Sometimes people say that water is removed from clothes in a spin dryer by centrq fnez:5fhw7t/w sr/+ifugaw 5:nfsfe7+/ /wtzqrhl force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when th *8w f-rs;+ xogim0emje car travels around a sharp curve at a constant 60 km/h as when it trj fer0+go -;8mwi*xsmavels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly rs1f(e;cc;iw( u;k mqn nn+y)voad. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bos;nv)1c( ;kcnnu m(feiy; q+wttom of a hill?

Describe all the forces acting on a child riding a horse on a merr nyiuj)dvl13 -y-go-round. Which of these forcedvji)n u1yl3-s provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the fjsyhgn +im98d706eg mxl5b, water spilling 8+xjeh5gm fdl07m9g,niyb6 s out, even at the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you havepmuvjz5k7 ( 6g u-*x-piaucvi .+8m vk in your car? There are at least three controls in the car which can bki 8+v5* uup g -xu m-ak.i(vvp7zcm6je used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small p49c2ee d-gjl hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this de-c9ljdg42 ep ecrease using Newton’s second law.

Why do bicycle riders lean inward when pb1z2 d9r s-rerounding a curve at high speed?

Why do airplanes bank when they turn? How would you cud mv3vjpn 588ompute the banking angle given its 8n3m u 5dvp8vjspeed and radius of the turn?

A girl is whirling a ball on a string around her headfq(56 ac2z ec3ebyp x3 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 6 5e3b23qcfzea( cyxpside of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If sonq et:r-1u7q v, how large a force? C1u7 :vetq-rqn onsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were dou6-vjz dnt zx slvq+q *z7/**kjble what it is, in what ways would the Moon’s orbit be dif *nvq 6+-lxsj*qvtzd7* kzzj/ferent?

Which pulls harder gravitatf m3i*s:tn)z kionally, the Earth on the Moon, or the Moon on the Earth? Whic*mf3tsz ni )k:h accelerates more?

The Sun's gravitational pull on the Earth is much larger oajpu0xx9e0 g/e 2q(rthan the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earep2e/ rxaoxg9j 0u q(0th to the other.]

Will an object weigh more at the equator or at the poles? What two 59d+ 9mw-z.n6 ,sndidnvtng leffects are at wor 95vgd ni.dlnw-m9n,+tsdn6zk? Do they oppose each other?

The gravitational force on the Moon due to the Earth is onloik 92su.hmp2e0 2o 2 2ag9cjyw8bfxt y about half the force on the Moon due to the Sun. Wh222x0ykeimpojacwf9 us8 o.9 2t bh2gy isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration tk9 t/adk2o9s/sg m2qyqe (h6of Mars in its orbit around the Sun larger or smaller than the centripetaqtsq(h2 e/y2t6mk ago9/ 9 sdkl acceleration of the Earth?

Would it require less speed to launch a satellite (a) towo saellb:;.9z:;hn o0dd yp, tard the east or (b) toward the , a:podtdlse;9;n yboh l.0 z:west? Consider the Earth’s rotation direction.

When will your apparent weight be the greatestrg 4;/0lt h6vr6fcw l sbmxj19, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, wvx 6h0f grl;6ltm1srbc j4/9 (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 are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in o)l)erha md.w c 4f5tu996rvqe uter 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 the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects falu c.fqd mw6r5l4 e)e9r)avth9l, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent weightlessnj tub0+ xfw:w4ess” betweeb:w t+xf 04wujn steps.

The Earth moves faster in its orbit around the Sun in January than in July. Iswb+)xw4xr7ae 9 v.qr9sj 3pzj the Earth closer to the Sun in January, or in July? Explain. [Note: This is not mu4 jz x+pqar.3v97rjxsw)w be 9ch 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 discovered to have a moon. Explaiv32r dg p.jn4w;+cgysc(:xvkn how this discovery enabled an estimate of Pluto’rxwcj v : p4gc(kd.2sn;yg v3+s mass.

