Sometimes people say that water is removedpck0(;) t wc3 /zmihfr from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this state) zic c(;rwpk03hm/tfment?

Will the acceleration of a car be the same when the car travels ar*1e47fiszu / rwol0 usound a sharp curve at a con/4 ui z sf*rs0o7uw1lestant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where do z1 gzi85ym-np )sxu* u/5xakdojf32jes the car exert the greatest and least forces on the road: (a) at the top of njau* k/ xy8poj5sz31 f2 i-zm dg5)uxa hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a horse on a mr4-u1xtoxt 6 xyyy) 8yerry-go-round. Which of these xur81oxt 6ytyy x-4)yforces provides the centripetal acceleration of the child?

A bucket of water can be whirled in a vertical circle without the6pl9 hre a6u7v water spilling out, even at the top of the circle when the buck6 pv7l 9ea6urhet is upside down. Explain.

How many “accelerators” do you have in your car? There a9 -)l/ v:3 snqyb9s gait fh,bq(e:nbmre at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do theybb :tvs g3s(a:,ly n-fb )e9hi mn9q/q produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fc4uv*3jdo:7 zl d ft2x (+phwjig. 5–31. His sled does not leave the ground (he does not achieve “air”), but heu7 2tjwxpv l+(d34cjf z:d *oh 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 curve at high speedy pv8 rcs04i +oco* mt)vuqn5;q6zik+?

Why do airplanes bank when they turn? How would you compute the bankintmjq6vjs091a v7hx ojrw*mh,h*; wq+ g angle given its speed and radius of x*q m,jjho9a*v71s t vqwm 6hrw;jh+0the turn?

A girl is whirling a ball on a string-it7t,mt,.t c;2djy j azcdl7 around her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the other side of the yard. When should cytjt mld;t7z2. j d,a tc-7,ishe let go of the string?

Does an apple exert a gravitational force on the Eart cjcp+ p:5rul(h? If so, how large a force? Consider an appl(jpc 5u+rpl :ce
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Moon’s odtkx5x;lmut- hpl3 8-rbit be differelxu-5 kxpm8; l ht-td3nt?

Which pulls harder gravitationally, the Earth on the Moon, or the s1m :( +lwhg1x3gvlfwkk6na 0 Moon on the Earth? Which aslakw 13m0l 6 +( wgx1h:vkgnfccelerates more?

The Sun's gravitational pull on the Earth is much larger tha u43ue(r9*h:/tzam9 kv/voqjuzoar ( n the Moon's. Yet the Moon's is mainly respo9rt o(4uer /jhv* z3 kqmvu9o( az:au/nsible for 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 equator1;(zbbvnrnzj5 :votp9 -nci 8k3n -4h.jn gq q or at the poles? What two effects are at work? Do they oppose eachoqgbn( n4jvc5.p:-qh1-z zt nbnr kivj8n; 39 other?

The gravitational force on the Moon due to tv)z0) ek gc)xlhe Earth is only about half the force on the Moon due to the Sun. Why isn’t the Moon pu) x)cl v)0gezklled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Sun larger f 1p8mlc53v 4gmxm:p way0r1z or smaller than the centripetal acceleraz4prm1 5gwp:fm ma03c x18yvltion of the Earth?

Would it require less speed to launch a satellite (a) towab,8 8u0vk lyly igw:i,rd the east or (b) toward the west? Consider the Earth’s rotation diregyi0k,wlvyl, b88u: i ction.

When will your apparent weight be the greatesqnphufi8576 wt, as measured by a scale in a moving elevator: w6hn5 87 ifuqpwhen the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods3 u2h1a9wk seh in outer space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship3e wk1suhh9 2a 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 experiences “free fallx 0,k h6boxp.el21ysc5ux ui0” or “apparent weightlessness” between ste5c, sxxhb k ui1y20.e0ouxl6pps.

The Earth moves faster in its orbit around the Sun in January than in July uz+iv464he;5m) poka: j(mgzevdaq6 . Is the Earth clo:v mju kmz6;z va diq46p+5(hg e)ea4oser 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 the plane of its orbit.]

The mass of Pluto wasg9tzi /aeag-uqv* p4. not known until it was discovered to have a moon. Explain how tpt9qg*vi -e4u./az g ahis discovery enabled an estimate of Pluto’s mass.

