Sometimes people say that water is removed from clothes n97umid,o r0eao3 ;cjin a spin dryer by centrifugal force throwing the w0d3 79uioj; rcmn, oaeater outward. What is wrong with this statement?

Will the acceleration of a car be tvplcgp)8x y+fjll qg 9894 w1mhe same when the car travels around a sharp curve ap p+1 mcv498wy8lxgj)gfll9q t a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly r6j .ix)eomzhyd1c- 7 uoad. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near7 h )oj-iyzm1.6cdeux the bottom of a hill?

Describe all the forces acting on a child riding a horse on a b inn39 z h/cnp5w;be7merry-go-round. Which of these forces provides the cz;h9n/n3b ib7 ec n5wpentripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle withi u(vrl,x y8p6wmj *)kd5lax 0out the water spilling out, evelxp0damr yu(v ,x56j iw )8*lkn at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are akaszc03*byv hld+2*n)vq -hft least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations docz ayfnk)3v *2bhshlvqd-*0 + they produce?

A child on a sled comes flying over the crest of a small hill, as showtip 56d f/kcap 9udv.j xae51:n in Fig. 5–31. His sled does not leave the ground /tk9ced p ai1ud6xpja:.v5f5 (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 when rounding a curve at high speezd by(g: 8atqv zf(5y-58r aeqd?

Why do airplanes bank when they turn? How would you compute the banking angle g15u(*zvf3w dhj ye0y qiven iu15w0zj(e3q fy* hdyv ts speed and radius of the turn?

A girl is whirling a ball on a string around he eh-1kb-lan*bizuw + s -ok)v2r 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 other side of the yard. Wh-v-ak)z2 i*+lhu w bn-o eskb1en should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how-;svxqh*cy0h r: ucdo0 ve7:n large a force? Consideoun h0 0-e:sdx:;hcr vv*q7cy r an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what iv 6ebyuu+d-u-w 2m:pqt is, in what ways would the Moon’s orbit be dqbwu- 6u:v2+de -pym uifferent?

Which pulls harder gravitationally, the Earth on .ty7(mrlyev1w7ra *4-w qkjhthe Moon, or the Moon on the Earth? Which accelerates morehk1qyrm.7wvewl t a*7j4-r(y?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet)uf/oe +,jydi thed +yuejoi,/f) 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.]

Will an object weigh morr 1zsot3 pv:n7( t2n5fxqpw7c e at the equator or at the poles? What two effects are at wopv n5nf q1(t :op7w3csr2x7tzrk? Do they oppose each other?

The gravitational force on the Moon due i 1 vz(po m /ph(esmc++vfn(s:to the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulled away from the 1( p:e+( inpvfc/ms o (hsm+vzEarth?

Is the centripetal acceleration of Mars in its orbit around the Sun ln9v tb;yfds76;a u.q warger or smaller than the centripetanys;.b 7qv; 9uf6tdw al acceleration of the Earth?

Would it require less speed mw o to0ob732h2mtq 5yto launch a satellite (a) toward the east or (b) towarm 35 2ob2wq0yom7 htotd the west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a:tfj 4lnf s f)5e.yy2kgn1rvb1 . ala+ scale in a moving elevator: when the e4 )avfn.+t2jg b.er15ksyf:y1 la l nflevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periodszgp* *s/ phbb:0c2zef in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) thep*h2*z/ s:ecbgzp0bf 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 wgag kg/,7s)up27hvyvk;4pk4 f 9ll ceeightlessness” between a) l 2k4g ;7 ypvkp sg/clkvgfhu7e,94steps.

