Sometimes people say that water is removed from clothei0rq)kd ec dkpa3(5/ 9htdn .g-cetbscw+-n9s in a spin dryer by centrifugal force throwing/(n wkiatq -c+909e5)cgrc-d. ed 3kt b pdshn the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around a sharp c kj9x0w +rjr2 byow3m:urve at a constant 60 km/h as wh r+9o :j2xy 3kwbjwr0men it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where de*og:5yr(oj48n1ozu n l, kgj/zip:hoes the car exert the greatest and least forces u8ri kz,*y z4hgo:ng1:o op(j5 enj/ lon the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-rnagp4+w5fh ojpic 9yi08;, q sound. Which of thes ,g;o i8j50s ynahf4wppq+9i ce forces provides the centripetal acceleration of the child?

A bucket of water can k88 xypvx8ag6 be whirled in a vertical circle without the water spilling out, even at the top of the circle wv86y pkgaxx 88hen the bucket is upside down. Explain.

How many “accelerators” do you have in your car? There are at least three cvb4l. mo0bx5w-hl)rp ontrols in the car which can be used to cause the car to accelerate. What are they? What accelerations wvox)bmr p45lb0. hl- do they produce?

A child on a sled comes flying over the crescfppn; 8 vw86kn96hjtt of a small hill, as shown in Fig. 5–31. His sled does not leave thpvnfw8 ;9 8n6phtk6jc e 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 second law.

Why do bicycle riders lean inward when roui/ucdx9 0yn9 , i8s wzfe7k y6z6q6efunding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle g q)/t wc,)t.vz4kaavvh2;nzviven its speed and ra2)kt q/z ,a. vcwt)4vvz nhv;adius of the turn?

A girl is whirling a ball on a strin- /qrspuhg ci34 mivtpg7b2sfw sm.8oa(2 +4 eg around her head in a horizontal plane. She wants to let go at precisely the riesv ti p+37ur2ogim4mb s q8c.4h2s(/p-waf gght time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on tompooln0- 5kxt7x le+;e,gx )it, jv+he Earth? If so, how large a force? Consider an apple e xm7 plo;otxj, +o5,-0t ig+lxk)v ne
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would 0bp :z)gfu-p 1a 7wcoithe Moon’s orbit be diffe )-ipoa:u17fzcbw g0prent?

Which pulls harder gravitationally, the Earth on the Moon, .c 06vp rer6exor the Moon on the Earth? Which accelerates m6cxe r.ver60 pore?

The Sun's gravitational pull on the Earthdy8v pl k5yi;3 is much larger than the Moon's. Yet the Moon's is mainly responsi8yk3 dlpi yv5;ble 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 equator wda4m-f-t+4 y *ywboxh,gx9mor at the poles? What two effects are at work? Do they yy4b*wo -wtm49,hfdam- xg+xoppose each other?

The gravitational force on the Moon due to the Earth is only about half 1we4(f6o, wgy:q 9z i;v wyolqthe force on the Moon due to the Sun. Why isn’t the Moon pulled aw o z,e1qg:q(l6o4vw w9wify y;ay from the Earth?

Is the centripetal acceleration of Marshm spk le .(vtndo2.;8 in its orbit around the Sun larger or smaller than the cen.lm;(sedtnphk 82vo .tripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) towardx ppv n1d9 4. xqi*hgs,;sy:qg the east or (b) toward the west? Consider thiqshvqdpy : xgp .g; *ns,x419e Earth’s rotation direction.

When will your apparent weight beks.ir(ehqq 984 /cwa/bnyq2a the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accee /q9ah(nsci 24 y.rwk8/aqqb lerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend longlqqo7eemp;3 :rtd2 8owxjb,r.3z8bv3lkd9l periods in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on therqqb rd8;e3jwl 7vxzolde:9l23.3kmo8 ,bt p 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 “ 1 rh,w.d2lj;wvk2ynjx ,sphv+nk (g2 free fall” or “apparent weightlessness” between+vw1.2y,gk2sxh rhd wpjn ,njk (v2l ; steps.

The Earth moves faster in itrqbw1q7( :dhsqav ,;ps orbit around the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: Thi , qh;v(s1rqbdap7:q ws is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovere djb52yzcb)0j d to have a moon. Explain how this discovery enabled an estimate of Pluto’s b2b)yj 0djcz5mass.

