Sometimes people say that water is removed from clothes in a spin dryer 0t+ataolbdci.c7m 11 f,3hk d by centrifugal force throwing the water outward. What is wrong with this statemdldiatf c +mt3 o1. a0hbk,1c7ent?

Will the acceleration of a car be the same when the car travels arouvy;k 8e mks/g-nd a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Explaine;y/m8gv ks-k .

Suppose a car moves at constant speed along a hilly road. Where do*:r.h9x o5xnkv1p mw8:oxwfdjf* cv 1es the car exert the greatest and least forces on the road: (a) atw.rn5px1m:**dhcfx kx wfj vvo9:8 1o the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-roua,ht 5( fkdyyl20rv 487d hjnknd. Which of these forces provides the centripe(d 4hvlka05h87yd rjk t ,yfn2tal acceleration of the child?

A bucket of water can be whirled in a vertical rau8f)s3 wk59 wh/hni circle without the water spilling out, even at the top of the circle when the bucket is upside doww/fuhr)sw hkn9i38a 5n. Explain.

How many “accelerators” do you have in your car? There are at least 4c0 tbp 6thtn+three controls in t tn+ c4th06tbphe car which can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fioedv304gt-m:p3 ec,8z.0j qrrql vadg. 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 sledq:4rvzevad0q 0 ,j -o3p ltrgcdem83. decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roundingki k 6iu qd1c3sc+w(xb/z3x0g a curve at high speed?

Why do airplanes bank wm 2 tn,b+l 1l-lrgoty/87achhhen they turn? How would you compute the banking angle given its speed and rad8bl7hytanh glm1l/+ -r 2cot,ius of the turn?

A girl is whirling a ball on a string around l9l+90gbuc0h nli px0x6t:pz her head in a horizontal plane. She wants to let go at precisely the right time so thap0lz 9 g6nt+xu ixp0lhcl0b:9 t 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? bx s4iuq4:n wxh4t (2yIf so, how large a force?i4 :n2qhwx(sx4u 4bty Consider 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 ):hx/ )lqj hzho,selw(g5 ic .orbit be differenl (/) he gxo:jc5.slhz)qwih ,t?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon oel hd,cmg5f4 .n the Earth? Which accelerates more?4cedm 5 .glf,h

The Sun's gravitational pull on the Eart (g8 1tavbo7quugg rm 6+ gtkhxv9+c78h is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the othxb6a+c8 h 7vu+gggq17(g to8r tukv9mer.]

Will an object weigh morgivgpl;pn2y.tw c1t ) *e:14ramek 9x e at the equator or at the poles? What two effects are at work? Do they oppose ) .9 2tgxae1;i*nlgp yr twkevp4mc:1each other?

The gravitational force on the Moon due to the Earth is only about half tv/:eo-t n a4chorxy ;1he force on the Moon due t; e:a ocx1n/o -yht4vro the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larg7 7g/y3axet9dkw:t vq er or smaller than the centripvak tyg/7q:d79 texw3 etal acceleration of the Earth?

Would it require less speed to launch a satello j:n99.p(*u rpxe gbqite (a) toward the east or (b) toward the west? Consider the Ej*o qbe g9:u(r. p9nxparth’s rotation direction.

When will your apparent weig6o 2uopr1of:5 liz3eg ht be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the f 5p2u:lreizo og613o 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 spamp4 k:,irlse 6ce could be adversely affected by weightlessness. One way to slsr4mk:, e pi6imulate 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 you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” betwee0 )mq02gqv .jw/y mcvvn stepv0/wqvj ygq.) 2mc0mvs.

The Earth moves faster in its orbit around the Sun in January than in July. x2 jkiw b8:xdbsfre g5: 716tjIs tf:jbb16wx d58 kg:jr27t xisehe 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 was disc gf pigy.c 7istw b9;i)h050bvovered to have a moon. Explain tw fi7sg) 9 0.c0ig5yibp ;hvbhow this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon'st8c d7+g8)j4svj1g ipi wn 0us. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.1pgiw7gduj8ts4 0n c 8s)j1+vi 0 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 1980 drvb3b(i ok.qfu-5ao 56a+ up$\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleafxdhaw+ f2kw 73a96f ration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1a w3d6xkh2wa+ffa f79 .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 exerte .gv h7v-e8kvh c7h4s5rd:vi kd on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of rh 4kvve-v7vd ghrhc 5 k:7si8.adius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is i/pq xrvv25 5;:;ac ku)5zqjr r:j ynhkn orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration 5jav5r: )jprh kykz; 5; 2qqu :/crxvnat the Earth's surface. $\approx$    g

