Sometimes people say that water is remo g ,dq/9-btg+ orhaz4fsux4; xved from clothes in a spin dryer by centrifu+,zxg u4hof/b 9q tg s4d-;raxgal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travels t5d:tj 4fk q9v0k,xpj around a sharp curve at a constant 60 km/h as when it travels around a gentle curve at the same speed? Expjk0kf q94x,5tt vdj:plain.

Suppose a car moves at constant speed along )1ve-ebh 6munhox2fzn+5 8 lwa hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom o)z ewm hnofu+eh-2lb1x8 5n6vf a hill?

Describe all the forces acting on a child riding aehzg408d vq+cd ye4q * horse on a merry-go-round. Which of these forces provides the centripetal acceleration of q+0 4 dygv*h4zqcede 8the child?

A bucket of water can be whirled in a vertica ckgpw-q 11bpj/q *w2/q.px dol circle without the water spilling out, even at the top of the circle when the bucket is upside down. Explaopk1qw cj2qq1- /gb/*px.pwd in.

How many “accelerators” do you have in your car? There areh6 n o9.0ngwjyub167yce f-hg at least three controls in the car which can be used to cause wn6yu1gjgyb.e- n 6970fhoch the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flyinfueap:tli m76tm)(hg (;5 utbg over the crest of a small hill, as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease using Nua( 6m;(g ftumithe7tl5 :p) bewton’s second law.

Why do bicycle riders lean inward when rounding a7m0z;l: h 8ezrer jc0a curve at high speed?

Why do airplanes bank when they turn? How would you compute the banking -q*d(x:v bkm jangle given its speed and radi*bj-:d mxqv(kus of the turn?

A girl is whirling a ball on a string around qzm z)q/ x(yy6her head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a)xyy q(zm6/zq 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 e,swfr8eypb7 l4* a-gso, how large a force? Conside4b8 s7pg-,l raf*ewyer an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double whayk n57hn8cn +lt it is, in what ways would the Moon’s orbit be differec7kn8n+hy l5 nnt?

Which pulls harder gravitationally, the,7r8povmjnx zy +yu-- Earth on the Moon, or the Moon on the Earth? Which acceleran-vymyu8x7+,o -zpr jtes more?

The Sun's gravitational pull on the Earth is much larger thanej ssia +:)*xn 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 ota:ins j +x*)esher.]

Will an object weigh more at the equator or at the poles? What two effe/g:*dn xr p4bqx w:*y(6 s3plsf+glgscts are at w:xg* w gn f:(qrbss l/4*sxl6dy3+gp pork? Do they oppose each other?

The gravitational fov gzbzbj8. xlem52-e8rce on the Moon due to the Earth is only about half the force 28ezeb-.8gv j x5lmz bon the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Suts2nshunfznruii,,y f63h5e r*n fp 3.1a9 f 9n larger or smaller ttu5 srni,anfnfy2 h9 3he .1*pn 96 uf3ifzsr,han the centripetal acceleration of the Earth?

Would it require less speed to lau-dv5jy vk hya8: cei4-nch a satellite (a) toward the east or (b) toward the w45 vk-aj 8civd: yh-eyest? Consider the Earth’s rotation direction.

When will your apparent weight be thei60e yt*:7tl/f mqzlq greatest, as measured by a scale in a moving elevator: when the elly qt:f6*l izte /0qm7evator (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 periods in outer space m 46yzkmkybt1xlb:*h r4 /ko; 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 om 61br*;ym/xy4 kok:th4 lz bkn the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free fall” or “apparent wwd g wk-(8+dhheightlessness” between stepd(wgdk -+h hw8s.

The Earth moves faster in its orbit aro*a6. dpcdi ndt*3 kr1g3vpm y8und the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Exp3ip*ny3*tc d.p vka8g6 rm1d dlain. [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 was discovered to have a moon. Esa to(xs4po6 -,hb (ul n1h3 wvrp4m,ij+wes6xplain how this discovery enabled an estima hw(v6spw,34roe-mi4l 6uo,thj(nss+ x ba1pte of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger i sz lp1t,feq7 7ckv/rbqcl.cc * vff39y 2o8)than the Moon's. Yet the Moon's is mainly responsible for lc7frk9 cfqvq, f/pvc. yi7scebl* z3)t2o 1 8the 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 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 1y7xyy + jq6g5u980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 agt11i wa/ mjrud-/0qncceleration of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on tdw 1/nimjqg u0a1r-/the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus as it rotates u-ns +24j hl kc goj;8g0ofli;aniformly in a horizontal circle (at arm’s length) of radius 0 0l g2;8ig4+csf jho-aj lo;nk.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Eart3i psc n g.* kkan*f6hcy4 r99k49kydnh's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answks 6r9a.* p9k*ci 4ngnyykh3df9nc k 4er 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 clay on th n0 l3xuxz:gm,e edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diam:0ln3zxgm xu, eter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rate in a v99g) pzxwqes-gc( s:( xbpho0ertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speed is 4h9qsbpgp0(-(e z9)wgx c:x os.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 cam g4vwkz0h : jvxn/2;an round a turn of radius 77 m on a flat road if the coefficient of stwz2m;nv :40/ axkjhgvatic 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 f9n7 7rzvl g 9w*qlvz*kriction be between the tires and the road if a car i zwgn7l7rk qlv*v*z99s to round a level curve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pilots is designed to rog 84,xs;o4d,8mw l7 afipurr ftate a trainee in a horizontal circle of radius 12.0 g 8lf,r;fo7swdx m44pur8, aim . 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 k2bvtxh: :b5f2y8p qxcm from the axis of a rotating 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 reached and the coin slides off. What is the coefficientp x52qhv2xb :8bf:ykt of static friction between the coin and the turntable?   

