Sometimes people say that water is removed from clothes in a sa.wfe4 to q5ow*p5k*vpin dryer by centrifugal force throwing the water outward. What is wrong wpwov5e *o q.tk5 a*f4with this statement?

Will the acceleration of a car be the same when the car travels x-rv hcayb6 d0t-+; vyaround a sharp curve at a constant 60 km/h as when it travels around a ge vdh+ya;-r0bx-cty v6ntle curve at the same speed? Explain.

Suppose a car moves at constant speec5u+gyb xu4vj( :*j ltd along a hilly road. Where does the car exert the greatest and least forces on the road: (bgv+ t5y*:u4j c(juxl 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 forwq*(h4,z e* 25cna iqumysn3j ces acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of thes3qw*nn eqm,*yj24zu 5h(cai child?

A bucket of water can be whirled in a vertical circle without thewmpz( 7,pe5 dh water spilling outm, hpd 5wez7p(, 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 threc ,r 7rswdp)o5e controls in the car which o)5 cd7wr,psrcan 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 smallwd.59q .s9t vohuu;zn hill, as shown in Fig. 5–31. His sled does nodwu;.9 z9t s u.vh5onqt leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward r,/ sem8ovn8ywhen rounding a curve at high speed?

Why do airplanes bank when97+klzdfsh m 7pbdx*( they turn? How would you compute the banking angle given its speed and*zskd9 p+f7x hl(d m7b radius of the turn?

A girl is whirling a ball on a string aroundh5gja1eq; d6bmdh8 4 x her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the qhda 15hdb;6mgxe 4 j8other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If 1 dy1h0 :m4ynv2bp2*ucdfqiyso, how large a force?*1v d 4byuh0pqyim 2y:2nf1dc Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways p0bhg-t 7dao 3b0m(l rvbpc8f.g5ke /would the Moon’s orbit be difmtgrkpb0 3(b hvg50be .7dlfapco -/8ferent?

Which pulls harder gravitationally, the Earth .an+cb9ify;sdzre sq ; 67z 2r r1jv(hon the Moon, or the Moon on the Earth? Which accelerates mor.7rz; riarc ; sqbvefs+1h6njzd (92ye?

The Sun's gravitational pull on the Earth is wirf2sh/tn i0*zau/4e 3+ui x much larger than the Moon's. Yet the Moon's is ma n2sie*/h tar+xu/34wi 0zfuiinly 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 atl2* jdck4q7vls3 gz2a pk6ej 2 the poles? What two effects are at work? Do they oppose each other?kalgjd426 ce qjlkvs72p3* z2

The gravitational force on the Moon due to the Earth is only abou og7jh,dzfn-3g yk,tyk550ho t half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from th-305kg,t y5ko,j7o fhdzn gyhe Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun lar ltc69pvqe. cpi59x6k:as8a)5lgtue ger or smaller than the centripetal acceler . qa 8p6c5ilg6t5vce)u sk:ltp a99xeation of the Earth?

Would it require less speed to launch a satellite (a) toward zv.y tjlqmw6jl1k 1:v we9c-94k2nzxthe east or (b) toward the west? Consider the Earth’s .lj9vzylz49j vctkw:-2 wq1 1en6xkmrotation direction.

When will your apparent weight be the greatest, as measured by a sca-6a5hv40 j,uf,prk g)bi 4q7n byg cnule 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 b64u 57fak uryc qbbv,-ginh,0 4npjg)e 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 l4wt h)r,zo l3fong periods in outer space could be adversely affected by weightlessness. One o),3rh l f4wtzway to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how 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” bdvo//1yz jq0mprv- g0etween s-y/v0 rjp d0mogqvz /1teps.

The Earth moves faster in its orbit around the Sun in ap;2 iiyp+ld7 z5zk oor0.y dow,9w7bJanuary than in July. Is the Earth closer to the Sun in January, or in0o +z2iaoy dp.l zyp7,;i7 do5wb9 wkr 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 discovered to have a moon. Explain1d4g/mq,jg; az s wtw4 how this discovery enabled an estimate ojmws4a4,/ w1 ;g zdgqtf Pluto’s mass.