  The Sun's gravitational pul l(9 c9)ulh1bdeeo*q, ew1xr;il) pee fvg* f3l on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider tfee 1 d*;*eqrl,i ul h3 e o(cbgxle)w1fv)p99he 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 travelingv4(d d wjgzf,-zcc5 )m 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 Earo rc0pu,r(h*c th in its orbit around the Sun, and the net force exerted on the Earth. What exerts 0,*cucpohrr (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 di5d(l lvgur9 qp. 3ta)xscus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90ldx. u9)rtv3qa(gl5p m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 4dor5 q+f9b)fo 00 km from the 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 , o9dq+r of)5fbthe gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude o6bk4f 0cqdv1h f the acceleration of a speck of clay on the edge of a potq4hvbc01k6fd ter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a ver6 1jhzc harw-7le-eu42ggup4tical circle of radius p-ejl 4uz2r4u6wg cg-eahh7172.0 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 whichtr*v8o+(wwr tzz 0i4r a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires ani r*w8 wro (t4rvt+0zzd road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static ykql2:6e l7rcca 6 rk,friction be between the tires and the road if a car is to round a level curve of radius 85 m at aey 2rr ck:6c,l6lk7qa speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotatelz;m/uh:kyx ) y cf ,imtu:ecz(-x) i7 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, hcmux:zfz/,mk ;eycy (: )uxl-ht ii7)ow fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable f,ewp:sp5eq0i. f lwy.92ukf of variable speed. When the speed of the turntable is slowly increwqfwp2l5 f: p k09,yeuie.fs .ased, 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 traveling when upside dowurnp7r n)-pa8 g.d .ron at the t.d gpna7-u.8no)pr r rop 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 kgx+:g 98xzsnd lbw7gzj n(m)w . (including the driver) crosses the rounded top of a hill (radius =d z(wwb x9xjm) .l nn+s8zgg:795$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris w 0unhz efhp/g.wz9; a) exw0ga2no6 k2heel need to make for the passengers to feel “weightless” at the tow;fua 2.n z a )g/xk6ghhw0ez0pe2on9pmost point?    rpm

  A bucket of mass 2.00 kg is whirled in 90vf q f1eh)0tpfqz5 oa vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope suppot501 ff0vze)qp f9 hqorting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.05g4;)(u2is it akthmuut3g :u 0 cm from the axis of rotation is to experience an acceleratg2h(t35; i sutgu)u um:kiat 4ion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cyl,g ;u-pg/i,y t:26 daluy3iuh.eju voindrically walled "ro ulo,36uadgy -,jp;2t g:i.u/ihvue yom." (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 a (u r12jnmz;wdjxkdq4u5qd87 ir-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 52qwm;(18zk j dud ru7x 54jqdn-
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 thef;2u- s)avkre+f 78mmbkw o 2a weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of 8b )s ; mm-a7aef2rw2k+fvouk $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a 9.tc8s xe/rku(r(ctos9 j p8dcar 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 masse ngeq;fmuf g+) lk5.j j89bfk)s $ 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 diving vertically at q5thz;tw 6omiru,/nzk5s. v 9 310 $\mathrm{~m} / \mathrm{s}$ . 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 tangent/8mtn iyy5n tu7;tc,cial and centripetal components of the net force exerted on the car (by the gryn 7uyn; mt,cci t5t/8ound) 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 the pit gl/::h1rt en5nauf 9-nlce.5wb)kt marea, going from rest to 320km/h in a sem :luwftn)9cb5h.r-nela 1n/k 5t:gemicircular 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 . Ats(jod a9f+0u).zcga m a particular instant, its acceleration is 1dag s.(0 u)z+fa9 ojmc.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 spac:/k x-e2zoq,dfp,yxrecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass i:,qzk e/pdx2x,- fo yrs 1350 kg.   

  At the surface of a certain planet, the gravitational accelerikf4j3 ty+cm by.mq72 ation g has a magnitude of m2 ymqibk.4y7j +ft3c12 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 due55y u 98 k:/tz;eio njc7ugizd to gravity on the Moon. The Moon's radius is 1.74 7juoe8 5zgd cz t5/:9;nkiuiy $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 2br(- f-nuzo d1.5 times that of Earth, but has the same mass. What is the accelera(u 2z--nbdf ortion due to gravity near its surface?   

  A hypothetical planet has n9rd+jdlo f 84,4 y ud,gltr*ia mass 1.66 times that of Earth, but the same radius. What is g near its surfaytf,+*dl94ig 8 dnd or4l jur,ce?   

