Sometimes people say that water is removed from clothesc jck5ek t levf287.c99m9h ,oyj)hqg in a spin dryer by centrifugal forcg,oclemc5 hj) q8.kytc9hk9j vf729 e e throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be th2q1a(erws zt:e same when the car travels around a sharp curve at a constant 60 km/h as when sq1zaw2(e :tr it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant .a-d2fj s 2emdspeed along a hilly road. Where does the car exert the jde s2m.2 da-fgreatest 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?

Describe all the forces act*y2 i1j4hxq9cu fl,eiing on a child riding a horse on a merry-go-round. Which of these forces provides the cei9eh yj,u q*2ix4 c1flntripetal acceleration of the child?

A bucket of water can be whirled in a vertical cirbecj2ucq5a- m i *(gf.cle without the water spilling out,ebg qjcm ca2i*5.(u-f even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least 2d14cw jf 6kb+ld+ex dthree controls in the car which can be used to cause the car to acced bx164cfeld++kjd w2lerate. What are they? What accelerations do they produce?

A child on a sled comes flying over thej3xck :lrm o/6x wz-)tko*aqkg9 modv/ q64y7 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 slo4ya3r doo: v*z)j6 -/ml7gkx w9km6kcxq/q ted decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at hig im9unapjr q up*90::wh speed?

Why do airplanes bank when they turn? Ho;e 0z1a x h*ut/esds*ow would you compute the banking angle given its speed au*t;s*0 da / zxh1oeesnd radius of the turn?

A girl is whirling a ball on a string around her head in a horizontal planyrl9lgo6,i ;e(jv) ei 5- ispye. She wants to let gopy,) i5r;vo(sgyie9l-l6 e j i at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a 3i7a ek ylm1ie9q63b: qdr2nfforce? Coqfk2y17 i 693q:ireem bn3dalnsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what wayssp6rp, m r89z3ldxtk; would the Moon’s orbit be,8 z3mpkp;t9rd l6srx different?

Which pulls harder gravitationv.(zk:u5 -ohv*x u.fd);oa p :zbzrmxally, the Earth on the Moon, or the Moon on the Earth? bfpu-:;k: odh maz.z5v.z r* (ox)vuxWhich accelerates more?

The Sun's gravitational pull on the Earth is much larger thagrq:no- t)t f2 w;h4fon the Moon's. Yet the Moon'qftf2r; 4ho-w)og nt :s is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? What two effects are ag2 gy,3em,dx ct work? Do they opposem,edgg 3c,y2 x each other?

The gravitational force on the Moon due to the Earth is only o i ab39drfp3g7 8v(xy,+nqisabout half the force on the Moon due to the Sun. Why isn f y73i8sq a,+vrig9 bpd3nox(’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger orvg1bw7t xnuj)c m8:, h smaller than the centripetal acceleration of h1xgnj7 )8w cv: ubt,mthe Earth?

Would it require less speez0v p)49 ikiyq;/debo d to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotatipv;k d)bi4eizqo9y0/ on direction.

When will your apparent weightbn0nb:vsz zindp a 0 7u))o6s4 zro-5a be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upwazoi7b0z on 54auvr asd)sn6zb-:0 p) nrd, (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 affected b5t p) bp5td:ck,.dz ody 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). Explat.dkc )tz,5 d:ppd bo5in 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 experieyul javz u/z*rkrhj;2 s c)7;2nces “free fall” or “apparent weightlessness” between st h;l)zjrcz7s;k/u2 j ra*2yu veps.

The Earth moves faster in its orbit around tt dm597b-tnqvhe Sun in January than in July. Is the Earth cl5t9qmtbvn d7- oser 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 unt43xkdqy 8b sc i,15v atn.zq40berh3nil it was discovered to have a moon. Explain how this1inn cz0v td.ay384 qrkebh3s5xq b,4 discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's-cw,x q-e 4mhj. 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.jxwqh,me- -c410 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 h)qoxmqru)*+u;ufd) $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 thqe iblrimmsex0/v6 4 x7,vs2,e Sun, and the net force exerted on the Earth. What exerts this force on the Earth? v e,4xl/0q x rbe,i2smi6ms7vAssume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus aj3vng ;9 ne*q;-eluulgow .m( s it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the ;gngv3 9wl q(o*-lnm eu uje.;discus.   

