Sometimes people say that water is ra/cz /bo0cq e1emoved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this qa/c0c/e boz1 statement?

Will the acceleration of a car bes55m6gpjowyyi. ) xf- the same when the car travels around a sharp curve at a constant 60 km/h as when it travels aroundjp omy-y).5 5x6wgf si a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alonro:b.nzs* r)avnk3s i-d 1f s,g a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hi. rb ,)d-os :3i*k1srszv nfanll, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse jary .lo2+csue-l-;k2 w-789i mg eduwmt:ozon a merry-go-round. Which of these forces provides the centripetal acceleration of+ 2zj ; c : 9-t-umw.ero-iyuo2wal mglsk8ed7 the child?

A bucket of water can be whirlea2.mjd,xvp3x*b7yehmp ;qp .g lt4f73w, fbtd in a vertical circle without the water spilling out, even at the top of the circle wh3ptf,yp .7.ltm*bj73xwdf4 ap hqgm ;b , evx2en the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There arezau5+z/j6hfarg j5 e toz5w /2 at least three controls in the car which can be used to cause the car to accelerate. What are they? What acceleru2za5or az/ +f/ 6 htjwej5g5zations do they produce?

A child on a sled comes flying over the crest of a small hill,.1nka 3 b 4(khc7yd(x m,pmwoj as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the no3hwmdc my1b7kxo(a p4n.,kj (rmal 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 ; 0z2xrvw gqdo6(a:nl lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? 9zbtni;3 l3t5go5cg mHow would you compute the banking angle given its5gm953zo3 tgt ;cl nbi speed and radius of the turn?

A girl is whirling a ball on a string i/hh ag s1 (rkx0v ceb1/i-ysl(e;m4xaround 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. Wh11yea(sel/kb0i(h gxhmc x4s -v ;r/ien should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how large a freg,*-5 nbxe norce? Consider an xgen5 e r-,bn*apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wh 50vdz0qnh h*oat ways would the Moon’s orbit be difzhh0 qv5*0nd oferent?

Which pulls harder gravitationally, the Earth on the Moon, or thehjpmnfz/ yl6v6-) oa9 Moon on the Earth? Which accelerate/o6fh av-nylz)j 9p 6ms more?

The Sun's gravitational pull on they*tj-c:- f jtp Earth is much larger than the Moon's. Yet the p-tjj yt* f:c-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 more at the ezn2y9nm 4sxdm:zn op(1 : sq6lquator or at the poles? What two effects are a1mpn2o:zds y9s(4qnmnzx6l:t work? Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about h3e fq/ ,c1rggaalf the force on theqag1/eg fc r3, Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun largnk/,0xcutpj))e vk e 5er or smaller than the centripetal acceleration of c5e,nv0u j)xkke t/)p the Earth?

Would it require less speed to launch a satellite (a) gsh8- 8cp;vqj zg7c +e*c byx(toward the east or (b) toward the west? Consider t;8qc s*v gbe-8z(pjcxycgh+7he Earth’s rotation direction.

When will your apparent weight be the greatest, as measured by a sca5a1u756xc1dzunt c fs+bb rz,le 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? Wher5 ubxsdfb a nz61,u1cct57z+ n 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 aff mh)*wm, oeezq0 9-qq+bm jl1eected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on b +q *weoqm,)1ee mj -q0l9zhmour feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “freet ts w,e wk j87vqvv.um:20v6h fall” or “apparent weightlessness” between steps.wt.kju,vv6v0 7m2ev8tws hq:

The Earth moves faster in its*f4sp mxn;8 dp orbit around the Sun 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 seasons — the main factor is the tilt of the Earth’s axis relative to the 84mfnspp;d * xplane of its orbit.]

The mass of Pluto was not known until it was discovered to haveij, jt9pb/.cz-yfs q5 a moon. Explain howj jzi9y /c,s.fq- bp5t this discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on9wvh188y(ppprqw5i g the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible foh8p wypq(19gir5p8v wr 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 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:s3i uz+x bs2s 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in vug ; hm1n5i qp hfim78.q9ma6its orbit around the Sun, and the net ffgi.;9 vqq7map8 51h h6iunmmorce exerted on the Earth. What exerts this force on the Earth? 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 210 N is exerted on a 2.0-kg dis6ret,ygr t 4qbzi:4y 2cus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate, r2:446ezyygqttr bi the speed of the discus.   