  Two objects attract each other gravitae3b4c culq5 d:tionally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of r/p;avv.hu x1gravity, at (a) 3200 mrh v .;a/p1vux    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earw97xhmk :ux)t r)e 9yath’s center to a point outside the Earth where thegravitational 7) 9wuyt:k9rm)e xxahacceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five timevk y6ud hsekk/3e9tl)(z2ntfhl.; t, s the mass of our Sun packed into a sphere about 10 km in radius. Estimate th3.se hvtkf;2hz6ke l kn yd )u(l,t/9te surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an averag mu(bzls.nj0-. n rx*ce star like our Sun but is now in the last stage of its evolution,l j m-z xcn*b0u(n.rs. 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 whilegv/0x+*cq1b2e h/5savq 2gjvfh kk4 a orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up hxk5c*v kgeq2v1 04vs jq /g/abh2 f+athere. 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 loca-e7oc moz/n7z ted at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total oc- zm7ozen /7gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most ofxa)q1- gakk3l+ (oo(g 1h xxjlu*3r sa the planets line up on the same side of the Sun. Calculate the total force 1 xs (u+hlal31a3)* qkk(ao r-gjxogxon 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 sf,*bnp87i zyy(jx(xk2wshb; ht *q/gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the bys* t7xz,(i 2 f*hp;hxbjsny(/kw q8mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for6hvbxy l-,fan 0dp f0jk9i1.w the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obta0kiba xj. h6wvl0y,dn-pf19fined using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a s3rzd-kbd jl 7 1.vh+w60lf d /byt4vrhtable circular orbit about the Earth at a height of 3600 zblh dkl631f t.wd-rdhj /+ry0 v4b7v km.    $\times 10^3$

  The space shuttle releases a satellite into ae;*uklia o k4b9szk3z3 wz nx- 2izu6, circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) wh-zk x9zo* 64k z3 3k;w us,2unazeibilen the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are tonyw 615h)/rv h/ kkmxf 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 revolutiofmwr kx vyh h15)n//k6n. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular g* *. xoe7;bo0 iuncpo“near-Earth” orbit. A g7;*ouoeco. p* b0xin“near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite ha.*-mb 28ncrmqk7+ n tz+pf fyqve to be launched from the top onzp7fc -b+rnmt2 +yf k.qmq *8f Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module cc npa2c-j2uf, ontinued to orbit the Moon at an alt2 ,jc-u2 fpnacitude of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks onx 4p h01:7mipm2grhmc gi:k) f ice that orbit the planet. The inner radius of the nkp7:xi mhg ih)2 c:4pgmr01m rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once every 15.5 s (see Fmh5lzc/ e +,dlig. 5–9). What is the ratio d lm/5+lec, hzof 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 of a 75-kg astronaut 4200 km from the center obwit g 7zk71a2p5/peff the Earth's Moon in a space vehicle (a) moving at w/akp2i gb75t7ep1 fz 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-oag o6l( da/omu ;pj 8;zrgi*9star system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is thogdjp*/8 (zgm ;orla;u96i oae mass of each?    $\times 10^{29}$

  What will a spring scale read for the weiv w4lc :q50m6pp xi8dqght of a 55-kg woman in an elevator that moves mx485qvpcp6l d i0qw :
(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 of an ek5/ox tde vd-c 2qm )w).-xl+vos 1xttlevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude mxxk)x-t-d.ov+stwt)q 1e c5/ dv l2oand direction)? a =   

Show that if a satellite orbits very near the surface ofbcngmhb3.4 xk z2r *7e a planet with period T , the density (mass/volume) of the plae b7nrm*xb zgh 24k.c3net 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 (27.0*na 2/lqdgf/r t4gr o4 d) to determine the period of an artificial satellite orbiting very near the Earthd 2arq/ /lntgr4o*gf0 ’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Su1yvbr kv+b +3in like the planets. Its period bi1y+rkv+v3b is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance5a *q:a g ql(w:f;fb)g1 zhnre 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 very clot(4 ru -o+q(l ujz b kd:gpp430*cywehse 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 bc4g qdpo l-u+zry3uj(kh 4(w0pe:t*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 about hob j xb1d65 v eu5gv5qk9g(f5the 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 largesq;su-x;4dyrvuv1 z gr q,zq/;t moons of Jupiter (those discovered by Galileo in 1609q/zqyd,u1 xqrr;;vz ;s- g vu4).
(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 Eand 9vmcf*d1n 5 h:ga8krth from the known period and distance of the Moon. a * m5ndgd9fc8khv: 1n   $\times 10^{24}$

  Determine the mean distance from Jupiter ie2)bpwa5(flj /5rlxt 2 hd,y6jivg5 for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the per5b5) l2(h yl2,x twga/e5jijpr i6vdf iods 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 Jupiter consists of many fragmeehowh7vpf d+(i5d */v nts (which some space scientists think came from a pla( dd5wei+vfhh*/v o7p net 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 tafn3unq4qx ;.f(b kvt 5le describes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this pl(bnn5u3 qfkt qx.vf;4 anet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fib;k/u9 qu 1.qc2 iwzo ib2+zsgg. 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 tc2b; .uuz gi+ /19kwbizo2sqqhe vine is 5.5 m long.   

