Sometimes people say wxn;ps5r(7v xtwc: -b that water is removed from clothes in a spin dryer by centrifugal force th s(v;brcxwnwt-5p:7x rowing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharehss-8;dgj g1pz )d;m d g90ctp curve at a constant 60 km/h as when it travels arousjztg 019 pd-)geg;;h scmd 8dnd a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed aluehc4 sa4mb5 +ong a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level u+b 54s ea4hcmstretch near the bottom of a hill?

Describe all the forces acting on a chilzjz34- dp5hmy d riding a horse on a merry-go-round. Which of these forces provides th43ypzh5-zjm de centripetal acceleration of the child?

A bucket of water can be whirled in a vertical ci52za p*sh5k c;copy6ircle without the water spilling out, even at the to25ikppacys5;o* zh6 c p of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are atrhe3.9xb ;+tx d(gwtr least three controls in the car which can be used to cause the car t g3wt;x+b rdxh9(r. eto accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the cres2bmlf8*gd a q,t of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sgdamb*f8, 2lq led decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at ory 32jjs.2x phigh speed?

Why do airplanes bank when they turn? How would you 3m8rgc mjzvg91 efwbo 6-.3 hocompute the banking angle given its speed3f zc o w3ogebjmvh98mg1.6 -r and radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal plan,avnfx6oy-eh5 s /5l le. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of lo,5e- x/n l 6favhy5sthe string?

Does an apple exert a gravitational force on the Earth? If so, how large xd jf:o,g b.q2a force? Consd q2fxgo. :j,bider 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 orbdaeq5qbkr0 v 3 (plejshfd7 t,/a .r-8it be different?3/.( ,k8 rfdsqeh 0dtal a7eqrp b-vj5

Which pulls harder gravitationally, the Earth on the Moj is;,iga0c*e: z+ djoon, or the Moon on the Earth? Which accel0ji* og;z:acs die,+jerates more?

The Sun's gravitational pull on the Earth is much larger tab.3 sh(i glf6zeps/ 3han the Moon's. Yet the Moon'hfl 33se./gbp6a i(zs s 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 at the equator or at the poles? What t k9zy( l jt6yg9:n)(xufcu lr4wo effects are at work? Do they oppose each otherl zjl(nxf)(r6tk94ug:y 9cy u?

The gravitational force on the Moon due to the zkd: :x154 a ergjkli9Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pial ekr:j1k z59 g4xd:ulled away from the Earth?

Is the centripetal a09 od mpwklx+7cceleration of Mars in its orbit around the Sun larger or smwk+p xdm7l 9o0aller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) to;)kq*;, am jrvz05uokcjz0j c6hq u4r as:x4dward the west? Consider the Earth’s rotation directiaj v0usxj;d) h cu:kjr4;rom4ka6z*q, cq50z on.

When will your apparent weight be the greatest, as measured by .er g *dwbkgja*)j8j* 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 *djbwa k8*.)r gje* gjbe the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long period d(kadf1hzb8,1 au8g1 i(dmjus in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cym(8(f aj1gdd8iuk u za,dh11blindrical 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, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “ axtc-(rrc kwcc.mu02l*f4rq3 .y s5gq5m bb5free fall” or “apparent weightlessness” between steps.54buwxk5lcf2-g0*rc.br r a q ( 3qts.m5cmcy

The Earth moves faster in its orbitnk ast /fq7,xis0 p2u/ 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 producing the seasons ,skq 2p7/fnx /s0it ua— 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 discoverefd1(qi+3 htljd to have a moon. Explain how this discovery enabled an estimate of Pluto’s masjt1 hdi 3q(+lfs.

  The Sun's gravitational pull on the Earth is much larger than the Moonk/b+k/w5cp tu4vzhb q +)6izrc)e i)z 's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the differenc ))ku5e)h bb+6/ zi z +z4pqtviwk/crce in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane travelin rw56g 1z7oiqlh31q u;hlcex,g 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 or9 f:-d sk8mesdbit around 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 kd fd8ms-e9:s circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotatvjkjbv 8fggb )h4 7/a0es uniformly in a horizontal circ ja hjgvgb0b8)v7f/4 kle (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, anzlmrc -im 0vwj4 iqdje7l00 1(d circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answee m0dzlmj cq-iwv070ri lj 1(4r 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 okq)1jbv:(dk upy r-84ubmc u0f a potter’s wheel turning0-p )cbr ujyuk1 vdk4(qu8b:m at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a stringcyd.fo- ;(v 9iqwkef* is revolved at a uniform rate in a vertical circle of radius 72.0 fqcy-9o. (f*i ; vkdewcm , 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 10 r;sd6t- ;;g4xuw* l7rtqon.p0smcsj50-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;-urq t o sms4 j0*ng;7s.cdwpx6;l tr.80? Is this result independent of the mass of the car?   

