Sometimes people say that water is removed from clothes in a spin dr-31sg 1soc5: 7fj dcboldcs0xyer by centrs7xgs-c :f1dobc jc1l3 50o sdifugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a c(9zq v49 2qyvsd *ub/coa b-yyh+eg y,ar be the same when the car travels around a sharp curve at a constant 60 km/h as when ie/yd +9b vqy9q gzh(vs 4yy*uc2 -,obat travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whaeot3 u)u91dbnuvh-v)85 hq i(b.mh nere 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 near the bottom of a hin5b.tuv-hdu8vei)q 39bo hm u h( )na1ll?

Describe all the forces ogb 239pxq ds3ujs z59vhlq7(acting on a child riding a horse on a merry-go-round. Which of these forces provides the centripetal acceleration of the child9x(l js 9527 q go3zbuh3dsvpq?

A bucket of water can be whirled in a vertical circle wit+yqyw9fo-nzn(nu /lrdw 7 c 7(hout the water spilling out, even at thl q n(yu 7w/oyfn zr7wc(n-+d9e top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at leastm,blc+j727wqqaf td.b/zi lvwjx *03sr,;w l three controls in the car which can be used to cause the car tob.lq wz+r7/jl cb 2*va3 x,0wi7lw,j;dtqmfs accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill,s5ga2+y +b 5 +jni o:zal4fxbd 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 sn4 fb:2o+ijdlaa+5zb+x5y g using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high sp+y:9d w kebdj3eed?

Why do airplanes bank wg) l6 r :83yjqqx1gswfhen they turn? How would you compute the banking angle given its speed and radius of ggw1fjy8q:3x 6lqrs) the turn?

A girl is whirling a ball on a string around her head in a horizontal u:d8v)jb0rp, f i+q1qbw x7q(qp4r jo 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 yaf18+ r p ,:dq uqbv7iqrx)woj40jbpq(rd. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? 3bsr3 ar4geu3If so, how large a force? Considbe3sg334 r ruaer an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would thh2gw.m2i hu7q e4nu)c e Moon’s orbit be diff2u.qum7h4n 2c hgi e)werent?

Which pulls harder gravitationally, the Earth on the Moon, or the Moon+h1ph*r wx go: on the Earth? Which accelerates morr g h*wph:o+1xe?

The Sun's gravitational pull on the tz9 y7hnilvz8r-i )3.vx/w lzEarth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Ea)h-znvirit l.lyvw/7x zz83 9rth to the other.]

Will an object weigh more at the eq 2)hav+ af-(ma2ivz dzuator or at the poles? What two effects are at work? Do dzf h v-v+im2za(2)aa they oppose each other?

The gravitational force on the Moon due to the Earth is oj5gihf ljs:,+ 3q3ayz nly about half the force on the M 3+,hqlji 5jyz:gfs 3aoon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its o cejbva8qr3 uu5+zv)-rbit around the Sun larger or smaller than the centripetal acceleratzuu-35 eajq+ )cb8rvvion of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (bb 19cg5d cx2 x6sjbw6p7c:r jb) toward the wes7j x2 gcc6bwx d5r9c pbb16js:t? Consider the Earth’s rotation direction.

When will your appareku4,, gl* :mcmlktd1wup:/u ent weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When woulumc41e d:l * uk:,utw,/glkpmd 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 sp;1yl 6gqwj a(fwfo25aace 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(f;6ayqwo15 2 jwalfg 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 weightlessnen4o:t hs7xdo*ss” betweenon7o :sdt 4*hx steps.

The Earth moves faster in its orbit around the Sun in January thanboxjoqyzd2m,t:96 ef1bq,4.p( xh p fs6dm-n in July. Is the Earth closer to1(pyo6.pf96,zt s 4e fm,dx-qdx bnbq: jmh2o the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known ue(u2k+ytcszo): q 7 a5eh) zqqntil it was discovered to have a moon. Explain how this di ys+e uz5kt))qeqq7z(ho2ca :scovery enabled an estimate of Pluto’s mass.

