Sometimes people say that water is remove8c e jdld6vkw ,m:s,5y8s:op ld from clothes in a spin dryer by centrifugal force throwing the water outward. Whae5:pkd8c8 w,mls lsy vjo ,:6dt is wrong with this statement?

Will the acceleration of a car be the same when the car travels j 3yur4tz9 i6sxr +bvzy::n+uaround a sharp curve azjn +vb+xyyzusri39:u r6 t4: t a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the u/jdqg,tx8 *hgj)tx( car exert the greatest and least forces on the roadj8x( ,h j/gtxtg)q ud*: (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+h+8*jmew f hl a horse on a merry-go-round. Which of these forces pr h+l jw+*he8mfovides the centripetal acceleration of the child?

A bucket of water can be whirled in a vg .oy)0y1mjzsertical circle without the water spilling out, even atmygo 0j .1z)sy the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do1b:w 2n9sse7.m0f;wzs4 kz(ia bde vb you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. Wh f2(z7sv kebmsa:4nbwei.09dsw; 1bz at are they? What accelerations do they produce?

A child on a sled comes flying over t zg:jk:l(+ dr.afimac+vsv7qy4 4gd, h ng) 0mhe crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sledhg:c 0:ksa z7jvmlq .dmv) fydig(n4a+4,gr+ decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward whi.j+w+ .yw4ey trnk*uen rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bankp*noj (k t1r9beovu f:6r9;,oy cj b8ning angle given its speedb1eo 8 uyt cn(;no *j9b:9k,pr6vfor j and radius of the turn?

A girl is whirling a ball on a string around her head in ak hxk o 8o- vm7*uvr-nei*ys;6 horizontal plane. She wants to let g u-o-8 n oe;6kvihs*y*mxk7rvo at precisely the right 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 gravitation d8:6 l8ighbsaal force on the Earth? If so, how large a force? Co88ahsb: g6dilnsider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in whauh p vz4rr7v(/t ways would the Moon’s orbit bezu7v( /rhr4 vp different?

Which pulls harder g/8ia81 l*yzqnr)cw zn6mcr o2ravitationally, the Earth on the Moon, or the Moon on the Earth? Which acceleratyn/wcr62 zqoc*8 zmi na)8r1 les more?

The Sun's gravitational pull on the Earth is much larger than the Moon's. Yeof) jn55n04 ( hrkyzret the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the o5)f zhj5(kren4r n 0ydifference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the poles? -,m-szbmd es:k .t2lw What two effects are at work? Do they oppz2 .,s m k:bes-wtdlm-ose each other?

The gravitational forceql(tm1 .e(c yvq-k3rcx;n 5mv on the Moon due to the Earth is only about half the force on the Moon due to r5;m(yvc xq e.3qm(1 n kvc-tlthe Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars t/lior)uw a;z lycz e(6 e4u*)in its orbit around the Sun larger or smaller than the centripetal accelu4zao /6u;zt*)eey )i(wr lcl eration of the Earth?

Would it require less speed to launch a satellite (a) towad/mv3k;+eygv rd the east or (b) toward mvk;gv/3d +ey the west? Consider the Earth’s rotation direction.

When will your apparent weight be tn.dz9vptby: wk 87a 5uhe 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 whe.5tv 7p 8nw:udz 9kbayn you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected by+*jelp vls;8yqmnd kp80x+7t 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 gravity you mq8n* vekp7p+ 0xl jl8 ;+stydcan think of.

Explain how a runner experiences “free fall” or “apparentwun5z9 ,y g 0i.l3faqp weightlessness” betweenlpq 0gw.53n,iyu9za f steps.

The Earth moves faster in its orbit aroundvwl e-o6x-in 9zy )7rk the Sun in January than in July. Is the Earth closer to the x67 rkvle9w z-iy- )onSun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was008he m-yl4pt ik+xhb not known until it was discovered to have a moon. Explain how this discovery enabled an estimate of Pluto’s mass.h4y-tbx0m+i hle80p k

  The Sun's gravitational pull on the Earth is m vckh9u;p ;b*uop8vike 8m*w *uch larger 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 Earkvowc*uv ikpm u*;b9* 88eph;th 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 198b d-lgn-.e;k r0 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accat 10 x bsvr1lhaia(12eleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assu10(bixh1tv2s1a a a lrme 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-kgfw -n,stz 24fl discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed ofn f,z- 2tslf4w the discus.   