  How large must the coefficient of statie mvj okvzg,6dtrp9-yd;( i17c friction be between the tires and the road if a 1kdi-7;j, (v6t gdm9orye zvpcar is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots ,h4gq 65melhd1 xjml55 jex-s is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the forc5emll,45 1h6- h5mj xeqgdxj se 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 r,dpk/v18 xb seg m33(6yyzyiof variable speed. When the speed of the turntable is slowly iny gsy(kmi 3z8,rpd361b/vxye creased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at thedl*2 0vp rfp.0x:p (qiz,i htr top of*:fhrr02v,d. p(p0ptilixqz a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses 5c7w s/ z:hyl) c vzwikr*;0withe rounded top of)i* cwlkww :50 scirzy7z;/vh 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 per minutf ndu3u)khoe h43 4y7td3-qj ge would a 15-m-diameter Ferris wheel need to make for the pasd7h o)4fdky-thgj u33 eq34nusengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a ve2k n3r 8ns,d3cm zz2r/gqvpj,rtical circle of radius 1.10 m. At the lowesjr8zc3/kg vmp22 qn3sd,rn z,t 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 - mqsz.ezcr8 m0sq*8k hz mb:m,)skwv(1 buv 0a centrifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accelerati scs-.z(mm) mqhe ,ubwv z8r80 :k*s0q 1mzbvkon of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a c4 o:)xtwtwxoz b-4 :faylindrically walled "room." (See Fig. 5-35.) x):x-4wwz 4 ft:toao b
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 frictionlz1y4uhz2bu g6ess air-hockey tabletop, and is held in this orbit by a l4 u2ghzybu16zight cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, v5lbjm*x -e2 zby not ignoring the weight of the ball which revolves on a string 0.600 m long. In m5vl*e-xb 2j zparticular, 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,v6z y/w-dmyuy4i).8q odvj3 uoa ru- 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 masses *rd5 fhhh 31(3k+ltwnky rb *w$ 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 vertical)quotg-pwvh45 01ryk/ ohmgj6wyt 12 ly 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 onw 8d5tp* iah.7onu pig ,*8rxf the net force exerted on the car (by the ground) in Example 5-8 when its speed dnh5 *a8u.twp*,8ong iip r7xis 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit area, goingie)5ffxpb 9* n 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 acceleration f*exp f 9n5i)bwith no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radiuv-li:zl)plaju- :7p:y t-zy ps 2.90 m . At a particular instant,p)p:ypll::u zv7-- jlti -ya z its 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 4 k:w vcih1rx-9fw7tj(2 Earth radii) above the Earth’s surface if its mass is 1j1 hw :-4xci9t rk7wfv350 kg.   

  At the surface of a certag *zg 6nzd;mvl7.0u(eo: xa j/r)ffyzin planet, the gravitational acceleration g has a magnitud*j;v(fnu ryx l:aogz.)e/0f 6z zdm7 ge 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.x zrl-5l0h+lyc .so3n The Moon's radius is 1.74 ny c-xl+o0s.hll3r5 z$\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 hax 2,eg ;biu + upirgebc26o67vs the same mass. What is the acceleration due to grave2ubu2 e76+obgxrvp g,; ci6iity near its surface?   

  A hypothetical planet has a mass k/lsm uwj;bvos60 ;m0 1.66 times that of Earth, but the same radius. /s;ku 06 ;smobl0vwj mWhat is g near its surface?   

