Sometimes people say that water is removed from clothes in a spin drysdqnptgl1 7 +d ;x9g3xer by centrifugal force throwing the water outward. 31+dgxpxsn gql7 d9t; What is wrong with this statement?

Will the acceleration of a car be the same when the car travelu(tjcy oq fe.uvr6*6/s around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explut ufr yv.oecj6/q*(6ain.

Suppose a car moves at cons.yge pbfo-5 )mtant speed along 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 stretch near the bottog5ympo e)b- f.m of a hill?

Describe all the forces acting on a child riding a horse on a me 3ww 1rx3of9bjyy itf- iz+e62rry-go-round. Which of these forces provides the ce wxifiy6+ 2z3tje3f1w-b y o9rntripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle wi7su6t(nz r:q kthout the water spilling out, even at t76ns( qu r:tkzhe top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you haveh3i;fweipnhc.icn52n5k bl;+p9 mq0 x 6v6 ex in your car? There are at least three controls in the car which can be used to cause the car tl9hxxmkii3p+e vc6 cq 05;w n.i 2 6efh5pbn;no accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying oveb8 2zy z+bvzx*r the crest 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 sled decrease as he goes over the hill. Explain this decrease using Newton8y +*zzbzxbv2’s second law.

Why do bicycle riders lean inward wh +d9k ubos:)muen rounding a curve at high speed?

Why do airplanes bank when they turn? How woulkua*n v() an-ed you compute the banking angle given its speed and radius of teu nav(n*k a-)he turn?

A girl is whirling a yimyt1lo-i+hgfau(k 2tz8+ + ball on a string around her head in a horizontal plane. She wants to let go at1 iofik l z+8y+ty(amh-+gu2t 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 the string?

Does an apple exert a gravitational force on the Earth? If j j jppj; kh,c.e/k0:xso, how large a force? Consider an aj jckjp pkej,x.h/;:0pple
(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 orbpis l:/0jpvay md2 fbgc*uv+y)7 u)7bit ljva+)p*2dc )u/b:7u bsyfv7py gim 0be different?

Which pulls harder gravitationally, thea3/wh 4y(4 xuta5z swp4wen-ky8 crv5jf 3x 9h Earth on the Moon, or the Moon on the Earth? Which acceleratha zxa xn4 5c( w-9wuvs3hf8kp4e/y35 j4rwyt es more?

The Sun's gravitational pull on the Earth is mur m2s-k( :,escuh1cmvch larger than the Moon's. Yet the Moon's is mainlyu(v 1 m2,sh :reccmk-s 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 two effects are aasi2v0dx, g)bp 3mr-/eqnrc+ t work? Do they o spm2-)vci+ /qn3rr ,0bg xaedppose each other?

The gravitational force on the Moon due to the Earth is only about h xm jdbh3r+ /+1:qafgirjp2i)alf the force on the Mox/mhq1jfaiig3 p)+rrj+ 2 :b don due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around thex xp0ex5u /d d1 cgv-zb39wrs2 Sun larger or smaller than the centripetal eupz0swbxg3/5r-29c 1xxd d vacceleration of the Earth?

Would it require less speed to launch a sqof*vvtlt gtktn9 (/2xp/0 *jatellite (a) toward the east or (b) toward the wet0nkj f 2tx lvtt9 q*//(*vpgost? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a l,g 8,t sbo4huscale in a movins8h,u4t logb,g elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affecte 9lpr.+ze jfjr-m v-(hd 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 obj.z -l9- m(h+refrvjpjects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiv ft+dhp 5rs)9ences “free fall” or “apparent weightlessness” between st9sp5rtdhf )+v eps.

