Sometimes people say that rw-cgpa-9o (m3o ycl:water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with thca-gr -lycp(wo mo:93is statement?

Will the acceleration of a car be the same when the car travels arou 2oq8 . w9z)xoytvo-gz*ff,v mnd a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? E*8o - yvx2vffo 9zqgtow).,zm xplain.

Suppose a car moves at constant ssi6lwjwh4. xjq + 0j6mpeed along a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level 60l wqj msj+ hw.6ix4jstretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a merry-go-rouc:7pa w2gd 2bdnd. Which of these forces provides the centr72gp a:dw2dcbipetal acceleration of the child?

A bucket of water can be whirled in a vertical circln v0)0zgup2whe without the water spilling out, even at the top of the v0)wg hpznu0 2circle when the bucket is upside down. Explain.

How many “accelerators” do you have 0 97nl/u; eyycwpeg+f in your car? There are at least three controls ncg;y pf+yu9 7lw0ee /in the car which can be 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 hill, as shown in Fyiyp:7bbihp,* h 4 mm c:x1lf*ig. 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 thispy4pf:i b* :xl*imc1hmh,y7b decrease using Newton’s second law.

Why do bicycle riders lean i.bp9e(f4yql dz8/wq jts*z:w nward when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking angle q 7t7;;zvx(pj 4gmoy hgiven its spee;xmvt 7jg z;qp7 y(4hod and radius of the turn?

A girl is whirling a ball on a string aroundqmvj :i 9p) s7dc(5s7+l xlyoa her head in a horizontal plane. She wants to let go at precisely xqi7js vp7l ao :+sc)5lmy(9dthe 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, bwhl :an /kvhrs2h4qabg .wp - 1b5/0nhow large a force? Consider an apple5q24wkghvrs 0/ab . 1 :nlw npbb/h-ha
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’sl stzx5 ;(r. ad2 hxrg gn01dfu -k.dr1w54xhw orbit be differentr 45 .tz51(wsdd-xd;nf . axlu10wr 2gx kghhr?

Which pulls harder gravitationally, the Earth on the Moon, or gwy * p c46mxi+-qh2crthe Moon on the Eahiw*q6c2gpm4c+ xyr - rth? Which accelerates more?

The Sun's gravitational pul(r f+-4k .x9zpymhyvhl on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference infzhk(4 +h9px v.yrm-y gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equa0bx/ wzq 7cbh5tor or at the poles? What two effects are at work? Do bxc50 7qzhbw /they oppose each other?

The gravitational force on the Moon due ton63tj-,d eq xa the Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pulleaqtje3 -n, 6xdd away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger izm +i b9t5 rcd9d;sfy6l:ps,w g/s3hor smaller than the centripetal acceleration of t s c ,9fy ;dlwp/si :zh6m3s9dg+i5tbrhe Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) towz c;96e3x6 pn z(q3hvf h8q10lreyspward th8vwe9fqc(qhzh0x3y 6 prp1 zs 6;nl3ee west? Consider the Earth’s rotation direction.

When will your apparent )i2581tqfrp yb 8f)hybfayh4 weight be the 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 at12hytby85fhq )f48pf)y b air 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 outer space co72phj0jji q +9im )pukuld be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a i qpum 20i+)9jp7 hkjjcylindrical 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 experiences “free fall” or “apparent weighti x r-8b) z7 gpom12*zadngirueiu,-3lessness” between sn* 8x7,u1)muibzr3rzgi-- p2ieag d oteps.

The Earth moves faster il3 -0 lr jg.q v tl;xb3o96bh5mw/lqynn its orbit around the Sun in January than in July. Is the Earth closer to the Sun 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 thelbmx3.gnwl/;v -6l 3tb5y9l0oqhjqr plane of its orbit.]

The mass of Pluto was not known until it was diw3zwt6o6y +ief+aj5w scovered to have a moon. Explain how this discovery enabled an estimfzjw 5++oaiw 3e t6yw6ate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than thymtmc, *l,bc0(9wex e e Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Cotc, e,bmleym( *cw 0x9nsider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves with a speed of 1.25 $\mathrm{~m} / \mathrm{s}$ . Calculate (a) the centripetal acceleration of the child,   
(b) the net horizontal force exerted on the child ( mass =25.0 $\mathrm{~kg}$)   

  A jet plane traveling 1980cs9yh n+b3op8wg ezo5*) ;;mrc f +zqt $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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(yl3h:3rvm;eb f5ebb: ibb wl nul6+0 Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that t(iybnu :h3b ;6wef3re bl5+lbbm:vl 0he 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 unic, (h z/sh vl9f53rkkcformly in a horizontal circle (at arm’s length) of radius 0.90 m. Ca,k9ch h3cl / rz5vksf(lculate the speed of the discus.   

