Sometimes people say that water is removed from cd/ y2ys0r 9 m)9ibgllolothes in a spin dryer by centrifugal foryo0dl ybmr99/ls2)gice throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car trav z13fceah7+, zc rz*lc6-zb3+jh bmoj els around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Ex+ r c azz *h3jhmz6eof,b17cjzlb3c +-plain.

Suppose a car moves at constant speed along a hilly road. Where does the a23m k51x6vz i n/csrlcar exert the greatest and least forces on the road: (a) at thv1rlm6 3/na izsx5 kc2e 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 actinpuqm9vt6w-fg7jv7 ) svzn-r *g on a child riding a horse on a merry-go-round. Which of these forcvfvr -)t q*9wg-6p 7v uznm7jses provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical cirndxp .ot -jv656i 8zdacle without the water spilling out, even at the top of the circle when tvotpz8xd 6-j a5i.d6nhe bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least t*a(boj x3c98n .(flynejbq6sn2j h( ( +oprbthree controls in the car which can be used to cause the car to accelerate. What are t +jb*n (eo .o csa(jb38jh2nyp(n6rf9 tlxb(qhey? What accelerations do they produce?

A child on a sled comes flying over qtz. )c7m+cfm og 6,yithe 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 us.q7+6mcg, ) o itfczyming Newton’s second law.

Why do bicycle riders lean inward when roun;e+t 6vinjf/.gb2u+kj q k g(tding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking a8 p5b1: 4leuwpf zf0ejngle given its speed and radius of the turn?p8e1p40f5 wb :zufej l

A girl is whirling a b q8y h.;h; scgeex0u(qall on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the balle0 xcs;yhe; gqh8q.u( 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 the7(fa ik g3on+bi trb7jq+m21 m Earth? If so, how large a force? Consider an applem (n7b72 gt1bi+ kfq3iam+ roj
(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 xi3a m22rna.dqev 9o0orbit be diina9mqv02dx.23 oear fferent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the yeq,qg*m- (plb,yw0 yf.cz- sEarth? Which accelerates q,qep yf c-z(*lwbgy,.sy m-0 more?

The Sun's gravitational pull on the Earth is much larg;tu m6doea 1fjjum): )er than the Moon's. Yet the Moon's is mainly responsible for the ju ):6u)joate;1mmf dtides. 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 a/4rl) fr* 0hz atqk /pldv6 qwfsb735tre at work? Do they opposedlfps*l z5b 3k/r/ tw7)t64va0qqhf r each other?

The gravitational force on the Moon due to2gsy ,80tj8m zfg(yf j the Earth is only about half the force on the Moon due to thejj (ztgf 2ysg,f8 my80 Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit aroun;c,f v f)va0uis.s ow;4bl17r jmg;nnd the Sun larger or smaller than the centripetal acceleration. r;4sowjm;7g; v)cnbavul0f f1,nis of the Earth?

Would it require less speed to launch a satellite (a) toward the east om91me 5 7l.ycinaal n7r (b) toward the west?5an717llm.e ncia9y m Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measur(ngr cnh19s m14r g;ezed 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 1mhr(nsgegr cz9 41;n 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 adverso- ,xr v:e7q,iyd 0 dkyndf9b4ely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with 0dbr y qdk en,o-7i4y,x:v df9the 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 weightlessneuhdy-5(mgu:qunc o4 8ss” betweed:muu4uhy -5o8nc gq(n steps.

The Earth moves faster in its orbit around the Sun in January than in July. Isd smj7v(cdr5 p8n5n n2 the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor jm 2ndc(dr5p5 v 7s8nnin 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 dz +9,mfe; tzo2 )l*l w8c mkgsg1gr zst3p8qh9iscovered to have a moon. Explain how* ;gps8+ 9l92 wmfl gzqrm83),gztezktocs1h this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitationasteultpbt m(8;hp5:ww)9a8 f l pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly respons8) t 5epth98 (f:b mw;ulwaptsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 19)jdrn5 nwh 3m380 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 orbiof5jh-uw 6-6 j lxt(wct around the Sun, and the net force exerted on the Earth. What exerts this fjl-j-o665w c wuht(x force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg d/,y50 q qfif1jng9 g oyac50deiscus as it rotates uniformly in a horizontal circle (ata/,g5n qf ic5je9fqoyg100y d arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 4(ohof.+8 )h h9t iyyhl00 km from the Earth's surface, and circles the Earth about once evelyfi8( 9hhh.hytoo+ )ry 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on the edge of dkze-b79t ;pi-weenj)r8g; c a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is e c 9ke)w8j;;i rtb--zg 7dnep32 cm?   