  The Sun's gravitational pulnkai my:qzo/*t2aprs)ot(x( r4 ; bc0l 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 in gravitational pull from one sido am;tt cr(*b i r q)04a/yk(sn:2zpoxe 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 19bz,uw8 h*x )jgpo;b7bj7 h ,qu80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Earty+v p4 hgy)x a.eu:9-rzf; hlch in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radil-h94vzg c:exfru +p)y.;yahus 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 exertq:v0)f)whie zx*yi x-8 zrk w7ed on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate zqf:)-h08ewwk *zi x yvx)7ir the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from acd0g;a+ zm t4x.yn c.the Earth's surface, and circles the Earth about once evta+.c.na0 mzy;c4 xdg ery 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a s 8 td,d+fjrd-rix njna kd/.2(peck of clay on the edge of a potter’s wheel turning at 45 rpm (revolufi xdk,.da drj/n+n2 r(8td- jtions 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 b:iaspfv w09 p hi*,0mvertical circle of radius 72.0asp0im 9:p vhb,* i0fw cm , as shown in Fig. 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 sar l;meepgagkir h4 97: zt0*)peed with which a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between t7 azret0k9ie) rhg4pmgl* :;a ires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction b 8quju20gx7j i-fu/lbe between the tires and the road if a car is to round a lu uu7 g8lqbf2i /-xjj0evel curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter f ht9vfg(hl/ (pilots is designed to rotate a trainee in a horizontal circle o f9(fhgt lv(h/f radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating tura3f yi(,npa+m-p 6 qhuntable of variable speed. When the speed of the turntable is slowly increased, the coin remains fipu(qa6y ia+pnh -3mf, xed 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 g 3 - kzkrv riosq5g15ds*9 zc7q.h.lwroller coaster be traveling when upside down at the top of a ci5 ..kgsg-kz r59q*3r h1qovd s7 zcliwrcle
(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) crosse u*ymx/*ikrh0 s the rounded top of a hill (radius kxu rmy /ih*0*=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-dit:;)pv sos d/bameter Ferris wheel need to make for the passengers to feel “weightless” at the topmob/v :)osp ;stdst point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical ryz1mk9 adpd,6utq*: circle of radius 1.10 m. At the lowest point of its tz*9dup d a,r1yqm 6k:motion the 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 rotate if a particle 9.00 cm from the axis o))zov 39e cewif rotation is to expezcv)wi3) e9 oerience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, peopfo8or.ttwk-n y 6e)- ule are rotated in a cylindrically walled "room." (See Fig. 5-35f-o wye.nu t tk-o68)r.)
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 ) -9vef q0e.)s hciz5o pis rotated in a circle on a frictionless air-hockey tabletop, and is held vp z-)se0f5ciq e 9oh.in this orbit by a light 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 timesk1h (n 7 7df*wkzos0l, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of z1* sfs 7n(lkowkd h70 $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 radiu/r n;6em s3qzda h01ees of 88 m is perfectly 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 5y6lk :xbl * w vb-li6htf3me,bvc,t9$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertically at mmz0jn,:dks 9 310 $\mathrm{~m} / \mathrm{s}$ . 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 components of the net force exermb0c5r f3ixe/ted on the car (by the ground) in Example 5-8 wh5f/0e im rbcx3en 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, goingda8s- tvvz;v ;z.okg- 9bijj9 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 accelerati9b kiv-jv s zt8gov9d.;-j;azon. 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 radv n*s(o -qbm0aius 2.90 m . At a particular instant, its acceleration nmv0bqs *-(oa is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’s gravity on a spa f))bh/v mcp7tg-28 jo edj ccse*9o(jcecraft 12,800 km (2 Earth radii) above the Earth’s surface eeg2/(jc 9pv)o ob cjmc 8t*f-jdh)s7if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitationu m3g3w-w2lie al acceleration g has a magnitude u 33-eglmw2iwof 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 th 8b7gy(2wq2ykzf2p js e Moon. The Moon's radius is 1.7zsyfy( pgk b8w2j72 2q4 $\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, bfejmqe58gdgdbc.+ 1 .ut has the same mass. What is the acceleration due to gravity neare1 fgb8 g.d dcq.jm5+e its surface?   

  A hypothetical planet has a mass 1.66 times0dcac/) k3zlt0 tivfx mo +mkxg)*- s3 that of Earth, but the same radius. What is g near kckx0xlga-tv )/3mi)*oz0dsc m tf3 +its surface?   