  Suppose the space shuttle is in orbit a p;m1qldg8egkyy3/ s ;mm;e5400 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 yom mg/q5ee;la8gysy;1p3m;d kur answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of c 4a m 3uuxa/w4:emu,swlay on the edge of a potter’s wheel turnwae/u3xm: umu4wa4, sing at 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a strinf ) frbn;-uy o*+lg+*hvci u)ng is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fg n)+v+ n fi* uou*r)ly-;cbhfig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

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

  What is the maximum speed with which a 1050-kg car can wtzw+i*bls,d. ju9; w round a turn of radius 77 m on a flat road if the coefficient of static friction bez b,l.9*ji +sww;dtuwtween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficienx 0 jxx/- w3pxa1kp qsjf0n2u+t of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of xf0q 231/n jxjpw0xps kux-a+95km/h ?   

  A device for training astronauts and jerin p+e 73+hwrp 6ler3t fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee+3ewr3h i+6rlpp7n re 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 axis of a rotating turntab:jv0 9(eg yi/ rifvobo 7gpv;(le of variable speed. When the speed of the turntable is slogp7j(oe/vi9v:fbi ;( yrg0 ovwly 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 dpp.msbxev1 i *f/)9l pown at the top 91esl v.*bx)mpp /fpi of a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses the rounded top-3 u( qfblv+mr+wz5 y*slb)xl of a (ull 3*f-vb+5xs)mqw lr +zy bhill (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 1z pkkl)3:e)r y/gydk(j wl6x*5-m-diameter Ferris wheel need to make for the passengee/pz gkl 3dklr:y(kyj xw6* ))rs to feel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At th1yrpm+ so0gw 8e lowest point of its motion tr 8powsm+g 1y0he tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifubyynk37r2.iry9fgq 3 ge rotate if a particle 9.00 cm from the axis of rotation is to experien i3fg2.37 y9rqyybkrnce an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricafg z6s+ft/3plrf ot2;lly walled "room." (Setgol2 +z6r f/pf ft;s3e Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless air-hockey hceq50nel:llqos//w 9k5 y gp-3ka 7n tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig.k9e o70q3/aq ng/ lec-h:nl l5y pks5w 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 t ohov0 /w4*tasyjz.w: ime, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find ov /*z:w.a 0wyosh j4tthe 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 bam(h hr3hmoui6-z.z8 ;z, n hmpnked 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 t 9+4..bi1w5 x x hdisao7akdf$ 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 man yrza62 ;/ra/i)djnxreuver by diving 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 tangential and centrxmre;g,x 5j dt dl2d/d7-l/rwipetal components of the net force exerted on the car (byedl/-mdtrj;7,dl5 /2xdrxgw the ground) 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 uniformxq f2 9 tq gv)t)he-i9negd9g9ly from the pit area, going from rest to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flg-t x qi9nhvegqg) 2d9e 9t)9fat, 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 ofx3pjez nx65fi fa.r2 . radius 2.90 m . At a particular instant, its acceleration is fp2 izxf .e.5nr3 x6ja1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 kmn7k8 yl5/ u 3u6wqbmhb (2 Earth radii) abq5b7lhwm b638un/u kyove the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g hashtvg mq/. .wz -*;)vxso n: rk::vbdpw a magnitude nwp/x)dk: b.v;:zq*wvg .s oht-: m vrof 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 d9p wzzeqt,m9kbe31l: vr y49sy5 auh/ ue to gravity on the Moon. The Moon's radius is 1.74 tz a9,sh9e 4p5zy 93yebur/wm klq:1v$\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 10r5sb. ikquo)0 .i o7u7mzlt:k3d oqb .5 times that of Earth, but has the same mass. What is the acceleration due tbmb0to 0)r:oduz7. ku i 3so5qiql7k.o gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that p-pg/(qn yhhmvx)hss f:qr2 yh315 )f ) weod;of Earth, but the same radius. What is g near:fm)h-esoh5pq( 2nxdg) )s pv1y hy 3whf/q;r its surface?   