  A ball on the end of a string is revolved at a uniform rate insu* t7a ry(z5i)a kcjt21zs4o74 f +ghtei-ds a vertical circle of radius 72.0 cm , as shoe5uz2cga-7ryif i17*(ssz h4 j oatdt+t)4ks wn in Fig. 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 speedr8bodr .w5uu *bs5rh; with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient orod5 r8 hb5u.ur;bsw*f static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires zyd0y*t p gbbh-+t:8v and the road if a car is*vdt g+ yh:bt8ypz-0 b to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is de- )mjxf9qmu3)hy6g7da2 o mrlsigned to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7ud)7xm-a9 hol6jg f32 mmqy r).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 frkg6zz -ycaeaa1+q8s-qsd u3 x-ipduk *5m 78xom the axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between thecyakkg qd -a 3e-+x8zq-uu5i msax*687dp1sz coin and the turntable?   

  At what minimum speed muszpvgp;msc 1dlk4 z45p0u j 5v5t a roller coaster be traveling when upside down at the top of a cir5vjvcu gzk5 44;l0pm5d1ppsz cle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the drivnmci iasqg1)009l i8e2h w)p ier) crosses the rounded top of a hill (r9ngi)w2slhe qm1c 0ii a)i8 0padius =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 mlu/e1(evt(rd.p3w; . nqs wa2yfb:k zinute would a 15-m-diameter Ferris wheel need to make for the passengers to feel “vkf3s ;2ulbwqa.(. y/1:ezwn drte( p weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirly,o cvh4bw,/ +2w+prevz8c aw ch9f.sed in a vertical circle of radius 1.10 m. At the lowest 8,b ww/s+ v9czyaf.hr,ce2+vow4p c hpoint of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifu,q1vh k kt garhg 25d:u/.;eztge rotate if a particle 9.00 cm from the axis of rotation is to experience an guz,t5ak/e khh2 :rtqv.g; 1 dacceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in3i/jz lgnrys- .4f1vimk* u 2w a cylindrically walled "room." (S43 i*ivskmfj lr1-./2ugzw nyee Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M )hvcdf ui- n 6)ec7p:)n is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dpf)7c:nn-uhd e c6) ivangling 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 ignorin yttug5( x9;v.y8vwa8zh0neq g the weight of the ball which revolves on a string 0.600 m long. In particular, find the .0xygenyh ;u88z( aqv9v5twt magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius ofq9i7gn .w 8 twdu93h0(,o 1rplhw;ujl lh g6gr 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 ham /7 +3hqzvv/9/i6l zxvxapy/wim0$ 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 ) r5klmvhjr.ofa0g2, evasive 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 centrimwzhc ye4u)) fi09(it petal components of the net force exerted on the car (by the ground) in Example 5-8 when its spezc ih4m(y0)u)9w eitfed 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 fsfo,o 1)zlw7aqf2 2c tlgd*i3rom 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 coeffic*tsf2w )cz1,f i3adgqool 2l7ient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horis(5g4u*m4 m eh.vn9vxxf fn8 azontal circle of radius 2.90 m . At a particular instant, its accelns(8 fx*f4mm9xeuva nvh 4.g5eration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spa;91 owerlj. 8f9 j;n8htwjotbcecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass isrj1ef;;hj8. w jtt8 ow9ob n9l 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a ma ;.pd6v*p(27oquvkbgefbtvic( 5(amgnitude o p(imvd.vcvu( (2 bgfobe ptakq5*67;f 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 on the Moon. The Moon's radius iszmfb y 2rr*39p 1.74 frb2 yr3 9m*pz$\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, but has th cjc jmnno8c++a)9gl;8lb n*fgd87kj*yo*qwe same mass. What is the acceleration due to gravity ne o n jc;yfj 8n8lal*ckqogb8mwgdj 7n)c*+* +9ar its surface?   

  A hypothetical planet has a mass 1.66 times that of Ear8nu. nhoj *m-uth, but the same radius. W8n- *nmh jo.uuhat is g near its surface?   

