Sometimes people sayn37ln .)ynojq that water is removed from clothes in a spin dryer by centrifugal .qn3 7nyj n)olforce throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharo6 jxb5:6co bn6e0 wymp curve at a constant 60 km/h a06x:woy j6oc e 6bmbn5s when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly r nw-36:aal vs9q wdbs8oad. 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 stretch near the bottom of a hill?n 3la asbwwsq:8d-v9 6

Describe all the forces actiyxw dg 7d*0 fq6ba.7m g8ew:zgng on a child riding a horse on a merry-go-round. Which ofe.70*7yzdga d8mggb:ww x6 fq these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled in z8t;-z1um qoe a vertical circle without the water spilling out, even at the top of the mtu;8ezo-1 zqcircle when the bucket is upside down. Explain.

How many “accelerators” do y.u dm7b ok.xad . ekhs2+a;l-eou have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they prodx2;+ok.db .lkuh -.ea ms7aeduce?

A child on a sled comes flying over the crea u4 t2hvrl7pt4m)2dl6/ jir7b /nshust of a small hill, as shown in Fig. 5–31. His sled does notjr47lna/ hp2tt/ mulbuv )rih 6 42s7d leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward w (* 6(cwrp c+ahrhxj)jhen rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle gj8.gk+ xhu 88nidakb: iven its speed and radius of the turnjkhk.a 8un:ib+88dg x ?

A girl is whirling a ball on a string around her 2vw+unur+v m:. xsv7ihead in a horizontal plane. She wants to let go at precisely the right time so that th 7mxv2.n+uusv v+wi :re ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on hxk 7(r hhm3r/the Earth? If so, how large a force? hx h r(h/r7k3mConsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s orbit wxc;ub09e a 8cbe0auc9; x bwce8 different?

Which pulls harder gravitationally, the Earth on the Moon, or tujclbf9yz* ekojb,f 98 h7:m-he Moon on the Ear89bf:b9*l7umoj-,ckfhj y ez th? Which accelerates more?

The Sun's gravitational pull on the r-r9 qdnq ye.r0+c9qso0uv* d Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pulsu 99*n rdqorec0r.q+-dvy0q l from one side of the Earth to the other.]

Will an object weigh more at */xd 7h hjf zn0q)k txj0h:5amthe equator or at the poles? What two effects are at work? Do thkaxqh5/xh0 zt*f)j :70 dmhn jey oppose each other?

The gravitational force on 3v 2qzzvhw42rthe Moon due to the Earth is only about half the force on the Moon due to the v rhzvz22q w43Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larodqnu64 we . 4:puwn3sger or smaller than the centripe. ueodpn6us4 q3n:4w wtal acceleration of the Earth?

Would it require less speed to launch a sat4gsr .cak/.oantyz; t a3 f/t1qe ,uh)ellite (a) toward the east or (b) toward the west? Con.a.;th/et/u,ak1 say ng) fqz43c ort sider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in a gf(f5h bkqo 26moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free falb(fko qf62 5ghl, (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 long periods in oumf3 +2 ooanr+i8yggs 3ter space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a g23 ma yg++3iors8ofn 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 you can think of.

Explain how a runner experieo tj:0zn a:g-jnces “free fall” or “apparent weightlessness” between steps-z:o j:jagnt0 .

The Earth moves faster b jf(.+jzyui d5kaks79 0lm9xin its orbit around the Sun in January than in July. Is t95xak(sjzmud+i7j0 k fy .b9 lhe Earth closer to the Sun in 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 web: he73lvdg fsc7y-,hx cm7,as discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s massy h v 7c,-lbsc e3fxe:,d7m7hg.

  The Sun's gravitational pull on the Earth i;j,un v6 n-txts much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Cox,t ;un6vt-jn nsider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . 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 19* +m)l dptxxabsqv+0nt 50d +z80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around 3 wpjs9;cn kk.the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle k wpcn9;s k.j3of 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 exerthd yprb8 ib733ed on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) d3 y3hpbr7i8bof radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Ea )rq9 8rfzx-irrth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Expres9)rzxrf i8rq-s 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 g.ja iiu/2 ih gn s2*/awn84g:chz5udthe edge of a potter’s wheel turning at 45 rpm (revolutii :ia/u5g c8 d 2*gnasjz/4igw.n2uhhons per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a .k4utv; kiq y9vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its q9it kyv .;4ukspeed 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 whip 0pf- pn1xpth/-t60kjzl ,xgch a 1050-kg car can round a turn of radius 77 m on a flat road if the ckn0xp g06,fxtlztp-hj-/1 pp oefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of stashcpqgs;z 71 s:9ypy+wh4e3zqxv67 d d61jhxtic friction be between the tires and the road if a car is to round a level w sgzhs 7 p+:q6q h;4d y9p6s1d1x3e7vzxhyjccurve of radius 85 m at a speed of 95km/h ?   