  The Sun's gravitationaoue yw.-il,f(g*b2v k l pull on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explalv(,o*yfb u -wge2i .kin. [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 1x b-i ti-dz1v7980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 thofk74z: o *glre Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? :g7 ooklz*r4fAssume 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 i8skfe-ud9ijcv: 6rn 4*aizmkk0g*t39 cw 6qls exerted on a 2.0-kg discus as it rotates uniformlyjkdwnm9 vez ucr*t36*46q8 giaf09lk-:ksci in a horizontal 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 tf0rq l q6,p5y qnm/+v48ei2:7p evdcsl xmu:ghe Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms ofd7gsnqv/qe5le, :rqumixyfv86c 0p+4 ml:2p g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude 0 wi9p wst1o6bpr,ty,ju pv.0of the acceleration of a speck of clay on the edge of a pottewpy,bt, j6w v0 o.9pis1rpu0tr’s wheel turning 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 uniform rate in a ik d*/ w650yt0ocj;*jf )5kzoxxiv uvvertical circle of radius 72.0 cm , as shown jtk60/xx0o 5kw f)d5o*vj yzci*uiv; 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 speed with which a 105es+h io; iv9g(0-kg car can round 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 ma (ogiv9; ih+sess of the car?   

  How large must the c6 4xcl6 banq+p)yk6e l/:wiwdoefficient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a spex6ac / wp l :)kd6nqy4e+6bliwed of 95km/h ?   

  A device for training astronk.i 4 u46zk/c ;vljjvqp 8qa0dauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.8jvu/c;i0a qdl6vk4 zq.jkp40 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 turntable of variable h(..k1dm mwe mspeed. 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. Wh(dm.1w.m hkm eat is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must alndv ps4ym zqp1f,oz 04j0 ;l2b):nfk roller coaster be traveling when upside down at the top of a pv: 0lj 1nsf0pbd, nm4lf;2 o)yzz4kq 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 driver) crosses th4fx+0v52hpn(gp j g mne rounded top of a hill (radius xm4ggh ppfn( 5j+0nv 2=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 n ivl*zhw67-*a ptq8 oleed to make for the passengers to feel “weightless” at the topmost poiniwapvth ol67* zql8 -*t?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circt. yps,2 8*vhjsxp 3ntle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting t .h8s spv3xpj,tny*2the 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 cmb)tn z5ga1;lxh n+2is from the axis of rotation is to experience an ;2tsz5)+nxhli1 bg naacceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically wa jwovtu+o 19o 4edb)vsyf9;5vlled "room." (See Fig. 5-3+vwv4o j b ytv 9f95dos)1uoe;5.)
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 cir,v46 hf)ane udvrru(kzve5 6)9i d lu3cle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown idz 4e 3 66k9 vd,(aivfu5ruhrlu )nv)en 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 lh4ng* c buvg9:sg3 s9this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, findvg gbsn4g*:9h l39scu 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 ,bs r5:y:v deais 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 r xy0ayfx+9 yuyzt-)nme m,1l i44d )g$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver /14x6hgyapoz dd w89jby 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 exerted o8w i;szn -fz1zn the car (by the ground) in Example 8isnz;z f1w- z 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 from5 9a7 ib9bjjbg 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 ogj a95ij97b bbf 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 skidding? $\approx$   

  A particle revolves i,wny7j-jmvk 1n a horizontal circle of radius 2.90 m . At a particular in v-jw km,ynj17stant, 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 gr aw1vk:-tbb o.avity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if vwkb1o a.t- :bits mass is 1350 kg.   

  At the surface of a certain plang.eqr4zip iw s:elc90e4q-;:q y 1uanet, the gravitational acceleration g has a magnitude of 1. qeaw;iy q:4ensu-l0eci 4z:g 9p1qr2 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 M7gl doh+1: hle1r2jpg*xn/ vv)af27eze jt+coon. The Moon's radius is 1.74 + xv2ga1nr fc ee1l2o :pjd/t7 ehvh)+g7jlz*$\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, ,knp*j:: qloibut has the same mass. What is the acceleratiqn*j:,lk: pioon due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, b;e:zq psfe y+6ut the same radius. pqe fs 6y:+;zeWhat is g near its surface?   

