Sometimes people say that water is removed from clothes in a spini*p kjdzo*u.+ b3(k8 d3ohkqn dryer by centrifugal force throwib* k8un*d3o dk3p.kj o+(qhz ing the water outward. What is wrong with this statement?

Will the acceleration of a6.ciskc,s2 r;ju pn 7z car be the same when the car travels around a sharp curve at a constant 60 km/h asnu;.p7i2 zr c ,kj6scs when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where doesi 59h itbm5r-oam9nvbx8b 3 s- 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 nea5iho-nm m5i r8 bst9ab-v x39br the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-round.(4ls :rlu fuazxa4z 4l+dj8z2 Which of these forces ajlz8:lz u4sz2xad4( rl4+uf provides the centripetal acceleration of the child?

A bucket of water can be whirlepi btt/ukhq78mf( 6 1td in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explai6b uqph i(t71t/k mf8tn.

How many “accelerators” do you have in your car? There are at least three 87 8-jcshrsdwunl46udd* ; ns controls in the car which can be used to cause the car to accelerate.s-8nw*c rj 4dhu 6;8u nsddls7 What are they? What accelerations do they produce?

A child on a sled comes flying over the cret movhj,2 afasauu t3v:18+(f *hz(x nst of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he haxzvuv8a, u:t(fs 3ha (nmf t2+j*1odoes 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 inward w *h d.:zhxts c6yfkx02hen rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banrf y *4l.m93+ban.f)ukl ;asa3 buyoxking angle given its speer bna4as9 .ambf oyuxly;+ .l*uf)3k3 d and radius of the turn?

A girl is whirling a ball on a string around hendb-.uqg .n-rk ti4z) r head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When shouz)b.trn4u kq- gi d-n.ld she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how largjz2op djhz5vr 03t- y/e a force? C do/ 0zr2 3y5pthjz-jvonsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublr07 u pk +f,nczu5jf9/ku 5o/l,qbddve what it is, in what ways would the Moon’s orbit be du+ ub jq9f/5 n0vkkol/5uzdrcfp,d,7 ifferent?

Which pulls harder gravitationally, the Earth on tk9 cq, -y d1a+z5viiwqhe Moon, or the Moon on the Earw+ idqk5a1-yi9zv cq,th? Which accelerates more?

The Sun's gravitation40p :ijo c b)nh1 /ug .2cpicv ug2la-th(v*hwal pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly a0ubhcg4-.(c p c2ji)*w t1g h2vin /vpuol:hresponsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh mor aa):zijytr1(5n i,3s e1iflb5y y tf1e at the equator or at the poles? What two effects are at work? Doi:byl1aiy )a(5zfy5in3 sjfr 11 tte, they oppose each other?

The gravitational force on the Moon due to the Earth is only about hals z-i 9 c-ldq3i5cpsdyo ; ;1aprb+4)wndyd,gf the force on the Moon due to the Sun. Why isn’t the Ms5sw dpdi91 ;n+c-cldp;) -3b yq4doai zry,goon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger+kw7wdq-lgra n/,pwr, ph9; ag yjx60g x/;fk or smaller tf9,gyak;jr0ghr- ;x,gwww+/k x dl/ 7nqpa6 p han the centripetal acceleration of the Earth?

Would it require les* un, yj*(pa*o0;ptrcntuys i pxy( 0,s speed to launch a satellite (a) toward the east or (b) toward the wecypriya0(t** sjytu *pox; (pn, nu,0st? Consider the Earth’s rotation direction.

When will your apparent weight be th kkm- ,le1tel 2 ;vk)ur9kcd5pe greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) l k9 )k kmctk;e2-e5pu, rvdl1is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend loeblhf9mrn0-adc 6 y4s(3 (gmjng periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the 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 yancdrb(m0j hy 3lf6e-smg9 4(ou can think of.

Explain how a runner experiences “free uwdnj0tse h-h6y2) l2 fall” or “apparent weightlessness” between steps u-d)jeyls 0wht22n6h.

