Sometimes people say tha +gxa1iw158n 0a habgct water is removed from clothes in a spin dryer by centrifugal force throwing the water out80a1nab1wh 5+x iggcaward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels a qn,qi08:dy mtk,zom9round a sharp curve at a constant 60 km/h y,qk,diq80nm9 mo:t z as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant sp nd4imni hlv/v2 30na;eed along a hilly road. 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 near the bottom;h 0m i3nv/ naldv4n2i of a hill?

Describe all the forces acting on a child ri7w(s 5/om9e dhq 1ixmxding a horse on a merry-go-round. Which of these forces provides xhsd omiwx/(91 5m 7qethe centripetal acceleration of the child?

A bucket of water can o*ea+,67fn z8p tdffube whirled in a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside dowap+8fz6,ndu*f7 fe ot n. Explain.

How many “accelerators” do you have xq)m:3x8fk mbin your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do tm 3kq:8xm)x fbhey produce?

A child on a sled comes flying over the crest of a small hill, as shown in xja)1e,g: fkl Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), bfxg)jake l 1:,ut 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 g3 tt0xi.hppwyu.2 . lwhen rounding a curve at high speed?

Why do airplanes bank when they turn? How would ppe:8l b gxs49-l8ccp you compute the banking angle given its speed and rad- cg8lpscl8 :ex94bpp ius of the turn?

A girl is whirling a ball on a string around her head in a hoj3b1wu6 /xrfiprfl,jn q+ d0;rizontal 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. When shoul, r+lx 0d/ fbu1j q3winjf;r6pd she let go of the string?

Does an apple exert y6 v8ki,i:.x kva+ fiya gravitational force on the Earth? If so, how large a force? :,vk+ivy. iyxa fk 6i8Consider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the q( g yws)x/a8k5r2c reMoon’s orbit byrs/ g() c8aqre2k x5we different?

Which pulls harder gravitationally, the Earth on the Moon, or the Mooezpol5u a nv wu/15/,an on the Earthv auz a/ 1w5ol5pen/u,? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than ree .pq//7( bdsqipe/the Moon's. Yet the/e(peqbd/ ep.7iq/ r s 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 jjm2 o2xng 16a 5zy.8+rggsxsmore at the equator or at the poles? What two effects are at work? Do they oppose each sys.o ja2zjg8 2+5mx1gnr6x g other?

The gravitational force on the Moon due to the Earth is oq3csp4/: vq6/zex1l7 whsirl v 3*jal nly about half the force on thec1wsejvqzq: arp/73h/svxli 46*3 l l Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbi2 8)1 fj yrz3crpoa9vit around the Sun larger or sma9ri acf p)28yv1zr3oj ller than the centripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) t jd-ofsw3g rz(2n8sc (oward the-nc(swo 3(sfd 8jzg2r west? Consider the Earth’s rotation direction.

When will your apparent weight pl; ob4ocw v 8kmj;4m1be 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 ckov 18mp;bj m4;lw4 ocase would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected byh sp,+dqan 8z4ggcir6-( u1+ sx+szo y weightlessness. One way to simulate gravity is to shape the spaceship-a4s1dsyphr +g z+nc sxzqg+6uo,8 i( 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 weightlesek 0f)oetd1( p 4vg:xkiz /ln2sness” between steps.kp)k0oif exz1vt4(2e/d n:lg

The Earth moves faster in its orbit around the Sun in January than ccw 8ti,.v4sus07iu d 2z44dvjgzs7rin July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the svz rvs ,sw2.c7i0u 74sjugdtz4 48diceasons — 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 di6hqn-+kw b5 dgr:0zpzmt-1(g / zkmgnscovered to have a moon. Explain hog0 (/-gt q5-zzz 1rd: pnwkk6nmg+mbhw this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger th(p x x)q:zsbm l8x,6cwan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one sidbx s8,m(p c)6:xq lwzxe 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 d;f(4ekvb)tz4 mhn7 h 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 accehj+q jyjwx :-k0e l/w6ul/k d(leration of the Earth 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.jyk+whl 6wejq0 /dx(l/ :u-kj50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N i) mch-z,vb j9k (bswyham )0c(s exerted on a 2.0-kg discus as it rotates uniformly in a hormyb(z))hkh-s c0vacb 9j(mw ,izontal 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 tlwu,vw)p ;b+9lvx9b 2ikygkbq(*z4 rhe 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 of g , the gravitational2,v ur 4ybbibw)qlx9kpzg9*( kl+;vw acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay o nhd;1,crb pq+n the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s d+p,hr n1;b dqciameter is 32 cm?   

