Sometimes people say that water is removed from clothes in uf 1)pi u/et8na spin dryer by centrifugal force throwing the waten/if epu)1tu 8r outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travel:: fpbt0f3 nnus around a sharp curve at a constant 60 km/h as when it traveunf0 tbn:pf3:ls around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly2ongf, m 8p,4aykgsa.+ m4brg 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 lbs8o g2g pa +yk4mrma 4.,nfg,evel stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-zwj97 f4q sb2jround. Which of these forces provides the centripe7bj9q4jw fz2 stal acceleration of the child?

A bucket of water can be whirled in a vertical circle wit s 5mx(pfbyc 4m5+nt9ehout the water spilling out, even at the top ofe+ nx5yp4mf9bs5(cmt the circle when the bucket is upside down. Explain.

How many “accelerators” do you have +w mdtyck (tte*i.ef m*dc0 oj.2h.:nin your car? There are at least three controls in the car w2et.tc0y kn(hdo .*c.t f mdjem *iw+:hich can be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crestwffw v+smr6 vsc- yk5xy2stxk:6,6: y of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s secx+fyw:vm tkfs,wy:- 6 cvyx2r5s66s kond law.

Why do bicycle riders leaey 4qy6jfe 4 02gq1qb.w11 yhj o9mmvhn inward when rounding a curve at high speed?

Why do airplanes bank when they turn? Ht/g3; lru)rzczn dxy5f6v92 y ow would you compute the banking angle given its speed and ryt2 cr9v5 y;nzuf gl/ x3)6dzradius of the turn?

A girl is whirling a ball on a string ,nye zm;z7v5varound her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let g mz;7 5vyvnze,o of the string?

Does an apple exert a gravitatiae/ c7 6e srrbtqe8-f-onal force on the Earth? If so, how large a force? Consider an aectrefqae6/r8--s7 bpple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doubleqwmskef/um.hv6+9 dp3 sv ))h what it is, in what ways would the Moon’s orbit be differe+ wuh p hv3sm9v)dmq e.f)sk/6nt?

Which pulls harder gravitationall 0md -tb inhc*.f(glvjv2mr 4)y, the Earth on the Moon, or the Moon on the Earth?2j v ld.i mg4fv)tmb 0*-hrnc( Which accelerates more?

The Sun's gravitational pull on the Earth is.* ghlkul-.m9m myguov9-d9g much larger than the Moon's. Yet the Moon's is mainly responsible for thy9 .. g-glgdvu-mo9*hklm 9m ue tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at th0l8ta w;t fnw*1ri,takf9zfc0m e1uy 1 8wpu5 e poles? What two effects are at work? Do they oppose eacha 0tt1 l t18yrfae9 0 *ww1nuf,5kz8wfimc;up other?

The gravitational force on the Moon due to the Earth7qdw*yfd xy/+ is only about half the force on the Mfxy/d 7yd* +wqoon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around thvf*4owp5r vdam+jx)a) ufmi v8olx25ycr3 2,e Sun larger or smaller than the centripetal acceleration of the wvljvp8f+5m , 3xfxa y *v2m5o4ioa2)crd )ruEarth?

Would it require less speed to launch a satellite (a) toward the east or (b, j1nuh5 qf4/yud37shhuzv; e) toward the west? Conss1huhf57uq; n4/vhzej y,d3uider the Earth’s rotation direction.

When will your apparent weight be the greatest, as measured byiv,ro gf*i1to u57vpl67vkr ; 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 bp;ig*u71ik6o 7fovr lvt,5 vre 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 adversedxpkvbd -93t - 5f jartnyao/5-*q 1nily 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. Cf-dbr*n1 d -av9 kay qoix3/ 5pn-tj5tonsider (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 “apparenukp)lj84,54mul fuwa t weightlessness” between smup5j),ak4 ul84fwu lteps.

The Earth moves faster in its orbit around the S85 -w0wz2btlabuz3by f 9y3nq7kqu( a un in January than in 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 seaso7znqk 9aw -5t 0b2 fub(3w 8aluqzbyy3ns — 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 was51e4la .tl. o mxpia:l discovered to have a moon. Explain how this discovery enabled a a5 .:i etamlxo.1l4pln estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yegf r 33 vvgo p4n,g9ppt(9ts nf-m mc*1hdo:j:t 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 sitting 1.10 m from the ce*s pdmgvh m:n:jt vn3f p9fop(, 3rg-gto94 c1nter 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 (kvzy/hm(bipz vbb 0+ hi:)d-)+zsxy, 1ccgy 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 acc;q(7pvh g hu1d26l llveleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? l plg72d(h6v;uql1vh Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 2 13 xkl29hnsflrko uwfo-;2*a10 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus;21 l 9h-fnwf*a2ul r kkoosx3.   