  Two objects attract each ode* ); /o nai)xnaro)* xw91c2 slqnucther 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 gravf+ jw1lwodk4;:/ qipj0rx8 hjr7qws5ity, at (a) 3200 m :j+ i 71rqlwf48dh /5p; wjjrxwq0osk   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside tx7+/ relnna 1xk4ayc.he Earth where thegravitational acceleration due to the Earth is ak.a /nxc +lner1yx74$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed inxf96k i)s(2wp 3p vnqpstn9fk4sm 3 :ito a sphere about 10 km in radius. Estimate the surface gravity on this monstefi 2 np ) p q4:6nt(s93piws3s9vmkkxfr.    $\times10^12$

  A typical white-dwarf 9q0tm3 +hvwa e2 fo1wfv sz8v2star, which once was an average star like our Sun but is now in the last stage oh8 vf2v9s31e +q zw mafw20tovf its 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 weightlessbzeuv u 9)ppl3wyxva7u5,,f lkv23 a: while orbiting in the 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 ca2uvp53we,f7,:z9ul byavp )a3 xkulvlculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located5g at1ygq-gjq5n;p /d at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by the other thr1agq;ng-qj5 pt /g5d yee.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years us+ 2qjc,a,las:.0qk2h r xxcud* r 2tmost of the planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in xaucchqs 0.*+sj2kl2,q 2x :,dtaru r 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 accelerationsnhfbml60 jc12z: u;g of gravity at the surface of Mars is 0.38 of what it is on hl 6jb mnz:0s1gf; u2cEarth, and 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 perir o)xtokvt9))od of the Earth and its distance from the Sun. [Note: Compare your answer to that obx))tov9ot )krtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable cir7/r v.fx4ed:cjet0w ecular orbit about the Earth at a height of 3600 kvxjc.74fee: 0r/ wet dm.    $\times 10^3$

  The space shuttle releasesxq2q baw+,of4 a satellite into a circular orbit 650 km above the Eart +o4a2fwq xb,qh. How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experw5e) v1f-up lk 6iccr6ience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as5ccik 1w6l)6evp-ur f the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the f5w+.w j.sni l;xrk f.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 compasnf. lk.+. ;rwx ifw5jred to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity ws1dds z8 b4f7e inqw*1ould a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earf 1dq ni d1bwz4*7se8sth?   

  During an Apollo lunar landing mission, the command module continu rjq-byqy*3oq17v61vcnz h (ned to orbit the Moon at an altitude of about 100 km7vq1yq z(r3-v 1oyqn n *jcbh6. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of cbpy /t3vz4bi4 skrz8g+ g9jo9hunks of ice that orbit the planet. The inner radius og yb jvig3rk4 zb +st8949opz/f 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 : ws y2ydnmvt*m/ 1:drevery 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, an:ysdvr:2 1ym/n *tmw dd (b) at the bottom?
(a)    (b)   

  What is the apparent w3ufeqr fmqf m5h(b30ob);b f 7eight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (bb3mf uef7)(bqforhq mf 5 ;03a) 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-s xchkx7;e zff4v 0h+8ftar system consists of two stars of equal mass. They are observed to be separated by 360fx z8;7hhfvx+4cf0k e 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-ki/ rpiwe:j0.wz9 6xoh g woman in an elevator that movw.96 e:rihjxo / piwz0es
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an en2zrt; szhl,kv 5:8ln levator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What wt8l nl :n,z2;5khzvr sas the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite3b9bepy(g 3a7e9n k 0h jdzi8 ha:+bnz orbits very near the surface of a planet with period T , t3eke :hj y3 bz9nba(0d+ai8npgh7z9 b he density (mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the periodmn v(zqzm b.:hd/l n93 of the Moon (27.4 d) to determine the period of an artificia v3:lbd/ h9zzn( .qmnml satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun likvrd 0t,e)/v7 s mh/pmfe the planets. Its p t/rfdm,s/7mv ) 0epvheriod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averageij9;jx yov9;rlao4l / 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 onccm9qrd4nd qz *waah0bf q9*ih6r t (*5e every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is newrda0th ai 9*9frd*q nzm(q q5bc*4 6harest 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 Galas//6 1z-.ctkqloiis xxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, ktyfc/kxu 9fiz++;3l and mean distance for the four largest moons of Jupi kf;x ktil3u/zfc9+ y+ter (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 period and distance of the Moonipl8chw17g/ w . 1w/g78iplh wc    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupityowyhg 70(, l8 mzusx,er’s moons, using Kepler’s third law. Use the distance of Io and the periods given inhz,0 (ys,7 gmuy lxo8w 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 consist 5:jm5rwl(sgjs of many fragments (which some space scientists think came from a planej5:w5lm(s j rgt 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 "planet" in the r*evlf5w70s 4vx z- nmform of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the drxw *50-4 sfvlnvzm e7istance 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 hang;9 qm;a3pdcvmi a9e u1ing vine (Fig. 5–419uma ;dp i9vq3ec ;am1). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration o acq03u gps1ux0cpf93 f gravity be half what it is on thccx0 f g0uap3q3s9 1upe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual*; 7x si2kgt6t o5u/fns3sipb 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, how5;* uosi bngkpi237 fst st6/x hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration 3ehbb)zn:zu )+j4p5 r2 uerk qof gravity at the equator isrz+n32 5 e)q4u bjebkrp:uhz) slightly less than it would be if the 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 dio,2rk99-odawi vyh)l b zb 4n5rectly from the Earth to the Moon experience zero net force because the Ea n42ohr 9o-,z5l9 adw yikbbv)rth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass isse6,pcytr75k- 8xb bs 65 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in whic-6 bby,te k57xprs8s ch direction?     ----待选择----upwartddown 