  How far above the Earth’y(6ib7 woq0l0 gb xg5ss surface will the acceleration of gravity be half what it is on th50byls gqwi (6 g7obx0e surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hann l;n-mhr tgj1d i rn-y+78q0kds and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard areh1lg nt --dryi8nqjkr07 m+n ; they pulling on one another?    $\times 10^2$

  Because the Earth rotates oncy 4ozm-83 t oezhmbpo(ft7 82ze 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 ofte8 3t -2fz ozh(opym m7oz8b4 this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraftya p0nd)b-s d. traveling directly from the Earth to the Moon experienc-ys)ba. pn0 dde zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an el9er:xc0jd+3k:f yqr eevator, it says your mass is 82 kg. What is the acceleration of the elevator, and ::yrdxe 0+9kr 3 jqcfein which direction?     ----待选择----upwartddown 

  A projected space station conswwhrrl:t89 .csh( kq;ists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gra:;8wqrsh r h.l (twkc9vity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his airs,8 5xeye2lbecraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in term-4xuaq .fi tbf (a48l):qd awqs of its radius r, the acceleration l i:afb4x.)qq -a tq8uw(d4af due to gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hangq3 8thc q9g;b z , /.twoy/7qsez41b-ihzehsc ing on a string) is deflected from the vertical by a;ybsh.gqezi3zoetbz4 wq-c/h9 ,/7c1st 8h qn angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of If the coeffic;:a5 dzij +az1t6m3 gvn*ifq d dm+t0xient of static fric+jtix d+ vd*zi5fa mg0qtznda :;3 1m6tion 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 objects at 1, /sj8zt;pcvh+ miaj the equator were appa1vmpc+jj 8 h; ts,/zairently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant diw,5 iyp nymn;swrc/qu. nke1/n 5h1 s+stance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve ofmz7k2cqwc0 w,pm4,ucz c 1baq3 rke 98 radius 235 m. A lamp suspended from the ceiling swings out to an anzmw q1e93uba0 c,mkr2cc zpw7,c48 qkgle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times ascu/dcd )1dj ) 6xqfp-weo) z*w massive as the Earth. Thus, it has been claimed that a person wp1je)x cqu-w o)fd /)*6z ddcwould be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced thze nm56(o hqr:e presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from whicrqn(5 ho: mz6eh 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 traverlegv09p1; b 7oj),isimms n:nses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How dible n):np01 ;o mm9g,s7i vsjo 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 contact with the road at A?

  The Navstar Global Positiphv,00v 3bxurcya:.y;19 wfd3c n w, 5 wqumgroning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,w0hudbfqyc,v3;51g:y rpar9uwx wcm3,v0 n . 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), aftenw8tw a26zkg2r traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros i2a 6kwz8wgtn2 s 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 th6(ei v1d,t-nsqj8s vde space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km abotde, sv1-n8v dijqs (6ve 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 mean distance frfpl 0oilj f e9yeu43 *dm087lyom the Sun?i3*fey lfm0j e498ly p0 7dluo   
(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 actually "poh( toh 47v6qfeel" yourseq6(o7ph 4hovtlf 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 Gala0l ke0y gdup9.xy (Fig. 5-46) at a distance of about 30,000 lighte9 0gpkd0ly.u-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 ow/: .nhfq 7w6z.tlj qmf a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpointl.hnq6 j/ .twmw7f:zq of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kh8;v/y- y-ju0 hjvw *fvz sfu9g orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experien v8jo(:qf e-mdced by the tip of the 1.5-cm-long sweep second hand on your wrist watch? qdvfo:-j(em 8    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinkvm rj(be ullm4 u*bb*:yp86l p n6*ha/er weight around in a circle below you on a 0.25-m piece of fishing line. The weight makes av:6pybb bluj(/r8 *u m6meph l*4*anl complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radzrr y jnw2xw-gt5*g*a7:p7 ulius R in a new highway is designed so that a car traveling a5pw* j:ug a*l7rzyx - 72rwntgt 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 trasnp( 6zig t* i *kjg(;uqr4f8ain, the Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the (izi6na sgu8(f r*jp gq k4*t;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.$\approx$    $\times 10^2$