  The Sun's gravitational pull on the Earthh su*5qry,l0,g /ytgd4lkuad+ lvx6sp2f;c / is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravita dfxsqugv6t d 5h2plca,u/l0;g l+* yrk,y 4/stional pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling h,7h9c k .7xge)khfel 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around thj:vvl:r6w / f; z k.n)fu(psore Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's.:vvrr)w fn k:oszfp(l / uj;6 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 21j;iiu 8qks xth47 2ld20 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at armdi 2skjhu4;87til qx 2’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and ms-o2qy*fwz d/u 80lr myclw5j8+ u 6fcircles the Earth abo*c 8wj8q5 /-ul wdf yyflzmo+u6s2 0mrut 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 at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on0 kast1)bo ay2 the edge of a potter’s wheel t0baok 1s ya)2turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform8dzb3 5phwwpbf 77t+f9w l-uh rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5wl7pd-f+ 5fhuzw 9w3p87hb bt-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 which a 1050-kg car can round /q4e6 z uejv/u:a)dps a turn of radius 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 mass of the car? a/qj vdu e4z6:/) suep  

  How large must the coefficient of static friction be between the tires and theju kl dpr*0(95x dsts* road if a car is to rosjxks0*9ltu*5 ( drp dund a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astr(3(v4mmi kkbw onauts and jet fighter pilots is designed to rotate a trainee in a hor(bw i43(mvkk mizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntableerq x dyf ,b,ep /xu2.8dp17u8p opd9a 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 the coin an, fxybp 2a 8d/u.r8qx,7p1depode9up d the turntable?   

  At what minimum speed must a rlldqmh de,0 1 nmn)pv-wn.:d 9oller coaster be traveling when upside down at the top of a1q:hd) ,pde nnl mv-09d.wmln 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 (including the/.swovdgm l +6, c6fcx driver) crosses the rounded top ofvwsc,+g d x./mc6l 6of a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel ne9e, rsu8 4luzoed to make for the passengers to feel “weightless” at the topmost u4,z sr9e8lou point?    rpm

  A bucket of mass 2.00 kg isyvo,b-mt fig.s n3 .c)6 *9vfhbh+fpjuybh7 7 whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion tsn ff t+f37bvjbbvhcp 9*oy. . ,yhmuh-g 6i7)he 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 the axqzdr:.rn0e aqs t6 cvp5a231 yis of rotation is to experience an acceler2 pvrz0 q3a6qa5cyr1s te.:dnation of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peopt1ifh n fme ax2a;h.degu7+;3le are rotated in a cylindrically walled "room." (See Fig.guh71fh maa3ief+2x ;. ne;td 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 on a frict-va huly4vf)tl l y-ht+.,nz:9mt ,ymf2iu7lionless air-hockey tabletop, and is held in this orbit by a light cord conney7 nhmlt),-a f lv,mltht-i:fyuzuvl+.y 942 cted 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 , pr.n: s edvw0-lbecisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude 0debn-. lwv:sof $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 tf*rgrl - fip,o+n2fh,688q1lq*dpc qjdq-a88 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 massesfr5w;qp a4 ok3 $ 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 mtjg5 tvwkm n48hp,c4tg5j8u1aneuver 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 lzk7n((5m xrnwh8 u +sthe net force exerted on the car (by the ground) in Exw x r+nnh5ul78skm ((zample 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 Indianapolip,l jyf0bm5tu ch *4-ts 500 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 of static friction have to be between the tires and the road to provide this acceleration with not54u-c,jfmhy btl p 0* slipping or skidding? $\approx$   

  A particle revolves in a hori0oav./emir1 :ze pd 6jzontal circle of radius 2.90 m . At a particular inseapozj/ 6r0edv i.:m1tant, its 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 grav+lwmb c2bn5p8d1t m; nity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass c +d8mn 2bwtp5 mn1bl;is 1350 kg.   

  At the surface of a certain planet, the grlrg vfq:v0mo7r19xq0 qu c gd 5lv))3ravitational acceleration g has a magnitude of 12 m/l7m5xlvd v 9rf0rq0o3cq ) )q ggurv:1s$^2$ 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 acceleratk/g mmfz4secg3,2h kr9y i8g3ion due to gravity on the Moon. The Moon's radius is 1.7 kk g492e m83sihyg,/ gmfcrz34 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet, u 9kcvve8+ndi spz6+pv+n9-ghl o7n has a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due d9innv+ lvhv-9p,u++oe g 8c7 np zs6kto gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but tvj.hpt1+ )qx 9ue.gsg he same radius. What is g near its surface? 1+g9)stj vhpeq.u g .x  

  Two objects attract (cr;7 etsx.p(3yb segk o)c a:each other gravitationally 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)dxmoy01isd k; 7yn )b of g , the acceleration of gravity, at (a) 3200 m ;y mnsbko xyd) i10d7)   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wh: s8q5b6nyaux6 .e r7h*3ekzbbkast+ere thegravitational acceleration due to 35*8u6r :e 7 kzbayknseashb6.tbx q+ the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has f-u f1rrbf 8;bgive times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surffg-8b1urrf ;bace gravity on this monster.    $\times10^12$