  The Sun's gravitational pull on the Earth is much larger ; t abb7dor3h;raw,u baar ,;;than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a mer,w buobaa;ar ;73r;bh ,rt a;dry-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 travelino fpa n7:6)sjmg 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 its orbit aroundv 5qc;dgds4 hi4r 5kejuhri *1kzh;+2 the Sun, and the net force exerted on the Earthiud 1*v dskkjeih2q hzchgrr4;5+; 54. 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 discus as it rota scn2d)-6 kjwktes uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus. cnk2d6)-j wsk   

  Suppose the space shuttle is in orbit 400 km from the Eakdk0 t)0 dhyadyn0;ps7tc33v rth'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 d hkc0 )07;vk0 yat3tndspdy3of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration ohsi9hv gl 7+/nf a speck of clay on the edge of a pottern+h/gl79iv h s’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 rfazz n x4em 556b3yy7w*xsv2svt-tw8ate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4.00wvvzwy6-t xfbex4s* sz3 nmy 85 7at25 $\mathrm{~m} / \mathrm{s}$ 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 turnz7-ie u9p ky*09xd jox of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result9 d-z97ip0 kxue y*jxo independent of the mass of the car?   

  How large must the coefficient of statggg5uodf45 *ug h,,tfic friction be between the tires and the road if a car is to round a level g,f*t,d5uf oghgu 5 g4curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to n.e 1agqzl(m6 rotate a trainee in a horizonme 1.g azn(ql6tal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is 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 mxjl9 8g(ecg7axis of a rotating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static fgmcg(9je xl87 riction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travelie )izayzb +(e.ng when upside down at the top of a circle ib)zaez (.+ye
(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 950i1o b1 6sf2tr/mu1-ayb h u*ny kg (including the driver) crosses the rounded top of a hill (iutumy61yf1a/ r n1 bo2hs-*bradius =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 kt8 0gfg3qry 71y )ybjFerris wheel need to make for the passengers to feel “weightless” at the toygf)gq837ykj r 1bt0ypmost point?    rpm

  A bucket of mass 2.00 kg is cngq2;0sdk w.h1 aq yxa(4xx )whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the buck1hqw anys cx().ka2g q; xxd04et 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 9.00 cm rz(:. qmy+x2x t8m ad7s2ibq0sa*hnufrom the axis of rotation is to experience an acceleration2 qb (smz:t*nx28xsh0 +arydam i. 7uq of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, pe0wxo8wkj3c5n2 yg ou o)lvwb.r 8ugtk.e.5v,ople are rotated in a cylindrically walled "r5o8nv,3ww)2508 er l j.bokucguoyv..x kwtg oom." (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 a6pb 4rlobm5f0 circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a cent 5pb4m f6blo0rral 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 nqp 7jbie5k 7y/ot ignoring the weight of the ball which5 iby k/j7p7qe revolves 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 6,sxibcfaq:y; n: i)+ yitjd 4$\mathrm{~km} / \mathrm{h}$ , 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 8iaw v(/9mfims $ 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 ve*: p)znvt gnfc(n 3d(ertically 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 andz+vliayp +s+ m crk0)wws 0azi-32 6sp centripetal components of the net force exerted on the car (by the ground)-pmwr3 s0 y +az+v)k+ais zl w2csip60 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 unifel0 4lx9c1 4ufo1jl m)a hl bx2csxq:1ormly 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 throcj2l )qob4:hx0e1x l1c xa1f9 sl4ulmugh 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 . A2g)w b 1jsp,dnt a particular instant, its accn,sdp)j1wg2b eleration 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 Earvl7eqj n gsv8u3r m2+)th’s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1 ug78lqevvrn) +sj3m2 350 kg.   

  At the surface of a certain planet, the gravitational accelera/a,sn6s*im; .z t0gt-vv +dgol)iwpction g has a magni -i *tnv)wadmtz igl .s0/cvpos+;g6,tude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to grdt/zw9m gkkktbz.vrzm .9d5a/1 / i5 cavity on the Moon. The Moon's radius is 1.7zvk.5czr 9 k.aimbgk td 9m z//5/tw1d4 $\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 E*hgdh-8.yu0mx /zd n;rmdn6t;ops ;rarth, but has the same mass. What d.;6d mn;mtrnyr o*;ps h xd80 zhug-/is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earthu bd :67ctma8vj*cdm5, but the same radius. What is g near its surfam8c:6mucad7b j 5t vd*ce?   