  At what minimum speed must y818ts yxffr;a5 lh-ua roller coaster be traveling when upside down at ther 8 y5lh;fuf ysa1xt8- 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 (including the drs (j -((yn5x jm;/wpnprjkqd zb, 9t2qv1 vka;iver) crosses the rounded top of a hill (radius(qabvy2(zx/q(j9nd njtr1- ,; pkj vk;m 5 swp =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-diam,jr. -zq0aulceter Ferris wheel need to make for the passengers to feel “wz, a .lcjr-q0ueightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At 7meyk, a,yksh ( 6a+pkthe lowest point of its motion the tension in the rope sk(+e,ap 6 sm y7hkky,aupporting 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 ro1b0i gvw w:-/s,c- n dhtqw/wntate if a particle 9.00 cm from the axis of rotation is to experience an acceleration of wicdbgt0w qn:, 1nh-w/w-/vs115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival oqqns97 /, vkhu m*,s:med.sp, people are rotated in a cylindrically walled "room u7pv/9qk so:e*dsmn qh,,m.s." (See Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a ci 3stnc)wuj 5w5v hgdm39fz), arcle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord cog9wnvfjs)du5wah5,3 t) c3mz nnected 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 ignoring tq.x5 4bioojs7 he weight of the ball which revolves on a string 0.600 m long. In partbq. sj 5x4io7oicular, 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 cariv8 , 4, ku(+ai urgzt-2zqwva 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 masse iqhj ,3pnukxfxx:78 +s $ 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 maneuvds uwn9(waw z3 +jf96,sl:sybie3r6k er 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 force3f.jmlp v,mq 6 exerted on the fv63j, qmplm. car (by the ground) in Example 5-8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates uniformly from r-nhk-+ ug k:nthe pit area, going from+ g:k-n-n ruhk 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 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 (n++vdmw64ea g q k-xsk. zcn:radius 2.90 m . At a particular instant, its sze+( dwnkn6xa.+kmv c4: q-gacceleration 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 spacecraftgc5 gf .w,x,zgl8olli6dji-+aq bw+2 12,800 km (2 Earth radii) above the Earth’s surface if ji-+zd,olww8 ,gg +qb5 x ag ci2l.6flits mass is 1350 kg.   

  At the surface of a cert 45f l2sq)j g0jsd7z 6mstd4kkain planet, the gravitational acceleration g has a magnitude of 5qmdds0j skk 64l z4s2g7f j)t12 m/s$^2$ A 21.0-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet   
(b) the weight of the brass ball on the Earth and on the planet? $W_{Earth}$   $W_{planet}$  

  Calculate the acceleration due to gravity on the Moon. The Moon's radius f: k1h.dez1g kis 1.71kefd.hk:1z g4 $\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 ofz*1:zd(jovsgrv tr l 9v2s;(q Earth, but has the same mass. Wh2jqd:r1;vg (lz v9(zrsto*vsat is the acceleration due to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of E((vab dz2 m/pvp3wy:carth, but the same radius. What is g near its bdv w3za2/ (vpmyp:(csurface?   