  Suppose the space shuttle is in orbit 400 km from the otw6;swd)mp b4k3a 2iEarth'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 gravitatioi 23bwta;6dk oms4pw )nal acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelp.b t0q *(gx vvzemkdg7;,+rceration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per p +7c* vrqm0kgb(z,ve;gx.tdminute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vertical circf ui ayd7;57oe:k bo7l/mvq 8yle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.007: ;i87q oyvoeub/kfl d7a5y m $\mathrm{~m} / \mathrm{s}$ 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 qpdk+rqnx,:dh cn 1ut/2rn r.73je0j a turn of radius 77 m on a c0jn nqhr.t13, qpr u k2jd7 rxe+:d/nflat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between th ,o pyxqux3 )-zmb40nae tires and the road if a car -0y abq3xnp ,ux4)moz is to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training as3e5;z9dxh;sqe9pf qr1kksa+ o (-bl itronauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is s(s qi+x d9eolk5;p 3e -qkzrsbhf;a91he 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 8s3jvu:p)uz:ue:l oh e6m) m ecm 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 coefficient of statiuz3)e: ):lsu j:evep mu86homc friction between the coin and the turntable?   

  At what minimum speed m d+o/dk9c ;-nktjzdn-f c 75kzust a roller coaster be traveling when upside down at the top of a ci+dzkz9 /j k-;n tfk 7cdd-nco5rcle
(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 the ro. cifriaii 14 g5adk17unded top of a hi1f. agii5 rc7id1kia4ll (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferri imomqpb6 9,,os wheel need to make forb9o iopm6,mq , the passengers to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg ismv3- vo+emr ;vp)5h qa whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion therq vo+ )maph3v e-5;vm 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 ce;w2 k/ ej s1h2f70y.wtzrrthbdm,6cvc ,f3 ht ntrifuge rotate if a particle 9.00 cm from the axis of rotation i;r3r yc.2,ktd 2 c/ jbve61,mhsh zwwt07ftfhs to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are ro *dlz;8uku5qd vm7v c)tated in a cylindrically walled "room."v* d; dcl)uum 85qkz7v (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 ct;rk((z y e b8bn*)rznc3 ;hkbircle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through hcbb3 brn t; )zrze;*y(kn(k8a 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 , pre3t+ 4 :xr.-f(bofe e-opmy-o-lzcwzt cisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the mag.wp+x:t y-tzo e -o4-f bo3l cefm(-zrnitude 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 radiuvw hn8 mhf8l00afni *5s of 88 m is perfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses)bsh ,x(hr9tlqn6 pvl;* ,d ii7swe1j $ 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 evasiv0i2unvod;8rc+ sd)(e u;rnal e 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 exerte7ur/7 w,t xttzs sw6gif7,e;nd on the car (by the ground) in Example 5-8 when its, t7w ws7i6 ftzs/tr ;g7nuex, speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 an n3.ts 7x-ljtccelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, w.s3t jlt7 nx-nhat 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 parti def-s68a mwq,h 1h:tscular instant, its acceleration is 1.05f t-m a, hq:w1dh8e6ss $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Earth radii:qjl /cd8nhp9:.w jim) above then:.pc9 hj:m ji/8wdlq Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratiodz e -fiz-c7.sn g has a magnitude of 7edczf i-z -s.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 rkanmtc.v1*yr zu2 v.8adius is 1.74mct1y.*r.kv2a unz v 8 $\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 Eakjcp +xs s/gf8mo;.4 urth, but has the same mass. What ip fcso. xjgu/;sk48+ ms the acceleration due to gravity near its surface?   

  A hypothetical planet 9zz rk2wwc*oe;hy7r8:ho / g:a9 ha sfhas a mass 1.66 times that of Earth, but the same radius. What isc* ho2so8h/wgeayhwrz ;k9af:9z r:7 g near its surface?   

