Sometimes people say that water is removed from clothes ia5hlased-ncw:r 8 p*5x8k az3n a spin dryer by centrifugal force throwing the water outward. What ish8z3xrk l a55e:w d*- acs8pan wrong with this statement?

Will the acceleration of a1tlgwv 0b gz3m9btp +( car be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speedzg9b pb+g0lv3mt w1t( ? Explain.

Suppose a car moves at constant speed along a hilly roa2j j 50nmw,drh(d;3advwmt; qd. 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; njvtmdw0 5(a2, 3;mdrqhjwd stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse onsskdl ; h*ms10pw4x9e a merry-go-round. Which of these fows;ms e9hpd 14*k x0lsrces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the water sp qu4kg x3.6qol8jb p:s9xgy i h1/x:bpilling out, even at the top of the circle when the bucket is upsidk xoggy b jhux6p 84spqb 139i/q.x:l:e down. Explain.

How many “accelerators” do you have in your ch4 gdpuy p*7 pffn :z dq/lnrjsp)1;/3ar? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do tjnd1ngr*/zfq hlfp37up dy4s; / )pp:hey produce?

A child on a sled comqi;l0j)ebdyyr aa ) -+es flying over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (h-eb ay+r;al ) iy)q0dje does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when roundi rou-b+*b)ylmda2if8b7 hxf id37er: ng a curve at high speed?

Why do airplanes bank when th6 x )kr9az/chpbmh+.hey turn? How would you compute the banking angle given its speed and radius of the th6h9kh z). pcmxa/+br urn?

A girl is whirling a ball on a string around her head in 1gp;w ;sf 6zkja horizontal plane. She wants to let go at precisely s1f; jkzwg6p;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 gravitational force on the Earth? If so, how luk1 wmox yz*3kn6a+z(l3p 7 hharge a force? Consider o*y63k7+xazpmz3 huhn (k1l wan apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways woul*6nvn24y wnt w i.hww uvw 1v;/nr+5aqd the Moon’s orbit bew4wn/6a2w5;vnh+yi .vw w vt r1q*un n different?

Which pulls harder gravi d ge 8,t+bvn5gh1vlnr8ts.w;tationally, the Earth on the Moon, or the Moon on the Ear ,dv+n1 5be tntr8sl.whg ;8vgth? Which accelerates more?

The Sun's gravitational pull on the Earth is much larger than the Moon'q,d5e)c/5x +am h liaks. Yet the Moon's is mainly responsible feq/ h5)da+mlaxk,5i cor the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at the pu4wl8, kv +3hrr:i; cbp: nrsmoles? What two effects are at work? ksrc+, ib8 ulwr4 :mpv3:hr;n Do they oppose each other?

The gravitational force on the Moon due to the Earth is only about half thk ua .74susf-he force on the Moon due to the Sun. Why isn’t the Mo4uusha fk.s -7on pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sugc .h7p*u z 11gviyx m.dlkobe. 1(-ain larger or smaller than the centripetal acceleration of the Eakg ( ei-*lzdpmgvca.x.o1yhb u. 1i71rth?

Would it require less speed to launch a mkn87 fq9iqij pk/a;g;s+rv 9satellite (a) toward the east or (b) toward the west8;f ak vs;jqimi9 7 rq9kg/pn+? Consider the Earth’s rotation direction.

When will your apparent weight be the greatest, 8qax9p+l1a:qb *vs u hd f,j*krii9z)e*-sln 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 woz9)s e*h*i8jrf+a 9uxd1spnqibak*,- q:lvluld it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer m u*0fy3k9udyd5d az+space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spacesy9 dk+u35mz d*yau0 fdhip 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 can think of.

Explain how a runner experie:k(9r/61 : .uffaf/mv6 sinlhlzwm lxnces “free fall” or “apparent weightlessness” between stepsuzm l69f/ lmv: k:1( nfr. hilx/wfas6.

The Earth moves faster in its orbit around the Sun in January t(jsea1t . vhf:han in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much ofe1sht(a : .vjf 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. Explain 9s5ig(+ a vabfhow this dis i5fv+sb9 aa(gcovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much hv-lvng0z4 o1 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 Earth to the other.]A child sitting 1v 1-ghon l40zv.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 19 )ykyk-n5o wtbjeaz4x ep) *4/80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 the S5p fczyiu7hnz:k vz2e)d6 5 du9o0lm+ un, and the net force exerted on the Earth. What exerts5mh o z7:fdk9+yv0 56z2ucipzudnl)e 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 rotates uniforbq iu,m3),6xdb dm0q dmly in a horizontal circle (at arm’s length) of radius 0m,d bdm i)d63u0x ,bqq.90 m. Calculate the speed of the discus.   