The Earth moves faster in its orbit aro6rrg9m jouq-.:a1+l tt fb(t0 wds1jrund 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 — the main factor10otsjl-r( .qmb:w91trtu j a+ d gf6r 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 discoverdwp; r)28ks pj id(/p-cb pj2sed to have a moon. Explain how this discovery enabled an estimate / j)w 2pp8s;brdds2p-c(kp jiof Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger t (at+ g2:vy7j x8fmfzey 5lhk5han the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider 8 ljfemv+ g xah:kyt2z5(f5 7ythe 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 h*rkso5f .9pl 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 ii.6 o4ko;b x46d col z*q-tw0lssg3 rets orbit around the Sun, and the net force exerted on the Earth. 6sxl;o drqc g3 0k4siw*e6tozo b.4l- What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 Nv/+8dlq-96oy 2:k t a6t dpghz0jbccx is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of rh2bjzlokc d atqy p/ vt6:8g-x 90d6c+adius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Ea*w pgc2m4wk *zrth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the spa kg*mpzcw4*2 wce 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 accelero- iihe.*p kcv::8d ization of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel *hpi8e:vzd:i i ck.o-’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circwm7thsg; p7hjirgju6h cr y-a6 z1 3;.le of radius 72.0 cm , as shown in Fig. 5-33. If its speedguhy7j th z6w; -6gpr h.csi;j3a7r1m 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 1050-kg ca i41p(;o,ymcpz 5gqitr can round a turn of radius 77 m on a flat road if the coefficient of static friction between ip( m;4o51pgti ,zcqytires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of statim . y,2johix-zc friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95km/ xyzimj, o.2-hh ?   

  A device for training astronauts and jet dp)zya hzd kt ..j68-qfighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trad q -ht) a6.8jzdykz.pinee 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 turnte+44yvfq iqg gv(8n:hx)q ;x xable of variable speed. When the speed of qhn;8eiyxqg )xgv 4 :qxf v(+4the turntable is slowly increased, 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 co:sm4. my*yu/z pc3wptaster be traveling when upside down at the top of a circm34 *m.: /csuypz pwtyle
(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 4t*o :llvu0 /uh;opf fthe driver) crosses the rounded top of a hill (radius*ufo; :tfv0phluo /4 l =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 6z /93swyse tnminute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost tsszyw/93 6 enpoint?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circc-g(ej s+ 2cucle of radius 1.10 m. At the lowest point of its motion the tension in thu g(c 2e+cj-cse 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 centrifevxtxtwi h12y; wrza8 36 bx:8uge rotate if a particle 9.00 cm from the axis of rotation is to experienbiaxwt2exr;x:v z 18w8 63htyce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindri2 5kcc) 5 yrz.jn03xhcpjyo s0cally walled "room." (See Figs55c.y0jp)yc2hcr 0 okz3 x nj. 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 )*noiagju55.q 4noq t a circle on a frictionless air-hockey tabletop, and is held in n*ogoua)ij5q4t5. qn 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, by not ignb ie v zz6xan( o09tic*e4rn+(oring the weight of the ball which revolves on a stri c(ben6 0rza4oinv9i+xzt (e*ng 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radiusr/ixdeg+ 9x g:)b le2l of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of massess( 01yadpf )8iqrh)kw $ 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 maneufxpjy 5ts, g0): u(e+yggvgq.ver 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 tangenti :r5nxwd* o-tnal and centripetal components of the net force exerted on the car (by the ground)do x-:5*nrtwn in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates unifo;1d 2tj p02 1u4vusqtmts+cy kj+5upjrmly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to providej4 2+ksps yqum;1 5 jpt1d tvjcu02+tu this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horu cwbo6/0le, ,zt4mydizontal circle of radius 2.90 m . At a particular instant, its 6oulz,wc /,t0 ybe4 mdacceleration 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 ppu5 t9gh/4m ca spacecraft 12,800 km (2 Earth radii) a tppmhc/59u4g bove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitatizha,g0t r8eedr36znyl,m :/f onal acceleration g has a magnitudehezg/y ,8dt,zlemr:a60 r f3n 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 o.myjno xc)1 a)n the Moon. The Moon's radius is 1.74 ya c.xo1) mj)n$\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 thal *kk wvz1ie;j+4brh(t of Earth, but has the same mass. What is the accelera1ekrhblz*k +( jwiv4;tion due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, o: mklou 9i+4cjb;apv- 88xzwbut the same radius. Whatjx +k8ipvbw4c;-ula oo: 8 z9m is g near its surface?   

