Sometimes people say that water is removed from clothes in a spi)(7uk: ;dacrimfk,at n dryer by centrit,: ;ukia c(rka7mfd)fugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car trave24;i mg37uw5dmf 7/5ukryg /mf(ns ibzz pf6 bls around a sharp curve at a constant 60 km/h as when it travels around a gent rb3y26f4 ids/ m/f;k7mubifz pg(g7zn 5uw5mle curve at the same speed? Explain.

Suppose a car moves at constacmxxed1;d7wy ,bz.96tu, y yant speed along a hilly road. Where does the car exert the greatest and least forces on the romd wt6bx ,,u yc7;1 e.ydza9yxad: (a) at the top of a 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 chicdtsl s.r3h;xf ( (o6ild riding a horse on a merry-go-round. Which of these forces provides the centripetal accelef x3d (rch;isl.to s6(ration of the child?

A bucket of water can be whirled in a vertic/ chfa2 e9q n,cs*6gpzbt:+vial circle without the water spilling out, even at the top of the circle when the bucket is upside dohs :,ebpznivc /a*f 2q9+tc6gwn. Explain.

How many “acceleratoeb*xnf2cs c 6n0ic zs.k0d9)grs” do you have in your car? There are at least three controls in the car which can be used to cause the car to accelerate. What are02 )i znd6sgbxsn9ec*.c 0fkc they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hill, as shown in Fi48;uoshbp-t b g. 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 Newton’s secon 4 ;hupsbo8tb-d law.

Why do bicycle riders lean inward when j-q wyjh3s.8jrounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute tl a ;sgzczq3(y0x1kg6he banking angle given its speed andcs3 6 ky0aqx;gzz1l(g radius of the turn?

A girl is whirling a ball on a s5e qs,w+ 1mg6w a.bc9e6nsmxntring around her head in a horizontal plane. She wants to let gomb 9nw s656 cseegqw.mx1n+,a at precisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational forc ip2 eqt :z.jq482pvdke on the Earth? If so, how large a force? Consider an a tj:peqkv8qz.p4 i 2d2pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways woulqgrkvzj h e*, i5vfg17d:hd84 d the Moon’s orbit be differ4*r jq7dv8i5kgzhe f v :h1g,dent?

Which pulls harder gravitationally, the Earth on the Moon, or thee6hh9wim ):u g Moon on the Earth? Which accelerates moew:6ghh9umi ) re?

The Sun's gravitational pull oj)xndy7+as/kh0 ll( s/ 2cxpfn 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/ x0cflajk)s2hy7/s+dxpl ( n from one side of the Earth to the other.]

Will an object weigh more at the equator,o baet1fu19 p or at the poles? What two effects are at work? Do theyae fot9,u 1bp1 oppose each other?

The gravitational force on the Moon due tj jc)op6-o9bu4klou0 o the Earth is only about half the force on the Moon due to the Sun. Why isn’t thpoo uo-6ub9ljj4 k)0 ce Moon pulled away from the Earth?

Is the centripetal acceleration of M7e4 y xwlm+wh)ars in its orbit around the Sun larger or smaller than the centyxl)mw +7w4 heripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the moo/s2 ,d k;4tea gqv1d-j de+east or (b) toward the west? Consider the Earth’s rotation tojo-q dv ;s4d1ageme,dk+ /2direction.

When will your appareqyov0f wfz5c;+) clz(nt weight be the greatest, as measured by a scale in a moving elevator: when the elevator (a) accelerates downward, (b) accelerates upward, (c) is in free fall, (d) moves upward at qw fclczvyz)f(;o+05constant speed? In which case would your weight be the least? When would it be the same as when you are on the ground?

What keeps a satellite up in its orbit around theEarth?

Astronauts who spend long periods in outer space could be adversely affected bw1pgor )u 6ag0y weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on thep) 0wg1au 6ogr 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 experiencepln:k0sk w b( ax5.(ozs “free fall” or “apparent weightlessness” betweenk o( klw(p.0sab n:5zx steps.