  Suppose the space shhdauuk/ ajk w hv3ha *zu0.u6rd ao*,:+q3 ao3uttle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the graviqd0aa*o3 a a3v 3hk6u*w.ud/ u+aro uhz:j,hk tational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a sp 3fetiu2d dwry-o3y6fx n98f/ux)7 sg eck of clay on the edge of a potter’s wheel turning at 45 rpm (revoltx3o6w3 s n x9yeu)/ffiu278dd- ygr futions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a vevkvm7 3ia p.n.* )yi;1agopkr8wg *vtrtical circle of radius 72.0 cm , as shown in Fig. 5-33. If ik ni7av3kov 8pg*yi *.w1tvap)m; .rgts speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed wi3+p pzas pu:*fth which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of pu f3*s:ppz+ athe car?   

  How large must the coefficient of stati6i )g6 gpw8tvy5u7dga c friction be between the tires and the road if a car is to round a level curve ofug ig w)8vtda6g 57y6p radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighte*:tsk d 7tn9fer pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If d9st: tfenk7*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 f0 vx: 9pqt+atz,k gq/the axis of a rotating turntable of variable speed. When the /z, xqqtg9fa:+p0k tvspeed 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 friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside downuvd ;q/oqlq0m :2us 8w;zdz c3 at the top of a cd qqs q ol0dv ;2/m3zz8c;uu:wircle
(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 (includingd*fj/tzd /(n n the driver) crosses the rounded top of a nt(*// zn ddfjhill (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-diametee /du3re sycrqnqf2cs +6a 8zgr;6; 9)qyx0jbr Ferris wheel need to make for the passengers to feel “weightless” at theq8qy6 cs ry6cbrxzjnfeg+2)rs e039/ ;ad ;qu topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle ofjznpo-mdk m5o hho9;*a) kh 55 radius 1.10 m. At the lowest point of its motion the tension in the rope supporting the bucket is *zp9j okm)mono;dhh5- ka5 h525.0 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 pasl4 -c1qti1ggrticle 9.00 cm from the axis of rotation si g4cq1g -t1lis to experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peoplezr 6 rp2pqscy q+2,uj8 are rotated in a cylindrically walled "room." (See Fig. zuysq2pp 6r+cr j,2 8q5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a fric lvptw6u21 6.a.h kpm+0prnlf tionless air-hockey tabletop, and is held in this orbit by a light m.vlp1t 0ku26rf +hpnlw a p.6cord 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 jl u3f7p6rny9b q-zxl3di4 dl: knc*4this time, by not ignoring the weight of the ball which revolves on a fj-nxll6c93zrl ky743n* d4d:q upbistring 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 pp +bd,vd- l5kperfectly banked for a car traveling 75 $\mathrm{~km} / \mathrm{h}$ , what must be the coefficient of static friction for a car not to skid when traveling at 95 $\mathrm{~km} / \mathrm{h}$ ?   

  A 1200$-\mathrm{kg}$ car rounds a curve of radius 67 m banked at an angle of 12$^{\circ}$ . If the car is traveling at 95$ \mathrm{~km} / \mathrm{h}$ , will a friction force be required? If so, how much and in what direction? $\approx$    down the plane

Two blocks, of masses goz ,ngc-*sfzo )+y0d p5 wk4t$ 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 divibrm9,s a zl.f2tnch36n 4dd8yng vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangentiahjmc2ia8 +9rri d(4m yl and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 when2a 49yrdjm8 i+irhm c( its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from the pit 6go nuif7+euy3 i okh7d1;)qrwg1pz +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 accelerat6 3q uiehnz7u r7 )o1 ;p+iggk1oy+fwdion. 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 hori670d sn5cnfckh l0zk) 3mhy 2ezontal circle of radius 2.90 m . At a particular instant, its acceleration is 1.0h s k 52yhckem3f6dzncn7l0)05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spacecraft 12,800 km (2 Eart*wjc,xc8a e8t kf1kp3h radii) above the Eax13a k8kftwc* cj e8,prth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravita fves9xw4m tsr9p9:7b7a z(xotional acceleration g has a magnitudtx7a9opfz 4xb9m9:evsw (7sr e 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 gravity on the Moon. The Moon's j)g vyus 7h+o-radius is 1.74)g sh-u+7ojy v $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 timesxm n ,*elu)hy; that of Earth, but has the same mass. What um;e)yxn ,h *lis the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius. 5nlpidz(9nt2 What is g near itslnd92p z(5nti surface?   

