Sometimes people say that water is removed from crhw fy 2+yu9)zc2rod+lothes in a spin dryer by centrifugal force throwing the water f2d9rc u)2y r+zywho+ outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels a+j pkpx 9p6s62lqz pbd:d 4q+6ovkcz, round a sharp curve at a constant 60 km/h kdb6:pq9pd6q v xzcslok +pzj2+,6 4p as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly*d2750a:t m,h f 8bdyi.ryvsg hax8dc 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 stretch near the bottom of a hibdfds2d c : ytm8rahyg,*vh85i.x 70all?

Describe all the forces acting on a child riding a horse on a merry-go-roupzb0omibn-em+8eg1 ; f9gj 1gnd. Which of these forces provides the centripetal acceleratzg9pboj81;ig- enfb 1 g0e+mm ion of the child?

A bucket of water can be whirled in a vertical circle 5ah ifxq5v31 j1; vvx ph;w-f jaavwls3nb(/8without the water spilling out, even at the top of the circle when the bucket is upside down. ;v/35 nv ;v35v qjxl1 aaws 8f(phabx1wh-fi jExplain.

How many “accelerators” doz6 dy a 7y*g-(ostjzfrzn2;q; you have in your car? There are at least three controls in the car whigzza7j;osyy q-n*2 (6dtrfz; ch 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*0ot jnmk )hvp80i.hu, as shown in Fig. 5–31. His sled does not leave the grok8h0jnv.poit* )u h0m und (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curvehs r+a 8u;-mqj at high speed?

Why do airplanes bank wh.hj a7ugv/9 znen they turn? How would you compute the banking angle given its speed and radi 7 vha9/zg.jnuus of the turn?

A girl is whirling a ball on a string around her head in a horizontal pli5(1v2xvsnju ane. She wants to let go at precisely ins5j2u(x vv1 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 large a fobo1o82/5 sy.yf zy4u ho n3uqfhfgx-6rce? Cons gx ffn-y4s hq/6z.15 o y23uofo8hybuider an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what 43 qc6gpmi)xm it is, in what ways would the Moon’s orbit be different?mx) g3mq 6p4ic

Which pulls harder gb jx)pzp: tdj76t 72iet)akw( ravitationally, the Earth on the Moon, or the Moon on the Earth? Whz 6 ta):x)e7k(t2b jjp7twi pdich accelerates more?

The Sun's gravitational pultuy0 j, ba4v;p.a/jhyl on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hiy 4a jb ,p/h.vu0jy;tant: 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 poles? What two efferx 3*jc b-v(sqcts are at work? Do they oppose each -c(xj*sqb 3r vother?

The gravitational fo*6z+yn;8u se * akfn4hj nss,bwh 9ds3rce on the Moon due to the Earth is only about half the force onkez8 an * f ns3jnhybh +ss,*ds;469wu the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration.tskl1+mk(br16kpl1mm /*ryv 0( ssf -guaxm of Mars in its orbit around the Sun larger or smaller than the cenbk/sm fap61+rmumlx0gyl - (r1vk*.1tk mss(tripetal acceleration of the Earth?

Would it require less speed to launch a sate 90rw5xyokt 8ullite (a) toward the east or (b) toward tr0 98y xout5kwhe west? Consider the Earth’s rotation direction.

When will your apparent w4rwl zt0vo*1+o 5x yuk4qh .upeight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates 1o.+pyqwu r4o4t*hlx05k vzu downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be a5 krbcbl0z, *vdversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspectkcbvr5,b z* l0s of gravity you can think of.

Explain how a runner experiences6;/mvc 4 nygm:x3uqz j “free fall” or “apparent weightlessness” between stepsxc y: u6m;/4zvgm3q jn.