  Two objects attract each other gravitationalljic49) iy t tj5c2xe3kf14am u gj*l :suw1lq:y 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 ,wcplqv2 w/f6 wxmx f-d v520xu 8awb1* the acceleration of gravity, at (a) 3200 m uw*v 6f20w xm2dqw xlpcav f51b8xw/-   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’sjn0g 2,8cys xx7vzrb-a6qnd 1 center to a point outside the Earth where thegravitational accelery dnabvc6-2z0 gnxq7s, 8rj1xation due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times 9y9 sjirzkb, -0z 3j.v: rircdthe mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravi 99zrb3ryivs0,z.jdjk i-r c:ty on this monster.    $\times10^12$

  A typical white-dwarf star, which once w/) vhea*9tg.znn2 csd 5mc;zpas an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. Whap*)nzahtme9 s;z d /2c.gnvc5t is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while orbi-vjvxfn* x 2-lting 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 gravity 250 km above the Earth’s surface in txf -v 2*lx-jvnerms of g.   

  Four 9.5-kg spheres are located at the corners of a square of side 0.60 m. C 1iqde)qjf50talculate the magnitude and direc)1qfje5q 0 tdition 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 tdv bkfe89*pu-jms +o1he planets line up 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 (Figjudf emv 18ok+* -p9bs. 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 Mars is 0.38 + 9idjt yes;u,of what it is on Earth, and that Mars’ radius ut,9ejsd; y+i is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known h.o( c47o wdpo4jwa s36pgt2ivalue for the period of the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, 3g.tpcap jio47s2dw 6o wo4h(Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a sv0n d.l7v 88a-tv ro3lnu eu/uatellite moving in a stable circular orbit about the Earth at a height of 3600 km. vt-0dvvor.l e/7auu8u 3n l8n   $\times 10^3$

  The space shuttle releases a satellite izhv5 hogyrb7vs,0au j44ew)p 5raa ,,nto a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the 4hv v, 7p4 azaa)o5g,5whury, sej br0release occurs?    $\times 10^3$

  At what rate must a cylindrical spacesy-dqf gni d;pu 7s0q+.p6kg2 mhip rotate if occupants 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 revolution. . ;dfgnqg-impk67 u0py+2sdq (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Ea5uz6m+ qx-zl krth 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 t+qk- l5zumx6 zo the radius of 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-;/s-xgs.w+ tuwa1 y -cmpy sr the top of Mt. Everest to be placed in a circular orbit a- cy+r st.wu/s1;wxgsp m-ay-round the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit ted;pn6 9y81)jfu yuwe he Moon at an altitude of abou1)yj6;pe 8fd nyuweu9 t 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. The i45-cztpzy nmyu93; l q:r6czdnn6 mclyz-5d:q;3ru94 zpzt yc ner 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. n *m sho0:wm: rzrj-rj s5r3q-ecww2* 5–9). What is the ratio of a person’s apparent weight to her reawj**ze:n-5 j: rq3 hro srm-ww2s0rcml weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from t 7t/rdm( +:n05fonsmf -npw5uq ns4oehe center of the Earth's Moon osn+ne-45p oq07dst f (n:5frmwn um /in a 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 ofem x26( 2oyv.wgi 6zf d0chpo* 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 0dg *poex iyv(owh 2f2c.z66mis the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55 w8rw:s)2)f9huces/dj2 9i ol knxer3-kg woman in an elevator tha93 /i:fn suw2rorewhj82)k9xlc )sedt moves
(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 el97d u37wgbj x9yjx,hc evator. The cord can withstand a tension of 220 N and j7 hdb,g9yux97wjcx3breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satelliteq0 fyi(m 2hp0g orbits very near the surface of a planet with period T , the density (mass/volume) ofqgpfi( 0h0my2 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*fhc. 9 kbsl-k4e 2acv the period of the Moon (27.4 d) to determine the period of an afk.hle -k4 c2*vb9 ascrtificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hi. h 3f1f3kwt4vqm5 e180oytjz ;i vilundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance ;8zo01m vew tiyjkifql31i3v ht5.f4from the Sun?    $\times 10^{11}$

  Neptune is an average -1 ,sccj znab/z)qv qnc9+zw: distance 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 ;dit x7/pxs0b*ue *.lov zyu3jyt 3d:ha uc9 2comes very close to the surface of the Sun on its closest appro 93uz;etvh0sjp3ba 2 lxy uddux/i.* yto*c7:ach (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 theev5;k1bf.sz e 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, an056p+l( o0q,n wj gse/hytjhz d mean distance for the four largest moons of Jupiter (those discovq ,6y j epwgt0 sjl0(n+hzh/5oered 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 knowxpuvsew+v l:dy- p,0 ,r8en0zn period and distance of the Moon. ,yvw pld:-z8 0r0xne+pvu es ,   $\times 10^{24}$