  Two objects attract each other gravitationally with a forcub66n(js 2v76kx ygi 6v5aqhue 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 ac h 7 24bjyvt8vtlmr.++tla j5yceleration of gravity, at (a) 3200 m ++vj yjllbhyt4t2 t7var m85.   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside the Earth wher ija1q249 l y qrof5g3ojqh82te thegravitational acceler fq8l2ro24o 1j qygj39qi5h atation due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has fivepqs e2 2sw*ox. times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monsteosew 2*q .s2pxr.    $\times10^12$

  A typical white-dwarf star, which once was an average sta*bs9d*pulx7)wc (,trtmzg7 cr like our Sun but is now in the last stage of9 mgt7bdwscl,** uxzp 7t)r(c 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 wearaxz5t4bf7 r4nnmh.uu 1 5l; ightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earazr 154l xn.n fu;7bh4rtm a5uth’s surface in terms of g.   

  Four 9.5-kg spheres are lq1 ;)uchre1jx edr r5rxq +5f.ocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere by q x r+fe151x.eqjhd5)r;r uc rthe other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of l(q*6.vt nze /mdei m ::z-)h:igexrmthe planets line up on the same side of the Sun. Calculate the total force on the Earth due to (.ie6zxm :-n/g hze*ltv) red:i:mm q 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 gravity m)a tve:b4y+ ,-bgyfjat the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the masg)m:4+eya-b j tfyv,bs of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known vzep6/i /kzua 1alue for the period of the Earth and its distance from the Sun. [Note: Compare you1 6k/ua zpe/izr answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in ad suidmb, 9f15;do() :amfew m stable circular orbit about the Eartdedm1fb)w ( uf;:od m95,ma sih at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into avm,fr-dz /e f4 circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when fde-r/z4vm f ,the release occurs?    $\times 10^3$

  At what rate must a cylindrical+mi/vj-.vdo f spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give jo d/vimv+. f-your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellt+ hda h a90cvdfwn8/k9.uv84g: owulite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth which is ver4ulv /hcvfwahogddu .90 t8w+8 a nk:9y 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 rwd*21ryx tc)x q/7ula satellite have to be launched from the top of Mt. /uw7rx) t* 21r ylxdcqEverest to be placed in a circular orbit around the Earth?   

  During an Apollo lunav tb8r nw0zogo3g7f72r landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it tagonr3t fbz802gw7v 7oke to go around the Moon once?    s

  The rings of Saturn are cos- l20 zh +h.;vb9(lfgyfpi ezmposed of chunks of ice that orbit the planet. The inner radius of the rings is 73,00sz-l gh9yz(b+ fip 0fl;h.ve2 0 $\mathrm{~km}$ , 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 diameteirmvr*),vv :fr rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to hv v:vm,r f)ir*er real 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 the center ofd nbgr p5fm+sdm7phj1n:) h., the Earth's Moon in a space vehicle (a) moving at constant velocity, hn srbpm+d5gd7,1fhjm): np .    ----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 areab q/6nz+) 1yo0khy jcn4drq 1 observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point m1khannoj06rb/1qdyq)+ cz y4idway 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 iny:b.ul * ep5vb an elevator that moves l:b5bv y*eu.p
(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 susp fgy)v( mkial 5o3w79sended from the ceiling of an elevator. The cord can withstandyg(siw av 7o f3l)mk95 a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface nl7:d) y z5h) wpfelil6trs3)of a planet with period T , the density (mass/volume) of pe ):6ir s7h3flly5tnz )lw)dthe planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period : tuwd7smao) a.*m:fv of the Moon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s surfaced a.f vm w:m)7t*u:aos.    s