The Earth moves faster in its orbit around the Sun in January t2i7; tqvyesl41 )z+s0it9dh hib8q j than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factqjttii8v i+ 0e hsb1zqst729dy;l4)hor 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 a moon m/ey zi9xithh-aq;s6fe 9,k1. Explain how thi kezia t6f-eiqh1m9,s/h9x ;ys discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than ( bzogp8 6 g jm8gqv8z/;f-tq0n*s jrjthe 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 sitting8vqnzgqg bt8 *j86-r;omg spz(0j/ jf 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 traveling6*e/niqlkpk.zcq*x/jlq gb :*7 mf u: 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 khq r1nn))ql,je8dl 3dq773 a7g igilEarth in its orbit around the Sun, and the net force exerted on the Earth. What exertslr1q8n, q7j3idande3l)h ql7g) gk 7 i 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 qb8oa l6mmeka5 8h 7u9/uo;twfmi*j8a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’k*8o5mh9ua8bqam/ w7t ojfu 68i; mles length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle e4mmo an 7)z t/)v(0qig3zeobis in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal aqozn4oe bta7mev/zi) g0 m(3)cceleration 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 ofkcw60y mrwe77 lw*cf* clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s d*wm70wrkw*7ly 6 fc ceiameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate irfa. l :19kcjon a vertical circle of radius 72.0 cm , as shown in Fig. 5 jo9. 1kral:cf-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 whic 5(jdvqw- ,mbhh a 1050-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 independent of tqj,h bm -vdw5(he mass of the car?   

  How large must the coefficient of static friction be )d6 ugml3 ,dqubetween the tires and the road if a car imu63u)ld, gqds to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is desidiwvvjg;2m+cj)::m -pkj wg:gned to rotate a trainee in a horizontapv:i w2j:+ m-kw)md;cjg gjv:l 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 4vnex 0jghkd h/h8vu(b o48n5 cm from the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm iudhxvo4 hgh (4/0nnb8 vej5k8s reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must hldg ,h4ouf- y03any* a roller coaster be traveling when upside down at the top yfhuh n *gyo-ld40 3,aof 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 tn0 lx(3wtqueuu 9z3w6- rsp5zhe rounded top of a hill (radius 5 wt-zspqu6r0wln(39u uz3 xe =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 7j-a6;. v ffm rehq9vhper minute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at theha9;q6er 7jvh fvm-f. topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10qnt9*m:lb+smfxo 29t6 wtlm gd p -69r m. At the lowest point of its motion the tension in the rope supporting the bu6l mpdm r+sbg9 x9 :29wf6tomlt-* nqtcket 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 c/jd7ujr7*/ w*ku v ( hemsd8wparticle 9.00 cm from the axis of rotation is/uj*7u s(e7* cvjm/h kwd rd8w to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnivalqn j:+ ,wtkrm0, people are rotated in a cylindrically walled "room." (Srw,kn0j t :qm+ee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictxs1iyvz 0 ,4flionless air-hockey tabletop, and is hevsz xf,4yi10 lld in this orbit by a light 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 ,hrfr 1d*hndpec,4mu.v u7.q, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In partrn .dm,f1p4 hu.er,cu*qv7hdicular, 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 8a5d 36*-s; ys2 hm)bzhnsdg; pl o9yoo8 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 masses fa2l 8uxxg5h( $ 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 :j j;*vwiq+b c7tyy.l-ars7 yhiq.d2 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 components of the net force exeewy0aim,n *b-ux9 . dexlt6)urted on the car (by the ground) in Example 5-8 when its speed is ,0*)xn-x6dmt9ewube lu .iya 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, going e)mb z9q av4 aym9*(asfrom 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 thimzv9mb(aa ea*qy) 49 ss acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle ofa)5gjym , +5fsy yen6t radius 2.90 m . At a particular instant, itsy +5 myj6fn5,)etsagy 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 (2 Earth radiiu2k:ks n skfa2qb--)6s zew(q) above the Earth’s surface if its mass is 1350w)-s ak2e6:b z-sqsu2 kqn (fk kg.   

  At the surface of a certain planet, the gravitational acceleration gi88 w(0iofqvv r:)tyd has a magnitudevvrdfo ) 0i :ty8iqw8( 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 e6x4mip24,qu ut d1ypgravity on the Moon. The Moon's radius is 1.7umid4t14q up , x62pye4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiua bbt8,bt- 6hss 1.5 times that of Earth, but has the same mass. What is the acc-bas bt68 ht,beleration due to gravity near its surface?   

  A hypothetical planes lc9 ml/f1rhdrt1+/i t has a mass 1.66 times that of Earth, but the same radius. Whatifc /1r 9rh1+mdls /lt is g near its surface?   