  Two objects attract each other grfv8y deoy-k f(0/ s3ccavitationally 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 valumu cjg uocb;2t wguv :t7./d3l10k 9xhe of g , the acceleration of gravity, at (a) 3200 m 0c2v 1k 3gdjwmuht.7 g;l9:/ucbtxu o   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside th7lsjzj9 2n+o cjw59/yss/y wpe Earth where thegravitational acceleration due to the Earth spny959oy/ 7wssljjwj /2zc +is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times -ogb5 2r2nummzhs(rs2pvoax+4l: b7 the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surfaxm+:zr4maso lu 7gn22 vo25(-bb rhs pce gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was etn,a n5y83 shan average star like our Sun but is now in the last stage of its evolution, is the si,h3 ysn8ant5e ze of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbiting in the space05v2w9 ttm/ebhhv0c e shuttle. Your frbmth t2cvw9eh 0/5ev0iends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at th,v )k74iofpzt q8ck vhoh*3 7ze corners of a square of side 0.60 m. Calculatekv374iq hztvp k z,78fc oho*) the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side oc mm6e-50 3lx lha0oteco8em7f the Sun. Calculate the total force on the Earth due to Venus, Je0 6o3xca lm-cm0 mee8ht 57loupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the sury. mz.7tklf.q)e j0t nface of Mars is 0.38 of what it is o7 zjyt.en0.mtk f)lq .n Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the periodvdzz, q1)nkv / of the Earth and its distance from the Sun. [Note: Compare yourk ,q/v)n z1zdv answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satelliteo+dbx ugbr.e ,;n6o0owqd /6j moving in a stable circular orbit about the Earth at a heb0dej+ 6rq.xu gwoo6/;dnbo, ight of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km abovykrjdg-v 7vg)/ deod v7k,csei3: 4pe3i/p8me the Earc-7),eedr kk 8epviov3pdyd s3/v 4:jm7gg i/th. How fast must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if ocmcj.6 coigczg3/l* ;f cupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolutionl;j. zogcc/3* cm6i fg. (See Question 21, Fig 5–32.)   

  Determine the time iyas/jpv 8 5bs0t takes for a satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height ab ss/pjyv 0a58bove 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 satelli d 2 ibispkqh :lic(:3xpudun ic-rm4m7n(:7 7te have to be launched from the top of Mt. Everest to be placn2 ((cx:77qrhk4lms-i 7uiu:pibdi : pnc3mded in a circular orbit around the Earth?   

  During an Apollo lunar landing me jp*0gz/3*hi qgk7a jission, the command module continued to orbit the Moon at an altitude of about 100 km. How lon7pzhjq 3/*0eg *ikjg ag did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice tlsp nesw t7.cdnan4+8i6.jc .c*l q*dhat orbit the planet. The inner r 7tdwj*q4.lpcc.ndsl. 6ne*a8+in cs adius 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 /l yrli uw*f.syh7p+l b0-4z dm in diameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a l*lbw0hf4pl/y+.d r zyiu s-7 person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg a xg j:f86hlk+72 rmylgstronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity, hgr7gjy2k f +:xl8m6l     ----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. They a-nwh +57th 7ef*;hg*c dwr lihre obseh-t*fn ;iw 7 e7dwhhg+5lhrc*rved to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an yhe3jm ynj57+ ;7y:qi.pllulelevator that movejl5ehl7u+p yn.yylj :q3; m 7is
(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 from91qz- srtuenahod 3hnyk84;7 a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates.ond4qzyh8 n 7; tk-1 s39urhae What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orb;ptv tk*vu m o/p7b+t0its very near the surface of a planet with period T , the density (mass/volume) of the planet is v; tb+ utvo/k0mp t7p* $\rho=m / V=3 \pi / G T^{2}$ .
(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 u 6jl3y**lgk+rapi6 g7x0qg3zbktvf r2;q 8gperiod of the Moon (27.4 d) to determine the period of an artificial satellite org6lvkxf6;ggquip k7by+8lt r jrzg *3q*2a 30biting very near the Earth’s surface.    s

  The asteroid Icarus, though only j 8n9+xn grqns.u12j scqn5.. b omgs0a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fxnqrc5.ng9. jn s81 2jqmo0 .bs+gunsrom the Sun?    $\times 10^{11}$

  Neptune is an average distance owulnef 7; qkrcnk+63 56t;soql :fia,4 qg)usf 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 Squqb 5ak9rf*5++v/7g 4opsyf;wjh, t:ef glcun roughly once every 76 years. It comes very close to the su s:5+ ug ogcfwvplb79;q,4t* fejar+kfhq/ 5yrface 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.]    $\times 10^6$