  Two objects attract each other gravi )kd.7/hilvsitationally 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) vdb o3wey 4e913200 m9oe1v bdy3ew 4    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Es f3dlr,x: t+ mij-h3farth’s center to a point outside the Earth where thegravitatihl i ,fxt3sjr:m +-3fdonal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the maya9v o(r05 kvvss of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this mons59yov 0avvrk (ter.    $\times10^12$

  A typical white-dwarf s hcq2et+ q j 7ug-u2+qci-b wj0otw.v9tar, 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 gravit q7 vow0-w-+cj 9 uqg2q2jt ubthcei.+y on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless b6 y v6-ft1kyxtz:u:pakfs ;0while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s 6f1:uv-a0 tz;ky6y k btxsp:f surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side u1t; nfsu5 na;rwv/:y 0mvo s4(/igtl0.60 m. Calculate the magnitude and direction ;; 0/1 g5muvu(vn:trni/ sa4tlswfyoof the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Suhg9qi6d-;hl;*ihsf va d xn1axe b)+1n. Calculate the total force1) 6qaad*1 ;xx;d-sghhlhneivbf 9+i 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 Mars is 0.3akx2 z p; shf :5n8rr1cwzfqe,sp9f:0 8 of what it is on Earth, and that Mars’ radius isc08s sf5f:xkwrrz: ,np a 1qez2;pf9h 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 Ear36lh *9 l3;8f3- nq impvkupjpl3xfpz th and its distance h zlu9nfp333xvl;i*p kq-6 lpmj3pf8from 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 moeq ktzwysp;7 a8*9f8own3e 6nving in a stable circular orbit about the Earth at a heig;z8 wnte7*wes6n 3k9f qoayp 8ht of 3600 km.    $\times 10^3$

  The space shuttle releases a satellitcya+,0 yr25 l (zfaffva7ram:e into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when thvf ycr, aa5y+f 0(aafr72:zlme release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants ajhfk(8hn yv0.re to 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 (vjh0kny8h.f . (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit6cacn /:gt e )9nfkr7c 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 Earth. Does your result dependagnf6n e c9: krctc)7/ on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellit. felav22sv lq(02cnqe have to be launched from the top of Mt. Everest to be placed in a eq2s 2.fnv(0lvacq 2lcircular orbit around the Earth?   

  During an Apollo lunar landing mission, the commzvcjszm)(jv9:z.u.c 9n7 pxu*w n9zxand module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go arzsz7n 9(: c.xjzum w9czx)vu9. j*vnpound the Moon once?    s

  The rings of Saturn are composedwsrkrvl z ojze0k3 45st.+70c of chunks of ice that orbit the planet. The inner radiults r0kwv.o 53c7e z 0z+rj4kss of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diameter rotates once eveo)+jk x /(igbkry 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weig/)(ixokkg j b+ht (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of the :qth1mgq7k7. 6wt gdcEart6 7dq.:wgqh 1ttgm k7ch's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars k p7d )56cvlgpof equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway be 7p v6ckp)ldg5tween them. What is the mass of each?    $\times 10^{29}$

  What will a spring scaln.q zu8q((s.m5 fh qbqe read for the weight of a 55-kg woman in an elevator thazb.(quhs.5q(f 8 nqmq t 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 frmulpke) 9 m ;v5qfy9op*v/4bnom the ceiling of an elevator. The cord can withsfopv;9 ymmpe5 nq )/ b4*vlku9tand a tension 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 th;:6 uend9hs6 pwf,osm vpi,zs 2 hk2x)lm)4k ze surface of a planet with period T , the density (mass/volume) ofw96spn2p lhfmu ome, )s)dx, 2v:k6k sz4zhi; the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to detny uynsx+7q(cjs-i/ ,ermine the period of an artificial sateu(yjx q i n+/cs,sn-7yllite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, twj9gmkys5sdv g8c*f97ceyjau.j .-2i;5bfchough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Suj5fd7k y w5 ebfm9.g-a 2c;g9icy8.jc*sjsvun?    $\times 10^{11}$

  Neptune is an average jxn3(h4 f fehw,ew3o 5distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughlpf*rerxc9g- - .a,wh gy once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is negr,xe9. rchaw *- -pgfarest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of the/v4d0 npujy x8 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 m9* jc5il fewepfdk9+c:: g-gpass, period, and mean distance for the four largest moons of Jupiter (thos gw-fe*5pd:9 9c: cgf +jkeiple discovered 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 sfpdx8vtb7,9f d9(am* e6uzh Earth from the known period and distance of the Moon. 7(ez6ad b 8hm*vstf,9fud 9xp    $\times 10^{24}$