  Two objects attract each other gravitationally with a force of 2.5w1 y. ots uz-f,gm+yy/$ \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 (a) 3200 i n7*zuis ipet-r8w g/8vu,b5 m - p w8usiig/v r8*,tneizu7 5b   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cbxba,-53dne2a:04aco 7rol -syljrk enter to a point outside the Earth where thegravita54-r:yn r7dx k ljb0 3o eaao,abslc-2tional acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fiveo ku5ca tk n30jv5tu3jr9bnj)f/3wo 1 times the mass of our Sun packed into a sphere about353wc/9t1n kkuouf b0j5anjj3 ) ortv 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but+b,y*l ge bc*yze/)uq is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun.qeg/ ybb*yc ze*lu)+, What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless whl. 7 vbt8 7 -4ay:8jhbuynlffqile orbiting in the space shuttle. Your friends respond that they thought gravity lan -v .bhj4f7 : fybu88lty7qwas 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 corutyj 5.)xswlth6 ecq5n v/+p5ners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitatilsq +5utwp.h c) j5y 5/tenx6vonal force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planez4bu5 ta 1i;fzts line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and u1;t4za5b z fiSaturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of what 6ne4vs2cz/ dc+d ludw,4 zlr6it is on Earth, and that Mars’ radi z24+dlusd vwnd6erz6,cc /l4us is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of thbp4z +j- hg at-xkm)x)*kn;7;) cnbovlyid 6 re Sun using the known value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16z ix-or )gdm*natbx h)bc 64kn; p)v ;7-lyj+k.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circu-41 -9fg8qt pqcrl jiqlar orbit about the Eartjq1qrt9cl-fi48p- gqh at a height of 3600 km.    $\times 10^3$

  The space shuttle releases o*3qpx ne+dx, a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release nd+,3xeqp xo*occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if o 1tqz( 2x0ywikccupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s d1q(yi tkwx z20iameter 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 satellit,d21yt x0w fr8ty7 p8f)wwjobe 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 rarbtyowfp w 1tfx0w7d,2)yj88 dius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity woulsbpw-hyg/ d4k/0aj;o d a satellite have to be launched from the top of Mt. Everest td0p hsw/gjby-o k;a4 /o be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the cok + kqhlp3kb4 l2,dkq plw3j*1mmand module continued to orbit the Moon at an altitude of a*w3k1 lqdh3kp ,4j +l2plkbk qbout 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of c za,i3 edk )q;:qeq; zoreph3bt25(n ohunks of ice that orbit the planet. The inner radiusez;qehkqt 3 od qb),r on:api3(e2; z5 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 15.5 s (see Fig. 5:m vbj.kr (*um.:xjuy–9). What is the ratio of a person’s apparent weight to huk (bx:v m.:.*jjryumer real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight o:v( f oadj3jh3f a 75-kg astronaut 4200 km from the center of the Earth's Moon in a 3a (f:dhjj 3ovspace vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star sys.bo,4iz+fp6t i4da,4o da mcltem consists of two stars of equal mass. They are observed to be 6 44ltam4i. dd po+ibfcoz ,a,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 scaled8e7 ,-s d dg+svt2vab read for the weight of a 55-kg woman in an elevator that 2ebtga d7,ds+vdsv -8moves
(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 the3*2:z umgrvc: at lr+lfj8j jn4u9y:r ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s miyar:l: u:l8 j39urvrgzm4 ftj +n*c2j nimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of,pafe1+;w h: -8iuit1o msyi;mla )jy a planet with period T , thilht y1 m;isiepw8-o ,:j) 1y+mau;fae 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 period of the Moon (27.4 d) cc,vpq ( zg)gszp3(1b to determine the period of an artificial satellitevg,b3z (p zqs)cpcg 1( orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun 8ex:3 phf)x9hkj m:fylike t::9fx yjxehhk fpm8) 3he planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distancm+hil 9z2 w8)z6t5wtgx zgn) re 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 clygb q.e3z *hv6ose to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the 3gvzbhe.*6qy comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Gabci 6kc37*gm9 mgectp48 sz.zlaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 l3i e .38gayvpxnhv4 4aivt(n;da *o(nargest moons of Jupiter (thoseo3 4;x* y ( n4v3agtn.p hin8aeiv(dva 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 Moon.s pdz ):pz1qg;sl87a f 1;z)q7gsl 8sfa z :ppd   $\times 10^{24}$

