Sometimes people say that wo 73wvb7vq, mrio7wzp(x5 lf/ater is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wroi3r( / w775bopzlow7vmf q,xv ng with this statement?

Will the acceleration of a car be the same when the4ahjfc /dkw snf,wfe;) 3*6nx car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle cur4hdn wcnf3s k)w; xfa/*6 fej,ve at the same speed? Explain.

Suppose a car moves at constant speed2sq xntn8un.-: alrn7 along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a leu:r2q tn-nn l8as.xn7vel stretch near the bottom of a hill?

Describe all the forces actine pvk( i6d:lx xt ho7/5dchb:4g on a child riding a horse on a merry-go-round. Which of these forces pr/ckt7dbd(xx::oih lvhp4e 6 5 ovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without bcm(2x1 uf/stthe water spilling out, even at the top of the circle when the bucket is uubsc2x(/ 1mtf pside down. Explain.

How many “accelerators” do you have in yxtiq.evi 3t x633zel.up( 79ki ybd f(our car? There are at least three controls in the car which can be used to cause the car to accelerat.37vi(e t px3.3u69bklt qdfxy( eiize. What are they? What accelerations do they produce?

A child on a sled comes flying o. tqy*a;9 x vavczio6jjl*i 9ml1) r mk;)o)fvver the crest of a small hill, as shown in Fig. 5–l i)o)avt *l;6.)kqm vi9x ;r1f ca9zmoj yvj*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 second law.

Why do bicycle rider9 bc :*5noxbsys lean inward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking ang7, k(ip. *xikjwbdb: ule givenp* .b 7 ,kjxuid:wbik( its speed and radius of the turn?

A girl is whirling a ba,0ez kp5t )hv f8/b(5axt:fw5 fal imell on a string around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a targeth0elwx5e 5ffft/ (aziat, mv8p5b) k: on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so,rpm 8jl ,3:wi3eo9swt how large a force? Consider a li8e :o9tpwrs,m3j w3n apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whaqdq4 2.fb*ziu6gg i)tt ways would the Moon’s orbit bqgbq6i )2.4*dtgizu f e different?

Which pulls harder gravitationally, the Earth -,lx -s(oefomon the Moon, or the Moon on the Earth? Whic-(loe -ofmx,s h accelerates more?

The Sun's gravitational pull on thelyeths6 p 0o* bvza+49 Earth is much larger than the Moon's. Yet the Moon's is mainly responsible*sby9h6tv0o z 4a lpe+ 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 equatorh*x/fg r)c qyy+g b e2cnwuy8-ev:t // or at the poles? What two effects are at work? Do they oppose each othgrcyycu x qgnfy/+e/-8b: v tw*/e 2)her?

The gravitational force on the Moon due to the Earth is only about half the forc;d+oxqox-+j we on the Moon due to the Sun. Why isn’t the Moon puj xod ;-o+wx+qlled away from the Earth?

Is the centripetal acceleration of Mars in its orbio 7 v8ep0msf9xzg7dvbab7 m ,,t around the Sun larger or smaller than the centripetalx7 fazmmvo,d0vesbb, 787p 9g acceleration of the Earth?

Would it require less speed to launch a satellite (aekzv,+z fepk/r g tz fc;42 m2m+z0j2x) toward the east or (b) toward the west? Consider te;4zetxf2gzkvzm0 +p 2m zckjr,+f2/ he Earth’s rotation direction.

When will your apparent weight be the+k j1c;wa*sye r: vu7a greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you s 1+aw e;r *uy:avc7kjare 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,m* wiq 7jjd5qected 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 our feet, and (c) any other aspects of gravityq i7w5jjd ,qm* you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessness” bef7jpl q4r b*5:qf6jh ttween steps 6 j4bfjq:t7flr5hp*q.

