Sometimes people say that water is removed from clothes in a rw; 6jte8;uvh q46o ewspin dryer by centrifugal force throwing the water out e6twev8oj ;u w4r6hq;ward. What is wrong with this statement?

Will the acceleration of a car be the same when / ha:unqt):oe the car travels around a sharp curve at a constant 60 km/h as wh/eqoh :a:u t)nen it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where doe (z.e2zeho pv yxa(0s;s 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 z. ;yxp va2(s 0(ezeohbottom of a hill?

Describe all the forces acting on - .3nelvcpb6o7 t8es pa child riding a horse on a merry-go-round. Which of these forces prceo37p8 bens pt. 6lv-ovides the centripetal acceleration of the child?

A bucket of water can be whirlednviw6h:hd*)y 7 *tgcy in a vertical circle without the water spilling out, even at the top of the circle when thhw*yidn y6*) 7gctv:he bucket is upside down. Explain.

How many “accelerators” do you have in yourbonw,uk h4, c0 car? There are at least three controls in the car which can be used to cause the car to accelerate. What are they? What accelerations do they prodnubh 4 w0,o,kcuce?

A child on a sled comes flying over the crest of a smap i9-hj7hdkc. ll hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normalk.-dc7i9h p jh 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 9*5bwxcxgada:ryj;j 5+stt 5curve at high speed?

Why do airplanes bank wbwknjz9/s n(3hen they turn? How would you compute the banking angle given its b3z 9knws (n/jspeed and radius of the turn?

A girl is whirling a ball on a string aroj:zj fnr7l: 5hn7 o(oyund her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit 7 7zhjr5l:j:ony onf( a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitation/xd wtmlje6f2z13k9 gal force on the Earth? If so, how large a force? Consider ef1j mkw dx36t/lzg2 9an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass (5-c.hiimir g were double what it is, in what ways would the Moon’s orbit be -5 mrcg.iih (idifferent?

Which pulls harder gravitationally, thlykqtwxh04c t8 ft0 09x c6vi3n-8lgge Earth on the Moon, or the Moon on the Earth? Which accelerates more?cthk036 -n4 0xfg0 qlg x9cvwyil8tt8

The Sun's gravitational pull on the Earth is much l0vs58;nk i atharger than the Moon's. Yet the Moon's is mainly responsible for the tides.5;0hinkv at 8s Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator orxzb57gd3w xi2 at the poles? What two effects are at work? Do ix3g d x2w7z5bthey oppose each other?

The gravitational force on the Moon due to the Earth is z-ca ;dkgi(v/only about half the force on;g ckdvi( z/a- the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acc o/hkd b*8tl8w k56k/ lc 6.cq0osx9z cmnm(nkeleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of t8(cqx *6n k co.znkhds 6wblm0lm //ct8ok 59khe Earth?

Would it require less speed to launch a satellite (a) toward thc99 yunk ,0ilse east or (b) toward the west? Consider the Eaknul ic9ys,0 9rth’s rotation direction.

When will your apparent weight be the greatest, as measured by a scale in qxewm6+tm34c a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at constant speed? In which case would your weight be the least? W4qctwm e+3x m6hen 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 oumo01*hyf,g( ,vqr rjmrabx 6h/j.x e8 ter space could be adversely 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 ,j, (hyrm6eb r/* fg x0rmavjqx 1.ho8how 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 ;kwl+f o.ls j+6jv2qx“free fall” or “apparent weightlessness” between sxwk6+2+q oll. f; jsvjteps.

The Earth moves faster in its orbit around the Sun in January than in Julr2avtbq r6v+i7ambp.7wp9p 7y. Is the Earth closer to the Sunw7a9pp7 m2qr a6p.7bvrt ib+v 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 was not known until it 2f pl0if;rpu(1 qn cf9was discovered to have a moon. Explain how this discovery enabled an estim;lfcpn 2rf( uq0f9 p1iate of Pluto’s mass.

  The Sun's gravitational pull on the E zse1ha )1nv;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 side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves)a 1n1e ehvsz; 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 1942 l3uuels:fm80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 acceleroe;kvsve rhjy2+9ke 5o3q ;f,ation of the Earth 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 h,j;e9qo;f3e25v ksovk rye + 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 off5nqy0s9p +o4db w3 cw 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’ofwyb59s+4 pn03q wc ds length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuto*8v*ogp)f t:feow 0.ycfk a/ tle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms o8k : .fpvecgwa/f)*yfto0oo*f g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the accelerqq3mcskb0ijru0l r)g+s) 1k b *il;x0ation of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions c0sr3bq1 jlk0)u;rb +k miqxl gis*)0 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 vertical circe j:cb8brq(l.p57y x xle of radius 72.0 cm , as sho:5erp8x bx7qb.lc yj(wn 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 speed with which a 1050-kg car can rouc/ )ksq6(iyqmb py uc( ;b+3vbnd a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the6/ +qycbyvcm bpqb( )sk3(; iu car?   