  Determine the mean distance from Jupicgh g+mgx7 l7wp* e6 - hrrb0lu6c7b-eter for each of Jupiter’s moons, using Kepler’s third law. U-c+u elxlr6 *- r70wchb egp7gm7bgh6se 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 Jupitex hosc5ihlxgf;)3z )a*tdim 4:g,(2px)bnkq r consists of many fragments (which some space scientists think came)5 4h if) )xlsq3(b; gzan c*dxkgxpit:om2,h 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 "planet" in the form of a band co+)hk*c9snddcaj88fc)7 flg+h 7c va vmpletely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent grac+)+7*sh7 8d9fcnac lhvjdkgafv c)8vity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gome lk9qzi3x(6t31 rije5rv.grge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vitirg35m3 jlrx q(.1eezkv 96ine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half what i k6ad/ac-3te it /kaa3citd6e- is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutua:56/ f m-zyht: skugvovg69hvl circle once every 2.5 s. If we assume f 5mvvg69k: yv/g-6:zh tous htheir arms are each 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+sx e3cn) .j3*x ew0*dfdkswwtr 1jc( gravity at the equator is slightly less than it wdsr 1e+c.dwx0k w(3*)cj*wfst xen3jould 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 trak4fqai-i+;z 3lf7ap r veling directly from the Earth torzqa-afii7k l f p;3+4 the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass ishg)6cj iuc/sry 3j 9j* 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 elevhy)c*jugjr 936i sc/ jator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will 4 l: j+8t 85kd/ncx-esvqab5 vo/8 edj xit5jrrotate 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 t 5dtdi cj5 t-ejx 5x+r:skboja8/vq8lnv48/ e he Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43). 0xttm n0 x+a4z
(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 ofzp j*etnagf 9+*s 5.jf its radius r, the acceleration due to gravity at its surface an zg *p9.fjejn+s*a5tfd the gravitational constant G.

A plumb bob (a mass m hanging on a st x,x zpt.c+atz;n.o der( ;r3tring) is deflected from the vertical by an angle ;;cp (.zntt3d+ta,rzo x.rxe $\theta$ 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 bfk n:;oe x4dcv4)+gd1,nolkuanked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handle 4oe;fdg)o,1v: 4uxklcdnnk+ the curve?

  How long would a day be if t+h 5z 4t:cwgqphe Earth were rotating so fast that objects at the equator were apparently weighgw:45p tqz+chtless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 1 .fqp8qxx.3o)hqc;s0 g zyri 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 235 m. A lam-l6p h2xdtfssw 23 t)jp suspt2pwts6x2) df3jhs l-ended from 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. lp1y+;xc bt/m.9m:mj owg qg:yzi4 f;Thus, it has been claimed that j4b9;q .mzyi;fwg:mpt/ c1:xyl g+om a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data 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 1wj.xc:6:7 o6vmmda ijlrkr +the presence of an 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 by measuring the speed of gas clouds orbi+lm ojki67 arxd6: 1rv.jmc:w ting 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 asnqxmjwl7pqh: b a9-( : it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compaqp: blmjnx: -q7h w9(are? (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 Positioncqq/b38an0k,xt j gj iij34si 75a.yling System (GPS) utilizes a group of 24 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 satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. b8glj sqqjai3,jn.t45x/ i i07a y kc3(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 bil/ xx-aq(pum evdu/ ,i/lion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughp,u/uxv(ixde / a/mq-ly 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 satelli-t yzh q2:af0oi +,pngte in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above thn+a-2hfg y,qp ozit:0 e 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 had xr31:z 61cm7u+n.bqtmnjrso(f 5res a period of 3000 years. (a) What is its mean distance from the Sun?q(ref163 :nzub .1x dmn5ocr+mtsjr7   
(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 ya*om r;: ,8qwp3mlmdy ou could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumdym,l q8;3*:roaw mp mptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milk;m a pgz28 snh9n0:nrpywt:-g 5ml8e ka0lt, jy Way Galaxy (Fig. 5-46) at a distance omw :;n0a gh9lys2m8kgp ne- 0:l8nrtjz, 5tap f 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 a square 0.50 m on each sideb+:, y9uj4 nolyni1 stp vscse 6 cz,rh/10e5g. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at th s1py+,,6sjn /ugrv b yseo9etnc 40czihl:51e midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the E nna6osb55fl0ze)) b/ks: mmtarth $ \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 th 7 dyjnm.na:qs2khtozd(+a- )e tip of the 1.5-cm-long sweep second hand on yods:ayzmqon. -n27(kh+ )tajdur wrist watch?    $\times 10^{-4}$

  While fishing, you get bored osv6z87 o( u sb3sq1hy h8+fmkand start to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line.7s b y1v (+kf8 omz3ohquh68ss The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is3 d)ywxtky-ku5qtv p+ - 3 i+ww9x8)ah0iyzl s designed so that a car traveling at spet) +-+q- yl hwx39xaykz)0ywk5wt sdp 83uvi ied $ 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,v.p g4 xzc+3lhcw + rye*q*cx: 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 speed of (approximately ). (a) Calculate the friction for.r + gv*xp ccc4:leq3zwy*+xhce 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.$\approx$    $\times 10^2$