  Two objects attract each other gravitationally wit88ut; ayzwh6dft;fw*uv i )d*h 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 qx:m5dd tes wj824ii. of g , the acceleration of gravity, at (a) 3200 miid5we.msdxj 2 8:t4 q    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Eajz-c o .:w9 xux(/fnjhrth where thegravitatij. z9-x hcwof/:jnx (uonal acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass))2v:ckr aqr2rh y;ne of our Sun packed into a sphere abou)n ve2rq a;:crrky )h2t 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an ave2ai 8* 2vfx*w(e :g gclv,nfivrage 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 our Sun. What is the v8,in(x v cl*2* figafw2g:evsurface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the spa3l ga7v j-9ktbce 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 2503j -vt bag7l9k km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at th:sari71smu 4tj /lm(kvmba 2 (,xyl,ze corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one spheret a/a(i (yr4mkm:v17ms,bsx,u l2lzj by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on thky )gz;3vy8 swe same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assumzk vy 8s)3;ygwing all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Madotd8 thl01:urs is 0.38 of what itl 08:ho1u tdtd is 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 h484gk/q uhxy the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example84ygxqk4 /huh 5–16.]    $\times 10^{30}$

  Calculate the speed of a +skrw)m by6r5satellite moving in a stable circular orbit about the Ek bwsm+y6r r5)arth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a sate7op74w5jy9hb x . z7mc j: 5nqa8mwcjsllite into a circular orbit 650 km above the Earth. How fast must the shuttle be mov w ps wqm7 ma9z: 7558nb.xjy7h4cocjjing (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are to experiencej fh*)vn35u9 qrpk5pt simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution*u9) pfkjv n553 hqprt. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a gae 3oyiifn 5fi.qa* q,1*v (wwn-8bysatellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at ai fnyy ai,w- e8qn1f5*3*gv.i qbo(w 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 hafz(cj3 8c u0ydve to be launched from the top of Mt. Everest to be placed in a circular orbit around the Eartdj8zf0c c y3(uh?   

  During an Apollo lunar landing missixg lyd.y+ jg-t:z rcmb(rlgh7 7+:)yson, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to jgtl7+rs)gz y:dygy(+7xmcb.:rl -h go around the Moon once?    s

  The rings of Saturn are comyyzwimj /7 56u+t fb2cposed of chunks of ice that orbit the planet. The inn6m7z 5tuj2/fbc yi y+wer radius of the 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 Fig. 5–9). Wh,t+mp dp/ 03uibip0bmat is the ratio of a person’s apparent weight tib+d,0m3pbipumtp/ 0 o her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent l,o17ixkp,hqc * dbb*weight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in aqblik*o x cp*d7h,,1b space vehicle (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 consists of two stars of equal mass. T3t x.9.ih1nrzhc u+k ad0kl3rhey are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway 3+ul.tnhrhz r d3 0aicx19.kkbetween them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg7k8urv *q2ufjz6vxf 6 woman in an elevator that jx62u fkzvq8*fv67u rmoves
(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 a/g2jqit ir)*zud:l . from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was i/j*zar q l:2t.di)guthe elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits ver7rp.k8 9 orxb9fwa5lhy near the surface of a planet with period T , the density wr 9r8 7b.lfxoa95phk(mass/volume) of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the Mhsfjsy9u)p28 ( 6 no dbbq8)kvjg/8fc oon (27.4 d) to determine the period of an artq)29bj/db (v 6gucs8 f8s8jfknp)hy oificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though o,ecp 6szj+b-d nly a few hundred meters across, orbits the Sun like the planets. Itsbzjc p-es+6d, period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distae( *hd0 ti7amap 33jqgnce 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 comkr+t z0r qoxuf999 9yces very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s k9 99 +fzqu r0rcxt9oyorbit 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 the center of th*,yr+4pj zh1 o3ioreq /iqq/ mruo );ee 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 maswue tpn nz/+.)7d-szos, period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo)un tew.p7n/z+s -odz 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+uch7:gd4ou swn3+ ql from the known period and distance of the Moon. ns+ u43ohc q:gld u7+w   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons,biajpm mnu/ mnnxl12b+ . ,3w3 using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Tabl3l ,2 pnun/m .1 xm3a+ijmbwbne.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars andgvg5 -43vxd3 mswjm0 .vb prg9 Jupiter consists of many fragments (which some spacvsxr94vv0 5d3j.g3w mbggp m-e scientists 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" s d4t u+l-nuu5:vc 5y g-pblx7in the form of a band completbu-7s-u5l 5t ug nx: ycvd+p4lely 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 planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 5–/iw uu40lax *u41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he cu*0u wi4alux /an 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 acceler;b pdq3q qs/f1 rm:dw1ation of gravity be half what wfdr:pm 13 q s1dqb;q/it is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutuaty(c,51 a7z+ouyejzg l circle once every 2.5uz5( jaey7c+z1 ,ot yg s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gravi7o t*nl ;rmxs+ty at the equator is slightly less than it*7;+xsn ot lmr would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will3nstjff4abv: v.s dq i:*zn*, a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and oppostzv*,ifq:4v jbn3ns f* as .d:ite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in jq g0ga;w0n w/6ucza6fmkm 28an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which dirkzqw6m 6 fuw/0g20aaj;mc g8 nection?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotate ma+wxj- z,mvpr+74i,n-gwdtn,4 dj vabout 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 gravity at the surface of the Earth (1.0 g) is tv,p dw7-g m,x4+n4trinmdv a w,zjj+-o be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a verticagwu*-a3l 6) pb34skruek5 feeea* le /l 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 terms9k.x hkkk-igid)gmguqe; g, l-5 ,sj2 of its radius r, the acceleration due to gravity at its surface and the gravitational cons;di ik -lx 5,s2ehjkkq -ggu ggm,).k9tant G.