  A ball on the end of a string(.ov:;af7jra8fe+h / ruw cl45ym ol bums6i. is revolved at a uniform rate in a vertical circle of radius 72.0 c+wvc uyrmra(f om4j;8o e /uh5allsi.. b 6:f7m , as shown 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 1050-kg car can round a turn o5qffwh3 cl )qnh,n(k5*7i rxt f radius 77 m on a flat road if the c3q,wkh7nr t i*5x5c f)qnlh(f oefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffi ;q 5hfq ;l 7:t7wwgxuxseyc:)cient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at 5f :glhs;x :x7equw7ty;c) wqa speed of 95km/h ?   

  A device for traininbyx8u.x1j wajrm4 txt8q.kc 2;6im4pg astronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circ 6.4 xwrkp8xbj. mmxtayt 2j q1i84c;ule 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 o2t to9sc +to; nq/e*nnf a rotating turntable of variable speed. When the speed of the tur sqonen;t/ t+*9c not2ntable 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 and the turntable?   

  At what minimum speed must a roller coaster be traveli e ai xr4:40d/iip;lying when upside down at the tol4a:piy d ie4 i;0xi/rp 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 mass 950 kg (includityuz 31nm-s 3vng the driver) crosses the rounded top of a z-yu vmst3n31hill (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 minusgi**1nt. mex,rs5 1ii q gav+te would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmost point? rmtnq 5v*i11+gsa, eg*xsi. i    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 14 w6/ iv*d x2k6lja6v.swu dkv.10 m. At the lowest point of its motion the tension in the rope supportinl*6idak4vwvuw vj. 6k/s2 xd6g 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 g1.a rfqx 229mimb*l: 0 mpyqp9.00 cm from the axis of romgx2:p.0y9pq fa lib2m 1m* qrtation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carniva-uvd yigv0 f.(ee r4m2l, people are rotated in a cylindrically walled "room."fvyeg-2d rmie (0.vu4 (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 M ) is rotated in a circle on a frictionless ains34st r; nm wi;bbcxd;l3*6(g9pa xur-hockey tabletop, and is held in this orbit by a light con3 3tbxwmsa lp;4n*b(g cd9u;sr;i x 6rd 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 not ignoring the weight of thekxny es-+ yj4/ ball which revolves on a string 0.600 m long. In particular, find the magnitude of 4/y jx-+eskny$\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 88-9; i;89 h(pbibc pggbrzebowc,-dh ( 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 massesp i*t/.epiq.2fe ( vsf f(m*hd $ 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 maneuvca- kaz qe02w5f dj*/3fq qq3eer 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 net5 f9ciyv0sgt4yg j7x a6+0jo h5u,n2p-dwref force exerted on th0 dj anh2x6y+us-ef5twycgg57j p4v i0r9 ,o fe car (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from tozo nahk; 7-kj el7/h1he pit area, going from rest to 320km/h in a semhoa;nj - / k17lezok7hicircular 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 skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a p v0). :dfl6r;vxbydytarticular instant, it xylr .) 0dd6t;v:yvbfs 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 Eaya* ukx;fxp sh :y1c5 ;z08-d( jputfjrth’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surf 1duya(8jj ;0f:;ypfsuztxc kx*5 p -hace if its mass is 1350 kg.   

  At the surface of a certain planeltsr8r1 zol:d f 6e-f2t, the gravitational acceleration g has a magnitf2rdz: 6l-o 1 sfrt8leude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is v)ifm knkz/6n+p)vg . 1.74 vzn k i+n./)kfg6v)pm$\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, bu3dosx8;dvgil (p9s (if- k5 szt has the same mass. What is the acceleration due to g9 ldisg(vs;d-x(f3 8 5zkosip ravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the siwc5 )8 s*+4ze4crg9jvfv fxr ame radius. What 5z8r 9 vc g+)wjr4ce4fsx* vfiis g near its surface?   