  Suppose the space shuttle is in orbit 400 km from the69 uq0fg kb4trngg ;+s Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its r;g9skfg+4g unq b06t orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of ax 6; fv*e2njif ofs(0k potter’s wheel turning at 45 rpm nxfov*6i (sf20fj; ek(revolutions 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 ver zr8s9;:+ntxnd6k*h-kikdk3 jb zly7tical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.0jr6d 98- :kykz ixnb*t ;s7+nkh3lzdk0 $\mathrm{~m} / \mathrm{s}$ 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 car can round a turn of radi l(ta63qof;l1 yz;sceus 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the maac;y16 sz(f3lo;le q tss of the car?   

  How large must the coefficient of static friction be between the tiresfc6j/7 1bwl2hc ar 3yv and the road if a c2 lbcc/v7w31fajyrh6 ar is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training asnw8z f7xsdlm/ : vhia/6rp :)vtronauts and jet fighter pilots is designed 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 shnxiv /sp:lh:6dv/z )7 8wmrfae 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 variabldgaf 1y14 ,co 64.i tdn0:+psvim hkmue speed. When the speed of the turntable isys1 am: ,it4 vh+fckg6uodn4p1 m0i d. 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 coaster be travelintxj d+e5(i (u l4z2ciqk)eh 2kg when upside down at the top of a circlekj)c2lte 5d k iiu+ ehq(x2z4(
(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 masr++ly4y n 8deo7gd jw3s 950 kg (including the driver) crosses the rounded top of a hill (radigjnd4r w7+ ly eo8d3y+us =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-dms2eldv +h4: :7avhj tiameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost po +v ah:2jtedv7l 4msh:int?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m.8/8ux br4s 0e6yz;s:j mtskdn At the lowest point of its motm t 4sk/bzey:x;d js08s6nu r8ion 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 th4 ; pban0p e:u9wht/die axis of rotation is to experience an accelp/ 4bw;nh:t p0au 9eideration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at ,w 2 v8 8fwgman0uh*u5 chg3oqt/ 2ruia carnival, people are rotated in a cylindrically walled "room." (See Fig. 5-35.)h3qu tn gg8ua vru8woi2cm5fw*2 ,0/h
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 a*gyk).aq8i mcircle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole a kiaa.qyg*)m8 s 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 z2 3h w9g)4h+mxewdwxignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude hm34g2zew h dxx)9w+wof $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 rad/0mq yyo0ck0d ius 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 masses*g4;q kv;jal*-hc 0lw ahg8ph $ 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 evasi d/ -u9m-wwizpve maneuver 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 and centripetal components of the7w:tu)rc9pl(z mm3 klz6f- e v net force exerted on the car (by the grounde -m:6kczvw3 r f um9z7lp)l(t) 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 50; tq 4crw*ll+w0 accelerates uniformly 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 ow ;rq+*cl lwt4f 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 circle oae4 vl+l y4ouxp( whg b3/d5q/f radius 2.90 m . At a particular instant, itllp 5v3y /g uw4be 4/qhxd(+aos acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on jz:kwi(z:;qk a spacecraft 12,800 km (2 Earth radii) above the Eartkq :z; jz(k:iwh’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational accel y3pz3e g4lorek.g, y3eration g has a magnitudz4e ryk,ogpg 3eyl3 3.e 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 +r*5 c itkxr- whfh15kto gravity on the Moon. The Moon's radius is 1.7 *c15rtkhxkh +rf-w5i4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, butyb* 4ce m4z xodh,+uf 3m3;q u/hyxw1s has the same mass. What is the acceler c;x1ywu* qxyhz s3m md3/4 u4b+ohef,ation due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sx(i*4 bgsr)x yr .fyj27z oci0ame radius. Wha40j ).2 *yc(fr orgzs7xxyiibt is g near its surface?   