The Earth moves faster in its orbit around the Sun in January than in Jul)q;bnn q9de5 qn8did 6a (ub6cxa3oa,y. Is the Earth closer to the Sun in January, or 3udiqn dq)cn,anb6;ob5de8x a 96 qa(in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discoverevp9rx8eh ,: :cldms; sd to have a moon. Explain how this discovery enabled9v8r,sd:: phlscx ;em an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. zsk*ss 1p,i52b 9xmvpYet 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 sittx,smpiv*k5szp9 b21sing 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 6 rlm9uc uw2;v 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: bv0*ef knj1l in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50nlv1 f *ke0:jb$ \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 as ijmhv*g- eb+db aw)e :t) gar(+t rotates uniformly in a horizonte- tbvd+)(w*hg : ea)mbjar+g al circle (at arm’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, /htwnf qw8z v.l7hn* *)0 krt yww*zc4and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms /wnttz0nhy*k *4. )fw qzw*cwvl7h 8rof g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of thev). b-7,bffcg o1pbw x acceleration of a speck of clay on the edge of a pottexbcb f 1f.w gp,7obv)-r’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a str bt9w1ulrs7 wtv dbo 0oep347*ing is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.* ltwwd19u03oebrt s77 4bvp o00 $\mathrm{~m} / \mathrm{s}$ 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 m3vkil*mqf8 )x s eu3m+c:b 9fturn of radius 77 m on a flat road if the coefficient of static friction be8m u*xmq:)vmef3cbsk93l+ fitween 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 and the 94 z0vhwef .jjroad ih4j vwej.9f 0zf a car is 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 designed t1 c/ 3ribbvpl/,pq:o co rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee ,b/o/cvr1qic 3b :lppon 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 c q9e6g5ybo+s0 i;bq dxm from 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 coefficienb5d9qyqx6b eos;+ gi0t of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at tbm6hhnw285lz.mw5 g 0ntwh,g he togz82g5m.bh6 h mw5w,n htlwn0p of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of ma/tx3ev i6nh fg e,tu8v-gy:y. ss 950 kg (including the driver) crosses the rounded top of a hill x 6 vf/-y.38etng ei,thgyuv :(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-d,eaw g6cz 5p-r+ yf5qciameter Ferris wheel need to make for the passengega,czy5+ wc5-rfe p6qrs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertb v ;2m4qnppbv2h nc0:ical circle of radius 1.10 m. At the lowest pocpnbv m2hv0 bq;n2p4 :int 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 centrifuge rotate if a particle 9.00 cm from the aezd b0fuf ,rlp +f6b8x u5xa15xis of rotation is to experience an azfpe,ux51rfx0d ub 5f l 8ba+6cceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "yu/ ipje724 hfd8nuo l-ng, u:room." i8-:jhdn p4/lu ,y uge7fuo2n (See 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 Mzq4a7+b ea2w pl ;o dix5n8g:e ) is rotated in a circle on a frictionless air-hockey tabletop, and is hez2egbe ina :5o+xqa;487wdlpld in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by x*m 5xpir+hndudy bn:x-ys 8*t 4*r7snot ignoring the weight of the ball which revolves on a string 0.600 m long. In p:dr *r upi4xhs+57x -b ymn*yts8d*nxarticular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banke k p7a9 fuezmydvdbi7+728xl6 d 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 masse6tamzw4t / *my9cirj z+ar( 9+o+ tangs $ 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 eva6 z- w8jym 349+ bxlm:x0ry xbvxnhyc5sive 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 the net force exe (ftny r*e.6g+/ f p-kqebs77uaxk-ahrted on the car (by the ground) in r. tg-h(sae7kf7kb/ x qy+6afp-eu n*Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the6nz( .wwbw 3a h,1wmbolozd *. 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 no slipping or skiddibao,l* oz (.h3.wz1wnww db6 mng? $\approx$   

  A particle revolves o 3/vljmy6 oe ivdy6 .xuj)12lbd y,1ain a horizontal circle of radius 2.90 m . At a particular instant, its accelevlx6j.b1y6yjd vl,o 3 ueo )myid2a1/ration 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,br9*t( n rr5 d:8 lewvsqkl*sity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface i8rd:wrll(rs t **e5 q kvs9nb,f its mass is 1350 kg.   

  At the surface of a certain planet, the gravitatwbharq) wp/ bmn t yw1c70)/t+ional acceleration g has a magnitude of 1ny bpww 0tb+r1) aqmc) hw7//t2 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 dff 9)-ifx r0rjoh+ an)ue to gravity on the Moon. The Moon's radius is 1.74 ) -nrx+fo)aj0hrfi9f $\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 bw va018zqt n+that of Earth, but has the same mass. What is the acceleration due to gravin 8vt +aqz0bw1ty near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the sameqc +/4nniborg 4k(* pl radius. What po/+ rc *l(ikgn4qb4n is g near its surface?   