The Earth moves faster in its orbit around thecr,:nxu2whb9t7 yl (s pu,v xi- :(jar Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Nrx,:aw2 iyb ,lv:tc-(u 9p r7nxshu(jote: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to hq) 1n,xxe on+aave a moon. Explain how this discno)q, ea1x+n xovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is muw4 v o udl v25c 1piu(jalx:w 29r,ts-b,z2nywch 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 1.10 m from the center of a merry-go-round moves with a speed cr t xww,:v5sly a42l,2-(pdb92v1uuinwzjo 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 y -c zwlsysv0j+q9-u dg20/)qwp2zpl 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its oqk+fuy2 7 l+hgrbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth'f2 hquk+y7l+gs 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 210qr w1 6i5xbowp1hjfdu+ad d564u8fc5 ,ut j1w N is exerted on a 2.0-kg discus as it rotates uniformly in a,856o 41du wbwtxuq fcwjd6hpu dr ia5jf511+ horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfa/fsru 0v4cpp jdkox:)26so;mivh;u- vu94 xgce, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in ou;0/ud6c:sgs h 9prx;4fojk)p xuvmi4-vv2its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of cla ue; 5yc0hv)jky on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute)) yvc j;uek05h if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a verticih p*-z;h pbu6u qq5t4al circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed isi tp*uq5 b6-uh hp;zq4 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 spee(sfi z sciw2 r0u0y)z3d with which a 1050-kg car can round a turn of radius 77 m on a flat 0)yiuw3szsz f0ir(2c road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tcl.d a nc9+1 ypaq gb9r,zd(s5cv:lu 5ires and the road if a car is to round a level curve of radiusv:, 5gb.5 9(nylz+ raac9dulcqds1 pc 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilotszxphq km ybu .m(k)(/a*5ukk0 is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the traine.m p(u(/5k)khkuqxm kaby0 * ze 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 rwn( oc3 ,t1y+z h0fw nplrip20otating turntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reache p3tzwy1n0(n2 0+wpofl ,hcrid 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 z/xd5azmye k aj**b4)at theed*/m4b zy5x)ak*ajz top 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 (includq7u-j bnkakio+r9 p7/ing the driver) crosses the rounded top of a hilu/+bipqak9 ro7nkj-7 l (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 nmv+a4mw 7yi :zcw hm+6+dguh0eed to make for the passengers to feel “weightless”h+w6u07hwz m idycv+4+ mag: m at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radi0)cekwns. 9+ srr- u 0de-zlkius 1.10 m. At the lowest point of its motion theksw-- 0.0i rerns)lkud ecz9+ 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 centrifuge rotas.qvl *-yj:g. ;w ao7irla t0wte if a particle 9.00 cm from the axis of rotation is to experience an accelerat; :*0gawwat js.qr ov-i7y ll.ion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrica.ljchcp87yd c4la*-dlly walled "room." (See ap-c.*8y7j dhd clc4lFig. 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 62huq pf vny:-5kr:yhb7f3 qo on a frictionless air-hockey tabletop, and is held in this orbit by a lu6hq-qr7ff b5y32:k :y hvpo night cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

$v=\sqrt{\frac{m g R}{M}}$

  Redo Example 5-3 , precisely this time, by not ignorinct i/id;h o z6(t;p+cag the weight of the ball which revolves on a string 0.600 a(t/icic6ho ;dp zt;+ 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 1wke z+l *fofwji1way0--hk 9 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 ..vol*v bf pc/o5wfe) $ 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 ata q,;xp6ir 4-n zwe 2dwr2q*ir 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal componentsdw /:x-8x e(uexk.tcq ulxs 03 of the net force exerted on the car (by the ground) in Example c 0wx/e.8u(d l3 e:xs-ktxuqx 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 uniformly from the pit area, goizw 1wjvv4ct+)p6*n rm ng from rest to 320km/h in a semicircular arc with a radius of 220 w*tv m)v r4w1jn6p+c zm. 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 l( tdh28y :aeqm0 q5z+we/wgtn-t1ri 2.90 m . At a particular instant, its acceleration is 1.0n witzh rql+58td(-t0e/ :m2wegya1 q5 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 /mix e8t8nn/ac ;phrfu+dec( g2 ,fz. spacecraft 12,800 km (2 Earth radii) above the Earth’s dai8e/prh cfmtx un(e+z c/n 82g;f.,surface if its mass is 1350 kg.   

  At the surface of a cer ntqt(ecmxs)ga356wwg+y 9w-tain planet, the gravitational acceleration g has a magnitude of) ytc(wg xq3t+ ag6swenm5w- 9 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. T u,kbbcr 29)hy c,u9sshe Moon's radius is 1.74r,uu9k cys) ,bh9scb 2 $\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 the same mas da qatt5lbn,,;tdx(6s. What is the acceleration dult6a5q(,xtd;d,b tan e to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius/ arf )c; ,-hgpnsxx(r. What is g near its surh )frc ,xxa(g/p;r-n sface?   