  Determine the mean distance from Jupitmy/s1ih7ji:8omqdzbu . 6 l52xps q e0er for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods g/60 :zm8l d sq2i pu1qjx.osbheimy75iven 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(tir.qt sef s *8a1(lx Jupiter consists of many fragments (which some space scientists think came from a planet.flxe a tsqs( 8i1(*rt 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. 5*tyq,px*a;ejgv8kuitp ;a+y9qbu s an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the insi pbuek,+tgp.a;jqiq*9;a y*uvt yx5 8de 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 gc f 0al3cl*;jyorge by swinging in an arc from a hanging vine (Fig. 5–41). If his arms are capable of exerting a force c*l 3y ca;lfj0of 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 surlt*-h3 w-bhihface will the acceleration of gravity be half what it is on the surfaceh-3l-bth wih* ?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a m9e9z7m3bv 3e igfcdg92s73mq 5 v vvmtutual circle once every 2.5 s. If we assume their arms are each 0.80 m lo 79ecvg i5mmgq v23e7 9vdz3vf3t bsm9ng 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 ap8r ao72a: x+avri cq3cparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’q a oir3a:8rc+c2 7avxt 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 traveling directly fro r8 9w vh9 e1kh8ki7hzaek5*uim the Earth to the Moon experience zero net force because the Earth and Moon pul99vh85ekw 7e zkh8ukai h*1ril with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a b+;,jfz8jul it, 4ynwrathroom scale in an elevator, it says your mas,j lunirt4, f+wjy;z8s is 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 rotat.ouyre* q(t.ar n6o, qe 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 effeqronte.y.ro6,( a u*qct equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43) k 9ew8jex9t zo,1j7s 6ls1tuc.
(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 radius r, the acce77sh5nr,i b qj5+)gh/l gck sbleration due tlkgqcig7)n+/,ss 7bh j 55h rbo gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the p6)n wo 9 dg(b5a)vhykvertical by an abpw) )o9( 56kna hdgvyngle $\theta$ 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 670nllr76yry2k 9u r/ lx m is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds cr 29klrnr7l0y /lxy6u an a car safely handle the curve?

  How long would a day be if the Earth were rotating so fa/n 8jvzz.+0)q rmrvv bst that objects at the equator were apparently weightlezq/jbv+rz. )mv8v0 rnss?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance aparokkt wpct)0jr/ak -drm4 x;qqy+ +d .*t 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 cons6r34d9 inzel1ad(hnnvw *7yn tant speed rounds a curve of radius 235 m. A lamp suspe*ndnh a 6v4 (3lwy79iznd ner1nded from the ceiling 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 theb p oe80ohz. uhoy+(g2 Earth. Thus, it has been claimed that a o28ho(0 yophb e .z+ugperson 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 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 of an extrh02we6v 4w xl) sv9hkjemely 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 o9)kxlj4h 0h 2wwv 6evsrbiting 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 rxa 3wi3x:l/.aqh +c ngm85wr as it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature 5/mn8.a:3x qr w3i+g arlcx hwR. (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)uj m*dkf-b z() 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 nabzd -m )f(jk*uvigational “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 Rendezvousqr bnmczbqu9ecj) g 1)/cs0o: n*og +0 (NEAR), after traveling 2.1 billion km, is meant to orbit the astero0 jg 1q+gocn:b )/b0numoc*c)e qzs9rid 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 t3vgbtd8-*+s) j c(9ky khjicthe space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth)c 8ttcjgy)( -39vs+dj hkki*b, but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What t 0xp9uuovn(, is its mean distance fromu0n9ovu pxt (, 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 kj9nb*6nh9 matlag.p(pdp u/ hm9l ;2G would need to be if you could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumh;(99l/hj9lpnm .d6u*pb2pkma g ant ptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky q4w1 jo rhq0-,+:mtai1iwckgdsw cf;12pt : tWay Galaxy (Fig. 5-46) at a distance of about 30,00tgqcho1fjwmk ;w 2+sirc1t ::0-qdti4p, 1a w0 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a:.yfmcmv,zk qnpb,y-g l- .bja zc3vusj86: 8 square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass pk8.mb 8,q6 fv:sbzjcy, u --.3:mcpnajgv lyzlaced at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earth1kcd tk4. ;wc;x-zn kj7day s4 $ \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 accelerat-0w0 kyr,bu lf dvh,/qion experienced by the tip of the 1.5-cm-long sweep second hand on your wrilwhd,f, r/u0 q-vk0y bst watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight8 +xwe mv3x8ft around in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertic 8x3 fxvt+em8wal? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway;a utg /dwb-s5x.r 3;bp*wthd is designed so that a car traveling atp*.d;/ab; t uhdst5w-xg r3bw 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 when neg cc+ y;nlgh, +.w7g;kr,xpepmotiating 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 pr+;kwcle,c.+ ;yg, gnx7pm h(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.$\approx$    $\times 10^2$