  Suppose the space shuttle is tyd j)5au 6k, ea3dgc7in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of th5,c dgekj y7a )6da3tue 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 a0 zlwonfva g+,t8+ux -cceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diamet+ax0lt8zgnouw , - v+fer is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a v/w8h hqso5qt 0ertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speeh 5t/q 80whsqod is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can rouncrt gvd fh0a;;k qk(vm1-w;: ld a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0 q; ;tcw(0ka-v:kgfmvrdhl1;.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the ti+c8e(q uhm2z6qgbtq ev2x -c:res and the road if a car is to round a level curve of radius 85 m at a speed ofz(em2cqvbu+ 62- e8 tx:gcqhq 95km/h ?   

  A device for training astronauts and jet fightem s)gt+przr/eif- 8-j r pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the for/-jzf)mrgi-8stp +er ce 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 axizdjn3a4lye r9et7p-++k3/pry/z f xa s of a rotating turntable of variable speed. When the speed of the turntable is slowly incre3/y9fe l-xpz3e kj4 ta/++ 7darnzpyrased, 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 down alm r+ktkd2+3ab7rxt;b 4)js zt the top o+k )rbtak jz 4 +x;3tlrs2mbd7f 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 6udd,qx 0a-b lmass 950 kg (including the driver) crosses the rounded top of a hill uqdbda60 lx-,(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 sx0h7h.6u nk g9 jak6fneed to make for the passengers to feel “weightless” at6 ks 9kjhag. n76xfh0u the topmost point?    rpm

  A bucket of mass 2.00)g)oy y-*m8ymr; evxw kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is 2xremy) vg8 * )mwy;-yo5.0 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 wzkh99q0bg8-bv fk 0a rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of 115,0 8 gbfwq0k- 9ha9kvz0b00 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peopledd tpbx 2j y82dy.j.d- are rotated in a cylindrically walled "room." (See Fig. 5-35. -y2j tjydb. 2xdpd8d.)
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 fricti3lv w 3zl 8c+pucls4v1onless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling b3 +plc s41zu83 vwcllvlock (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 s6c7i9 vc r1ounx etaj3mju9i11 uo -;time, by not ignoring the weight of the ball which revolves on a strojao6un uuc9 ce1m91 i-r1 7t3; sjvixing 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 /e05mutmo.09 m vvkk hk-3svj75 $\mathrm{~km} / \mathrm{h}$ , 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 .fwch/sp8dzsdy6*v hxl 36-,kid 6lg$ 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 3chcvzy8p0 ue/ c829 zxo+a( xe10 $\mathrm{~m} / \mathrm{s}$ . 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 sy898q lqge2,gl5cg mforce exerted on the car (by the ground) in Example 5-8 when its spee, lq q28 cgg59y8smegld is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerateks0k..9-1bt+ ajq h ftdthsd+s uniformly from the pit area, going from rest to 320km/h in a semicircular arc with a radiujt1ft+bs-aq d0k t.k h.h s+9ds 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 . At a parti.b; hakdtj f1 ;zu,rt896hy jv.0b mmscular instant, its a.ju8bft.6tj;m b0,mkh s91v ;az r yhdcceleration 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 space ih:sje,ja e.(craft 12,800 km (2 Earth radii) above(as,hjei: je . the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a 6c;keg,qam ma +y ,s-vyj+l w*magnitude of ,sm +e kw;ay-a, ylc+qm6jg*v12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius is 1.ia5rz/d ,v ux*74 z,iadrvx* u/5$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but has thet k5z) x19sdsf(dbbsqn./ o k7 same mass. What is the acceleration due to gravity skt(1)okq f7s./bx z s 9db5dnnear its surface?   

  A hypothetical planet has a masctcjlt6( ,b 6ls 1.66 times that of Earth, but the same radius. Wha ltc6c,j 6t(blt is g near its surface?   