The Earth moves faster in its orbit ar w +s0mrmich7i9 ,wh4gound the Sun in January than in July. Is the Earth closer to the Sun in January, or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative tiwcr 0gi4h+ sm,wh 9m7o the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moon.b5t 33xmhxk-wp . 3r:qcfu0 gf Explain how this discovery enabled an estimate of Pluto’s mass.3-wfufqc5m x x :rkp03.h 3tgb

  The Sun's gravitational pull on/0 af molbt(,z 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 side of the Earth (t/ fbz0o,mlato 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 1980avuocowm j96tpg+l 2-6is ke .5v7do( $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 accelerati*v (r(rtru l o1u7xsq4on of the Earth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Ass *(u1lq st(r4vo 7rurxume 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 dq l0ik9s 4efirog7 u6;iscus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the4l9 eu0kfsg i76o;qri discus.   

  Suppose the space shuttle is in orbitp pciy8em o 2)fnyn,7( f(.uden,rl/ n 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. yn,(/ mn.)o,yfle8n r7(pfnue pdi c2 Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the 8v7 rw2onr. 15rq5curw9wmhw acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions 25vr1w5rm h .rqu89c nrwww7o per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniform rdeu9 bu1x e2k1ate in a vertical circle of radius 72.0 cm2uked9ex 11u b , 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 speed with which a 1050-kg car can round a tgsg.x xem34 2kurn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result ink s.23m egx4xgdependent of the mass of the car?   

  How large must the coefficientqa;3m l31wd+p;xozvl of static friction be between the tires and the road if a car is to round a level c1o3 q3zdlv;+m ;plaw xurve of radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet h4nhbbltk:5ux r*3 v,fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fa,lrthunkv x 34 5:bb*hst 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 frol4h - oogq y 5j,*uc6yoivz4:hm 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 coefficient of stao4yqv4 z- oc,uj65:lih hoy*g tic friction between the coin and the turntable?   

  At what minimum speed mustx qyki,e ;(9k ixxf:f6 a roller coaster be traveling when upside down at the topex x:; ,xi6f( ikyf9qk 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 drives 3rbgksiw90d +zhmiq /)oc,7r) crosses the rounded top ofiz,bis +3)c9m0s w/7qhd gkor a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameter Ferris wheel need tonbu4/r zwr* 3 svowg2rwt8a: 8 make for the passengers to feel8u wr2swzoba nwv 4/8rgr:*t3 “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirluvd39ux uk j 4ns8)t9v r iko+x+s1bi,ed in a vertical circle of radius 1.10 m. At the lob 9inv, s+dj3xxru+9uksoi8) u v t14kwest point of its 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:0s/ ;n qa 8flbtr4mgc of rotation is to experience/st0n lm8;: fbra4cg q an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival,. fy)ht2mbd+ 4 a(pul25r rxqr people are rotated in a cylindrically walled "room." (Setr.fl)25r muhp4r+ 2(q x adbye Fig. 5-35.)
The room radius is 4.6 m , and the rotation frequency is 0.50 revolutions per second when the floor drops out. What is the minimum coefficient of static friction so that the people will not slip down? People on this ride say they were "pressed against the wall." Is there really an outward force pressing them against the wall? If so, what is its source? If not, what is the proper description of their situation (besides "scary")? [Hint: First draw the free-body diagram for a person.]   

