 0jd hrs3kk3dg+f radius 1.10 m. At the lowes 3krh ads0k3,+j gd3hot point of its motion 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 from the axisn0mn0r iuz4ht i)78n mln.1nl of rotation is to n8n.4n 1mu0i7llz)i hrnt0m n experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people 0q9s jjxjul j :ijq)/.;)o geeare rotated in a cylindrically walled "room." (See Fig. 5-35.)) lij qjxgee.0qj9: ;s/uj j)o
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey t-zjgvq*,h mb geb6x5 5abletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a ceq v56mxjehb5 bg zg-*,ntral 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 ign7aqge1u z vd-a2v3(b5l lqvk4oring the weight of the ball which revolves on aqb7vgl(ak ad2q5e-vz 34 u1vl 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 bankes6uos .* 2dxqg/y;nxwd 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 masse *zq86 v)2vbsoi +sviu)c *fncs $ 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 b +o)y4w7b;zut5ezgoibi:4 c 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 components of the net b(h/01k*6yu rxsw dtc force exerted on the car (by the ground) in Example 5-8 1/ wksxht6r(cuby0d * 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 accn8r ;l3axtam 5elerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what n;83a m5xt rlawould 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 eda8f) (( ejloyvr)m ;x9rq/dparticular instant, its8xdj q )ev)le d ary(r9fo/m;( acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2u-c jmk9lp9ve8 p, b.aneg1;v Earth radii) above the Earth’s surface if its mass is 1350 .p lb ,c;9pmvunvk 1ja9-eg8ekg.   

  At the surface of a certain planet, the gravitational acceleration gylusdpz1 6 / i:;9kkdl has a magnitude oyldd1lkz; k :/p9 siu6f 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. Theq9a9 -pcv3b *5kh+g bq j;mnn7hgla;j Moon's radius is 1.7j 9jb*vg-chm9gpa+na ;k5hqq;l b37n4 $\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 Evqjd +uw /f*1aarth, but has the same mass. What is the accjfqv1+u a/ *dweleration due to gravity near its surface?   

  A hypothetical planejue,tz: b4lswyq;p2 e7ewm;6el3,( ao whg: lt has a mass 1.66 times that of Earth, but the same radius. What isely:h7ue sle,otm,34;( z6wlqajwew:;p2 bg g near its surface?   

  Two objects attract each other gravitationqu2 y7/g6q 37z oinpwzally 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 acceleraz7 v 2ip t;wpfg28qb-ation of gravity, at (a) 3200 mwb27 a-tf8pgv2; izq p    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point ouf(x7 4ck pyf7otside the Earth where thegravitational acceleration due (fx 7okycp7f4to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times they7 c7di p:h7go mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this mons7h7gc 7 opydi:ter.    $\times10^12$

  A typical white-dwarf star, whi;q3ipm:o: m1ep a tc.j(6jur bch once was an average star like our Sun but is now in the last stage of its mq:prupjc.;j b:a eto36i(m1 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 weightless while orbiting in thpy d /qwrdfojjbp4; i5o1u1nr)a 396we space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by r1;u j4)p1wq3ro f adn j/5 py6dw9oibcalculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at( 22n;*1mzlj6ci2fi kwo nqro the corners of a square of side 0.60 m. Calculate the magnito i2jnqwlc ; 6(r*2fz12i nmokude 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 ofh6rl7; i m*i..t* h1yinjzbwy 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 masses a yz b 7.6wl;ji*yi.rt* mi1hhnre $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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.t/m.0azlqj f ;38 of what it is on Earth, and .z/a;m0 flqtj that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the periodb r sal+l s0f,o0ffr)( of the Earth and its distancel raf+s0olsfb 0,rf () 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 satellite8yc dfx )9aoe2 moving in a stable circular orbit about the Earth at a height of 36009excydao28) f km.    $\times 10^3$

  The space shuttle releases a satelliteg fm 8kky w5*;poze)et)4)cla into a circular orbit 650 km above the Earth. How famteaz5p8;k4) ow* )k gefylc)st must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupantsgunk5t 73j2 xe are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and givxgeun k7 35tj2e your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for n jo)p sfq g0,utg)s. ;o dk(88c+imuwa satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the rd8n.j+)gs0 8u(to)f ug k,pioq; cm wsadius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the top x vcildr+3m7svd b6 bzkj 935h52mm3b of Mt. Everest to be placed in a circular orbi 56mv79bdds+b5v33chzmxjl ikm rb32t around the Earth?   