  Two objects attract each other gravitati8iil3e37dv -iio(:er4u3szppfhi: o, amda 1onally 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 o)lt9gm8h)m sc fl pc:/f gravity, at (a) 3200 mm: lmhl ftcg)s8)cp9/    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Eartw h 7 rkwojb-v,)d3p-l9 hwm6ch’s center to a point outside the Earth where thegravitational acceleration due to the Ev hhmr9wdp,-l6 3)oj- w7wkcb arth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sntrj5- 80:np9pan3 se nu8oh run packed into a sphere about 10tp8auj-ne 8 9nr0:nshp35 r on km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun b9jg5qom(,aqu ,lld i5v -pbd *ut is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is op5lgvdq9i j( qmd b-la,*,5 uthe surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feqp(q9ec 90mj-zy7d kkel weightless while orbiting in the space shuq7z k0jq-99(k medpyc ttle. 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 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m+uhtaworgngd.vx3(ta5 .7/ p. Calculate the magnitude and dax.d(/uw3gtt a rng5.7ph v+o irection 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 most of the planets line up on the same :y2aavmm0u9 xside of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. m9ux2a:vamy 05-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 ogdb45n kk( ;vjf what it is on Earth, and that Mars’ rjbdn vg4k;( 5kadius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun snkpxavz81e3.g),z w:nrhm wq9ab ) :using the known value for the period of the Earth and its distance frra1hsne. wb) g, wzpq :)v9kmnx:z83aom the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable ciratls nqpc,6h qeq6wk- ,uf-;2cular orbit about the Earth at a height of 3-, pse lh-;6nq6,cwf2aq ukqt600 km.    $\times 10^3$

  The space shuttle releases a satellite in6 cn5k+oi 1iguto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the releaki1u+o5c gi 6nse occurs?    $\times 10^3$

  At what rate must a cylindrical spacig8(8k8iz gjtkd7,aceship rotate if occupants are to experience simulated gravity of 0.60 g? As8d78 kgjcti(a, gizk 8sume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circuo6,, qbhg mtd 77vu3xqlar “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth w ,7quqthxbg7v36d, omhich 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 to be launched from the top ;3+7woa ul bhp,kr.eb of Mt. Everest to be placed in a circular orbit around the,7brwuk hl.o;b3 aep+ Earth?   

  During an Apollo lunar lanz:qrk53wfpq p64, ctpding mission, the command module continued to orbit the Motrc5: ,kq wpzpq64f3pon at an altitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks pvqnwkl5q+ 06j:xpje 1 )m)h nla0/gvof ice that orbit the planet. The inner radius of the rings0qv6 ) glmw/n h+5:npejv1lq0pajk x) 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 evaxvv4s84n5(g lupts 3s 6ojb +ery 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her re supg8ovtx 4(j4sbl3s5+vna 6al weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center 7)/u ++pzzs-zzgg yvo of the Earth's Moon in a space vehicle (a) moving at conss+zz7 / gp o-zv)gzu+ytant 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 consistsas; huqhdhw)po:o)6) of two stars of equal mass. They are observed to be separated by 360 millh)wqpoo )u: hh)sa;6 dion 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 fof8x8nofn.c yukqf .8 7r the weight of a 55-kg woman in an elevator that m q8fnk xo.8nyfc 8f.u7oves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of an k +vsdp08.g jqzm,pn7elevator. The cord can withstand a tension s80 dp,.qv+kzjgmnp 7 of 220 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 wiy 0axv7vksjv 7y2,t5wth period T , the density (mass/volume) of the planet iy2 75a t,xjvy vk0vs7ws $\rho=m / V=3 \pi / G T^{2}$ .
(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 thepflndrsjnmc 2 . 7+sb)ex 0z,1 Moon (27.4 d) to determine the period of an artificial satellite orbiting very ne c n.+p7j,ms)lersbdnx2z 0f1ar the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbitse g g0jy1 ukxa9t7-(hc2bgt -v the Sun like the planets. Its 12(xe0j7u ytgc9 gbtgh-k-vaperiod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of (vldjr+/; hry 5su a(f 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 t6 9hjxi 8j2i8i7aw dmm4ymsv3he Sun 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 dista28j4 mi9diyammjwvxh 3i8 7s6nce 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: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the Grt*7vvr8etzma /v09e7jip z/alaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, avqibm a :-9i3knd mean distance for the four largest moons of Jupiter (those discover9 :ikqa -ibvm3ed by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distancee;/0 enjjt; kf of the Moon. 0jfej; e /nkt;   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usinkng(:j oek4(/grx- oocc o1 ) v2skma.g Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to 1 kxkm(g(gc:ansre-4/) 2 . oco ovkjothe values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragmefv-b*ttheim :vc .fy4sg/ 6m8 nts (which some space scientists think came from a planet that onm6m c:.tv ftvfise*g8/h- y4bce orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "pl owb4. gvqe9bjkgeql9. 5u: 4lanet" 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 ri 4eub4vjqb.l5qg99 :gl k .ewong 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 a kctqnj,*:4 loxp06t orc 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 hpt4t l*k0x6o,jn :oqce can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Ea,t r+c uga4p* e3q1kttrth’s surface will the acceleration of gravity be half what it is on the surf kt4+g*tue tqa1pr,3cace?    $\times 10^6$