  The asteroid Icarus, though only a few hundred meters across, o qv-c 0 w(v,xq6iw0 p;fedogz0rbits the Sun like the planets. Its period is ed-;voq vwzc0p0f(i 0wq g6x,410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distanck 2sk cmk,-mt4e 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 on;/ pfn)au60zbe-eoxpi r)o .6 ttdy ;oce every 76 years. It comes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the );e d-ubefo.oz)p6/in 6ry;o0tptax nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the centq w s-g(amx5k onp(l0ly wxs.gbk :(*;er of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean dismror , v9mowbpo .q0fqp2x):0tance for the four largest moons of Jupiter (those o)xmq.,9: or 2vp 0wof0brqpmdiscovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and di64v2wakq8cd zzj 2r f9stance of the Moon. wvk29 rzfda 8246z cjq   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using ,cuec49ynl*gsfvu40)fmj wsv k;a. yu35k 0cKepler’s third law. Use the distance of Io and the pecmkc,yl j 54 sv.ucnw03ga )fu4ykv*fu0 ;es9riods 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 of many fragments (xn2hic-y;i:l7pw t 55ku2stm which some space 25ksiw2t-xtl7c n; uh5i ym:pscientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planetzm p0f we2.,uq" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the rin,f w2me.qz0pu g 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 v5lr+xsrvdul zfs1 6-qzl6,;r ine (Fig. 5–41). If his arms are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, aud1 lq xz,-5 rrs ;l6vr+l6zfsnd the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be half whbf 5xez 547uqiat it is on the surfqf7e 5 x4ib5zuace?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab h u6 kktha tppyv3//8g:ands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulli h/68up/ p:kyv3ttakgng on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent acceleration of grako7, sg52tlw (i xb2uhvity at the equator is slightly less than isx ih k2 (t,wuol72gb5t 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 spacecr4qj-k;3p g) t-pb *g uavm:qvtaft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon- 4q*gt;b)3 jvtkppa gv-umq : pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand vsyk1elacmchf6 z-fy72lgu((d f, 7-on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which-skl u6zcv7yf,d( mc1gl2(e f 7hfy-a direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube thaaekyjo,ttp:(g 2 )loe (g/:muv-*za tt will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) pt) :u,t e :v*(-ja2y/lkeg(gtza oomis to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertgj e0qw,h ny5+tpja60ical 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 radius r, the accigx rorw0yhj- *k 2p8d-0lq i3eleration due to gravioih gw*r pi lj-38 20d0-xyrqkty at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical bycw.m l1):urq0* pku who0 to0p ato*1k0o0ruc.luph:pw m w 0q)n angle $\theta$ 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 If the coeffjwg1hu-w9 m(d icient of static friction is 0.30 (wet pavement), at what -dg(1hjwwum 9 range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating sovw6f5x/z)sl9f w3dq c fast that objects at the equator were apparzw qvl d9)6w3f /sfx5cently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distancz0on;*n -kgt/olh us) e 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 curve of radiu8h4o8ptquqq ys/8rihl -( w *hs 235 m. A lamp suspended from the ceiling swings qhu l *q/88th8i sq-opy4( rwhout to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massi rl2+0;/ m/xil gifdbkve as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the sizf0lbl+2xm dg ki/ ;r/ie 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 exo,hch:s ci93(:oo erstremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by9ci:roe (o :c os,h3sh 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 speav8m(hb l8 ,tmc3p5dhchpl mz o3/ )(ned 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 is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightem3z(8b8cnamh, 5hp p3) m(/ hctvllodst? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning Sycb5h16ghxju 5 t-)eyr7: um s:g7c knbstem (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.”nyhgt uhc: r75:u5k cjeb1gxm- 7sb6) 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 5rilq vr3 d(r5;5o2ejwh/hbspt38e o(NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of about 15 km . Eros is hsr5hr3 je535 8lpb (ei/ v tr;o2dwqoroughly 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 /fqd 2f-9nbu j 7.vubqthe space shuttle pursuing a satellite in need of repair. You a9 uu7/.-q nvjfbfq2bdre in a circular orbit of the same radius 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 3000 years. (a) Wtwextxw-.o3 r2o *i6that is its mean distance from the Sunxw.oot 6-t2i3*t rwex ?   
(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 ttpsgql 63 h6o0o be if you could actually "feel" yourself gravitationallptl s6306oghq y attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of lo./+3qbpw6cxlc 5j f the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cente 6o fp3wqlx/bcj +5c.lr $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m o /m 6y*9rfccidycyeb9 1-c ux;n each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint ob9cy i/xc- ;y9d*y1mc er c6uff the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5u qv,2twnws:ltl(/si l, u 6q6500 kg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep second ur0sl6ao kky-(8 f 7rkhand on your wrist wrk6a kf7oky(u8 r -ls0atch?    $\times 10^{-4}$

  While fishing, you get bored and e4 ry2thq477k 4y urtcstart to swing a sinker weight around in a circle below you on a 0.25-m piece of fishing line. The weight make yrt7 reh qk4t424uy7cs 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 radiusza .,ziv* cw1i R in a new highway is designed so that a car traveling at wa*cz.,z v1iispeed $ 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 gygsl2fs -af 5t( *m6ytt,gw* 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 acceleratiofm6f* ,2 sgy*5ts-( ttylwa ggn, 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 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.$\approx$    $\times 10^2$