  Two objects attract each other gravit8*dpsdr 6+jo aationally 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 gr9gxtvk6vq/ 9e 8 omcj*avity, at (a) 3200 mmxo9 c/k96jev8gv t*q    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Eartk wzjzt5wo, xwx)n)- /h’s center to a point outside the Earth where thegravitational acceleration due tj)w, z tx 5knz/w)-wxoo the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the m4:p zbtnx qd13ass of our Sun packed into a sphere about 10 km in radius. Estimate the surfz td1np4:qx 3bace gravity on this monster.    $\times10^12$

  A typical white-dwarf st1be5nrqom.mvi n 0ix;k.8hg.ar, which once was an average star like our Sun but is nob;o58hmi0e.xign1 nm v .k.r qw in the last stage of its evolution, is the size 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 1:aq9q+k k6j.qevt yy+e 2ga norbiting in the space shuttle. Your friends respond that they thought:2 t +y9ge+q1qye vqk. kn6jaa 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 the corners of a squjyp/x+z 0igi 5are of side 0.60 m. Calculate the magnitude and direction x 5/0yzji+p igof 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 l6+zwjc . s-s2jqa t;bsame side of the Sun. Calcub;+ sq2a -6sjczjl .twlate 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 $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 ny5zprlr .xq9 b a6(f4gravity at the surface of Mars is 0.38 of what it is on Earth, andqyp 4nx.lzr (a5 fb96r 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 period 4fhncxx g87,tcha0u9k:pcj48ur1 dd of the Earth and its distance from the Sun. [Note: Compare your answer kpc 1 ,u:h a4ujcn9ddch xg 8xtf04r78to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in ao(os+ .z;7 ,ph dm ppw.cwshq) stable circular orbit about the Ear7 h.,p w os+hq)wdm(zocsp;.pth at a height of 3600 km.    $\times 10^3$

  The space shuttle releaseg3 jbt6 kpiy7:s a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the 6by: i7tj pkg3release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if occupants are pfgh 8ig-i25eptu6/ bto experience simgpup2i6 8 b-/t5gihfe ulated gravity 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 it takes for a satellite to orbit the Earth in a z+ 6jat+pg /(musy /wfcircular “near-Earth” orbit. A “near-Earth” orbit is one at a hsja+g ym f6+tz/wp(/ueight above the surface of the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched 6,d1 u;6s mer mptl8dlfrom the top of Mt. Everest to be placed in a circular oumdtp8r slme6;6l ,d1 rbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to orbit t h1 j+uql-l e()jobgi;rudk06he Moon at an altitude oq 6kj -jre(ou 0)ug ld1lb+;ihf about 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 pla ;mbt5b,j g*2wmqzp lcf6,( a1l-cjon net. The inner radius of the ring2jbc5f*qp 1cmtj(6m lzl; n, b-og,was 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 diskr,9 i95fhe. qp xob1ameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a persono9 i 5 .phfsxb,91rkeq’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent pdi y2x,y 3(5eklqfjzoj k2rk3-n)7jweight of a 75-kg astronaut 4200 km from the center of the Earth's Moon k 3xj2yq 73l 2p)kjniy,k(zje5rdf -o 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 of *rh jd+se+y,h1ik 2qdtwo stars of equal mass. They are obser y*,id2kq ++jdsheh1r ved 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 scak* daj w,4,hmale read for the weight of a 55-kg woman in an elevator that movesk*,aw 4 jda,mh
(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 suj8r+ 2 h3vs*woxz.3v ii48xfklc q3ph spended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleratix 8z 8h k x cwv*vhrji3.si+3pfo24ql3on (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface1tf m)5 h/ 7b*k2bd;c87b n taw rnboy8btqi;f of a planet with period T , the density (mass/volume) of the planet ioc)5 rt7 2bh8wbqmd;ta7nb 18;ifn /bt k*bfys $\rho=m / V=3 \pi / G T^{2}$ .
(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 perioxtxfh6vu /jc- :p+x 2m1e 18d3nuuwfsd of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very ne u eump11fn8:t36uwx- 2/ c+fxshjvd xar the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acrou (svq9y haj/-ss, orbits the Sun like the planets. Its period is 410 d. What is its mean dish/j9(vua yqs -tance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 .j8baxkv2xd ,20ss kt $\times 10^{9} \mathrm{~km}$ 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 76n6wgei1 -c11rdw m(vb bbbu79 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Esweb 71 wncv1bm gbri(-b9u61d timate 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- jlx ku8 -ce+m2fkii:0/lrcq 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, an lbew8o(9jd;jz tct)8d mean distance for the four largest moons of Jupiter (those discovered by Galileo in 1609). tl 98wztboc) dje;8j(
(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 ps n0 u,w7(b9un 0g vc9tpv-3e nci:rederiod and distance of the Moon. t(-vnens90u:9,re 0 d wg cpvu3c7 bin   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, us5mni- p7r l -myzlwf98ing Keplmlmw5izrp -8- fy9l7ner’s 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 cons: jun9p48n ;v4m3 y.wtqcbxkgte m9.p ists of many fragments (which some space scientists think came from a planet tha.mtt 4gup cen3xkp:.bjyv nmw8994 q ;t once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an ar nm c(.esv(:e rnnsw3;tificial "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 t;n(ns(cns3re mw v.: ehe 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 rle7) 0g;gx sjd5 g(vy0)tnuxhanging 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? Hilnxv )0x;)ggt7r5jg (0 u sedys mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleratio,1gpbxn6;p-u fb pj)mn of gravity be half what it is on t; bpn6gupj, )b1fmpx- he surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin i22/t yq r0x2kazd+ yktn a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual maxtka yr2d2+ z/q 2kt0ysses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of gra.b7t h4h psfa+ ny*m,mvity at the equator is slightly less than it would be if th4yps.h ah+tnf 7,b*mm e 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 wilmm8j0ove 9nz9c k0 7esl a spacecraft traveling directly from the Earth to the Moon experiennec 7oekjz98mm9s0v 0ce 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 in an eles:c,, sxfgw, gvator, it says your mass is 82 kg. What is the acceleration of th:,sf cw,g ,xgse elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rot.*z lp44)gyzo kfb o9tate about its center (like a tubular bicycle tire) (Fig. 5–42). The circz*kloyb) f4 o4 g9t.zple 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 felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43w0 i+lp3y gvi):i:.ydd2s clb ).
(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 planewihda5,+deo+ t etkt)k jsz(ph /6s57t in terms of its radius r, the acceleration due to gravity at its surface and tethop+ aj(,tz) /hk7i dstw d5+ek6s 5he gravitational constant G.