  What is the magnitude of the ai/qk4 o:et jzr /w-5gb i9qmi.cceleration of a speck of clay on the edge of a pott/qei :9iwji4ktbq.or-5z g/mer’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a sn03utfc;un 4 ntring is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fun4u0;3nf ntc ig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with whichy*e t *8ychd kc i)626em+oba1f8 2szr cq+hfv a 1050-kg car can round a turn of radius 77 m on a flat road 6vq1* ohzh8f2rdtacse2f*c+m)ik 86y+bc ye if the coefficient 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 ort ;t*g:7uier gm bb4 dtc r66k/7gii:f static friction be between the tires and the road if a car is to round * dgmur6t:k4 c7:gbgi breit7i;rt/ 6a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is destl;- dwy, 0ocgdnc*u( igned to rotate a trainee 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 dydcc n -,lugwt*;(0o 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.:uf: chctv(p,by ff42ilhf+ variable speed. When the speed of the turntable is slowly increased, the coin remains ff ch,y+v42f.p lbc(f :uit:hfixed 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 eube)s96t8g/ pnzer+ 4h xav(a roller coaster be traveling when upside down at the top ofbe/ nz8t(ha4xpgs )9r+6eu ve 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 (includi e6,)lrhl cs2bng the driver) crosses the rounded top of a hi lec2sb),rhl6 ll (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 wo+ op+49ws lqkxuld a 15-m-diameter Ferris wheel need to make for the pp4sko +x+9 qwlassengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 k7mph f:0 0axktg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the ro:mk0f70a t pxhpe 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 tc7c p-d;mszt/ he axis of rotation is to experience an acceleratiosc;/ -cpmdz7tn of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotaepu l5 3hmp7;n h7z4+dnsj a*bted in a cylindrically walled "room." (See Fig.sp 5n;b3dznumlhah+4p7je *7 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 q-yxrry;h:fhzg, bn+u 8dl 7,on a frictionless air-hockey tabletop, and is h8,ghh-7xbqyl; n:+ du yzr f,reld 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,h3gxqcb/k8 2e6ncj by sw: 1;v by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the mag wn2cce hsb831v /6yq:xk j;bgnitude 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 mru;h zzz(vr;8 s) ) pwtwrm.r(qgg;7w 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 2i2 1 lhpbb:gj$ 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 29hylv n8qrknn;a/ m8by 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 thm von3tjx:-:a o(uj 27ps2 xolqkfm77 6y+vr ke net force exerted on the car (by the ground) inq vvo7p okmu(ory2lxa3t j +7nkfj::m7-26xs 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 uniformly fv xf4 uig2y3o.b ,iz,oma7m4k rom 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 betweex7,23u iygvm ,4k4mbiof ao.z n the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a paroiym*9lnt pjr2 a 39j,;wqa s,ticular instant, its acceleration i9jjy*;l9o,2pq i ,rwatmn3a ss 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 Ep8q .zo71hy lk0pyg1u6sx :cparth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1pxhc1zy18gu l:qpp 6y.0 ko7s350 kg.   

  At the surface of a certain planet, the gravitationv 7fy51rd z.paal acceleration g has a magnitude of 12 m/sp a1zv.7 drfy5$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius tds .j-4kppc. f+ bty,is 1.74 . kp,jc+4 ts-t f.bdyp$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius / qutc42c-007ohug p. ntdiu3w, czam1.5 times that of Earth, but has the same mass. What is the acceleration ddm70pqhtzgc/ut. w2 on0i,cc 3 -a4uuue to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but ttb4 + g butc(l,,/tgtche same radius. What is g ntug4 ( t,bcc+ ,tgtl/bear its surface?   

  Two objects attract each other gravitationally i4ycycfe9s; 0 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 zft o07:nupda7mlk(t)l6q: rvalue of g , the acceleration of gravity, at (a) 3200 m m() 6tu:qzrf 7t pa7l:nokld0   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Ear 1km 4w;.so7dbwtt)oqth’s center to a point outside the Earth where thegravitational acceleration due to the Earth is wo7 .w)oksd q bt1;mt4$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun pac(cnscl,d)c9, h t1 cro-jxbo0ked into a sphere about 10 km in radius. Estimate the surface gravity on this monsc,o(0 bdlcc,x -)1rhc9s on tjter.    $\times10^12$