  Two objects attract each other gravitationally with a force o-vnh3nw* g;o hk ncs,*5/d mtif 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 uxckc q2(pl*c;jt-6 dacceleration of gravity, at (a) 3200 md*l jk 6tq;2p(-xu ccc    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outa*h lp/c0o x5zxtg,+ mside the Earth where thegravitational acceleration due to the Earth is 5xm lpgc z,/t0ox* h+a$\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron stabn qs6,;9rmve r has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the su;6re,vq sm9n brface gravity on this monster.    $\times10^12$

  A typical white-dwarf sta2ht bhsda26i b0z(l7n* e8adbr, which once 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. What is the surface gravity on this sta b 06tehdab2da(8 *nb7ihz2l sr?    $\times 10^7$

  You are explaining why astronts 1ch)o 6 ;1jmafs .s2t,g jgtup6:xkauts feel weightless while orbiting in the space shuttle. Your friends respondgcj,stj6gs21.xosh t1a )fk6:ptu ; m 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.eh5gcdty-j 59 60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere c-jd 9gt5 5heyby the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of th6apm/vf/ynz 4f l:qx0:tp5wme planets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupimq m 6tx:yn05wv/fpa/zfp :l4ter, 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 s -g4lm;gdf91k+oinskm t.(x the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 340og tds.x4 1ng;m (fim9-sl+ kk0 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun usingec7a-uo xw,u qp ,v.e+ the known value for the period of the Earth and its distance from the Sun. [Note: Compuo avxw.-e+p,7ce u,q are your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite)r.a6s6aas gw p/wixr hd/,x2 moving in a stable circular orbit about the Earth at a h/ s,xwg.ra26hdrwp)a asx6i /eight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above thzt.8v bn nscm34xs 3s3e Earth. How fast must the shuttle be moving (relative to Earth) when the .3tzns 338nvs4b mxsc release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experience (wf+r nya; jy23xv)z msimulated gra xfva+zwy (y3)rmn;j2vity 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, Fig 5–32.)   

  Determine the time it takes for a satellite to o1q+ sh0 .pkpasrbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth h+. k 0qs1spapwhich 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 oz: ).a5dmpov objq(k9 f Mt. Everest to be placed in a circular orbit a o.v(qb 5)kjdzom 9ap:round the Earth?   

  During an Apollo lunar landing mission, th3 jarvs /2kl6ve command module continued to orbit the Moon at an altitude of about 1jk 23/vv6srla 00 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit tp,bc219jzfzhr h9q 2e he planet. The inner radius of the ringszh1hrc9jz9 efp2 2,bq 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 diamehn;wwkbwo 3g+e9 sb( r *jf7a4ter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weighe7wb3+(nohwb r kga 4w9sf *j;t to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astrhcl; skx95) +zdf,z huikn7,z onaut 4200 km from the center of the Earth's Moon in a space vehicle (a) movi,lfz7kzh9 x5k,z+nhi; )cudsng 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 equal mass. Thece2 7yl)j 9kaoy are observed 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? j)lka 2o7y9ce   $\times 10^{29}$

  What will a spring scale read for the weight of a 55- 67y3gla2whbj kg woman in an elevator tha72yw 3a6jgl hbt 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 a cord suspended fr0i3 4gok9stll om the ceiling of an elevator. The cord can withstand a tension st0i9 34gklolof 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 with.9 r2qya jeo0o)g brecr47g8j period T , the density (mass/volumeo)04yr2. gj87rec 9 objgerqa ) 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 periolep jk6a-p( i2d of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Eaepp( al-k i6j2rth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, ov(iuu1zi 5 8h3gdwxj/ q6jd6bd )gj8drbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sunjdix 8/bzjq d)( vgi8huw5g66 u1 dj3d?    $\times 10^{11}$

  Neptune is an average distance of ut,j v;-7+1hmd zdsoofm;, ls4.5 $\times 10^{9} \mathrm{~km}$ 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 Sub di*0p u9ab(svql*rn9bp)7xn 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 orb7*p9(ubx9 bsvi) b0lp* dan qrit 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 tqot-b*ony u wzc xj3p, 8 jvo0l)7.y;qb97fi ehe 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 distq nd c1ys+;n2*oy wn.kance for the four largest moons of Jupiter (those discovered by Galileo ink d*cq1 on2;+nys.ny w 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of th6 kbm43-zsbohqj9pz(kqn 2ze3 w 9xs,e Moon. nz3bs2wmeqp ozkh4(s 3 q-k69, b zj9x   $\times 10^{24}$