  A device for training astronaji f17p ubfrzwd3v 6),uts and jet fighter pilots is designed to rotate a trai ju1r3fi,b )wz d6fp7vnee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own 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 varim 5ym:6r *f.sww vac4lr ;/tsfable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the tu mf/t.vylsf m6a;ww r5*src:4rntable 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 a/-uzuodjn)/ 1 szj-x must a roller coaster be traveling when upside down at the top of a circleus/n-jd-zuz j a 1)/ox
(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 drivc((hhfo0tl 9 eqd: 4taer) crosses the rounded top of a hill 0(:laedf hq toht49c ((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 a 15-m-diamq6d;qc*ib5m0d hjt y: c8q9 wceter Ferris wheel need to make for the pajw0 ym;9cc6iqddbht cq85q * :ssengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled inm/o ; cesu;w, -5xbgxr a vertical circle of radius 1.10 m. At the lowest point of it5e;mcx wogr/,-bx;u ss 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 tmp u5nxd0r64f tm*ck6 he axis of rotation is to experience an acceleration of 115,000u4 cr05mmpnd k6*6t xf $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a ctask, jk6.g; garnival, people are rotated in a cylindrically walled "room." (See Fig. 5-g,sk6k;a gj t.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 fr.y9 y (zb5c3 *-nbtejvq frz.gictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown5bzn*b-vg9c3ftyz . erjq .y ( in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring t7t cdg 0lj-d*qhe weight of the ball which revolves on a string 0.600 m long.ddgtjq 7c*-0 l In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling2 u5-b. 6dmn7jmmtfhl o4/pbd 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 massesfevevk*f(5j/ $ 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 mnb:tlrth)r1r3xamy90e t 2be an-;k m2.ul(ianeuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential anluq0jx6dc u l14w e2*od centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when its xlqu4*0 1o6j wcd2ulespeed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniluvo7;f6) vhfn +yhzpwv))5 oformly 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 accelerof ) ;zhv hn67l fwuov5v+)p)yation. 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 with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal cid-m m-hrymqlu y , 1cd(p+fa-wpq03b9rcle of radius 2.90 m . At a particular instant, its acceleq(l my,- cwa0pdpy3f9dm-hbmr-u 1 +q ration 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 Eaje 4nho8v o9,9tn b,g/1olg uf q+:p:lr tcqw7rth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Eoop+8e1 tt7nb/lfugjq9:gvwq:4 , hnr,ocl9arth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a magag8 6lfabdo .*nitude of 12 m/sl.adg o*8f 6ab$^2$ 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 jv(f oqd l89:igravity on the Moon. The Moon's radius is 1.78(ofi lv jd:9q4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radi;s(3vrx;fj q nus 1.5 times that of Earth, but has the same mass. What is the acceleration due to gravitys;;f(x nrvj3q near its surface?   

  A hypothetical planet has yw6/ .r6kw4 th d(wjiesb l.h6a mass 1.66 times that of Earth, but the same radius. What kb 6sthih . 46w wwlj/(.d6ryeis g near its surface?   

  Two objects attract each other gravitationally*z 8szw ef iw0w(is;:n q**jus with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3200 v8ff; vo/ ki -ykv7h7cm /hovfv ci8k-; 7f7kyv   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wh rs ;i/ m1xsdav+0oc-xere thegravitational acceleration due to the Earth isod-s;1 s+0 vxai xmc/r $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our h;9efa dqs: )qSun packed into a sphere about 10 km in radius. Estimate the surface gravity on this f9d:aq)hs q; emonster.    $\times10^12$