  Suppose the space shuttle tk:ieyx+ g-e* is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in itsxety :e-g+ki* orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on tp .f30gj*mp7xgh+t t7r vr,h zhe edge of a potter’s wheel turning at 45 rpm (revolutions per minu7xhh0rgf ,z7j vt* p.3rmpg+tte) if the wheel’s diameter is 32 cm?   

  A ball on the end of a s-j7h 0*)hss*,,vowp ifimga itring is revolved at a uniform rate in a vertical circle of rai*-hv *gsi f i0who,ma 7pj)s,dius 72.0 cm , 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 of ra3r8jlgl.g- 2 .yu4y uh qnt8ngdius 77 m on a flat road if the coefficient of static friction betw j88rnglqhuugt g2n.-4 3ly. yeen tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and .vf/5 t6 an2h,l0wt-hq *noxav9; dp:g pnglcthe road if a car is to round a level curve f:qc p5.naow*6h a/ v l2 0,v x-ngttp;h9lngdof radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designedj4sri1r7e j( 1 yxcqtnsp)1p) to rotate a trainee in a horizontal circle of radius ts)j4i) eyn(rc1pq7p s 1rxj112.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating tur) /shg-65os ex4joexf ntable of variable speed. When the speed of the turntable is slowly increased, the coin rema osef)jgohs /4e -xx56ins 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 s72 1zjfqm,hg roller coaster be traveling when upside down at the top of a ci,1 f7jzgms2qh rcle
(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 (includi9h1i*r9mz mu )vm:lb b2a9 jchv,zx3lng the driver) crosses the rounded top of a hill (rad2)3, 1ubhbmrvl9mail x9z :v*z9jhm cius =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 minutqd o6yb:qj3 o hi;w+/le would a 15-m-diameter Ferris wheel need to make for the passengers to feel “weightless” at the topmos3qoh;o:w yld i6/ q+bjt point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle o.9hhve9 )h xljf radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucketx9h hl hv.e9j) 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 part(d,ej;z5xkvi ++cflc-utoz, 0 rb u9q icle 9.00 cm from the axis ofb(li- qr f;e ,u9d5 ktu+o vjc0,zx+cz rotation is to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a ca/ zzyd6 g+w-6ye*ss7ckwge t. )re3bbrnival, people are rotated in a cylindrically walled "room." (See Fig. tg63z7s/d6wb s ecek* e)b-yrzyw g+. 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 ) ihzy5b2yo kz 8x l3dx;9s rotated in a circle on a frictionless air-hockey tabletop, and is dz 8y 9l;ox2xb3yzkh5held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not ignoring the weigh g*) lrjufug yf/9 ug::3of/f7 azw;whb r1.lbt of the ball which revolves on a string 0.600 m long. In particular, find the magnitudbl f ogz/guu:u7wgy. *f;rwafh/fb3lr )9:1 je of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectlhp+(1iee1h+zgewj 7lvt 2t1 ly 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 dg-qzrr911b2zu v6te$ 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 by divingolvag-as -qej z310n/2vf*xe 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 nets7 f ysml4y 5weao+;f.5w1 nsj force exerted on the car (by the ground) in Exams57;.al sm+54ow fnjw1efsy yple 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 the pit area,zvk*h:nz*rl + going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this accelerationrk+z* *nvl hz: with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . At a particular intz37 0 6 h6sfbuwbxao4 bp*obab5tj:7st: z b0w afjb776465xaohut * obsbtpb3ant, 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 gravity on a spacecraft 12,800 km e+0bhp9 djic.74tol9w7ercp (2 Earth radii) above the Earth’s surface if its mass is hcepeo7 d w4j9+r07b i9.tp cl1350 kg.   

  At the surface of a certain planet, the gravitationt 8zl9tb t7.ll, bqb)jal acceleration g has a magnitude of 12 m/sb8 q9 t,jl7bzl).ttbl$^2$ 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 M0w).709 u.q3jqg ym7laoojv tlpf /qsoon. The Moon's radius is 1.74 qt.. o3 ml0gqj)vu0f 7y oq7s j9palw/$\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, but hrhr -4p92 lcfz* /zo5t ) dwqpgw9l*jhas the same mass. What is the acceleration due to gravity near its surface?*-4h5ph2 z9djrl* qt w 9fr/wzlgp)co   

  A hypothetical planet has a mass 1.66 timby 4h,0ttk3p tky:ly4es that of Earth, but the same radius. Whatlktybh40 kyt4,py: t3 is g near its surface?   