The Earth moves fastrkhh c4/ t,mg w3wga+y:/;ruger in its orbit around the Sun in January than in July. Is the Earth closer to the Sun in Ja,uh3garh t+gw/ rm/:;kw4 cy gnuary, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known mpg6 zi7)sqe0until it was discovered to have a moon. Explain how this discovery ena6)gz mepq70i sbled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth i*7upi.mv1m;blxx v*(6,soxa ulup n ,s much larger than the Moon's. Yet the Moon'x;vv (m.miuu,b**1 ls, x6pn xao 7upls 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 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 19gjs o, 0cu,ajt.tkaoqn 706;z80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 its orbit around t1rwyr) 4e:f neyo 3s.uhe Sun, and the net force exerted on the Earth. What exerts this force on the Eart)y y4: rw3eourfs 1ne.h? 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 discus as it rotates uniformjp2v ut8(z1fn ly in a horizontal circle (at arm’s lef p1uj(v2z8tn ngth) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is i-fwyr *4+wu c5jm j1kfn orbit 400 km from the Earth's surface, and circles the Earth about once every 9ffm54cw-yw uj1j+ *kr0 minutes. Find the centripetal acceleration of the space shuttle in its 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 c-z2ndkw9 lwp b:r(t0 olay on the edge of a potter’s wheelkwto:2-pr d(90 zlbn w 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 3u ye+k-mfw 0th*p5wqy7q+svuniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00y0 w5*3+uhy-qsmet7 +fq vpkw $\mathrm{~m} / \mathrm{s}$ 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 yc::w;f rcyq2 with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coeff:yfw2c:c;qy r icient 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 betwe4zsrkc7vxo*n* b08w 2ijan p:en the tires and the road if a car is to round za7s24wrvkbo8 pc*:i n nj0*x a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet figct4tm ncy) v41hter 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 t 41vtcymc4) nis 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 turntx s 1uv0i7*on;wlsb d+able 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. Wib+un;s vl1xds7 o*w0 hat is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside down at t29kthtrjqg5a:s:mush3) )c oeh2t s9 he top of a cirkqc29sh:5aogs m2tue) t s:) h r39thjcle
(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 rounded tov6pix x0t2knsn ;y9 0np of a hil 92 i0v60sxtn;yp knxnl (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 Ferris wheel need kr a 9v.9eknkl*.l*oi to make for the passengers to feel “weightlesslko v.ak9* n kerl.*i9” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle o;ld.wl8u u rivovzc.9a- q7k3 f radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 cr3 v; l8zul-.wuiaq. k79vdoN.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a particle 9.00 wo(x e(b yuxc6q2c:u:gyo7j 5cm from the axis of rotation is to experience an accelerac(u 5 oyx27j(xqwuob::ec 6gytion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, pv +7)/7 amr opk4woj a:jqj4yneople are rotated in a cylindrically walled "room." (See Fig.q4:j/jyro7 w n74+p)ak omavj 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 o vsr86aj4 zn1wv7 2ypqlwn30c n a frictionless air-hockey tableto84 cqwlsvnyw azn p7v0j26 r13p, 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. 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 n j,dsys zf-xw4z4vx-42rx ( faot ignoring the weight of the ball which revolvesfy4j-v4 z xw a,x 4zx(2d-rfss on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car traveling 75 azth7 m0/ysz7$\mathrm{~km} / \mathrm{h}$ , 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 i1iao)f);ck5l wa-kk $ 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 a pcql ,gw(2wh2t 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 exert248oo3hg soh- yt2 qfyed on the car (by the ground) in Example 5-8 woto8qh2-h3 2 yo4gsy fhen 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 acce 7f ,8tmmel*pf ue+:smlerates 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 ac8mm* 7 fl+f,usemep:tceleration. 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. 8bphzeq-o82b:c r,rz90 m . At a particular instant, its ac8rc 8b -q2zhe,:pbz roceleration 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* t 6-t5xwcz(eo(,n nxx tdxl8 km (2 Earth radii) tntd(x ex6 t *cn-wl8ox 5x,z(above the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitat )5; tdutnj2poional acceleration g has a magnitude of 12 m/d2uj)5nto ; pts$^2$ 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.fiawna;(, a7j The Moon's radius is 1.74(ja7;a fawi,n $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hajx 2 8,p;uq 7o(gi dm0vy89uurwl5 nvns a radius 1.5 times that of Earth, but has the same mass. What is the acceleration due to graum5n;qxgn,yv w l 7u2vordp 0ju9( 88ivity near its surface?   

  A hypothetical planet has a mass 1.66 times tha l7 qg az7lkx8wb5zq:/t of Earth, but the same radius. Whlw75a/lz87 qgk qx z:bat is g near its surface?   