  A typical white-dwarf star, which once was an averagj)jql2 fq2rcn(df ( av/8w a(ie star like our Sun but is now in the last stage of its evolution, is the size of o(ljf(ad 2frw ) qv2q(n8iajc/ur 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 w pue okmj,*nco7:*wg7b ;dgy4eightless 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 calculating the acceleration of gravity 250 k*,gjp *o4c7g b7un mdk;wo ey:m above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side q81p gn1svys .: g.qhy0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphey:snvqg..s8 h11qpyg re by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mostmmg1 -q7kv :pyatu 58v cfsj-9c42bih 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 allb-cfm7t:vshj g8mpk y2v i 5u91q-4ca 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 gq9 2 51 hk/2hgkctedjnd53do kravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius idd53dj2cge t nk o5/q2kh91hks 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using th w8r*r8di stbx.azd; 48emx3l e known value for the period of the Earth and its distance from the Sun. [Note: Compare youbxia88wm8rzs4; rd x.e dt*l3r answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular orbit .v /zcas.j cd* i:ez4zabout the Earth at a height of 360.*/ d.azejc4vs :iz zc0 km.    $\times 10^3$

  The space shuttle releases a satellite in go7f5tw)-5c 8eimitu pd3ca.to a circular orbit 650 km above the Earth. How fast must the shuttle be movingdtu -5gcpeiwa. mo)8fti3 c57 (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupan)m6h h*m tp 7p.uhsvz-ts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Q6*hptm.)hs -u pvzh7m uestion 21, Fig 5–32.)   

  Determine the time it takes for a satellite to o-lvxu6t 6d jfym,( 0e4b. tmpirbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surfjp0 ,6 mb diu.e6lx(ytftv4 m-ace of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity woul 9wo;)xa2aae dd a satellite have to be launched from the top of Mt. Everest to29 woaa;aexd ) be placed in a circular orbit around the Earth?   

  During an Apollo lunar landingbbhl (9,x3awh mission, the command module continued to orbit the Moon at an altitude of abxw,bh h l(9b3aout 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are compa 8xzmuxr t9-9osed of chunks of ice that orbit the planet. The inner radius of tx9 9xtr -ua8zmhe 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 15p 1q;+hpwmj, u.5 s (see Fig. 5–9). What is the ratio of a person’u; pwm1jp+q,hs 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 9byek) u;x;f(khio1e4200 km from the center of the Earth's Moon in a space vehicle (a) m9 eh uiekx;1o;yk(f b)oving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of twotie4crkp +o27 stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What i 2koe4p7+trc is the mass of each?    $\times 10^{29}$

  What will a spring scale read f 11nk ;fjj8 ydbk j/9mhc9l;feor the weight of a 55-kg woman in an elevator that moves 19j1fm djnkhe8k/b y9 fcj;l ;
(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 fx2i a/5 wgksi1i+,b sirom a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as t+is, swgbii5/i 2 akx1he elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satel,y trjezw/ce c1t04w+dzh ox+:z /c, vlite orbits very near the surface of a planet with period T , the density (mass//tc+ o4:x,yczewc,/e1d wrt+ zh v0j zvolume) 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 Moonzg.ep w))y. uv1p7oiu (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s vpi1euz y)7o.)u w .pgsurface.    s

  The asteroid Icarus, though only a few hundred me; i; eguy)s:wz mu8r(jters across, orbits the Sun like the planets. Its period is 410 d. Wha e zisjwu:u;y;r)8g (mt is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.wl7(i(icij4uvx +9q ya.tn)v5 $\times 10^{9} \mathrm{~km}$ 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 8 q:jsz8ef9r7 e+pcpwclose 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: Tcej+8rqp f8w spz e79:he 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 Galatw ( gy-l8f1vaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, ps8ccw)rzypzf 8qbwvx43( 98leriod, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in czl cw9 svfp 3z84(8w)qyrb8x1609).
(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 kaxh; mt:0sc :xnown period and distance of the Moon. :hxmc xa:;st0   $\times 10^{24}$