  Two objects attract each other graviteh+9h b-2:c a5r gjsfjop3m)kationally 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 accelerationkwd ja r et0oe2.mqpt 4)-8o;j of gravity, at (a) 3200 m e-ojt).oepmtk4j; r8 qd 2w0a   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance f2sdgdy cg -l.7ena n5yuq ed1ws95.f(rom the Earth’s center to a point outside the Earth where thegravitational acceleration due to g( uy.y wcenf.7 ndsqdla9s 5d-21g 5ethe 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 zs 1mj26jtz:xinto a sphere abouszjjz1 2xm:t6t 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but isb -imqs7 s+f--wal7 wo ug1x;k now in the last stw;b-fso+wu gm7--akl7 isq x1age 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 a- 2: whfnzd4sb z1;kdhstronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up ther2 1ds4hzd-h; :znbkwfe. 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 square of side 0.60 m. Clg ji (*85mjevfd1z p0alculat g ivp*8 dm15fl(0jzeje the magnitude and direction of the total gravitational force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred years most of the planets line up on the same side of the Sy y.;z :,gin,hiqhb swx ,span86k8o*un. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, asshna6ybk8wh:,qnp8x , os;zygi,.s *iuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surfaces)m abt gp2wq99q7 4w2zi eg2m of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass 9zq7 ew9mgwg 2224i atbm)qspof Mars.    $\times 10^{23}$

  Determine the mass of the Sun using tt 8obrt6b ok0)he known value for the period of the Earth and its distance from the Sun. [Noteb8k6boor) 0t t: Compare your answer to that obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in r w5y , 9tfbfvto7xa9-a stable circular orbit about the Earth at a height of xyto9ft7,9v- rb wfa53600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular pgsr:w pf-fx 4,p0b9 eorbit 650 km above the Earth. How fast must the shuttle be moving (relative t:pgx ef, sp-b9 fp0r4wo Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical bq4+cnt-3n mias:cgs u8v94u 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 needed for one revolution. (See Question 21, Fig4tim4u cg+u9sq : ns3a8n-bv c 5–32.)   

  Determine the time it takes1 wqca 3, umt(gz/2ryt for a satellite to orbit the Earth in a circular “near-/c (gr2u za 1,ttmwqy3Earth” orbit. A “near-Earth” orbit is one at a height 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 satell v(njeftg4c 9a2v d+/fite have to be launched from the top of Mt. Everest to be plvnda jc/ve24+g(t9f f aced in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module contin3jw jw5t;l.a4fqro 4h ued to orbit the Moon at an altitudewq4fhta oj ;45rw.3lj of about 100 km. How long did it take to go around the Moon once?    s

  The rings of Saturn are composed onc+.d f2yhnq.d2kn6l24:g u elw t8egf chunks of ice that orbit the planet. The inner radie2 gdnc2t2g.n4h : n. uyw+k8lq6l defus of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


$T_{\text {irner }} $ =   
$T_{\text {outer }} $ =   

  A Ferris wheel 24.0 m in diaeqwy au;(a i-5meter rotates once every 15.5 s (see Fig. 5–9). What is the rati wuqay5(aie; -o of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from t qdb6xy3w)o( 7gom8e the center of the Earth's Moon in a space vehicle (a) moving at constant 8tyqwxde 6 o7gm)3(obvelocity,     ----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. Thee xx)rdq-z3cmf5ptp7+ )4wzyy are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. dp4e 7cw+y5 zm3tr-)xxp) qzfWhat is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman - t*zo*t5iidv in an elevator that movest- 5ivo **dtiz
(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 xpbmuel7kdb- x5- + s5a 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 acbd 5 u-5 xmlexsp7-+bkceleration (magnitude and direction)? a =   

Show that if a satellite orbits f4t)qdjifmtp n0 e /z/ vjh593very near the surface of a planet with period T , the density (mass/volu05vn4/ p3 /j fe)dti mtz9fhjqme) of 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 Moon (27.4 d) to determine the period of( m7d czs,3idv an artificial satellite orbii, m z(dsd7cv3ting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters acrossaz.h f 5o:+ m.qhj3t kzx:pg6f, orbits the Sun like the planets. Its peri+ g aoptqhm 6 .:z:f5.zjf3hkxod is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average -fzcr 1lgjhcc+qv00x+m+ 75tdou ba8distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It comes very )7+hyj7ieh2i (qoocp-qd u *rclose 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 isj hy+u7o r7(2p-ieq)dcqio h* nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the cuo xohsxg/i a- y1cx+:w.nx1x, lg7y2enter 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 dc/ 5qofn u4(dfistance for the four largest moons of Jupiter (those d n4o qfu/f5c(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 Earth from t(/z hi nyw -*hgeoe0rojmh*/8he known period and distance of the Moon. rzohemj-y /hn 8e0(iow*g /h *   $\times 10^{24}$

  Determine the mean distance from n54ugwoy+5 qshbh+cerb54z) Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the peri w s+z b+o4u5qbhe5n4)rcgy h5ods 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 mav ty,zwo,9w0 psd/g ;fny fragments (which some space scientists think cap9wvyg0,;zo f /sdw t,me 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 aul ss-+osaed-r1 (dm4rtificial "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 Earth-sr1ss udl e(m4+- oda days?   