A plumb bob (a mass m hanging on a string) is deflecteg)umb d*y*nogv f+0. ud from the vertical by an angle bg0mdf+*)yg.vu*ou n $\theta$ 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 specxxrn;:+xr4 led of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely handl4rx;c:x + lrnxe the curve?

  How long would a day be if 0i92geqne /2 -mmoh dss4qgo2 the Earth were rotating so fast that objects at the equator were apparently weightd mh-mgs242oiqeo qs 0n2 /e9gless?    $\times 10^3$s

  Two equal-mass stars maintain a constant di o1 lita:2mpyje0,*ocstance 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 nayrebpx: xmrmh8 55 hc81i9/ speed rounds a curve of radius 235 m. A lamp suspended from the cei5 5m1:8e 9i8rbnphryxx cm/ah ling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thxf(wxm0 heck:5(ze*vgg; k m;us, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equm(e5*x;gg emhv kz0(w;: fcxkator 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 Spac6f pfe q)wb-g6e Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light ewfg e)6b -q6pfscapes). 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 asp:h kvzkub .8tkv 3n4) it traverses the hill and valley shown in Fig. 5–45. Both the hill and va t:hk vk3uk4v8 p.)znblley 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 a group of 24 satellites zuzmb;+: 8wf a2uirlz:nq1 y9 ep(.a xorbiting 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 ]. (a) Detn +y1fbzu9zaprq w a:z 2miuxl;.:(8eermine 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, f* f7.ikw+j1,t sq sd:7qwcgy is meant to orbit the asteroid Eros at a 1d7twsq7 .cf*,q k s:i+w jfygheight 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 pursuing t -xqzn34n fnw/t58lf -gws1ua 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 it8ftun w/-qnnlg1tz-5s 34 w xf.
(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 3000o it)1ctx)dx10 qgc7b n)r/ql years. (a) What is its mean distance from the Sc)x1bgdn0t)q qil) c/to7x1run?   
(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 ne:0o 1w :bg+zzk r w/lqdjl/g*ded to be if you could actually "feel" yourself gravitationally attracted to someone near you. Ma zrqld/*o:z1gwg/kjw d+lb:0 ke reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milkya8tzm7jjwte4qidp; cp6 h )s-v1b h-/ Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the centetdvq6 )-h;c-p817ti hjb p se mz/j4war $ \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 cornerj (f 3uw+i y*y3zp1hbefni)8y s of 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 midpoint of the bottom side of the sqw*yeiy13j yp8hui3n +(bfz) f uare.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 550h)b.r 1ee n (q(tnfsr60 kg 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 experienced by 91kbu2) cxcru.gt9x p;i6wlis(o9 quthe tip of the 1.5-cm-long sweep second hand on your wrist watxpuoc q9lxukbts.29i9 r)16w gi u(;cch?    $\times 10^{-4}$

  While fishing, you get bored ac 5m-0yk-(rb1o meo; 1lwdnaond start 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 t n- o-aceb0mm11o k rdwlo5;(yhe fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so0 fh/bew+g0bi.vo,)a ntzj+e that a car traveling at speejvzbf+e,t)0o +/ h0 bnei.w gad $ 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 4el z9n j.jq6bAcela, 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 comfortable9 jj.nb46 lzqe. 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 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.$\approx$    $\times 10^2$