  Determine the mean distance from Jupiter fodsd*i vp+q3royd znm 7u 62b(3r each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the pdqb3d 6vz (*37u+mrisnod 2yvalues 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 fragm r l (xlm7gn)m9kajhkhf-)9-oh *ru; fents (which some space scientist* j)g ah nfx- rull97m-ohkhf (m9r;)ks think came 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 den/ g6u6knktn in61ak+pf8a/ w96jcgmscribes an artificial "planet" in the form 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 distance to the band is the same as the Earth-Sun distance (to make the climate t ifku8 w gpk6/6gn+nt6a9/ 6 macnkn1jemperate), 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 vine (Fig.+4qjy7of )* 1mks:nwnlj+nvy 5–41). 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 lowew1+4fo*qjm: nnj 7snvl+ )yykst 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 aghjng**7wzyak..44 )-*kpxt ezbkx dcceleration of gravity be half what it)y.7*jx*d*eahkp4kgt bg. x- wkz4nz is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin inisw87b1u - a,ft8rxi f 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 i71asifxt8-f , uw 8brpulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelej-db w gc.)qv9e(rgg+ ration of gravity at the equator.)+gwegjr-d qc (b9vg is 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 directly fromc1dk(6w uya j7 the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces? a6uy17wjck d(    $\times 10^8$

  You know your mass is 65 kg, but when you stand u6+jpqwdgamzs hc *;+nu8 91zil2k6z on a bathroom scale in an elevator,nz9g+ml* cskhai1 ;q2uzd 6zw8 up6 j+ it says your mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circuld1 .busx9i ey3ar tube that will rotate about its center (lu193di.e yx sbike 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?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43). g eqdi/,zc9 m2/huuc6 ( glm3t
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the actipg-u7d 0tlk 022jihceleration due 0j p0ui2lt- k72ightd to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from tuf -lvq-kua3tm-a-f4it pc(7)x 1yx mhe vertical by an anxxqi--fa7 )( 1lktfmvm u-u3t- ac4py gle $\theta$ 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 bawp texa)ay7-js l)*2w nked for a design speed of If the coefficient of static friction i)wa p-laey 2wxj7 *st)s 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects ckt 2n8ty n:4h2xdc// i;kyx6 ghrve 7at the equator were apparently weightle ivynckg/nc 26t;7rx/x:yehtd4h82kss?    $\times 10^3$s

  Two equal-mass stars maintain i/h0t1vmo u+ r3f8wima constant distance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lq0y:rq8 a uecss8c5.55h lju hamp suspended from the ceiling swings sq5ru 0ea8hl5s8.h:jcyuc5q out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times asr;etsc, g7xz1bg3p) j massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive g pr x7s)g13c,; zbtjemore than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extremelaooip+/5go0knl8bq r jj 06p,le /;giy massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes)io; e6k8,jglj ag 5nbpolo/0+ 0pir/q. They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it trave1o;vjyl c)+k1qea d* hrses 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 compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest*h y v1jqc;a)k1+l ode? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System w:dkl *.51d wu / f8ewg0jlmgr(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 d l.kw0*m/g5eg1w8dur l fwj :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), after traveling 2.1 hk), e91e ovajo0njs: billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Erojk0o ae )e,vs1n j9oh:s 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 purs.( rojqw05 :9np+cjos goiyg; tk2e7buing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite pj: cgk5+o9g. 72be(oyq r t;nowjsi0(400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean disil.9 (*w v+yfnp+voczsbl2v+tance from the +wl.*++vciv 9(2zb p nvfsloy 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 n2.c1e sk8njqo4fii.k2u:p t +j0y nkd cd+sk4eed to be if you could actually "feel" yourself gravitc+0:sjq1d k.i4. ntc esp8k+j 2o42y nfiukdk ationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Wemc:()a zsg o1ay Galaxy (Fig. 5-46) at a distance of about 30,000 light-years fro1osm(ca ge ):zm 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 squar5axyb, )udrm y1+ e1 jkowp7( on9uqop,.7yore 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed atm.noryoou5bq1 r pxa y, yk71)wuo9 7jd,(p+e the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Eart/ai zi r:pe77uh $ \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 exp d+zd (st4isv e25i3afn1 k:tterienced by the tip of the 1.5-cm-long sweep second ta vd( s5nif 2e3d 4i+:z1ktsthand on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around inmj-r wg/v.ouj x9 ll44dmh +*n a circle below you on a 04m x/*lrj .g mj 9hvwuo-d4l+n.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: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so thatpv.r aq4,c jf2p9o;md a car traveling at speppmd4;jqr2foc, av. 9ed $ 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, utilqf(ewa,fj w9cn6m ty j +*p e*sye7)k7izes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provideewjme taqy9)fykp+j* *6 7 en,7w(sfc 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.$\approx$    $\times 10^2$