  How large must the coefficient of static friction be p s:srg/h53/hqb1fk tbetween the tires and the road if a car is s/fhq1rg:k3 bh/ ps 5tto round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilryv3z7) x; j 8:mbmf.z(m sshcots is designed to rotate a trainee in a horizontal circle of radius 12.0 m .z jz:)yrc8b7xvm s;mm3 h(f s. 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 turntable of variable speayxfb l+ +14(8q tjyfged. When the speed +fyygq (lj4f+b tax8 1of the turntable is slowly increased, the coin remains fixed on the turntable until a rate of 36 rpm is reached and the coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a rf k*hg/jn)5x d+ mtnj1oller coaster be traveling when upside down at the top ofj *kfgdjtnhx1)m/5n + 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) cr7h9tbo c33, *0k ucuyx37ew cdhz,byeee8 (jh osses the rounded top of a hill (radic(hhwocu, juc37e 8etd0x b,ey3 yh9ze bk*73us =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 wheeljw -xa n7g4h3x 7rh:3csv s8cm need to make for the passengers to f3jc7rwa4m7 hnx 8s: vc3g-hx seel “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 -t*ckvmp+w(g4 f1k hz kg is whirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in the rope suppot *-mgpz k1kfv +(h4cwrting 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 centrsd;wh;oa,y08 aa 9wv o1d led2ifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleradyaao892;0 wo l 1vseda;hdw, tion of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a 1wc d.y1hl 8xpcylindrically walled "room." (See Fig. 5-35dx1c1.hp wyl 8.)
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 y9+3 98zp.poc ls bukttabletop, 9+zlc 3.ppyubs o9kt8 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. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , 8rgxb)kizbrev9 -v/r3/csr 2 precisely this time, by not ignoring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitudvx)bz8cbe rrrrg-v9/ /ki 3s2e of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectly banked for a car vqdajb6 vanxbf.7 t,:*; kr f-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 masselm,0 j08oi-n tc jpd/ps $ 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*et) (g,stx dj4/njoivdw+)yyt8h* 4g pk7 ajeuver 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 centripetal components of the net force exe +4zf wskn.qm0rted on the car (by the sqk n0.+f mz4wground) 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 accelerap;y9,g5as a xw-f7tn pehi:9ates uniformly 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 flat, what would the coaw-gyn:f9;p9i tasha,xp e57efficient 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 horizonumb : vlykx6)4 wspr+app,e/h3s* 7 obtal circle of radius 2.90 m . At a particular instant, it p+umky bo/vsblrpp 3,aex 4h*)67: sws acceleration 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 spacecraft 1dzowo fia y7 ,0/-t. wl;l,ejy2,800 km (2 Earth radii) above the Earth’s surface if its mass is 0-,;l aft. ojo,wi y/w7zed ly1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has9cr2ro oe5x 5k a magni5 kx9eo roc52rtude of 12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration dusd dd7g4jb;jl4buh :c2jm1w7e to gravity on the Moon. The Moon's radius is 1.7h1jj4db2 cdbdj: ;m 774ugslw4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 tim9129p e/m doc+utl.p0x ut ljp 1nii9nes that of Earth, but has the same mass. What is the acceleration due to gravity near its su eouppx9t120tp+ jl/9.nn di 1 lc9iumrface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but the same radius2+ vsydpq.o6n- ln,jmtv xc v2v 5-na7. Wy ns+,xdlmn6 -vv. o2- na tjqpv527vchat is g near its surface?   

  Two objects attract each otoatee8(x:4 pm-v8 uuuo yv f*,fob;i9her gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the aq9kx8x)),wu4rrm7 rtjw(: i uo s;ezgcceleration of gravity, at (a) 3200 m rw ,m(ux 7ogqx4t8;ewik su9 :)rzjr)   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Eart;86n q(z;au)i lf ksejh’s center to a point outside the Earth where thegravitational acceleration 6niz(u ef)8qka;s; jl due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphere a s*2 4idp42cpye tr(scbout 10 km in radius. Estimate the suri cep (2t44srpsdc2y* face gravity on this monster.    $\times10^12$

  A typical white-dwarf starm;;ds)jc8rb j9 t m1c-ukb qa j)jsx2+ yj)4uy, which once was an average star like our Sun but is now in the last stage of its e )uqs jmby)c-u;aj9cs1+j2 rdjm8)4 xbky;tj volution, 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 weightle(l./-aq v ci+b-oocvlv 6n :mrss 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 Eartaiqv-nbc+ o(6c r.m /vol- :vlh’s surface in terms of g.   