  Our Sun rotates about the center of the Galaxej /r/0brz4 bi2bpn 0uy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, pvqi )1/e n(.2l 1bj4lk iahhgqeriod, and mean distance for the four largest moons of Jupiter (those i2 agh1nleq) bkh(vl i.qj14/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 Ea iohybhwi otyykv5q4;;46,;v rth from the known period and distance of the Moon. i4tk;4vviyh, ybq h;6o wy5;o   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using g5(fi 3ngbx4pKepler’sp5gib( xng 43f third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists ofk5sh,rfie xo7-m+ 9oh many fragments (which some space scientists think came from a planet that once orbited tmhi-7e osf+ ,9ko5rhxhe 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 "planetc 3fem yx7b()t" 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 E7ef)xyb( 3ct marth-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. qs: mw19 vncws8sv73m*2g ytw5–41). If his arms are capabls 7 m*w9 1gnwt32vyqw: s8cmsve of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the accel uwx2mvn7e, u*/(oou*b )lj mheration of gravity be half what it *vjuuh 7nom e o*blx,wm() 2/uis on the surface?    $\times 10^6$

  On an ice rink, two skaters of g7 8wblur8:6ju8tpde ;q1eksequal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each sbj6 g8k r8; wq8elpdu17: uet0.80 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 acceleratt dp 6qu4-e(s )fpiyf+ion of gravity at the equator is t qp)sf d6f-+pe(y4ui slightly less than it 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 will a spacecraft travro45lohk7(cq9f ev,r z +ym x9eling directly from the Earth to the Moon experience zero net force brlczq h+oko9(rxy9m4f7 , 5 veecause 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 sl 44eb3vk-oc1k ys p6o 8v59p2kuoqxj *z9suscale in an elevator, it says your mass p k- z*9ps938b5oelqv2u14oscv6skoyjkx 4uis 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotagofub5729dccc8r f,ctz yx9 :3id0 bite 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.gu57idffyx,cirbcc9 :t8z3ob2 9d 0 c 0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in4- dje n9bbvu)lip6mq0 g3f*p 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 of its*ekumr* y+d)5z ohn exv7fl (pc;f+7a radius r, the acceleration due to gravity at ituz)y5a o+*k;e(+drh7 f lpnx cv*m7 fes surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is defle-onlmr1*41 )bv sg nclcted from the vertical by an angles*v-n n1lgmr) c l1b4o $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of Ifn,qt.ojvb,8 i1i ,2oewafj7z the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a c,8 ebf jv. ,otoiza2jwqn i7,1ar safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects ruziv)2d 4d5h u/k vq9at the equator were app4 rdkud h)v/viz9q2 u5arently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant dv+4-n5a .y hj wzccr76(f 1cvoev.omyistance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a :4e*pitkj 2jacurve of radius 235 m. A lamp suspended from the :j*e4ia k2jt pceiling swings out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 time 6ewit/-s u 7t9)xq3cfqxz c*os as massive as the Earth. Thus, it has been claimed that a person would be crushed bu-oz / 7) qies69q3w txctxc*fy the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presku.cd ao16vf uh6 l)5cyv,gp9ence of an extremely massive core in the distant galaxy 9fv c,vlch6)gou. u165pyk a dM87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and v)4e 6wktv:knj9hmzo2 alley 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 compar 2ktzm: )vek6nj9wh4o e? (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 satellitesjw;rafh 9tsx.4/ca;yir7a 3 r orbiting the Earth. Using “triangulation” and signals transmittyfa9;rt a/.h 4c3i xrrj;7sawed 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) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), aftciyoa)cat,3tch 5 9)oumor.(er traveling 2.1 billion km, is meacoyi ac,(r)t)hoo5am 93 t.cu nt to orbit the asteroid Eros at 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 pursuing a satellite in need of ro ; ir1qt)*gsdcuqz uj:90gk /:v-ykfepair. You are in a circular orbit of the same radit/ 1kq9qvz:jc)0r k;fs oi:-d *uggu yus 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,2a sqz5;k shu 3000 years. (a) What is its mean distance fra,qsu s;h2k 5zom the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you yj jwf3g,p; .scould actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, lig.wj3, j;py sfke F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates aroun7y ,rfo/ey2pl d the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from2op7r, y/efl y 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 kt, *8 dr3:afl4bbsydof a square 0.50 m on each side. Find the magnitude al3 :dskb t 4yd*ab8rf,nd 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 orbitn veelku41,x:(6bw ruaw ,:eys 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 accelerationh)xm5rhl 9g t)k+x.) a, wyaun experienced by the tip of the 1.5-cm-long sweep second hand on x ahn)+urg hk.)wx 5 ya9l,)mtyour wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around in a circdz8zt9fn +g06cz +iqlle below you on a 0.25z9ngzc6dtqz l+i f+8 0-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 vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so that a car travefs*7rp0: driga51 y xbq,a7 rwy7j8nvling at speed01875,afav rq g7pry7xjrs:bd ywin* $ 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 thn x2gmbkb9 ):ge 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 track is not banked an9k: g)2mnbb xgd 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.$\approx$    $\times 10^2$