  A typical white-dwarf star, which oncem m j6( *bk8fnp8j3wqm was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. Wh mj386jw qb(mf*mknp8 at is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronau(vhztkhsr6 auqt3 7:etkx+ 08 ts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Conk0sq et t r(+z:hkx673h8tuvavince 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 corners tflgl3m0jry(pgc:,.c *be7 t ql3 2ue of a square of side 0.60 m. Calculate tq ,c0(trl3 .2bcl3eg7j *yfl m:egputhe magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years mostcv; i ag2a iyj.s nghco x-s8m:e5xd7h+u;c9. of the planets line up on the same side of the Sun. Calculate the total forhxia .eu;ymxcgi5cdn7shac gv; -so2. 8 +j:9ce on the Earth 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 of gravity at the su5 (o/ht pyg/;roa 5tuurface of Mars is 0.38 of what it is on Earth, and u gh55/;tu(o/tp yoa rthat Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knowgy+)9 tjm mo(nn value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Exgo(jmt)9y+ nm ample 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving bq2znz k:yjzqs9)c . 7in a stable circular orbit about the Earth at a height of 3600y. nz7j2czzs)k: b9qq km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km d *w mzejknd6yp9m++19haqw,( vaz tm*k y+c6above the Earth. How fast must the shuttle be moving (relative to Earth) when the relea y*a jd+,qvtzkph(dcme +y 699+am znk6*wwm1se occurs?    $\times 10^3$

  At what rate must a cylindrical spxiz(+scx) *gyt--kafda j ix/7 ; soz;aceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as theztk/ax-zj- )7*i;x+a xsys;cfg i ( od time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circu q,w+yoc 3 akr7p/rtv9lar “near-Earth” orbit. A “near-E/ rc3kt+wvo7 r,ap9qyarth” 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 result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to2hel58; rxorowu6pl3 ez3 5 pm be launched from the top of Mt. Everest to be placed in a circular orb e83hxp5ou zlom2r;6wrel p53it around the Earth?   

  During an Apollo lunar landing mission, y5jd)ob nb7/ ythe command module continued to orbit the Moon at an altitude of about 100 km. How long jbd)5/ y oyn7bdid it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks.rj w:(l ol8bs of ice that orbit the planet. The inner radius objlow:8 s r(.lf 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)ffw1 r(6(t1toyj2c yc. What is the ratio 1 f6trfc2tcjo yw(y(1of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fr4 bw jw3xe/ws 8,a 4d44uhlbrxom the center of the Earth's Moon in a s wl h jbdsab4r/e4w8 u4,x4x3wpace 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 system consists of two stars of 8zsh 9i:ifh4q6h-el d equal mass. They are observe6l4 h9fqzh8- i e:ihdsd to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator t o-6nh.4dpqcl hat move4-poldq. n6 hcs
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of h b(wmnvaqivf9o c5 +i,o6t 6)an elevator. The cord can withstand a tension of 2+miqt(5 ico ov6nv)b ,ha9w 6f20 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with pmyikx rrqpkdz3gs (.4 v x674;eriod T , the des6; 7v grxkxrkd3pz miy(44. qnsity (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 9r n2f/*pr2z7m y 9fuphg8 olhdetermine the period of an artificial satellite orbiting very near them9y rl* 82gppzo/2 79urffhh n Earth’s surface.    s

  The asteroid Icarus, though only a few hun6gat57nbfv pw*b,p;2io9 2a g0uq)v6rj lb ajdred meters across, orbits the Sun like the planets. g ; ja9b7qvrwpbu t)ba26gj v65a , ilf2p0o*nIts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averag s*oi*ztyofp x zpm:8st37o8 5e distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun j .dpd(;ij dx;roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out thei ddp( ;.xj;jdre? [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/2ir2w p0v hqh center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean di e ghvpek- :1cd*.xz2dstance for the four largest moons of Jupiter (those discovered by Galileo in 160cex-1ge k *ph zd:d2.v9).
(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 t4hfac7- y bf tc.*b+nMoon. t.yaf-chb 4nfbc7t* +   $\times 10^{24}$