  Two objects attract each othcsz1-.lakcz9h,t l 11wc o b.; nt;jwwer gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gri-(0( 9a -phsggali3v(ziv xcavity, at (a) 3200 m3 i(0 -ahlax(igsc v(i9gp vz-    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s cezfa-;wtf:a( 417z + rv4)vzx 0xccybskoqr3onter to a point outside the Earth where thegravitational acceleration due tosba;r a w0c)ff z4rx(o 3voq4t+yk7vxc:z -z1 the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron st,bup.j4 mms08 sj 3nyyar has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface g j0s.8sy4m jb np3u,ymravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sunwxu3dt i-v6abm uba 7)25za -b but is now in the last stage of its evolution, is the size of our Moon but has t2wb-3ax )b -mv6daaiu 5zub7 the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel wekswln .k3n3 15n-pw7ixe x ih4+bqj p3ightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gx.4 xp - new3 37nb+hkp53ins1wiq kljravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corners of a square of sc:5h kr 9v ;u6g4pw3,ybxhwtside 0.60 m. Calculate the magnitude and ds 5 cb6prxh:wt,g39;vhwuky4irection of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line u5qh6 y l/e;r jfga9wv0p on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are h5ry0q;/ ef9algv6j w$M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surface of Mars ishy*54h*)gjd wz m gll4 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determinewg zjl4*gy*)d lmh45h the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for tsj2yf)pjxk/ho7xs+ ,he period of the Earth and its distankpysxh2f+j),oxs j7 / ce from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circular or) 1hf8k6+ si0 zn:to o4sy2rgtjrm-dpbit about the Eartdfy82ihn -o) mtgrr 60t:z1 +spo skj4h at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abovpb csk*t9 ib*,e the Earth.p *k,sbct i9b* How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship i5/g *yel379p v fbvpwrotate if occupants are to experience simulated grevfpwp *vi5 l 7yb/39gavity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time i5ixfug+m b39ut takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is very small compared to the radius of fbg9 uium 53x+the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from the t ugt.ong1w93+d ;wkinop of Mt. Everest to be placed in a circular orbit around the o+wdun1n ;twg9. gk3iEarth?   

  During an Apollo lunar landing mission, the command mo;oj3ys 4j0mg eqgb 6.ldule continued to orbit the Moon at an altitude of about 100 km. How long did it tqjyg j 6g4elm 0;s3.obake to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice th3 rq9e*(md gkqctgu6e. x5j7yat orbit the planet. The inner radius of the r3y5ue cr*(7 gjqed9gtkmx q.6ings 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 every9d)vhj72wavj: jid/t+)l kby 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her rj)wvl+j:v2h dd)jk 9ib/ ty7aeal weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 42f)t 3x(1 irk61 zgazar00 km from the center of the Earth's Moon in a space vehicle (a) moving at c i3gxz rr(t)1a afk6z1onstant 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-swcsboq27t+4oj 2 bk e7oo5v-j qe/t 8ntar 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 thbsotj+wqnot5jv- ooq c 7 e4 e/72kb28e mass of each?    $\times 10^{29}$

  What will a spring scaleps v7bnd,ds,ra hf;2)-gxg(r read for the weight of a 55-kg woman in an elevator that moves ng,dvaxp2r ;-f( dss)br ,7 gh
(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 elevator. j d z ou/pyvbxaa6o83dw9 64uyojpf:579 dh-tThe cord can withstand a tension of 220 N a9v:by pyhxpzoawt3j -/d76 9jdud ao86ufo54 nd breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planem8c mg1.ud o(p46 u pmtkro;o-t with period T , the density (mass/volu1u4okpt.m6og-r c ;(d o8pm mume) 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 tmq(kru+( ek70 l)acfriv7l ow)gn( b8he period of the Moon (27.4 d) to determine the period of an ar ng ll (r+7mr0v)k u)ebi7(kw(qcfoa 8tificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hun - l2ro:*+ywxvl5x- qh u/nzqa.k gb.gdred meters across, orbits the Sun like the n:.v--*xo . bal l2zggyqwu kr/+xhq5planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average dist6o70t b gwmw79.ni-fnmfa /nv ance 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 roug:rm +5u ls/d1mlv :zhnhly once every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.] s1nl:h5mzld mu:/r+ v    $\times 10^6$

  Our Sun rotates about* qk7pu8b4ohy the center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean *.ms6x lc4pv( nek8kpdistance for the four largest moons of Jupiter (those ppv.8cl sk*e k 64nmx(discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and dissyz2ppy) be4( tance of the Moon. 4y) (ypzpe2bs   $\times 10^{24}$