  Two objects attract each othercl,o7aghe3iu7r4 w),cdldy3 gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effectiv3b wt. -5-7wmposzptu.w r8mn e value of g , the acceleration of gravity, at (a) 3200 m8w.-uw7pz5 bm .wot s-n 3mptr    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center tv w4cfuz**jmp -+fmc u m.5-kxo a point outside the Earth where thegravitationp c4+vkmc-f- wfz.uj5 * mxu*mal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five tqv101 rij:3t n(jjmp- mo z/g/x1ap vcimes the mass of our Sun packed into a sphere about 10 km in r vmngo1j1mpz3: iq/j-v crx/pa1 ( j0tadius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an avervkkvq ;8h3;g fage star like our Sun but is now in the last stage of ifkg ;qh8;kv3vts evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbitilxwg5 b(1n5eung 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 surface in terms l(51g xebu 5nwof g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. /i k o--kzcq-rCalculate the magnit i/kkrz- --cqoude 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 pahic-5 * g5-bmhct 5gylanets line up on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiterai5*h c 5ygmh-b-t5cg, 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 grvh p b 83/,eospp;q6*ejbn/hai 3zay0 avity at the surface of Mars is 0.38 of what it i 3h8 ;/ehpb pb/0* paq,y63vzaji osens on Earth, and 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 perioddq2. j2e mxg:v of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained usqgx.j2de m2: ving Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving inaa 4c8;nx /f72zl0qa -reh qmxmex,l6 a stable circular orbit about the Earth at a height of 360 -,rlx qam4hxl2f6nx qm ;ze a/ac0e870 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the Eaasz5kw2 nc166t4slk alzwt, ) 1nr2oirth. How fast must the shuttle be moving (relative to Earno czr i25nsa l)w1wask64z6,k1t2 ltth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotall ;- jq.bg4brsd i;l:te if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, .-bb sqi4l; d: gr;lljand give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satelo19k ie zl;oh p;2ef7f rgy gft/7s7p8lite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Eae9p/r f y1 f7; ozik ;727osgptfglhe8rth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched frdw espcts).2l9g6v, j om the top of Mt. Everest to be placed in a circular orbid.6s pc2t ,) 9vgsjewlt around the Earth?   

  During an Apollo lunar landing mw m51-m2dckjmission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around1 kwmmd2c-5jm the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planetd*kl;g n:38bzag/hq tr )+tnnvd dmx(m*x ,x :. The inner radius of the rings is +zd :dr, 83qgt ;a:*nxgxm(k)x nh*b d/n tmvl73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (seeu2tc.rqg pvb-7dqz+ * (myi0 y Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) at the top, and (bzv0qur qyyb2+*pti.m( d7 cg-) at the bottom?
(a)    (b)   

  What is the apparent weight ofpp wn)0:ujmf 2 7ux1vbv a 4yusx1f0c. a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicvs0w2 au yux1p0 bfxj.)fnu m417pc:vle (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 consist6.yho1rb au( (vw:csys of two stars of equal mass. They are obse(yu6a.s cvhow y r(:1brved to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in a*e7;bh zi k71pqb+ .y ;hkmgkfn elevator that moves hk *iq eb;zb7h k7y;mg p+.1kf
(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 cek2q; *td(ffh ;kgvo7 piling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum accelerakfdqg( f ;;*khov2tp7 tion (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet with ujxv )qk*4zj*q u8cs-period T , the density (mass/volume) of 4-qv) cxjuq**js uz8kthe 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 thzq)o a6koet)+e period of the Moon (27.4 d) to determine the period of an artificial satelo)q+)6ke z oatlite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, t9fhdcrst 1i3y k1e5 w(hough only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What 1seyfrwd5( ct9i3k1 his its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an averag 8m9b dn+wb7w5,lb qig o** szapo:)vae distance 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 comes qco ld6 (80be7lz2u4g/ ngrll-piv.g very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sp qg74bz /g2v.c6 -ler0(i nulolldg8un. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates abou yiv.zdnehh-u53 +ap6lzrr j //5 upd+:gqm8ct 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, anrx,vnca u;0 yh:rf(z *d mean distance for the four largest moons of Jc * zy(r0v:hf,ruxa; nupiter (those 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 thexjdj 5 n 5bh6z:lf4c1u Earth from the known period and distance of the Moon. bldh6n545 :f1j xzj uc   $\times 10^{24}$

  Determine the mean distance from Jupiter for ese8i 3hi5di+mach of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periodsh5 se3+ i8idmi 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 between Mars and Juph1h q+su(kwpg7 k++)z qbw6vpiter consists of many fragments (which some space scishpv kkz7+)gb 6pu w1(whq+q+ entists think 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 the form of a band co8qxixnvfqm v94q s0xr/v l3) kyh/1 +nmpletely encircling a sun (Fig. 5-40). The inhabitants livekxq+xxl/fvqh) 4n n 09v1r8qs3 im yv/ on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging ve of f)y6 yh/:*lp8(u k9evktiine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine isk/6eu kv8l9(et) fyh :o fyp*i 5.5 m long.   