  A typical white-dwarf scz3l5qy/t l1mx 6w51 xfpm.ypz;-ujstar, 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 mzqs pjy3 6f1zuxmx 5t/15-cl.l;mpywass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in tb)( sjc) kdrtkoyrmjv0: n3c+j0d3 .ghe space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t r) kj.sbdgjkmtc:y)jrn 03od c(0+v3 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 iox2wic r l.tjz3i09 -0.60 m. Calculate the magnitude and direction of 0cij2xotz w. 93il i-rthe 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 si izcjf,n:jrgl.jr5,h kh v q6 33qfx/8de of the Sun. Calc3 v lqh.nfx:c3jk q/f6h85ji,gz ,jrrulate the total force 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 surface of Mac5h.p(g86orvt+ r+ fzyoiy u *rs is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mgr+ *6+hyyzfvru8 o ioc5(.ptass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using thel4ni f9 usnqz6svi+t y 9m434v known value for the period of the Earth and its distain sv 6zsv9tfy l43m9q 4u+n4ince from 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 circular bmr 3g bwy)2jr-g +(ehorbit about the Earth at a height jr(bhm g-gwrb+y 2e)3of 3600 km.    $\times 10^3$

  The space shuttle releases a satel p-iv9fh iz)d(hcm 9j1f; f2bclite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release omcf 9fh vhdf1-j cp29ib;i(z)ccurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate s x) ,e0w9slr-f51fepb: qzdqif occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answf,b dw-sqs0:9lrxpqz)5 e1fe er as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a saqo*js-udvf 6 yq:;cd37 uz7lrtellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Eaudrc3-zl d o:*yqu s6q7 fvj7;rth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velockltqn2cw0i 41u2yl0cvnfd2j pc+ b94 ity would a satellite have to be launched from the top of Mt. Everest to b4pn01dcl0ni ycc9jl2f4wk t2 q b+v 2ue placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbibtp5*(jmxl)fac+l0o o5dp2 a t the Moon at an altitude of about 100 km. How longjm *2fabocpo xtl+ l)(dpa50 5 did it take to go around the Moon once?    s

  The rings of Saturn are composed of chy;vd.r: i2h)vh9b az aunks of ice that orbit the planet. The inner radius of the ring i:a9v ; hzvbahyd2.r)s 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). Whatt.gy45 g5 w75cmpku4rn6um wv5p0o au iapu5kw55v 6g ptryw4mmg0o 5u47nc .us the ratio of 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 km40em*jc,h; z/vhddz +ar u- xl,p wnu* from the center of the Earth's Moon in a space vehicle (a) moving j 4v+e,,zhxm 0 wr-a*uchlu/dp zd*;nat 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 m 5psa jw: w3lelf1y5v ,il/;fdass. They are ovyf a:wsilj,5d3wl/lp;e 51 fbserved 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 zmtrqvg 2nrn (2ahx 2p,lxf32rh .8 5sfor the weight of a 55-kg woman in an elevator thathhm3zrqp.nl 228,g2rv2 5a txs nrfx( 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 from the cei -i0 qrj jz9e:ebg7eidvx7b 4.ling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevato 0 ee7dbe x9b v.4riqi7gj:jz-r accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planezwquu kqo w/ yjb-:0fg593rf/ t with period T , the density (mass/volume) of the planet is jbu/okf:3 r 5gw 0zfq9/ywu-q $\rho=m / V=3 \pi / G T^{2}$ .
(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 t.5y8h gfetnd 5 y3lio dukbdi-/m z810he period of the Moon (27.4 d) to determine the period of an artificial satellite orbiting ve0dk.8 md3hnue i t5f/- igby81zody l5ry near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun lik2)q7c0ydfc lkyd+fx, aq ct0 k34 mpf/e the planets. Its periodt 0q7df / x 4kcf03ycldp 2q,)y+afkcm is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of srm -zmns3)(3pi-b8tnlz *dl 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 roughly once e l6p mz7e0wiy:very 76 years. It comes very close to the surfac70el6i :zm ywpe of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: 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 t. 1crc14h8 t/kvfvrwmbdej +ky2gpo6s fh /2.he 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 distance for the four largest m:z)21m rzrwxqlso 3o 1oons of Jupiter (those discovzw1 z3)2:1rxoql smorered 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 of9v*-2g27 pruhp.jt-nb sd olch+dq9p the Earth from the known period and distance of the Moon. p9cd2l.r t-s+ *v7n -u hdphbg qpj92o   $\times 10^{24}$

  Determine the mean distance fromz:qedwp59*rahg3rx hf 717v m Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in 9phrazx:7f71d3 g h*5eqvr mwTable 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 M++xf;gdcwnw 7v p2lsks1u 3lwv,y,72g 2w x gnars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destru;+xdls1 7vsygwckfw, lnp 7 gvwn2 g,w32+x2oyed).
(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 describes9d0 goegvgx+/ an artificial "planet" in the form of a band comeg0+x9 d/ ggvopletely 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 g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gor2 xyxb+o mx..ujf3z,w ge by 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? His mass is 80 kg, and th3zx2x .,y.wojxu+fm b e vine is 5.5 m long.   