A flat puck (mass M ) is rotated in a circle on a frictionless awpn *r.sk fg 3.eayx27ir-hockey tabletop, and is held in this orbit by a light cord connectedy. k3ng.2esr axwf7p* 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 notw6y1nhwwe vfit .c2 a()8x8 cs ignoring the weight of the ball wh waxhw8cn .s2(ciw1 v6)ft8y eich revolves on a string 0.600 m long. In particular, find the magnitude of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , and the angle it makes with the horizontal. [Hint: Set the horizontal component of $\overrightarrow{\mathrm{F}}_{\mathrm{T}}$ equal to m $a_{\mathrm{R}}$ ; also, since there is no vertical motion, what can you say about the vertical component of $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ ?] $\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ =    the angle =   

  If a curve with a radius of 88 m is perfectl6mz +:uypts6xp 5j8 tky 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 9 hnp)ki ud((zmw/8zk$ 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 maneuverad62n1cc5 fmi 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,mb7 bdqv14g)v x18qrt 5d zj+t/ae et of the net force exerted on the car (by thet zg 41)bd,jd/ ere7t5q8vabxmv t+1q 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 505r we)hex2lg; x3w2vdq;-x su0 accelerates 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 coefficient of static fric2;xl h2x ed-wws3r5e;vg)xqution have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 mh (i390xm. iqdz*jca:u;blhz . At a particular instant, it(u bcx9:z*q i; h zhd.j3i0mals 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 Eak-vvq 1+ch5l irth’s gravity on a spacecraft 12,800 km (2 Earth radii) above-v h1 ik+v5qlc the Earth’s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleration g has a p.we6: )(at4 lppgst mmagnitud6mt4.:e s()pw a ptpgle 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 dueuojg *(gc-(kvkv ;ny 5 to gravity on the Moon. The Moon's radius is 1.74 vc*5yvu-o;gk((nkjg $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet hf7kgp4bt 7, qeas a radius 1.5 times that of Earth, but has the same mass. What is the acceleration d, egq77kp 4ftbue to gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth,mi *sqo3o3ik2 but the same radius. What is g ni mo3q3*i2ok sear its surface?   

  Two objects attract each other gravitationally with a force of p)-*v)gk:jp1hx g rjw*1 efkh 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effective value of g , the acceleration of gravity, at (a) 3200 ct)f 7 ;vnd.neac;oz9m ota.v;c) cfn ;n9ze7d   , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center 2sr1c1sp7u m1gxzhipt rt2, 0to a point outside the Earth where thegravitationasmps,c72 01 urixg21 zrpt1 thl acceleration due to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five .s wtzaxmr:yo k60/aycf 9n: -times the mass of our Sun packed into a sphere about - m6y:co9/ akns:xwyr.z 0tfa10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, ;xk0xndpc g;b m 8cg)5ercv-: which once was an average star like our Sun but is now in the last stage of its evolution, 8); n:;drcbe5vpm c-gxcxk g0 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 gcgu3e: mu bqqqy:4/6stronauts feel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Convince them and yourself th36ygu: gquqc/4 qe:m bat 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/aqcohe 1)9 8t7(p3) cmycqsaxz3 tdg at the corners of a square of side 0.60 m. Calculate the magnitude ansx 3qyotd h7zcp/3mtac )agce( 98q) 1d 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 Sp v3 x0belp1g(un. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a liev3p 01bg( lpxne (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 surface of Mars is 0.p l2(2fh kfk,t21awzj38 of what it is on Earth, and that Mars’ radius is 3400 km, p ( kl2t w1a2fj2,hfzkdetermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known val 7cbjkuhgb0d lvhbw-y)* 0w)/ue for the period of the Earth and its d0) j-w*/kw0bh)lhubcybgvd7 istance 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 movi5a3iej 9cin c*v3jd*b ng in a stable circular orbit about the Earth at a height of 3600 kj*5 bi*d v 3ic9ejnca3m.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km above the 8k mz, )9+hz-vcktrr ejuhu4.Earth. How fast must vkhzz+ckrh9)j8. etm uru ,-4 the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical svsv;sg0 c-;h 26 d;g8evhlvmk paceship rotate if occupants are to experience simulated s2ch mg;khvvlv806vs;-e gd ;gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for ,otd80 vh 2lcha satellite to orbit the Earth in a circular “near-Earth” orbit. A “near-E0h 8o vcdl,2tharth” 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 satellite hanh2w1y)j 5,jnloaqq :ve to be launched from the top of Mt. qwj njhq) o1:alyn2, 5Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the commap8 hhjjxd7:q2* scg :knd module continued to orbit the Moon at an altitude of about 100 km. How long did iqk*:gcdphx8s 2:7 jjht take to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit5s, wxcx4b/i a the planet. The inner radi 5bix, 4xc/wsaus of the rings is 73,000 $\mathrm{~km}$ , while the outer radius is 170,000$ \mathrm{~km}$ . Find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.7 $\times 10^{26} \mathrm{~kg}$ .