  How far above the Earth’s surface will the acceleratio o.) l2/g jkoxd ex o5py7/z5qt0gsc6in of gravity be half what it is on the surf5/tcgylk5 o ep0 zq.s /xi 7ojgo62)dxace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin cu k2f3makujnhm 4:) (in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0u 2h k:j3mmf4)ncak(u kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accele8i qk:i6,5m c krarii55z:kl y(qa3syration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of 3(ry5islki56 5:8qi:r mkiac z,kayq this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directqm;t4 hj58oi lly from the Eari5; htm4olj8 qth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, bqxu6.gsflz)5gpmev va 1 2,5tut when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleratiop s2qeg,avflt )z5g uv6x5 1m.n of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that q,e- gmn5wtzx-8p+vqfa )(n ewill rotate about its center (like a tub-( w vfgn- nm8ezpxet,q5q +a)ular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a venqs +jehje(, 5rtical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accelerwohux(/7k xy0y:7 k oyation due to k (7wyuxyhk0oy7x:/o gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflecte0p37g nj ku3uv jr h+dv7tpwi1 u8e/dcf9)na(d from the vertical by an angle cj+ 8 e wdna3hp)uvp k 9r(di73t0g7v1u fj/un$\theta$ 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 I, f/d adj/nqvt6g,sop40f fbv81 n9rrf the coefficient of static friction is 0.30 (wet pavement), at what ran nr vd6pn 8fvr,4a10 tj/gfd,sof/9bq ge of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at tt48 pcu ,crdm/he equator were apparently weightlecp48tcu /rmd,ss?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of zb fje /vy3nx(gl17y3 4aywa-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 consx p;.mpt(ypj c ymd:g40ww(e ,tant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swinwt0ycdp4py mw.pxgmj:;,(e( gs 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 b572cp54tcqj)tl x f rh;vq5uthat 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 would experience at the equator of such a planet. Use the following data uc )h;4j2p5f5t q7qtvlx5brc 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 suy86 vxw . p3 mdjwku.3v+ik:w3 tc3ySpace Telescope deduced the presence of an extremely massive co vt :duswux yvp+3m3cjw8.wikk.33y 6re in the distant galaxy M87, so dense that it could be a black hole (from which no light 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 hill and valle1)djexr rba06.e ex2h y shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting )e a1 jbr.de06xh xre2on 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 contact with the road at A?

  The Navstar Global Positioning System (GPS) utili. :ce8 bzmckc)zes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by m8kc:cze.)bcthese 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 satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Aster/q (lc-3oyza 0 v8h*cjkr6uy koid Rendezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a hecz(y0c*8kyk3lvr uj h/qo a-6 ight 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 the space shuttle p dlhipd(k2 ke:c k(,3mursuing 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 behind it. i (c(,mh:kklp3d2ekd
(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 iinreg-o6f8+psh . z l1ts mean distance fro+fs opnre .1glz86-him the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actual2ufc(8gylay thf21:u ly "feel" you c :uuyhfy8tal2(12gfrself gravitationally 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 )bbt r :yhewa;a(bla-n(s3j8. 5-46) at a distance of about 30,000 light-yearsn3( - bhl(8b;bw):reyt jsa aa 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 sq .r ,q4l6x2g/mugklhu uare 0.50 m on each side. Find the magnitude and directx2, uggmr.qll6k/ hu4 ion of the gravitational 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 Earth j)u(r ibh0mruc5vc0ano3e-. tv ( tn:$ \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 ochp+;u w15f qrf the 1.5-cm-long sweep second hand+1 phuf;w cqr5 on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing 2lnuq8 -1w(0jt eskwwa sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing lsj k1 l2e-(8twunwqw0ine makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway i.uj( hzkg92 nvs designed so that a car traveling at speedn9g 2kz hu.j(v $ 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 the car b :d* wxxc84/jcatxl(4awn0ds 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 wwc8cantb0:( / a4dx 4jd*lxxof (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.$\approx$    $\times 10^2$