  Determine the mean distance from Jupiter fofwenty6g0z)bczryp-e: f o 2 ql/(f47r each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given- b: go)q 4yr6zywc 2fff np(l/7et0ze 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 0/wb2(me j edq grxb m cz z-ip908m1o.iws)x8of many fragments (which some space scientists think came from a planeo2d8-bz(szimmbj w 0 ei 1xp.x/c0qm)we r98 gt 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 describe b) ent2-ld1uljhwa4f1c j7,v 3a2d mfs 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 Eartcb1nt)fm2a1jl2ld4uf ,dw7 3 v-ejh ah. 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 y; x 2)-qrb gdvn,ssc6uczo)o4d/ p,kfrom a hanging vine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His z;pbyv 6r, 4)o cdsu/ xoks,n-c2)dqgmass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be hal.exw +*iz9spx f what it is on tzxseiwp.9x +* he surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mut u.bay) eau7v5ual circle once every 2.5 s. If we assume their arms are each 0. 7y5va. ube)ua80 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 app i42e a; f:.yxpc30jk rkm9qyfarent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of3qcykkr;4 y.fip92f :x e aj0m this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth -uz1 ,b5cqhnw+ml q2z w4 svk*will a spacecraft traveling directly from the Eartw,521 4 u-zqqvs*ml+wk bnzh ch to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale inbvaq4aldgqj3 w8+ffh ye//fwhq( , ijk+4+q) an elevator, it says your mass is 82 kg. What is the acceleration of the elevator,b+i3+d/8+faqhy ) evww hjfaqg lk qf j4q,/(4 and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will ro48s xx,,s;nchiv c e-ltate 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 gravity at the surface of the Earth (1.0 g) is to be felh,escv8 4 x-nxc, ;lsit?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in 49nr e4qv:ov.g gos;ka 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 ma 4*xu4vy +m8hrgs:iiass of a planet in terms of its radius r, the acceleration due to gra i4hv8gia:yx4r mus+* vity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected fro7h 0hdudj d0 5*/j-x ayz0mxrem the vertical by an angle 0hxh -y0e mr5/xaj0dj*uzd7 d$\theta$ 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 desig) b3h ml.docnd3w:rqzim( 78fn speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a qro m73d )m(.h:n bdiwl3cf8zcar safely handle the curve?

  How long would a day be if the Earth were rot.x32h pf ct4npating so fast that objects at the equator wt2cpx4.nfp h3 ere apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a covd7febqnp); 6flo p/k t z(78gnstant distance 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 round: dll:ym s:v5(eo lh4ts a curve of radius 235 m. A lamp suspended from the ceiling swings out to e( l th:o mys54ll:dv:an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times1 .pmc3f;zxau *ctai, as massive as the Earth. Thus, 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 .a;ctizf1 ,mu3x*pa c 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 presence h yv-hgus,1smee/x y7 8qg ab*jdn765of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds oeyy75eamsh*us,nx8 q bg- 17/v gdh6jrbiting 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 hilor f ui8lo)/fy)uc 03ll and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is larges oc38ou0)f) l uf/rlyit? 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 Positiony0c u5m-c7t iking 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 11,000 nautical miles k5ticc0m u 7-y[1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after travelima)xz6.:i : pe:h cuc/xt-tpyng 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is roughly 40 x cxc:-/:zy p)tiu.p m6te:ha $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in n8l(a1zj 4.gywwhpe4 g eed of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind ipjeyw1g 8.l44z hgw (at.
(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 meana4 u+ s47q:ohp*mp a hefg)nsv44cg ;z distance from thg e4:m4ozsq;*vp 7)s+ ac4fnphhu 4age Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you coulce m( :cfi78vsy,azv g:z2z,gd actually "feel" yourself gravitationally attracted to someone near you. Make reasonabli,c(: z: 7 mfgz2ec8v y,sgavze assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milkeg6o1v ta-p(by Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the61ga evp(b o-t 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 45k az96ezcra m on each side. Find t654cazzare 9 khe 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 w6z4l3v0d c q 0fbp c 32hbdzp6fudv.6kg 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:jbyk 36vvwuv;y8,h nced by the tip of the 1.5-cm-long sweep second hand 3vy:86hw jv ubnkvy,;on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a 1jzbt- pjj0t8sinker 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 ltpz1j 0-bjt 8jine makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is design 52olihg-z)-leobl y 5ed so that a car travelin2-g illobe5oz yh5) l-g at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the cars whbdaoxyqo) 6gc)x3/m2 ,j ku5wen 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 ,3oxu/bao gqwj2k)cd y) m6x 5). (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.$\approx$    $\times 10^2$