  Two objects attract each other gravitationally with a force of 3fflao9ow-u4ev o/n6/o c 4yh 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 oq:ldo3o :pbm l2fv14 , the acceleration of gravity, at (a) 3200 mb ldop1v:4oo lq2f3m:    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a ph50a o oztjqqw(e-5d-oint outside the Earth where thegravitational acceleration a o50t zwq -(ojh-5edqdue to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sunz3 sh-9e+w cn8i:mwb2oa:r.rr7m heh packed into a sphere about 10 km in radius. Estimate the surface szrmr8hh2wneb 3 e rwaoh:m-:9+ ic7.gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun butpgj:)9q 8a0r0fe3s * n ,i umbhda/lzfj)p6f r is now in the last stage of its evolution, is the size of our Moon3irm0)napseah* jfg /z 9rbupfq 8j:)ldf0 ,6 but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronaukovil c54*iafps zuj8;07q k,ts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravopz *ikuj0l4k 8 iva,7qsf;c 5ity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. Calccmzp4+gmo,txi3zxyj 44 6de6 i;ak 7ln/eri5ulate the magnitude and direction of the total gravitatio l7;ckei5 pm/jaze6 +dxr 3,y64igz n44xmit onal force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the plant)p-9/f nymv1ls4y tk ets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four p4v1n) p /mlt9-kyyftslanets 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 acceleratilkd e /)g9vjcj.g bb,3on of gravity at the surface of Mars is 0.38 of what it is on Earth, d/bj.cgk39,blj) g veand that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the p 5 f6kg:m0dlec (ycj(qeriod of the Earth and its distance from the Sugy6c5dlq( m(kejc:0 fn. [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 k4vxiswr,1q 2 Earth at a height of 362sxiv rqk ,14w00 km.    $\times 10^3$

  The space shuttle releases a saj r s5d(wqzt*:o42 ncstellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the c2rzd o4j (t *sw:5nsqrelease occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupantc j,d nvxwjd-k:bu;0.o+sh+ ns are to experience sibdw:;+, j.u no-hn0+sjv cxkd mulated 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 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in 5fyp1iwp(z/x 0+ zs lxa circular “near-Earth” orbit. A “near-Ea / z+xxf0pz5silw(1py rth” 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 depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have tob5k qq /;gbrtx*c/dj 1 be launched from the top of Mt. Everest to be placed in a circular orbit around thkd/gqxqb;1jrtb *5/ ce Earth?   

  During an Apollo lunar landing mission, the command module 3a8h p *goxesmp iv :f7,wju fgz/f/.+continued to orbit the Moon at an altitude of about 100 km. How long did8xs*3hf:/z,fgga/+ouemvp j ip .f7w it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The inm.+)vx6 1omfaxhwcs5 ner radius of the rings is 73,000 5c.1+)hs6ax xvwomm f $\mathrm{~km}$ , 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). k dcdvxs/02z(What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (bd(zk/0cv 2sx d) at the bottom?
(a)    (b)   

  What is the apparent weight of a 7iqw4b0d -fab.5-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity, 0w -i4.b abfqd     ----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 q6zt r7of4wfaq; y7*bof two stars of equal mass. They are observed to be separatedr*qtaf;6qfb77 4 y woz 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 for the weight of a 55-kn*j(+tphzgr8 ys)n 6+q. cs hemp/wue8nd 7i+g woman in an elevator that moves +s cjewmu+7gnd)pn68y/ hzp+qr8 sni*t. (he
(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 fromx)p*wtd2 28 bo4ng5 kft ngc-r the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What wasdk5rxopw c4-nt8n*ggf )2tb2 the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satelliteptp9 d a 2+aqcck,g14lhzv94yy i57 dk orbits very near the surface of a planet with period T , the density (mass/1y kvd4d7+hq c4a pc9zg, pt592ayk ilvolume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Moon (27.4 d) to determin5w3xakkz 8wx(e the period of an arti kk(83waw5zxxficial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though j:-8ql2o 2ayv sko0nq 8yu8ixonly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the i sa:ouqq-vkj8 2yol088y nx 2Sun?    $\times 10^{11}$