  On an ice rink, two skaters x eaf2.rlfp9/t 0 ujv0of equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and theirr.ea fp 20fxv 9uj0/lt individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravity x 0toq*7yc( jz5wgts8at the equator (x8t7tjo*qy50sgwzc 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 spgf, 9h jb89,tab5 zo;ho:lxrsacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppo,x gsj;8hthb,ol959r f ab:zo site forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in*riy6aa ask/ 7 an elevator, 6s*y7 /ai akarit 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 (ji(:g: w abwjcircular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formj wwa (jg(:b:ied 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). 28bd;+ii(+ cnk.zqhi 9 x8zr hgtb.m q
(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 ry5xh9 d*prq,tp a x63x1c6zgsadius r, the acceleratiodazr, h pqgx*x53tspxy6c 961n due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflecteujfkgi/).a) 9wi;ezy e 4b5uf d from the vertical by angaf)/yjwk ie9 45z. u)ubf;ei angle $\theta$ 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 coefzkx41zd 8mr :qficient of s4mz 8dxrq:1zk tatic friction is 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 tnbgs)-:( g6 eqs6 e3h i:imjuthat objects at the equator we:h6qi3gm j i-s(t6eusn ) beg:re apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintai0uv)khto:v n ov,y,*o tgra::n a 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 0sm+hsof85h+ eqj,l:a 2owyu of radius 235 m. A lamp suso m 2+ f8yoqe: jhw0su5l,has+pended from the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320(eam0v4 jvx;u times as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet v(m0xuavj4e ;the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble .d2j w/ zjdnn:Space Telescope 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 ord./d2wj jnzn: biting 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 traverx qp sw gyne.u++w7)dl0aq2; 0btux g)ses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do thwsqq n 7b) gwu.t ly+)00p;xgu2ead x+e normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a groeca;m6pw (*i uup of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, emiw;*p (6 acuthe 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 satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion kmbr:d oj-m/z-x, is meant to orbit the asteroid Eros at a height of about 15 km . Erosjo/ bmzx-:dr- is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite i oo/kbl d-sf8:n need of repair. You are in kl8 obd:-s/ ofa circular orbit 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 5r xpnydk1,v/ 3000 years. (a) What is its mean distance from the Sup ndx5y1r k,/vn?   
(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 ogh+ (bqx+ w.x 5 *c7 cga-th5bs4lprkzf G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reg7 bh.*(qx c+rptl+zk5-5haxcb gs 4wasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a dbwd6k)c 2:f dwbqc48n istance of6fwq8: c n )bd2cb4dkw about 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners ofmdmyp*a nm q7b/;6ww - a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the sm w/mp6qmd7;b awn y-*quare.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits51-qj8 y *f dydviozs9 the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of r*-2iotkp xg1 the 1.5-cm-long sweep second hand ok-i2 t*r1gpxon your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinketlc, n* i5x:umr 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 vt,* lxn 5umc:iertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highwa s1 hy4jmn3 q1)at;te1teua 1wy is designed so that a car traveling at speedt4 )tm anwet3u1qa1;11shyje $ 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 negotiatinlx5 ;le z+zh.jg curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the frictijxe.;zzl 5+l hon 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.$\approx$    $\times 10^2$