  Four 9.5-kg spheres are lzz q lk(.;tdi4ocated at the corners of a square of side 0.60 m. Calculate the magnitude and direction of the total. i(kdlq4zz;t 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 upfbjlw+ -n j.d8 on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses ar- j+w.j 8lfnbde $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , 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 rvecpaq6 *1qpsdh ,9)0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of1* q6 ds9prhpaec,v q) Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for mn d(en.fe46xg14li j the period of the Earth and its distancegn4en 1 6djim(.lfe4 x from the Sun. [Note: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving i 245e pbvpgl*dplrtqy594at7n a stable circular orbit about the Earth at a height of 3600 k257rp9pey 45 4l ltpqgdb t*vam.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 6mt;qzqw*0 ja15 zd8pm50 km above the Earth. How fast must thed 18zqz0a tqjwpmm5 ;* shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylpus jpvhnf()us,/*b :indrical spaceship 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 needepnpbss) vf ,uj */hu(:d for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a .m*5x+v45nb2y fv)yt39z s hocly aalsatellite to orbit the Earth in a circular “near-Earth” orbit. A “near-Earth” orbit is one at a height ac al9.y+)hs*yfyt mvz52bl3o 4 nxv5above 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 from the 7 3byj blhu 29cb3j/qytop of Mt. Everest to be placed inbl3 u37 bqh9cyjb jy/2 a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command hhi+18hz/ fxdmodule continued to orbit the Moon at an altitude of about 100 km. Howhd hi8 xfz+/h1 long did it take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planeo ;18a-5.rnr)ailg ns5z epkdt. The inner radius of t e)a- s 5npia8drzgn.k5r 1;lohe 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 di7wyfh*+xpw w .ameter rotates once every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent weight to her real weight (a) atpwwwx7*y .hf + the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the cenv3lz dgfi4s3u r -l86lter of the Earth's Moon in a space vehicle (a) mo3lrzdu4 fis-lgl 836v ving 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 two stars :pkvjdb opb ixo,e+ *mw(a9*jmm :*v8of equal mass. They are observed t,j:pjv(mo o*b* apkd w8embm iv:x*+9o be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg hjlf3 ba1bco4y1ndn)d1ph 5* woman in an elevator that moves 4hc1nd1hay*b n)j3l5 o1fpbd
(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 frhuw-8oy +1jqb om a cord suspended 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 accel wyuo+-jhbq18eration (magnitude and direction)? a =   

Show that if a satellite orbits very near the su, cc0el7t 8kfe.h-9ka k5ibwkpir(i9k- a8dg rface of a planet with period T , the density (mass/volume) 8i,(k5k.7awefkpi 9gctkkb-i da9 lhrc - 8e0of 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 the period of the *s*xy/x hacx 0Moon (27.4 d) to determine the period of an artificial satellite orbiting very near txxx0ayh/* cs *he Earth’s surface.    s

  The asteroid Icarus, though only a f)qv06z9n4s2 sgwpa9 f caux.dew hundred meters across, orbits the Sun like the planets. Its period is 410 d. What isu0 n qw9z9fg624 pdvx)aass.c its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance os -c)lt,flx,p+fu dg +g.hi2gf 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 year5 ;nw/wx*cuz7 f2 shq k/ufxg6s. It comes very close to the surface of the Sun on its clhf fug/u;zw*w76/c52xs k xqnosest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about b.bn+ wm)us2a the center of the Galaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ at a distance of about 3 $\times 10^{4}$ light-years $\left(1 \mathrm{ly}=3 \times 10^{8} \mathrm{~m} / \mathrm{s} \times 3.16 \times 10^{7} \mathrm{~s} / \mathrm{y} \times 1 y\right)$ . What is the period of our orbital motion about the center of the Galaxy? $\approx$   $\times 10^8$

  Table 5–3 gives the mass, period, and mean distance for the four largest moons o u,bf78ue33ndtim0rp5gq1u/ i+ rpkcf Jupiter ium0e8ki1qn7 5cr,+g tf3dbp r/ uu3p(those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the e;h0v3f xtmtd -: img3Earth from the known period and distance of the Moon. m ftd3i-0e: 3;hmxg vt   $\times 10^{24}$

  Determine the mean distance from Jupitc q1qkss aa 5-:n.bx0aer for each of Jupiter’s moons, using Kepler’s third law. Use the distance of qa-aqxs:0s b.k5an 1c Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of many fragments (which socele31 wh. th;q ifk;0me space scientisfk;0;eih3. cwq 1telh ts 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 ar4szew ni .4 fjpyl552itificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Ea445. wiiyzs2nef5 pjlrth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. mp*pb9hm 16gu 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, and the vine is 5.5 m lonpm1b u9pg6h* mg.   