  Determine the mean distanchyt/7 0z jrbm4e from Jupiter for each of Jupiter’s moons, using Kepler’s thi/h 7m j4ty0zbrrd 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 between Ma0s6uz8;qxy piuisj 63 /x)ov nrs and Jupiter consists of many fragments (which some space scien6vi6 qus ;syxipo0jnzx )8 3u/tists 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:sgzgonn0j;4;r/y*rqsv. r x describes 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 alwayn0:j4s rn.vryoqxgrz* ;g /; ss 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 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 swingingwme .fi9:+rr z in an arc from a hanging vine (Fig. 5–41). If his arms are capable of e f9:mre+i .wrzxerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of;y+isse; p mm6yd6e4v gravity be half what it vmi;6sme6d 4+ eps;yy is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circle t* zb6v;i)atudn:z.n once every 2.5 s. If bzna: it vu6d *;)zt.nwe assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleras,llyf m)0 sg/tion of gravity at the equator is slightly less than it would be /llsm, )gs0yf 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 thucrt r9dmr6xd g-uf1 9t6 y9u2e Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth a26ud 1u6tgc y-rrfd99x9trumnd Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an elevagkr p 06yqx)r8tor, it says your mass is 82 kg. What is the86p gqrkxyr)0 acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that willru516(y3b4xkwikliv)f u w2jaw e 6z1 rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be thklufxz31vuw6( 4eariy) 6iw5 jkb 2w 1e 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.etuk -ynur,y96++;dft+r* pk zd w2bb 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 it u,(y8ek9izil,icj) ts radius r, the acceleration due to gravity at its surface kui ) te,i(8lj, zc9yi and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is d+dd5r7a )vo nkeflected from the vertical by an anglea dvk57ro d)n+ $\theta$ 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 si37kf7 8e 3sslotd8l speed of If the coefficient of static friction is 0.30 (wet pavemenks8los8l fits3 7 d7e3t), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objx-ic02y:/n8kc g-ai8z:2xfwget+vmcl 6 tdwects at the equator were apparently w agx 6 wcwtv0 f+2incey:zx/lmdic8g2:- 8 k-teightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dilg/qtd) pay xnt+7q8/stance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lrra: e.z k5x3dx7 be,s7t)oqzamp sus)z3 ,7erskxqa 7:.tz e xr5odbpended 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 timeso5our8( :q vjhs,jp,s as massive as the Earth. Thus, it has been claimed that a person would be crushhj p s,q:ov8jsru (o,5ed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Spac.ll*k:-ekzvglhol1cives(r . nj : w .r8;w6be 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 escapes8vk6:o.bzl wij.e :l-n1g vh *k; w .(erlclrs). 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 shown4v,2y 0vfpbox 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?)yb,0xvf4 2 opv 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 Positionr-2m4 gbpm( txing 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 naviga4( gmb2r xtpm-tional “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 kjdzc i ;*2o;wym, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rougc; ;*2wzy ojdihly 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 btajqysf+t,y:qw o4aaxh,; v 02m57m pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the s:yqwhs jtqv t2b5x;ayoma4a+f,0m ,7atellite (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 pepbh(+ nplxq *-riod of 3000 years. (a) What is its mean distance from thebh *pxqn-p (l+ Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G 3/ uglif+tyk9 would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, lg yut i9k+/f3like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) aty )ee )puuh;:h a distance of;h)uh):eye pu 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 o goiwpqc;):bx kh -o )n.sb/6okc/fm4 f 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 twxk i pmfc);/ :6hb).oq/kbonc-go s4he square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Ea nll648s9 mo(lw5 yxqgrth $ \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 the 1.5-zl x. wo2vb4f5cm-long sweep second hand on you4v lf2. 5zobxwr wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker wo cal5emm0r1w gh;ruv-q t5cr*c3:8feight 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 Fig-f;c eut: cwr8vrrl 1 h*qmo 53ma50gc. 5–10.]    $^{\circ}$

A circular curve of radius *w+txu8wuqkpt wg. rk )i./6m xh6kz2 R in a new highway is designed so that a car traveling g k .t ukqt)xhwr6u8*+p/kmxwwiz26. 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+w8fh.q r-cezch t8 l( 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 acc-+ .8hlrc 8cqehf (wzteleration, 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.$\approx$    $\times 10^2$