  Two objects attract each other gravi qpzmksc bqm9:ui, e2.d, et4jzh /:a.tationally 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 of gravity, at (a) 3200yi7hizjw-q rl1k b:,50iw k) m m )i1 hykbiw ,0- mjq7zi:5 wklr   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth whqpfdg9.(i e 4p ui79xgere thegravitational a 4f(dxue .9qpgip9g7icceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron st7r/ :8mjelua(k afysij5gh cu2,- -cfar has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this luf a5-g:yj ac h ,csfrk28eum7j-/i(monster.    $\times10^12$

  A typical white-dwarf star, which once was an averadr41 7qap12 ( 1lx7rmpuuc focge star like our Sun but is now in the last stage of d2 1rcl747rm qu x1u(aoppfc1 its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitin u96 fjg3o7ncgsd 07jug in the space shuttle. Your friends resp0n7cj9g 3fjud67ousg ond 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 sc,,l h 2lv-/8.p3 bkw :uc:fmwvedq3 ej mv4fuquare of side 0.60 m. Calculate the magnitude and direction of the total gravitat: -wvjc d,3e3kmcv.u8b,m /e l pwv24u:hflfq ional 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 u2ow ksd/+o6n side of the Sun. Calculate the total force on th+uos ow/n kd62e 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 Mars is z+4 tggslv3utkn.06q -+up it0.38 of what it is on Earth, and that Malg3sktqzit0 u -+4+g .upn6vtrs’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Eartk8i7imi,zwg.ca7j v4 h and its distaicaw., 4 7g zji8imk7vnce 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 orbit about the/*bhr-oap l:v Earth at a height of 3600 km. bl r:oa p-*h/v   $\times 10^3$

  The space shuttle releases a satellite int yu-ng+5cqc (1rp2 d pv;/lihxo a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) whenuqlhpxn;pvy/r d-1 i(5 ccg2+ the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to /eoc)r9y1,;pydi g ja experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–321ygpj ed/r oa );ic,9y.)   

  Determine the time it ta.lsoma om+ 0p5rs gnsq+0u/5skes for a satellite 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 r05msu qolrg+pma0 ss+s . 5/noadius 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 launcho5dqnuy, 6 c+hed from the top of Mt. Everest to be placed inuhndo ,y5q+ c6 a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the comman* gb*1x qgphiw/pmx7ma8z/ f7 d module continued to orbit the Moon at an altitq1pgfzmw* ha/ xb 7 x/gm*8ip7ude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice:gpfeym sdw u+w.42qu ke:.dn 50 tnp, that orbit the planet. The inner radius of the rings is 7eyu24 :ugd.f.nk+ps,mnt5p e q0 d :ww3,000 $\mathrm{~km}$ , 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–zhe9 nj/fg:5;y 1y b)ewymean 8 1frl79). What is the ratio of a person’s apparent weight to her real wn e fnf1g/lz)rm;hbyy:7ae8w1j9 ey 5eight (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 ceny 9gcwmr 0yyhgwom;ju .yx5y c. (q4/-ter of the Earth's Moon in a space vehigmc.w r(o0;4jwychy/.yyy95gmu- xq cle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They 40um;mk5w huaox8btp 8i2u+fare observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between th 8+0aw85tfou i2 mkhbmu p4x;uem. What is the mass of each?    $\times 10^{29}$

  What will a spring scale re5p ,/cinivon7 ad for the weight of a 55-kg woman in an elevator that mon i7o/,cn5 pivves
(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 sugj 03 fwmsrp11u/qe e;spended from the ceiling of an elevator. The cord can withstand a tensupr;/wq3s gm e1ef 0j1ion 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 +qb ed )i08nbrw )dnl8 goo+7msurface of a planet with period T , the density (mass/volume) of the planet bbni 0enl+ 8 m7dd+gowq)o8) ris $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the M3y;()gp jp zuzoon (27.4 d) to determine the period of an artificial satellite orbiting very near the E;jz) pyzp(g3uarth’s surface.    s

  The asteroid Icarus, though only a few(spf ru2:ih38togk3*/c tb nw hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is io3*fr8/kh:btc 2 pu t3gn ws(its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance olwo)d* xyu:.bf 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 Sunln ny;0qhi, 1dr5r3 *f9 ceyki roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Es 5nq r0 9k*y;,cneli3hdir 1yftimate 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 aboup6e*9lka:sdprwm* 4weg rw 9gd.+,d dt the center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moonk/5qs 5 )z rkxm.mohs0s of Jupiter (those diksrmshk5z 0m5 x/oq.)scovered 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 pe-vh+ ms 2f rqo2hd.0cq.cmn7t ymiw 8:riod and distance of the Moon. tim+csrhq2mdm0fq.nhw .8v:y o-2 c7   $\times 10^{24}$