  Determine the mean distance from Jupowe;:tt+ 8hg jiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the perhtg+;j:owt 8 eiods 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 betwe ()hmthdr*k4/x7sxw v gqiq +6en Mars and Jupiter consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but wash+q 74xvd i)6(k wqgtsrm*/h x destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in the form of apng*m 6-m-rs p 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 g-nsp6 *- rmpmexactly 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 swinging in an arc k7l.1yx5vxl,ue6nrl from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on r,un llx.e 67v1ylkx5 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 gravitjuiyj8j1x rv l/s66i5y be half what it is on the surface/5xy j6j6uiv1 r8jls i?    $\times 10^6$

  On an ice rink, two skaters of equal mass be:4ex(ubo tud uc8)w 7k;;qzgrab 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 bucw 4: kzx;u (te;b8e du7o)qmasses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acqe f8mxhpn 17gk/r 36yceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?py1fn 6 h8re k/7xqmg3    $\times 10^{-1}$

  At what distance from the Earth will a spacec g ekn+q)l:ooo.pg3;m raft traveling directly from the Earth to the Moon experience zero net force becausemp)l oq3k.:ggo;+ on e the Earth and 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.ry(4,ee wxlo an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, a e.4r,(yoewlxnd in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circul sh,89sf22+el5gwlr pa f3fslar 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 (rev8lsf92 sg+ pf2 hr5l w,ea3flsolutions 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 loopj ( * pbdobaw9ner2jwgr1h93+ (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 terms of its jujj5u o1h4.kradius r, the acceleration due to gravity at its surface and the gravitation5uh4okj1ju .j al constant G.

A plumb bob (a mass m ha l65)wr0tbkv vnging on a string) is deflected from the vertical by an 5l6vtvrw kb)0 angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coefficient of akz;qs1p.cfr ;(f1yfg1psh5 static fricsfs11q(;rfy.p 1zchp 5 kfa; gtion 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 Eartj9 hrv. csom+l97xwu/ h were rotating so fast that objects at the equar ljm7xv9w u .+9ohcs/tor were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distay*i *ah tn.s1z 4g;msz( oz8yxbz:m+rnce 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 ofpcd q (94d5hlt radius 235 m. A lamp suspended from the ceiling9dc5dtlh 4qp( swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Th osq:gxqc6,,6 n 3pduom:wmb+s g5:xwus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate th+ w ,ggobx6 o,m:5x sn:u6m d3cqs:qwpe 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 Telesco7zd7 witk0;g k5q,cl9l 7gsz ipe deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did thsli9cglk0k7 w 7t7i5z,qz dg; is 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 varrtqxl bea69 jp/4brh0)*hah0l xk5 +lley 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 largl qh/9trbhaa5 bx *) l0ep4x0 jkr+6hrest? 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 Pxm0g.agr(ef1 dk89 vxositioning 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 navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each mvx9a8d kr ( 0fxg1eg.satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rende r8eh jgg+h6h o 5p;idqm .)6j/astd.vzvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . ;65ev 8gth s i/djqmo.d gh).+ rp6hajEros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in tmgwz2o4iv/ .: h/zoo qmh k1b1wj6( t0f;joed he space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behindh1 bjkv:0z.;t eof4 6/mohogwz w o1dmi j(2q/ 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)- gy r.aop/4p1v0jo/ hhtj b9k What is its mean distance from the Sun?-g/ph0vyoj.jk/ th1r 9 b 4poa   
(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 chpej n4i2r fs0vhb2.2ould actually "feel" yourself gravitationally attracted to someone near you. Make re2shj evni4br2.h0p f2asonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (nv,ho od1/,yy0 i u*sfFig. 5-46) at a distance of abouthsufy 0i1oy*d,n/vo, 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 av1qzfmbdez .uf(uqid,2 :, u/t the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a zf:dufud,1me q(q.z,uiv2b / fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass v*l2kng:uki 65 i wpd45500 kg 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 secon/tztpe0j5,av7, z xl o r (gxgg8jg/z-d h5toj0 ggjzg-r7 (g zxxp8 ,,zav/et/ land on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker 6-6 h/u/t6 sh /q5-ezjbr:rsq y yyigcweight 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 fi /ijrb:sr y -tsh-yq6qg6 zyc5/u 6e/hshing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in ago+)cho w: ptjy9 lks)ae+ +9x new highway is designed so that a car traveling at sptao9xsop+9keh+ ))w: cygj l+eed $ 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 traa55q u yp r8raz-1c0edin, the Acela, utilizes tilt 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 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 til qp805zu5r1arcyd-e at. $\approx$    $\times 10^2$
(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.$\approx$    $\times 10^2$