  How far above the Earth’s surface will the ac90y + jq1tce 2xxaep*n cxw0l,celeration of gravity be half what it is on the surface? tw c j1 c0x+yeex,anx029p*q l   $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circle 9e 7dfv9b 9pa2cw7di rxxr,a. once every 2.5 s. If we assume their arms are each 0.80 m long and their indi vriex9c.9b,f x 7a2p7dr 9dwavidual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once p2lhf 3 ht+lp6iitra 6*yxcj 8)er day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this e jhrh 3cp)6littf8a y+ *ilx62ffect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earu t*oo;r 1idb3pjk)l8 th will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon purd ui*13o)b; l8p otjkll with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in anakg+ 0; c6,bu 3*w vppat:lpeh elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direcew:0 *6 hv3 ,aupcbk gapp+;tltion?     ----待选择----upwartddown 

  A projected space station consistszbi zoa9j,s8 7 of a circular tube that will 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 the rotation speed (revolutions per day) if an effect equal to gravity at t7z,iazo bjs89 he surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical ;+ c2e 0id5 zl7qt2naf1bogceloop (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 planet in t)m nxe9u eo b8iu )*f)c/3amuterms of its radius r, the acceleration due to gravity at its surface and the gravio8)9uu/teimu b* en mc)fx)3atational constant G.

A plumb bob (a mass m hanging on a string) is deflected from tk.0 08iw ,o+ilxnxc:w4ra j uwhe vertical by an 4:wi+ucw , .l0kaxrn o8x 0iwjangle $\theta$ 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 coefficient oaa-3q)4 wdfb.)x olj jf statifadwba xj4qo)3l-j.) c 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 fa2b1:biukot r8crd 7x 6st that objects at the equator wereb1iu6xctob2rr 8: d k7 apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain. o8 zxb p6lys8i3j7ww 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 of radius 235 m. A la.yg7j,yh 2b6loo cca)y, +zpo mp suspended from the ceiling swings out g,o) o.p6cboaylz, h2 +jy7ycto an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massivaz5;p rt8gdg7*cl ( rve as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planzp5v8ra d(g 7;r *cgtlet 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 Space Telescope deduced the presence oqf6tke6)i ) ccbw. tp0j2y9 mqf an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no lji09q 6mk)bwtf.pe t2q c6) ycight 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 trave4qf4*l n,w e7a(pxid erses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast caniw4* f4p a(qdnee7,lx the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) uthecf-mnf ( 06:taf+kn ilizes 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 centn f0fka(cnt+6:h -mefimeters. 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 (NEARp kq 5plcf-53g), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is rougg5 c qp5fl-k3phly 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 in nex0i f re:70r1jcqw 3xoed of repair. You arr0r cxqiwo 1f037:x jee in a 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 3000 years. (a) What is its mean distasl1e .3 bui3fvln )h5ynce from thv13 )sn 3ilyebfl 5.uhe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could acthrru 2hq m( xw4/+8eg4,;tw 3oxaitkbually "feel" yourself gravitationally attracted to someone near you. Make reasonable assw;xt +axgm / q o8h2tb4w34r,kr(eihu umptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (F.-7evaoi ch- cig. 5-46) at a distance of about 30,000 light-yecv -.ecahio7- ars 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 0.50 m oe+s jgt su46),yzo .mkn each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed a. )zgt 4 j6esyuo,msk+t the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kdb -t3wv9ky,ryxx: - zg orbits 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 the 1.5-cm-long sweep second j6hto n vc3)(95w;2ggw0p f*ckzq st khand on your wr 593 pggcqzj hf;0kv k*)6c w(st2twnoist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker bvb)l/xt.g r ,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 fistb,v /rx lg.b)hing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car trutb h6hr.(i-mtf rf3,aveling atrrf3,if.b-hmt th 6(u 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 A ueaf -s54 )yqzg:nfl9cela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exa 45-efn 9zgusqf:y)lerted 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 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.$\approx$    $\times 10^2$