  Determine the mean distance from Jupi4 7pe k.v9x tfu:.4z+ey.k smfeh,jw qter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to they .s t:.v 4z9kuewf+7pxkj,fe emh.q4 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 consistgpe efc/wjka:ce.;5 5dfn. 42wg(ndxs of many fragments (which some space scientists think came from a planet that g. ecj.knxp w5ng fee/df25da;w 4(c: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 ta:tei;bim+m+ ka rud06w/a fx (le 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 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 off iub6/+0:ai;at +rmew (mdxk revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorgcw, mc0/+frwq e 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 mawcfwq, 0c+mr/ss is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gra .)h8rj:kjk0*kncuji8 rz *o fvity be half what it is on the sujn)8 kruk*h :j8f0r .*joizck rface?    $\times 10^6$

  On an ice rink, two sjq5z.f3w fy 6v,gyc mq.00go-y ;nueykaters of 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 their individual masses are 60.0 kg, how hard are th;0,y.jygfqf. 0o z6y3qcmy 5 uwvne- gey pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration o*fehb7m:ueqw- ut:q6i x(f.vf gravity at the equator is slightly x:-t*f7q (evuhfm:iqe . bw6uless than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travelin6i xp/yl p,wl8g directly from the Earth to the Moon experpwp6il , /l8yxience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg,imy(1 bi7b7+x+ewiv *wzt:rq but when you stand on a bathroom scale in an elevator, it says yourw(ix y1+ vewrib7+zm7ibq t*: mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consistdjc2a;d8tb ;ms of a circular tube that will rotate about its center (like a tubulardmdcj;;8b a2t bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft innoyc7n+ qn 2l;- bt(hxbz+/xt a vertical loop (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 tes)vt7jgucj i,5l 4x,t rms of its radius r, the acceleration due to gravity at its surface and the gravigxu )t7j,jtilc4s,v 5tational constant G.

A plumb bob (a mass m hanging on a string) is deflected from jqo5un( 2lme0 lqs/ g;gus 1w6the vertical by an angle1m 2oe/qjlq swunsu; gl5 6g0( $\theta$ 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 designl l q,*)rkhzrw)gieo9;3 eew7 speed of If the coefficient of static friction ie9, iz; l)3)e7wr rhlgkeqwo *s 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Eart5vfve d xdoao km12/+*h were rotating so fast that objects at the equator were apparently wedxfk ov+2m v /eoad51*ightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart ofj 1 x7q9i+7xpp m+ gq-aaoqxc8 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 x2 fq9 gqrlar(pd60j *lamp suspended from the ceiling swings out to an la r9fx q*6dqjr(g 2p0angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as v7z7u(vx cmd)ojypid ,ls)7,the Earth. Thus, it has been claimed that a person woul) ),umi7pxlzvs ,dyo7cvd 7 (jd be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for 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 dedosw.g3hd-mci0 r jk6/ uced 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 measuri3k0-o/scrh6wd i .gj mng 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 oatm)t+unu 9 :up/ j+f as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is larumn/ a+tjopt9u+: f) ugest? 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 group ofpr +x yngt9wp5r gm1-zay*.2a 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 accmr5r ayp.y+x* 1-2wztg ap9gnuracy 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 traveli wup4iot -le ( yeoekg-w4) 957e*uuxing 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros i-yeiee9tuw7p -w(*eo ku 4xu4l)o 5gis 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 th*t*ytu:kjo l/ e space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius *: ky/ olttju*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) g,p o*mi:,eedWhat is its mean distance from t i*,mpedg, :oehe 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 kvjj/u 10m0 lhactually "feel" yourself gravitationallhkjl1/u v0 mj0y attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates aroundv4a.jqcn;p43 q9 ztk :rg. hnd the center of the Milky Way Galaxy (Fig. 5-46) at a distance ofv 3nrct4zhg.qd.ak :4j9;npq 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 of a square 0.50 m najt 95hva o(u 00vqj6on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg nvv 9t6jj0h5q(uo 0a amass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbitscm,w,)h kl8kg1yq e y5 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.(q. .vqx2ama lll;i m85-cm-long sweep second hand on your wrist watch?mq.l va28l maqli. ;(x    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around inrn0ecjai89/:i c8 gd p93aasi 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: Sj s9a3ina 9: ecgpc0 i8r/dai8ee Fig. 5–10.]    $^{\circ}$

A circular curve of rad33-ux ievxqqjb1g755s8 te lmius R in a new highway is designed so that a car travelingb -vx3q s753i8e5x1 emjutqgl 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, utilizebsb60-tq r; tpsdu 2afn(o9 j(s tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main foapsj9o0;qd fn62b(b s u ttr(-rce 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 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.$\approx$    $\times 10^2$