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

  A Ferris wheel 24.0 m in diameter rotates once evupf 9ac wbt8m(( 6- /2wmtbmuwery 15.5 s (see Fig. 5–9). What is the ratio of a c9mtbf6bm2(w 8w-m(p uw t/auperson’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 astronaq5 mw wu3mv*8nxi(ssh( 3nx)sut 4200 km from the center of the Earth's Mo(nvh mw3u3xx5 is8s*qsm(n) won in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal:yvzzlbkacfa78* f 5)2k o+qf mass. They are observef cffk ly8aqozb2a z)*7:vk +5d to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in ans6;ztusxv lcg* (c3r8a6i 1z*v au;o y elevator that molzca;cy;1(*a ut *s vs6uriz3v 6 gox8ves
(a) upward with constant speed of 6.0m./s   
(b) downward with constant speed of 6.0m./s   
(c) upward with acceleration of 0.33 g,   
(d) downward with acceleration 0.33 g   
(e) in free fall?   

  A 17.0-kg monkey hangs from a cord suspended from the ceiling of aj -ue /w(-;ym)qd-uy*sbtbpvn elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and directiosqp y(mt ;e/ wjb-uu-*b-ydv)n)? a =   

Show that if a satellite orbits very near the surface of a planet withvj.v*m/bm -9/ gtecv a period T , the density (mass/volume) of the planet at* vv/gjv/c9.- bme mis $\rho=m / V=3 \pi / G T^{2}$ .
(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 determ 6u ibprmgy7xix l(w-x)1 o(o.ine the period of an artificial x ib(rl(-wmuox)7yp6 1i x.ogsatellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundredj l g2g9i4r1 j/g/ gxnxch6kglm- e:9a meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance fromcllg/max:r en1g9 jikg-6g h 94x2/ jg the Sun?    $\times 10^{11}$

  Neptune is an averag qb3v) -h7ucjlxvgb9 4o3ouv7e distance of 4.5 $\times 10^{9} \mathrm{~km}$ from the Sun. Estimate the length of the Neptunian
year given that the Earth is 1.50 $\times 10^{8} \mathrm{~km}$ from the Sun on the average.    $\times 10^2$