  Two objects attract each other gry( rx+)x i6-cdfbga6v avitationally 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 0 jn+m;vhd08j6 erj0hl a d-spacceleration of gravity, at (a) 3200 m e-jad0s0; pd+jh8lrv n h06jm   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outsp4w1pm cito d9, agc76d/+m lg pw)bl4ide the Earth where thegravitational acceleration due to the Earth is m /wl94w,a6 dgopb mgc4p+idl 71)tpc$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed intu)0,ic zmw+4yduv,u.70 /dlda csl+huh 2ppbo a sphere about 10 km in radius. Estimate the surface gravity on thicu0p/4ddduh li,b)c z0 .+,uuma72+shwl v pys monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun b --xr,vumh ;oout is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?;m ho-u xr-,vo    $\times 10^7$

  You are explaining why astronauts feel weightless while 0o/ 0*) ukwc0um9atqxbxpm6w orbiting in the space shuttle. Your friends respond that they thought grax)cm uka6q9*0/umw ptx ow0 b0vity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are loti1rh ro6 y s,(khz*a2cated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on onei2yh6 otr(1* zkr,sh a sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of th5 c3ip h s/q2 *oc3c9 yjvoopw).)ypaqe planets line up on the same side of the Sun. Calculate the total force on the Ep9q3y2oiqcpc s)5 cavo.oh 3/*py j)warth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration (e8s(,zaj m mgof gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determme ,8j(szm( gaine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using m2rm 9zco8:p/j j)gjh9bbhz 9the known value for the period of the Earth and its distance from the Sun. [Note: Compare you9c 2ghj/9 )jmbhzr:jozbm 8 p9r answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satdti5m fbxg/een(mbz o8s 0r5 h -n/fgt:k66d-ellite moving in a stable circular orbit about the Earth at a height of 3r6e n 58 d:ftzf50i6g/sxdkehgtn mo/-b-( mb600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above th+w:: .kzo,lwmkxzeb* e Earth. How fast must the shuttle be moving (relative to Eam. x,: zkw+*we: zokblrth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience y09t4 o) rvfni mlw:h8 :iluw0c.w z3lsimulated 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 Question 21, Figf.03hu wtl:y 8zvcrl4o il m9iw)w n:0 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circu o5 +*pqnr t/i9rxhjq-lar “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 radius of the Earth. Does your 5i*h9j -+/nr qoqxtpr result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched fr 8qx-4fcmid j4om the top of Mt. Everest to be placed in a circulacjdi 4m8x4q f-r orbit around the Earth?   

  During an Apollo lunar landing mission, th7 exduq (cs xlq.aty098.imm .( vyki5e command module continued to orbit the Mooksv.udm qy0(m 85 iex..9cq 7(tlaix yn at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are c ev(8n(1 ws ek vnby9lr43o9vgomposed of chunks of ice that orbit the planet. The inner rae(1rsy4 (og n9vklvvb ew 389ndius 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. 5–9). Wh h;6f5/xqgr ,d 9fsiowat is the ratio of a person’s apparent weight to her real weightrg ds95/o xfqh, ;wf6i (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from t d * tzqhrs5urwj768r8he center of the Earth's Moon rr8 *jtd us 6qhr8z7w5in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-statpv u81kswxfuvdna tj-g 5* 093frx7 4r system consists of two 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 xv ts8t7 kf-gufrx439 v1p*0jnwdua5them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for thef /j6, o3b*n2epul sdx weight of a 55-kg woman in an elevator thatsf,d*p3/x o2n ebuj6 l moves
(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 ): rqz; ng+gdia cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minim+gg : n;)qrizdum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with period w7 m b5pl80v)py.lllp T , the5p)l08l.l ymp plw7vb 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) to determinsnrlr(: n 5m/me the period of an artific mn s:5l(mnrr/ial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred mf*puvc5nk7e 5eters across, orbits the Sun like the planets. Its period is 410 d. What k n55p*7 cfvueis its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5,5 d0 whea3alf $\times 10^{9} \mathrm{~km}$ 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 3oyb7(6y yeqt z,ls+r76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of t + ltor(ys67yy3qe,bz he 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 cm0;jx85 7ldm6 syp zpwenter of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean1c t(dk42yw uo distance for the four largest moons of Jupk(w 12 o4dycutiter (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 c mw5t*-rs2p8d)m a2h7gt nsqand distance of the Moon. p)qw2h 5msmtn tgr c82*a -sd7   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons,eox-u 8wqzl8y* b0h q5q0co-o using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the va0q*q5clx 8 -o0oqw-yobhuze 8lues 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 consistnu,o n*luo0,q s of many fragments (which some lun 0,n*,uo qospace scientists 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 dshim5)6pf +vh t4sro;oej *l;escribes 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 temperate), and that the + l hef r *)p6tovjho;s;4im5sring 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 bnj als/fv0()5fl z j7a hanging vine (Fig. 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 lowbfl70szv /5j)ajnf (lest 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 z6jb9e yj7qwtxe p;:j;d0ag) be half what it is on the surfa t;6;dzq)xe0j7ab:y e pgj jw9ce?    $\times 10^6$