  Two objects attract each other gravitationallxtfg.ku22h/l u65;f- akh af :mczjz6y 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 ac 3jj ,whl:qv62fk1ug uceleration of gravity, at (a) 3200 m f gv,j1qk2l j3h:wuu6    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wheyc4z5*pje,z j re thegravitational acczpe*jycj54z, eleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fi/rtmjmz 6 fs- wtn49p9zey t-/ 9fx8lgve times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the su/yne mm s gz96fxjwf/ z9-4tlt-pt8r9rface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, whjl c izbxi( z:;d *r-lbp0fj+v:t5v7 fich once was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of ourx dz:-; j7(l5ff:bvbv*l jtciz+i0pr Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting inn+,kmpqjw:-lh4s4cc zu1 k +h 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 th+kswz :nhqp-h l+4k4 u1cjcm,e acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the coapnc n0mzx:. (rners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere nxz:a (nmc.0pby the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planetw5cf5v 9fz/ 23af ucmm+uu;rb s line up on the same side of the Sun. Calculate the total force on the Earthbfu/f32uc5; 5+mz fm 9wrcvu a 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 accele eyr5:gpt 2-hjration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius isy-j2pe:r5th g 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of e6 cs6ogy: qy1:rvih-the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kep6e :crg1hyo- :iy6qvsler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular oru 11l)lh:h fgnbit about the Earth at a height of 36h llguf1 ):nh100 km.    $\times 10^3$

  The space shuttle releases a satellite into t4s 3r(vdot(ea circular orbit 650 km above the Earth. How fast must the shuttle be moving (r4 s3(tdtoev(r elative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupani tz9m7v2z-ixts are to experience simulated gravity of 0.60 g? Assume the spaceship’s diamem2vitx i9-z 7zter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orb/su3lytr t- g.( x6h b6eff*upit 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- e t3tuy6. (*sxugbpflfh 6/r very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity74;q96 -epecrw xgll o would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around 6;rg 9l 7eql4p-wxcoe the Earth?   

  During an Apollo lunar landing mission, the command module continjzr887 e ,xj3caa+vy dued to orbit the Moon at an altitude of about 100 km. How long did it 3rac8y z+ e, djajv78xtake to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. T6arq4;yu+sgcm0 oft- he inner radius of the rin o+umyg s6aqr4fc0t; -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 every 15.5 s (see Fig. 5–9). Whati;4: t8wsux (2hg/ i3pt rqpic is the ratio of a person’s apparent weight to her real weight (a) at the top, and i3(tipirs/ 8 4u;gw2:pctxh q(b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 kb l,3 m3kfngq4,/ rae1(cajyim from the center of the Earth's Moon in a space vehlm,c/er(g,3kb 4 niaa1q yjf3icle (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-s9/ 0 oif o d2vjds qg4awucbwg+,i(5w1tar 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 th5o/(gg+jo,c29 ddvb0wf4iiu1wsa w qe mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevk*ozpjq. v :am;;n4w vator that moves4okq; *wzjav; pm:.nv
(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 xgf3q3; p p9bj0icw yoi3 w5d4a cord suspended from the ceiling of an elevator. The cord can withstand a tensio39d y5 4cxwiqfpo i0wjg3 ;3bpn of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satelli kif;+e*ykgt9 te orbits very near the surface of a planet with period T , the density (mass/volumek* gyekt; fi9+) 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 Moon6xa.uw*3bml2 y wb0us (27.4 d) to determine the period of an artificial satellite orbiting very near the Earaxum0b us wl2w.63by*th’s surface.    s

  The asteroid Icarus, though on 2.9u7kusjbmi ly a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distmiuk7. 9 sju2bance from the Sun?    $\times 10^{11}$

  Neptune is an average di 8/ )-m:egdxoazs+2c7nb bhzfstance 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 clo rh9dxr5eaerru5,on 6tj0.s7 se 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 p,r7x0r rdrt6.95o5u ahejsne lanet’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 about 7o-): /qj *: aht -q*lh1ehbatz / .wvxbvtvgethe 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 t5cx-7ym x) nkmol:.uvw xi9z ac04tw .he four largest moons of Jupiter (those d0 x) 4kno. lz5vucwmwit9y:xca. -m 7xiscovered 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 Moon. 6 a8utxgz)bz-f/ g,pp2r)t9 nicp(kh zg9 facp bpr6)tkx /i- g upz8n2(,t)h   $\times 10^{24}$