  Halley’s comet orbits the Sun roughly once every 76 years. It come 0r-dywhvhzo m/t0g65s 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”6hz oh-ywv0/5 mg0drt 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 the center of the Gq5a *4 w11ltpgqlm,mzalaxy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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 meatq a:zqkj m 232ip7v4tn distance for the four largest moons of Jupiter (those discovered by Galil:27t qpza tqkm243jvieo 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 knji* bai6 ,;4s6z6 dmyeygv/j.dy k1jnown period and distance of the Moon. ;j,6.my a gd46nj/v 6kidbsiye jz*y1   $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiter’s moons, using xm0 .b-iz 5kqoKepler’s third lxo 5iqzk. mb-0aw. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and Jupiter consists of o0hn;gb, wxrucs4b5z js 5+ b4many fragments (which some space scientistrg4nhob bc; sb s5j0u5w,x +z4s 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 "planet" in the form of a barx 8xpu3r :le3nd completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where itux3pe x8 :3rlr is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in an arc from a hanging vine (Fig. 5ks6d)*ta;e0 zh 7exrx –41). If his arms are capable of exerting a force of 1400 N on the vine, wh ;arkz*)6 0d stxe7xehat is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will2hty/ a /hxr511ch gmx the acceleration of gravity be half what it is on thcy51tr 2h1hmhaxgx/ /e surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grao g4pdc*9)e.v vmdf)92pg fnl b hands and spin in a mutual circle once every 2.5 s. If we a9)9gd epvv*.m)g od plf ncf24ssume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates once :0owc ltrk6vix50wxle-c 3g-per day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is thisv lclkwx 6c ert3gxo: 05i-0w-?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft travegpxtd:jackq3 ( s( ;z5ling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with;:(5tack xd( z3pgsjq equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom scale in an elxof *mw76lyuga0 :ua2dt 88q mevator, it says your mass is 82 kg. Wh2*uaw8g :yf7qm 86u tdla0x moat is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube thati 1k;d)7hla o- iu7ywk will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circ7 ua;ko 7kiyw)d ih1-lle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an effect equal to gravity at the surface of the Earth (1.0 g) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop (Fig)qsg ( 9i06wkyw2--dfp rx cuzoqo(y,. 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 .4 *kac3cnpt kof its radius r, the acceleration due to gravity at its surfacn.p k 3tcka4*ce and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the vertical by aqfg6h .a+jz- b1do3 rmyi 8yi0n angir3+mg o80- y a.1fijhb6dzyqle $\theta$ 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 coeffici/kr0ji5a;r rx09u apgent of static friction is 0.30/ k;a 059p0i grruxrja (wet pavement), at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earh fg u0gc304oa1 usf)pth were rotating so fast that objects at the equator werguuocsf) 0p fg 3a0h41e apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a consta 0dh ouj yh.walko12./nt distance 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 spes+ m0 w,.jf1kr0yx ncfed rounds a curve of radius 235 m. A lamp suspended from the ceiling swin+sf m crn0w10 fkxyj,.gs out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earthur eu9xm v/-9g. Thus, it has been claimed that a person-9rvmugx /eu 9 would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced if4n 2vx7qer 5the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbiting qfvn42x i57erthe 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 traversesg s.e6th5kx fy67i8kah pc -5k the hill and valley shown in Fic 658 7.5ftepxyhhks-k 6kagig. 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? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioniymjb)5d)jo9 tng System (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.” The satellitesmjod) 5jb)9y t 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, i+p 7y9xce-ae bvsn)0: ug *rkjs meant to orbit the asteroid Eros at a hc-yej9: s enp0kv ga)ru*7b x+eight 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 satellit qwys.yb+ wer x(w3)c8e in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the s +(xe 3.w8bw y)wrcyqEarth), 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 jbpzpr140mv,3e2d1uwl2xp5 qzjz5 s is its mean distance fru312qj 5wmpes2xrb zz, jp1 0l4dz5pvom the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value o) e uckd.x2x+wzl ,u6cf G would need to be if you could actually "feel" yourself gravitationax 6u.c, 2 klud+cwze)xlly attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Mi16m ddnf z vkscqww4c .sb4v,cc:w445lky Way Galaxy (Fig. 5-46) at a distance of abouw44wcb5 wsm. s kcnq4:4dc6cf ,dv 1vzt 30,000 light-years from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each a 96y+if5q8t vgik+nfi, x8frside. Find therqit9+ayfv6,+8 f8nig xfik 5 magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the e 2*x,zbium 1n(f8nspEarth $ \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-lo 1 unw m:byb7kfwo p)1x8a9d1dng sweep second hand by81 dfk1ab:un pxm1o)9 dw 7won your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker690i 60puctixwhfo fj o*k4n6 weight around in a circle belowf hot0n*oj6icf069u wxip k46 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 akksipt35ln f: c)g bwp-d45u jz;i ;;p new highway is designed so that a car traveling at spg 3 cjsp45 ;-klnz) ;:kub5fi;dtpp iweed $ 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 theypa:d16 awwz+9v8ui:idkln t u 6(mj / cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against th9wua lpjk(d:i+w81z i 6m6d n/:yautve 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.$\approx$    $\times 10^2$