  On an ice rink, two skaters of equal mass v(cdy7 pc)j*hgrab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulvc *)dj7h(cpy ling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravu 1;p: 7n(q6, wwqhl0srld pnwity at the(pq6hn:wqru pnw, l 0d ls17w; equator 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 tbw ;*7f5b6k.zahqpk sraveling directly from the Earth to the Moon experience zero net force because the Eart57*sapfkw bbz; qk6.hh and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scalfyd ib(5jtd6 fdq/4f(e in an elevator, it says your mass is 82 kg. What is the acceleration j5if/qty 4fdd ( 6fd(bof the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotatehq4lqg2*t w.p about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about q24ghlw p*t.q 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 (F)v*ug :ec(zcmw )j*o s2 t;nw*egpl0zx04jhw ig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius h x 4oew/o.fj8bjxm02 r, the acceleration due to gravity at its surf/o oxfb.ewh4j m20 xj8ace and the gravitational constant G.

A plumb bob (a mass m havg(6 9ao 0beosa3v*3d ;nknddnging on a string) is deflected from the vertical by an angle d(6oa3bs 9anv g*dokn03dev; $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a.diu s29s3 mbpukz8u 0 design speed of If the coefficient of static friction is 0.30 (wet pavement), atdiz9m0s bu8up2 s.3k u what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so ux)1 b8b2vso58+-,x pvym;pok n6tj evg w4dvfast that objects at the equator weemog-4jox dkvvvsw x uy8p2;n,t 61+b58 ) vpbre apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dis xxle-og+t7i/m- kcetg 7:n/ztance 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 acac(qc /5uvk1 constant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swings oua( 51ukq ccvc/t to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive n-k4: widtf;8 o1hrt.8olfw:a3kkxg as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would explwfa:.t 8tw- kghk8kx1foo;43 r: ndierience 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 Tzm x9b)pj2)ey l /ksd 9-1hxqhelescope deduced 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 orbiting the core to be 2b - zejs1yxmhk)lhxq9d)/9p 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 speedn+-d07 cug l:jnahwp+ as 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 compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel h7h- pg+cjun wdanl+ 0:eaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioz, sb-lqx. ci 8yh67; nc-xkryning 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 ]. (a) Determine the speed of each satelli8xy7snlc- c ;6r,x q-h .zibykte.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is m3labi 0t9 hlh;u(,cnfjhgb/8 eant to orbit the asteroi/i,hfhb9 lu8tncb 3 g0lh; j(ad Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the spa4ds8ueiwk 8y 7ce shuttle pursuing a satellite in need of repair. You are in a circular yswu8k4 8 di7eorbit of the same radius as the satellite (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 distana kh z.y; n;z57ndl b;ao:nq2mce from the Sun;d; q7knza2;ln5.:ma by onhz?   
(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 coubuf8mmwy 6l/8 ld actually "feel" yourself gravitational /8mwbl6mfyu8 ly 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 Way Galaxy (Fig8xo5s1ibus wntlm;dt(02p6 vft06 z vs3d9ij. 5-46) at a distance of about 30,000 light-years from the centez81ov39tts wju( 0;m5bi 0 6ln6ftsspivd dx2r $ \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 th/hqt;jjita-3t ch+su .is 6 s9e corners of a square 0.50 m on each side. Find the3.9 cihjihta / q;us-t+tsjs6 magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits thex/b8 n7u h(drr(xa-mh yu6h9ofc 5kz 9 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 experiencedvuxs ig3)kc **hg0whq7- gnn. by the tip of the 1.5-cm-long sweep second hand on q* k uwgghn-x7)03cig n.*s vhyour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to sw.vdnvn 96j r4zmb6,g3 a7bdhp ing 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: See Fig4jrga7dz 6n9 ,vb hdv6.m nbp3. 5–10.]    $^{\circ}$

A circular curve of radimgprouk ws0dtc98z+m--k 28a us R in a new highway is designed so that a car travelinkr8mdam89-c2 s0guwzp ok+t-g at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the y2oqu7 qo7:t96yui 3q dmfgz (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 speed of (approximately ). (a) Calculate:f9y7tu y6io gqu mo(73qzqd 2 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.$\approx$    $\times 10^2$