  Two objects attract each other gravitationally with w8 kpri4 i3fg rhv0+f/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)b;eko 5x fkcgd.;j/sm q 001tw 3200 mc kkstmxj/d 5o1;;eg0.qfw 0b    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from th b* r5y:jsrhmn*g10vne Earth’s center to a point outside the Earth where thegravitational acceleration due to the Earth vysr1:m nn0bh5g**rjis $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed ik5 5*8zgrb*l bna9wl,x3vu3ce (qdhknto a sphere ablqx5 3he*c l9,bwur5ag*zn( kv83dk bout 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like o vhi f:11ut7xbkzsy96 ur Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our h6 f19vx ykitsubz71:Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightlendnkvk 9v33p(ss while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weakerpnd n9k 3v3(vk 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 +,- kl elxfqqj1 4j6mx1kw*oxside 0.60 m. Calculate the ma1+ lqjxmj x-lko*14 qxw6ef,kgnitude and direction of 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 planete,fzobod -g o,nry9 u29h,m7ks line up on the same side of the Sun.k2dz,o nmr,eo-y ou7 f,hgb99 Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars is 0.38 of wh4;jwt7cb ir(i at it is on Earth, (w bicrj t7;i4and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the knownn4 ebqso5k e*0s (c:b msep-h: value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using K s*:ces-0qbkb5m:( p4s he oneepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a sk.a,2 ml z;u+gh5e miytable circular orbit about the Earth at a heightm.ge; ,hamyzkl5+ i2u of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbi2+4q 3:dqv+ dwb.yh arihk vm/t 650 km above the Earth. Ho qi k+.yhbhq3amr d2wv +4:v/dw fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindricalj8 imd 0rxt/3eg2t 8zt spaceship rotate if occupants are 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. (See tdtrt03mzgi2exj 8 /8Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a ci8o./ffdu wx w :qn4dr(rcular “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 8d u4fw w.o/q drxn:(fradius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velou z. 8(yc ed9w*cd5h,m 5ylgjxcity would a satellite have to be launched from the top of Mt. Everest to be placed in ah, m8(y.5 *jl5duxzc9wcg dye circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit ttxj1e, 3iz ptnpsapfmf6+l7) sh(/9frj z( a:he Moon at an altitude of about fzhm jtal:ex(pff n6p /7apst3s)(, ji + 91rz100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are l 9*b0x2yivx1lwoqs)ikfe8l,2c- u c composed of chunks of ice that orbit the planet. The inner radius of the rinxl1 cle9 l8o2f20vcwqy *i, k-sbuix)gs 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 evepb4rw p:y426zbom*v3jfxo5 fry 15.5 s (see Fig. 5–9). What is the ratio of24m ozx5ovfb:jwf463 r y*bpp a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight vbo3i:z s5h6 -rwr n/ij.f+mlof a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) sjnihrl ozb5 +iw3-rv f m/:.6moving 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 systemudtf j-e5j(h3 vi) b6t consists of two stars of equal mass. They are observed to be separated by 360 milfutdj(3bh-j t5v6 ei) lion 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-kg woman in an elevatq;il f aib+ow6k+d;w4or that mo +4+o6;bwdlw i;qakifves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling p0nerz,gbs v:5z qn x0mj 0-u7of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directio ,mxp z5nn0r-7vjsb0: ugz e0qn)? a =   

Show that if a satellite orbits very nea7rew yy6-:7iyk-plc*l/ +i4iol iudfr the surface of a planet with period T , the density (mas 6lfeld 7cp :-y yk/+ir7ywoi-ii*4uls/volume) 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 determine the pe6xypqw* ozs5 (riod of an artifq6 pzox *ws(5yicial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred me.9w.c6 o v:7ax wruyzmters across, orbits the Sun like the planets. Its period is 410 d. What is i6 v.o7za9wwu .y: mxrcts mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dymk2 ,1v.gcr54pwt x:;.x s ooo(mivdistance 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 Suni ywb0 yfx12c0 roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third lw1xbf2 yy 0i0caw is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the ssb j)lg: o,j p1.lek*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 ll4: e qjgg( kr3y-td/sargest moons of Jupiter (those disco d-j(ggtslr:/ k43yqevered 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 period and distance of the M+/bopz+yj9qsp 7 u:mpoon. : mu+opj +y9/pszpb7q   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, usi6s d5nl dj/4kfng Kepler’s thi n6dsld4jk/f5rd law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt betr uhti b,gvddf;8/dj6wk+6 8 hween Mars and Jupiter consists of many fragments (which some space scientists thbkd 8rd6jthdw g+6 /fvh,u i;8ink came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in th yeqyt k+3j9dof g49x)e 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 quickkj+xfd)t43g o9 qyy9e ly 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 froco oe;ilj1 uzph.oal,6a .2l4m 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? .ul,aj.zol oi1 laoh2 6p;ce4His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’sr) sc(0nw5yl x surface will the acceleration of gravity be half what it i(0y) n5rs lxwcs on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hxf42j+n3 u;akm f gsge8i(ns 96gx; kgands 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 as ekgg269ukg mxxs(3if 8nng +j;;4f60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth roti4hk;7 uv*m4pc*a 1stk px+ybates once per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. W;*tp iua* yv+41x7bcp smkkh4hat fraction of g is this?    $\times 10^{-1}$