A plumb bob (a mass m hanging on a string) isz t:miv6, 9s:wdl n)i)bz/cay deflected from the vertical by an ait6s:/,9i)d n:)zm ya wz bcvlngle $\theta$ 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 f:.oh3pw zb6gf)( xhkm is banked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at6 3(go.)bhk z fph:xfw what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that oqx7t blnr;9 q4rod72s bjects at the eq 47bn9qd rxr; 2toqsl7uator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant di5zhit q1b(8op stance 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 rouno7c ;cctr*szsz7* xf9ds a curve of radius 235 m. A lamp suspended from the ceiling swings o zf* s xsct79rz*7cco;ut to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, it has been clai00 f xc0xjyca w44r/uwmed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupite04wj/ c4cxuay 0f0r xwr: 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 Tw j dv;2.ncwir1v83fk elescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by .wvid;rwn82k 3j 1cfvmeasuring 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 d)uq c gw)6g-o as it traverses the hill 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 )d )o qu-wgc6gis 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 Systemn3y jlu8.gu/ q (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 fourugj3/ y .nlqu8 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 Rendeq)* h+i6r.k0 gw1ddbt.oj gvizvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of abovd* w okh1jg .g).ir q0tdi+6but 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 satellit* zb ct,1aboi8e in need of repair. You are in a circular orbit of the same radius as the sat8bbcz o ta1i*,ellite (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 odi f0qohls1,gc .8(p bf 3000 years. (a) What is its mean distance from the Sun? q.0l1(dph, 8f bgiosc   
(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 yo ot( -+vviugkqp- 2fq;u could actually "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, like-k u+fipqq-go(;vtv 2 F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the 13xo9mxcso/gMilky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-yea mo9xco /13gxsrs 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 locatofp,txl6n. acfm;cw (w76z l28dvm:fry 7,hted at the corners of a square 0.50 m on each side. Find the magnit7cc 7tf.vorn h,wt6mml62,y:daf fp8x(l ; zwude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the nvbp8pk9f,n 5e :uno (3bl je(t (vwl)Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep se8f 3r(a71 3kf r6decdysve vq-cond hand on your wrist watc f- rr6e e yfc13qv(83avk7ddsh?    $\times 10^{-4}$

  While fishing, you get bored and start to swio,f/g tlq4:zgsm l24d ng a sinker weight around in a circle below you on a 0.25-m piece of fishing l :dg s, lolgmtzq24f4/ine. 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 b*,.)ly 7*d*n:ky89dnyy socuv s gjbin a new highway is designed so that a car travelinb8 lj*yd79ndg) b us,cy*y:nsy*o .v kg 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, th5k 7p 1:.ipmoi-bpwsme Acela, utilizes tilt of the cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more 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 andpb wsi:pk o5. pi-mm71 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.$\approx$    $\times 10^2$