  Tarzan plans to cross a gorge by swinging in an arc 1t-tyzi(p-df cq m)4pfrom a hanging 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? His mass p(tdi - 41)ftzp -cqymis 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration of gravity be halwdwi332w p ,n zie1dj o4pqr1;f what it is onnwj1w,e w1 34zdpdqi3p r ;i2o the surface?    $\times 10^6$

  On an ice rink, two skaters of1g- tu/n+v2,mq5czkd9yk mx k equal mass grab hands and spin in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their z-k/x1 +nykdut2,vgm5 cq9mkindividual 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 accelyb kta .slx:4iqj;q- w2 h(l ezz--yn+eration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. Whak y4q2 yx+.-- twjsial-qlzze :(;hbn t fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly /s0 cfokvms;(from the Earth to the Moon experience zero net force because the v;smkos( f0/cEarth 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 sg 0h 5:g1rqgcy655hk*(gi5x qojpcegi;s. p an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in whicg: epgch;5sr5s q(ggjp5 hg1yioxq 05c. k 6*ih direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tub eox6k 3zk5ii1e that 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) iekz 65kixi3o1s to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig. 5–43). 8jd usu.p 00w6x 2r1oa vb/b:s) yenlx
(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, tht(*2ge z8g bqie acceleration due to gravity at its su8* teigbqz2g( rface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by 0bo/0i*pyei h an angle /b *y0epio0hi$\theta$ 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 b7+ndsx kx o2+z 8igvf8anked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car +zi7kns82foxg8 dxv+safely handle the curve?

  How long would a day be if the Earth were rotating so fast that object1,j5fj50bg;g i3cq) rbheng ts at the equator were apparently 505)ngtbfqgic1hber ,g;jj 3 weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8.l8x3ppl0(7t wk1jqin+g3d p)jt q ql 70 $\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 ofld2rob36t - pf radius 235 m. A lamp suspended from the ceiling swings out to an af-tp l3b 62ordngle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mas1ni:8o a ty3/sic -iilsive 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 g 's a person would experience at the equator of such a planet. Use the foll:ti8 inli3as /oyi c-1owing 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 Hu /u ,7eadfk(*nx+x xpubble 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 x/d(u p,x*an +kx7 uefescapes). They did this by measuring the speed of gas clouds orbiting the core to be 780 $\mathrm{~km} / \mathrm{s}$ at a distance of 60 lightyears $ \left(5.7 \times 10^{17} \mathrm{~m}\right)$ from the core. Deduce the mass of the core, and compare it to the mass of our Sun. v =    $\times 10^{39}$solar masses =    $\times 10^9$

A car maintains a constant speed aso9t 29( rywlmk it traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a rr km(l29tw9oyadius 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? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satel8wsuqu5-m:5n ) xgs xalites orbiting the Earth. Using “triaamu)xqwxs:558 su g -nngulation” 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 satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]. (a) Determine the speed of each satellite.    $\times 10^3$
(b) Determine the period of each satellite. =    hours

  The Near Earth Asteroid Rendezvous (NEAR), after traveling 2.1 billion km, is me mrnhl1-qm3/ jant to orbit the asteroid Eros at a height of hmnmjq1l/ 3r-about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellite in need of rep gnba +g :yqqpwh12.nfi 949h+ jks8kiair. You are in a circular orbitkk js+afqii+g n:bh 9y4qg1npw9 2.h8 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) What is its mean dists o)n; kqqo)2sance from t osq;2sq on))khe Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" yozg9..wtzhcj *9 m9av aurself gravitationally attracted to someone near you. Make zwaj mv.*9.zt9 agc9hreasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates arounddt w5qoq 14o f:flfs ed5k()7dq4c ,dr the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the ce:51d cse fd7dwq)t(fo dr4q,5o qlk 4fnter $ \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 ; xy+cn+hrsa )the corners of a square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of ty;hnsr x+)c +ahe bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbnpg+/7b(4 o3halt j pdwt,*s hits 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(04 qmenu *d5rxe)yty by the tip of the 1.5-cm-long sweep second hand on un5x04e re*dty(my )q your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and stajp:u50zhe p,)+n 81g yqw)pz6uub drcrt to swing a sinker weight around in a circlhp6w:u dyzz gjuceur p5,+nb ) 18)0qpe below you on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is dem5 c3hlug7:lzx8 97j)u onwr esigned so that a car traveling aonrj g:z 9 u83l)x7c e7mlu5hwt 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 Acel 9qu0mw.ry7w t,/ 95cy3cokrj*tyhrj a, 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 forceo9 ,5.* cjrcyk3uw q/tyty70 9mhrrwj. 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.$\approx$    $\times 10^2$