  Determine the mean distance from Jupiterl0qpavfu( qc3; c8 yky((w ,fn for each of Jupiter’s moons, using Kepler’s thi(q 3(puyyavf0( cn;f k,8qwl crd law. Use 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 bet7v0m nevkun 8(r*7ew aween Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but v8(nu 7e*vreakwmn70was 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 95+eztmaz 0r1;fw( 7hbodi fha 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 ring rotates quickly enough to produce an apparent gravity of ow0 +1 zedtirb5ha 9z ;7(fmhfg as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge n::io-t /:xim 0+asv nlmas alb/9v.pby 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 vine, what is the maximum speed he can tolerate at the lowest point of his swing? tv xs/ lami+pbi.lva:n:o0n:/as9m - His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accele suvdv5* hy*lro3)snxs87 pzrfm y9;6ration of gravity be half what it is on the surfrm6sus vypz*3y 8) nvh7s*;lo d5rxf9 ace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grabdgn cum w27 :ch*uo*v8hrc h*8 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 vhcc8 2nh7gr**8muu w* : codhkg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelers,st43q:m:/hias3 wrn. f ywqation of gravity at the equator is slightly less than it would be if the Earth didn’t rotat3n. w3w4tqm/ aqh:isr :y fs,se. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will 2drvn 4v9t ljyht:8p5 a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and vtvd 54y9jtl8r pn:2 hopposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scalem* zu/blvo:m40c w 4ta in an elevator, it says your mass is 82 kg. What is the acceleration of the elevatot*:4 0mm4cu wba/lz vor, and in which direction?     ----待选择----upwartddown 

  A projected space stati0f vpptlehg80x havi65 . o(/un8/y iwon consists of a circular tube that will rotate about its /iv.gwpat/yexv08puh l of8ni056 h (center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop ,yf 1u yit2f4a(Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planetr5 )kgdj4ryxfg2e2k4 in terms of its radius r, the acceleration due to gravity at its surface and the gravitatry52k kxg 424jdrgf) eional constant G.

A plumb bob (a mass m hanging on a string) is deflectzi-0x0u)oj)x4 t a4p*3q0my uo jjolp ed from the vertical by an angomppju4joyxtx0aj4u3)*i lq-00 )zole $\theta$ 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 design speed of If the co/y6 q98hwlx z5f7ldx 2hr 1gcuefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely hry/h8xq2gdh5lw zu71x9 l6fcandle the curve?

  How long would a day be if the Earth were rotat r0f.j/x4);muhg6bx1vwspz ning so fast that objects at the eqv. fng04/;bzmu)x1phxs wjr 6uator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dnk5(jj;o wu-d:zqqd)8 os m o,istance 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 consnr:b y;ji-2 g 8z7cm15qh gqoktant speed rounds a curve of radius 235 m. A lamp suspended fror5k2qqz8j7niy h-o g:b m; gc1m 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 Eartht8(wo :p4w v-6y0xm e)ke xxbh. 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 experience at the equator of such a planet. Use the following data for Ju4(p 8x-6hxbm oewe:yvx)t k 0wpiter: 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 Hubbl i:(udpf o2w5je Space Telescope deduced the presence of an extremely massive core in the distanoi( :5wuj2dfpt 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 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley shdk 3ik6l1 w-kvnwl flgh 93;m0own 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 comph19kdfv6k n0wg;k3mw3l-lli 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 Positioning System (GPS) utixk))b 4)ws ,iirjs k.:nx ,qmnlizes 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 altitu ,4nixjk,) ) .k)imqwsbrxs :nde 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 Rendeztn 3 x82( cf/js cn0y;zr6dz6bo vcs.fvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroivxjb2s(f 8cdct;3znnf sy .60 o6 z/crd 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 space shuttlev6sl2 /k37v jdhewahn6- .xll vujc(7 pursuing a satellite in need of repair. You are in a circular orbitlkj( c . 6wv-3v7/nesahx7ljldh2vu6 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 distmn fk4p ra)vb5d fbm/ij9.r8e+3e 9taance from the Sun4m)893/.+9neejkbbirdf amp 5 arftv?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actugx3jl+ 2 axbtu. rghox 1;;f:bally "feel" yourself gravitationally attracted to someone near you. b j;gt.r3fu xo+: h1ga ;2bxlxMake reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fdo1 +qbc w x2bb(t)0zbig. 5-46) at a distance of about 30,000 li+xt bbd1b20bqcoz)w (ght-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 0.5v quwuo ;n9/thau953imt1 /v d0 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpv91/vd wutunm/ o5 3 ;atqih9uoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits f6)-dt4l/xlrz+h jy o the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experi,rp.qcdk;i0a 0mo0ve4vwm 3ienced by the tip of the 1.5-cm-long sweep second ha,pvi o ak. 0rv; 3qcw0d40miemnd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a izi vah ;:wdpcywhi-t+ 691k *h,0ewjsinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight ma-*adijt wzpch9i06wv hyei: k,1h;w + kes 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 designedfb6 9sx*4r+n q76rfwevb/ ovi so that a car travelin69ie7 f oqb+v/sx6bfvw rnr*4 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 Acela, utilizes tilt of the cars when negotuh a r/g5o7mphj (d9v*iating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to r p9oa57 (d*/uhjhmv gprovide 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.$\approx$    $\times 10^2$