  How far above the Earth’s surface will the acceleration of gravity be haluf5z :n)nqc 31:e+ vv.ibdkfif what it 1 )eub+in.vcqvz 5f d:ni3fk:is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and sm. k e cc4xh*o.uht49hpin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m ltxhcu9ekhh *m. c4.o4ong and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once per day, the apparent accelng5ijj;7fw: bbhcvu1 l2 0te1eration of gravity at the equator is slightly less than it would be ifw 1f1tgb2u0n;c: e ivljh b75j the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft nxj80iy /lr(ltraveling directly from the Earth to the Moon experience zero net lr8nixjy (l/0 force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kgae w,rg9)c qd jcof+l):7 a-yg, but when you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in which direct, d w fc+ly-7qj ec:agroa)g)9ion?     ----待选择----upwartddown 

  A projected space station consists of a circular tube tpkx7 //;p7nywo ,gz8j ekc/dahat 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 te,/an // cd kwx7g8kjo pz7py;he 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 air7 hrj 4)6 e0(qpu opshnj8zi5rcraft in a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of i vzuv06m+2xx hts radius r, the acceleration due to gravity at its surface and the gravitational cv+vx zu hm620xonstant G.

A plumb bob (a mass m hanginq5qknu:y*a 80wdozl /g on a string) is deflected from the vertical by anyz *: u 5anldq0/oqw8k 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 coysmk9l9p9h zkz.h8*p uy2 iy1efficient of static friction is 0k.1pyy zmh8p 99lus zhi9*2k y.30 (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were 4x;4e/o0 o 8 -nsd)52 ypkc ado u08oxpxjtkcwrotating so fast that objects at the equator were appp4 k0s; xod)e2 /j5a4w yduc k8txc 0xonoop-8arently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of cp :1cx8ox ++sl4fk qd8.0 $\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 curf h 1;)i 7z(wgalxlpkx82pb ,fve of radius 235 m. A lamp suspended from the ceiling swings outxff1gib2 ,hl)p lk(xw7z8;p a to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 3202y- (8 qtwqzur)p.zb ,jpj x(x times as massive as the Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of gz )pxq(t-rz.qpy(,x2bwu 8jj '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 Hi; rysu4bvj41*8m no gubble Space Telescope 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). Thejny8 i1;oumv*br4s 4 gy did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed as it traverses the hill and valley s,gw9w0pt c2b oa ;.nw8s0gbvmhown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the .9os0 wpbmwb gcag wv;t02,n8normal 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 (GP)kn+b u/m d:xmS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed evenly around the Earth, with four satellites in each of six orbits, allowing continuous navigational “fixes.” The samm:/n kub+d x)tellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion kmw+fq(::g,mot knc 23zrr9pz o , is meant to orr 9rt, z (:wp+nkz2q3gcoofm :bit the asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a swjae dw(4vq7( atellite in need of repair. You ad4wev7 (wj(aqre 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)-4e g *8schcqd What is its mean distance from the cc-e8q hg* d4sSun?   
(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 val*i0igi+b d 8dcue of G would need to be if you could actually "feel" yourself gravitationally attracted to someone n gciib*8d0 +diear you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center ofbmpke */i 42la the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light bpi/kl2a*4 em-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 of2o; pixalt- 1g a square 0.50 m on each side. Find the magnitude and direipx tg-ao12 ;lction 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 thwaq08hy /sd. re 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 tjk:+l 4k fbb-v/:i fgf,jae/whe tip of the 1.5-cm-long sweep second hand on your wrist b,jfg+/ajki:kfw : 4bf lv/ e-watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight arouas tl 7.gc3 yt))eakt7nd in a circle below you on a 0.25-m piece of fishing line. The weight makes a complete circle every l7at7y ktgcea )t3s).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 i/kjog //n-tm R in a new highway is designed so that a car travelin -/mkitg/no /jg at speed $ v_{0}$ can negotiate the turn safely on glare ice (zero friction). If a car travels too slowly, then it will slip toward the center of the circle. If it travels too fast, then it will slip away from the center of the circle. If the coefficient of static friction increases, a car can stay on the road while traveling at any speed within a range from $v_{\min }$ to $v_{\max }$ . Derive formulas for $ v_{\min }$ and $ v_{\max } $ as functions of $\mu_{s}, v_{0}$ , and R .

  Amtrak’s high speed train, the Acela, utilizes tilt of the c cboyb p2/e n1+hde8.aars when negotiating curves. The angle of tilt is adjusted so that the main b 82.ce+ba poe1nd /hyforce 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 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.$\approx$    $\times 10^2$