  At what distance from tz)7x5l bb(6,m lrikmg he Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moonbgmzx 65l(b7) mil,kr pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when yo ( q0kofp7qt)tl0hj(ku stand on a bathroom scale in an elevator, it says your (qp t (f7tjhl0k0k)qomass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotat8dw fllqfbnha4t i 89xt: )9w/e 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 ( d4l:8) xt9wf9n8ifwt b/hlaqrevolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 0fx:ms.inlx8a05e j1 vm f; es5–43).
(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 o 3i)krhudcyv 42*w8uof a planet in terms of its radius r, the acceleration due to gravity at its surface and thedi4*r28ch wy u )vku3o gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected froh0 x,njn p v7v2ils2/km the vertical by an angle sxi27vj 0 n/ vh,n2kpl$\theta$ 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 coeffz)dr+ rmcsd ,bs)e37 x,c, wluicient of static friction is 0.30 (wet pavement), at what range of speeds can a car b zmd,xsu+c,lrcr 7) 3,e d)wssafely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at )9y;18marwxr2n0(gs e(p2 aeoq pk krthe equator were apparentl08 pk21 ;earoeawr2psyxm9 (q)(kn rg y weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance nerm* 9jxs8hxi6n)aq ,onukru*01 4d 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 curvvi (;z jrltnb56+i 3zse of radius 235 m. A lamp suspended from the ceiling swinvt+ ;zzijsn 3l65(bi rgs 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. Thus, it has been claimed t */8 1oxmg*s kinib6tthat 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 person wou6*/ kbit*m g81ion tsxld 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 Hubbly v+4xr+2/b q+aobw.r9uriqs e 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+u r4a q9rb/ i.yqsvb rwo++2x escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the u);5gh/qfycb 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 without losing conhygbq)cf/u; 5 tact with the road at A?

  The Navstar Global Posiubvh0t5s6e5n9 g fg r)tioning 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 approximateug6v 5)rhges tb0n9f5 ly 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 trave;wg+venndzy 94/ll 2u ling 2.1 billion km, is meant to orbit the asteroid Eros at a height of abvn9leydl u4; 2z/wng+out 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 the space shuttle pursuing a satellite in+c:c qfi )ou c0 zr:pjrv6b4w/ need of repairfqp)rc6 :uc:iworj z/+04 bcv. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its p3(azip)l nce9d sfa8as0 r42*yh 5lhmean distance from the Snr *aypss d8(p al42 9h05 ehazf3icl)un?   
(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 l. ki ;. :wpbnc8i3:95bnpgk. qtpvh yneed to be if you could actually "feel" yourself gravitationally attracted to someone near you.pb: g :lb;c5n t9inkq..w.p3hvp8kiy Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around thr+tr h0y0,qlc1dz vw +e center of the Milky Way Galaxy (Fig. 5-46) at a distanc, 1lw+hqt+yvr0 d0rzce of 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 s,6 :y y7sk1vum*lwlcm on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kgm 7* sy6ly1uvs:,wckl 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 Ear4ca;jpfb24 1fp z pmq mq,a52sth $ \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 1b/zd3nw tbp:zp5e n 01.5-cm-long sweep second hanp:wnzpten3z15b/ b 0dd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a+65k kgoif3ucy(pzv: circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0 i5k3+(y pof6vguk: zc.50 s. What is the angle 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 that a car travely gfw+g yx7g/-6n phrsi;gg*5 ing agyyf;ghxg s- w657r/ g+i*pgnt speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of thr7fj/tvmm) j,a:9gq reie x.5e 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. ,a 5i):mmtrej 9j7/g f.ex vqrConsider 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.$\approx$    $\times 10^2$