  During an Apollo lunar landing mission, the command modug9 0 m3 l0 ;755x qihoxmdcft.qamt+zple continued to orbit the Moon at an altitude odmqipmo09hmtf7.;+x3g 5l 0 qxczt5af about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit6pi-jos-e dhg9fnx yw*ezlk125;( gv the planet. The inner radjyenk w-92 pz5v;( i-fh1g6egosdl*xius 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 dikas*5jjnl e65 yl;wj9 ameter rotates once every 15.5 s (see Fig. 5–9). What*y 9ln5j j6sjaelwk;5 is the ratio of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center v,e a5),xamksfy6zbg+ ew++ nof the Earth'swbe++yvs axzg, 5 )fka +nm,e6 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-stax1nj5vqsl 1y2ikbj:1g6k .sw r system consists of two stars of equal mass. They are observ2bn5qyj ikv1:1sg .6kljw s1 xed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg 9dok +lc.4ua2plq 2i1 ,zcwll woman in an elevator that moves 2.ul ,q+ll9cdkzwop12 4liac
(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 fd-q:dg 5 7:w)c da:kksj*ebnb rom a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleratine7w:)k5 b cdg sdaj d*qb-::kon (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with periaoxi czzi/p u2m4w/3,od T , the density (mass/volume) of the planet is po /4 uizax,/2wm3z ic $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determine thhozgju/ q1 b 7e*-dpe1l2wb5he period of an artificial satellqg7j puhe*h lbebw1dz-/ o125ite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters ac2u2,ke /e h2vc m j(;wkx;tfbtctk*3ty/epa 0ross, orbits the Sun like the planets. Its period is 410 d. What k2; xue 2, * ctbjf2tpwh3cy kaem;ve(/tt/0kis its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distzf9qx 3v4plzpph+m i2v+kua 8t9+)lv ance 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. It comes very cjcii ; ld9vsrjbqaws /: )10n kl+7ng0lose 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? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and f kd swc;l:jn1vl9 biqis ) /g7r00anj+arthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about tm .;oxoyx4d9the center 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 distance for the four largest moonskiya ;i4ao+9g:kj-e d of Jupiy9e :ikka -4ig;+joa dter (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 known pegjf1n h9ve(m6 xroi9t-r rfv 81k:u y*riod and distance of the Moon. eh*- vrjfk1x (frn8v96rim:goy tu91    $\times 10^{24}$

  Determine the mean dist7dfv :16ov-o,4 bz vjr3 spudjance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Us v7-puj sjozd6r:vbovf1 d,4 3e the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragmentshw: elc147sud .u igp /deux,7 (which some space scientists think came from a planet that once orbited the Sun but was desuhp e,dlg u .i e/ud:c77xs14wtroyed).
(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 /:7vmnq; khj ,cyls:e 3c ap6ba band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noonpvsjm6/a,:chc3l eb7q ;yn k:). 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 from a hanging viu xq3 s/1-kvkrpt, 9cnne (Fig. 5–41). If his,us9/ kqrv31 - ncpxtk 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 m long.   