  A projected space station consists of n dg3w-)5n bxba circular 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 grb-nn )3xwdb g5avity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his airczom *s:xv.ap-raft 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 aw,xe7t3q4 uwy5 ifs(:rq:p oq planet in terms of its radius r, the acceleration due to gravity at its surface andoqrqw45s3 e ,w:(x qyi7u :tfp the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected fr5awsufu duv +hr):+-kom the vertical by an wu uv s+a:-+r5hfu)kdangle $\theta$ 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 bankedu 0 rg) uemq3sy)x3 zoi-xe.)d for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speed-doemes) i. z) qxrgu3 3x0y)us can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast twt(*.fwkrhm3yp x46/9 qkmav hat objects at the equator wer y*.a m(kvr xkww3/649hfpqt me apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constqk yluqh00n0ybad/l8x- : 8q bant 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 conqk837fuhudsqs n 0 cx5ph5,o2stant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings out to an ang2u k05s3pn u5c fhh ,8os7qdqxle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as then- 5 bu43gr,bz +o1tpndg)yjh 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 gbogrubz41) hdp tny,+ -n53gj '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 ex .ro1cttr- or3f2jk4ntremely 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 meas1r2c -rn.t4 rjoft ko3uring 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 hill4p-e zd cp-+ry.h-7m/glym hy and valley shown in Fig. 5–45. Both the hill and valley have a radius of curr.d cy y4+h-p-zg7lm /m-pey hvature 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 contact with the road at A?

  The Navstar Global Positioning Systzcpopo ( 91ym;+a8bvp em (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position o1yvma ppo;(9 pb8c+z 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 np7t79ag 4gi, )j4 u2o dyvnvj(NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros 7t) i4guny4vn9aj2o, pjd g7v 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 in need of reb88 1ww6sxd ogpair. You are in a circular orbit of the same radius as the saowb 8wsd 1x6g8tellite (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 3fiytl51n ; ep8-s n0rjbcr *;i000 years. (a) What is its mean distance from tl5nc*;rsepri y - 0 tjbi;1fn8he 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 be if you could a5k o eqr1la+v*ctually "feel" yourself gravitationally attracted to someone near yo1a5vre oqk+ l*u. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milrzxpfnv-lvt. ;i wu p(f/p3k sb 11h94ky Way Galaxy (Fig. 5-46) at a distance ofzs1l t(f.wpxvk/nurf3b pv- 9h4i; 1p about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of arg5lrv*2cpcwjz l: .z3 xip;; 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 midpoinrpxlrg:j pc5i;wcv.zlz;2*3t of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 9gy.h d,dui-( uet g(hkg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tinz j.88tx l,wtp of the 1.5-cm-long sweep second hand on your wrist watc8twlxtn z,8 .jh?    $\times 10^{-4}$

  While fishing, you get bored and 7nxm7r; n5jj ostart to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint:mrxojj5;7n7n See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highb8dje b2mue,n6e6w l*way is designed so that a car traveling at s 6eejn6db*,bew8u ml 2peed $ 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, thecb)x(d nqcc6 6o4;hgw3;1hxhfrn un xhr10 w3 Acela, utilizes tilt of the cars 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 Acela train that rounds a curve with a radius of 620 m at a s1x g;nd c 3h4xcxwn;3rhchf6 )r0hwqo6n1bu( peed 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.$\approx$    $\times 10^2$