  Determine the mean distance from Jupiter for e d zdklq2 c4c3z4x cwxqz:x2;9ach of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Tad4;qzq xcl9x z2wkcx:c z423d ble 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 consuy1bk)4+g p7 bdg vzf5ists of many fragments (which some space scientists think camp+zd b7 vguk1f)y b4g5e 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 w:.i( du yg8q,fmui )z"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 Ea8 muzw(di .)ifu:g yq,rth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge bvy8ie2n+25 djj nrd ,gy swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 Nyin ev rg2dj 52,+8dnj on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravi60 hxwtlb 9ih+ty be half what it ist +h9l0 bxi6hw on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab handsu7p8a;.s ;kcv fv+zgi 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 are they pullina; v;p+cusvi . gf8k7zg on one another?    $\times 10^2$

  Because the Earth rotates once per day, the45 *vbkgshly) apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t ysb gv 5lh*4)krotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly from thf kof 6 5rc;9hz60bmdyqq 5xn/e Earth to the Moon experience zero net force because the Ed cyno 9;6zrh 5ff5bqx/ 6kqm0arth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 6pjpfpw j5m; h,5 niys 85a33rq5 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the accelerationp 5j3qs5mhpn5r,j; pw fa yi83 of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotat gde6y9hh/z9 ve 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 equag/ z9hv9hey6 dl to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraftfw 2m) :vihqpi-a,8we 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 terms j acz1 s-)hr i1kd.qhrr:d d;9of its radius r, the acceleration due to gravity at its sc 1-hdakrsrj1d:dh).9r;iq z urface and the gravitational constant G.

A plumb bob (a mass m hanging on a stri1lka e b2 hart;-,v(ybtj1 :xdng) is deflected from the vertical by anh;,txkrab2vlab et- 1: y1jd ( 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 isz1cy.6n xk:t+ d6-pwh exh*aa banked for a design speed of If the coefficient of static friction is 0.30 (wh-wzn 1+x6pad.:6kahce x*t y et pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were ro9aejz*iki*jx 8l v*; vtating so fast that objects at the equator were apparak xz 9jjeil*8i*v*;vently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance a, mma+g 5kccvuo)eo) 5part 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 c(98c,b5k8iu4z* a h cwl 3dkz:czmlm aurve of radius 235 m. A lamp suspended from the ceiling swings outk3zwcl ( m5b8z*aa4zc hdi9uml k:c8, 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 hqw(w +uxexi ly.5*jl 9as been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since peoxe (liwxq* lu.j5y w9+ple 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 the pro rvcn,zpm1. ;esence of an extremely massive core in the distant galaxy M87, so dense that it couzm,ro .1vn;p cld 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 valley s8lvf5 )o4l*ncl/ hiil)o4y kuhown in Fig. 5–45. Both the h)f 84lu5lnc*hl /li)o 4ovkyiill 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 contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes ak nnte wfm-l ka-ac-- jfr5)77 group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (jf-kc mnw-e a t)n-alk7rf57-a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km (3o: b5fg.p4naakv(y; h hpja, is meant to orbit the asteroid Eros ahf3 (;(.op nphaaabyvgk j:54 t a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle purpd g g;;cwof06suing a satellite in need of repair. Yowc0 f;gdo pg6;u 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 iti4a,l3 9b1tkcrlpwi 3 ecb4j*s mean distance from the j 3i*lk,tw b 43cpce1a9 rb4liSun?   
(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 ov7uts3 -j(rqneed to be if you could actually "feel" yourself graqs 7rtou 3j-v(vitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around td6g.efcds muqp: jd3+f5 ;)tq he center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,0 ; 5:mpdq )qcudeg+s6jfdft.300 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 mow2nhtu7+ bzn6oh(t 3ek3 d mp4ri7m , on each side. Find thnr(n+3e2u37d6wo p7m mzt b hkih,4toe magnitude and direction 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 oro q; 5b::jqvmj iqn,d9ir,fbni-xt , rno:j48 bits 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 accelera1. :ykv1 o4y l5fou flq8p8ygktion experienced by the tip of the 1.5-cm-long sweep second hand gfoy 1vf1p 4lyuyqkk.58o 8l: on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and s* :p87llp elostart to swing a 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 line makes with the verticaep7 8*slol:lp l? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car trav 4++kcdof 3yyw2h: jvieling at speedw43:ko+ d y2fcv +hyij $ 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, utili4zrz r)be vb1**y6 wf/ptkx* ezes 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 z61*ewbbv y * trerk)4*f/zpxtrack 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.$\approx$    $\times 10^2$