  How far above the Earth’s surface will t 2 yrqtz:;ydzo i(t3z8he acceleration of gravity be half what it is on8 ;2z iy: drqzo3zy(tt the surface?    $\times 10^6$

  On an ice rink, two 9u;rt ddmlwq p61to;b 3zl,9g+*gtaj skaters of equal mass grab 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 onultwg9mr+adltozq 3t61; jgdp9 *b;, e another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity ;ex-ws*j so(yl9f47t n ygsl/ at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction ofl sog94;xj -s7y/sy nw f(tle* g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spaceykxytj2xs +/kgw :seub7a3-b ( (:isg craft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull syykku+:a3 x ggs(x jb2b:-e s(7iw/twith equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bfpon k:)8 pzargo h u0+ywfe9l;o*vii :ou ;-)ut when you stand on a bathroom scale in an elevator, it says your mass nr ;age ) ook);p8oph*f9: fv+:i w- uzuoyl0iis 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a yx,m+*wbljjeh dbv w0f*-vykq .r 1+9circular tube 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 at the surface of the Earth (1.0 g) is to be felt. mxyf1h wjbv-y+b +,j*v0*de9qkwrl?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–433zgz fi2gul*8ize2 3c ).
(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 i6 h. x2ttfroo:u,sc. dts radius r, the acceleration due to gravity at its surface and the gravitational ch r ,o:cofdxt.t2us .6onstant G.

A plumb bob (a mass m hanging on a string) is deflected from x (lgd):6dv kp1m :u:it8wfcx the vertical by an angl:m(f1wivu6 d:tdc x):xlp gk 8e $\theta$ 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 bankedxb 4vydg,lhhu9i* f: * for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range*dl xu,h :b*i4y9vfgh of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so 9qzeguu7pf 1+ fast that objects at the eqfuq7 gz1eup9+ uator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of-kuip0xv1w yfq2 l.if y34hr6 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 cupca5 pfy2 9dd8p 6/c.ko+y ukkrve of radius 235 m. A lamp suspended frod dkp.y cup56+fp2k/a okc y89m 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 has been claimed tp2c+lk+ s/jnj hat a person would be crushed by the forcejk2+slp/ +cjn 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 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 annp:su5(: vrjqjp5ok+ vtr3 kk q2th.: extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this t5k:+:nqqp j .vsoh:v23j5ru (kpk trby 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 hilrttmhe: c dzc. 6o/*9rl 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 d:.9hozt6 e*ct /crmr the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Sycbqtzfpu*c) )i)*) hgin6 *ld6: dfz gstem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, tzi6g))nc:d lufdgt bpqf h**z )c)*6ihe position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), x(fzqfq() y,w 6yc clk/f+4vgq5*f yzafter traveling 2.1 billion km, is meant to orbitcf,q(q/f f fvx*wczz g)54y(yy6+lkq 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 satt1eq v ;jp i9csze/w s3p/(3pace shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 1/jpp t(9 sqwtiz3ea s3v/ce; 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 yeary,ai 2ijyke3:s. (a) What is its mean distance from the Sun?eji , yy:a2ki3   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you cm9 ; epko vrzd6ittw 86im8+4could actually "feel" yourself gravitationally attracted to someone near you. Mam6i8de wpmctk iz69rv t8;+ o4ke reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Gal1uhri:kg 7 g0oaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cent7 01:oigkguhr er $ \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 ta5p6zkm 0lc8n he corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint m0 a8 pkz6nc5lof the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500kycb(imoa2 pw- 26nd ) kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration exph,f* .u ve+reo xh.s1a,wmdz/ erienced by the tip of the 1.5-cm-long sweep second hand on you md*wzex1,oe+u .vfa.h/ r,hs r wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and startkv6 dpdpck ci-+2j 443ahw -hm to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50k c 2ajwhd d3+-k6 mhi-vp4p4c 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 highway is designed so fe rw ou,u-xj75n k8x,e)u)kk that a car traveling atx kx kk,)uj)ew nf,5 8-eur7ou 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 cays8(ha .;yiojdwos60 t+) kxvrs when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengersik;8ot +0)v jyh6y.ox(a sdsw , to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is not banked and the train does not tilt. $\approx$    $\times 10^2$
(b) Calculate the friction force on the passenger if the train tilts to its maximum tilt of 8.0º toward the center of the curve.$\approx$    $\times 10^2$