  Neptune is an average distanc ahl8 .(/tklbxe 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 roughly once every 76 years. It ,z/9 59ndn nissnyler/-cc5y 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 nearest whes cy5ls/, 9-/icynnn 9edrzn5n 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 abou6at(l cnw(r8 st 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 f ,0wd04ran d/b :hxrylour largest moons of Jupiter (those discovered by Galileah :d0rxb 4nr0/wy l,do in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period ann8tuhh 42qoc3w6up3t ;b n54dxqsie 6 d distance of the Moon. 2h 6h48o;butnp i6n43 cqqx dst ue53w   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using 5k t ,1al/po +6ocx/d4htjtp*s*pcg dgp /xt2Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the v hto1 4l/jtxt*/cd5p2cg /6sotdapk x+pg p*,alues in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments jdjhd86b7rfwt p2p )1)k)giryaui*3(which some space scientists think came from a planet that once orbited the Sunp26ipabrw*)1)3tdr8hf jg )ijk d7yu but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificiaigsn ge.mk,,z6xc 4 c1l "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 of revolutiocn1 z. xcim6,se4k g,gn, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinginxwuw rm4 .0ah6g in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 rwwa60x u4m.h N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will thez lw*. :xix;mj acceleration of gravity be half what it is w: z.x*xli m;jon the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circl9gax.tx gn1p+ e 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 x 1tnap.9gg+ xhard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apphs)-oz+an d*h6p l- toarent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the mag)-+ntsd -ha6h*z oo plnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly fryyg8+z*/f+p jncvfn) 6 sklgi--b - pgom the Earth to the Moon experience zero net force because the ly v 6nf-p8+gsg/-+ng*)kz-i bj ycfp 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 an elevatr8: tv c*jbh-nor, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direcvnjr*b8t h c:-tion?     ----待选择----upwartddown 

  A projected space station consists of a circular qb5pbx+3qc: x tube that will rotate about its center (like a tubular bicycle tirexc pbx5q :bq3+) (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 in a vertical loo3 umg)rk rp 7nfs7o.*ep (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 tcm/skeo8c ilf9 wzgk7 7n50h)he mass of a planet in terms of its radius r, the acceleration due to gravity at its surface and tmefwzlk7sc0/c 8)h75g 9oi knhe gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected :z-x ; m ej3gyjae;0ot4ntw;nfrom the vertical by an a e;nzwxj0jmae3:;;- t4nyotgngle $\theta$ 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 ;3j.b .btlkpiephd(*umh7 )vthe coefficient of static fricthi7 hpmkde (bjuv.plt;)*.b3ion is 0.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that obje,so*/ lsel.h2 u p.znxcts at the equator were axs. 2ze h*p.ul lo,/snpparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a conur1)q +189i3bawif i kbnvosf-km z71 stant 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 consg*cge v4. lvh3tant speed rounds a curve of radius 235 m. A lamp suspended f* 3vcg4gl e.vhrom the ceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive hz l4ktt+jznrhxh.) (8s 9c.b as the Earth. Thus, 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 the number of g 's a ztrn h. cl9 zx).4t(sjbhkh8+ 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 thmw0( f1czqdvkka,e,-e Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did the1mzq dv,-0ck a w,(kfis 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 tphhc 4 o)khedo6o)j5(he 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 can the car go with) p6 k5edo(4ohhcoh) jout losing contact with the road at A?

  The Navstar Global Pos(.da -1ul2s+ wqnyvm i+n8ubvitioning 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 eve vvn um-lbw8is( ynq du.21a++nly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 bi ,e+gr,/ hkmhdllion km, is meant to orbit the aster+h,g ,mhedrk /oid Eros at a height of about 15 km . Eros 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 t) ley bf e,a -u1xn(1z7saxhn-he space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satelli 1a) hnsl7y n,-e(1uzxexab-fte (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 y;az/ *ui pqp(rz.0b/gscit ( p9)duinears. (a) What is its mean distance from the Su*sc(pquz rtgan/p 9b0p ;d()z i.iiu/n?   
(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 value4q8 l(2r9y/sdefpuar of G would need to be if you could actually "feel" yourself gravi rs8q pdaey/l2 9(u4rftationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a di8y 5w84ip gnr)c qvxp)stance of about 30,0wpvi5)nc 4 )gyrqx p8800 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 locatg (qna4j( )do0-hliw.usy51rmh b nk; ed at the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitat-qhb(a .ml(ykd1o4hn 5 igs0njrwu;) ional force on a 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 5500 kg orbits the Eah 2/qefnhyk20aq 2jfv.r6l 4wrth $ \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 experie2;f eoy1q l9chnced by the tip of the 1.5-cm-long sweep second hand on youry;h fe12ocql9 wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight p8akd7iz j i;x l zg97gk6b3o6around 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 og lb8ax6d3iz6j7gk7p i9kz; that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so thatm. a4 y7w4k k ,xldze0bg6,yec a car traveling at spe bkkmey6,w4.0ay zc lg,xe47ded $ 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 iy5g1h 48qayk 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 (approximatelyi54hqk g8ya 1y ). (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.$\approx$    $\times 10^2$