Sometimes people say tha2:cq1*qa:(e8fwzon; e wt yzj t water is removed from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statemen*qz azqc1e:oj8t fe (2ynww:; t?

Will the acceleration of a car be the same when tqi;-yf 9lkycm2 i7l 5yhe car travels around a sharp curve at a constant 60 km/h as when it travels around a gentle cuyii-9y kllf75cy;2 m qrve at the same speed? Explain.

Suppose a car moves at constant speed along a hic pm33st+0e r8tnzinv5,dhn) lly 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, (en t5s +vp,iztnh 0c)d83n3rmc) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a h b ;t 6e pqluykdu31c+m 8.q)tlsrj:1torse on a merry-go-round. Which of these forces provides the centripetal acceleration ofkc.t+ttl)1uqe:yj; b6um3 p8 lq 1 drs the child?

A bucket of water can be whirled in a vertical cwwzdm 8tak;i5o 6: jl)ircle without the water spilling out, even at the top of the circle when t:6wz) wtakil o58 j;dmhe bucket is upside down. Explain.

How many “accelerators” do you have in your car? There arxk sl;:o/f6t 4yt3tr we at least three controls in the car which ca;t st6k x4yflt /:row3n be used to cause the car to accelerate. What are they? What accelerations do they produce?

A child on a sled comes flying over the crest of a small hil7.rhhlffuu 9(l, 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 sleu fl uh9f.h7(rd decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a cur 1idg0a q)t4duku61(niit sp2ve at high speed?

Why do airplanes bank when they80c0fq ecgf5p turn? How would you compute the banking angle given its speed and radius of the turq cfpf g085e0cn?

A girl is whirling a ball on a sti47* u 6kzyryjring around her head in a horizontal plane. She wants to let go at precisely the right time i uj7y*ryk4 z6so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how,z 6zl 1fdro6y7;qtyv large a force? Considerl1 vqz;f7d ,tyz6oy 6r an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in wha:p 5 ,dc1pma njnmb40zt ways would the Moon’s orbit be dim a n, b5pzdjm:nc410pfferent?

Which pulls harder gravitationally, the Earth on cei ;b9k zu(9lthe Moon, or the Moon on the Earth? W(bl zi9ke cu;9hich accelerates more?

The Sun's gravitational pull on the Earth is muchkjram+i/y/2q)zx 1c nsq 9 p/b larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Cob xy)q acs/m /1rk+n9/pqzij 2nsider the difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or at tq4pc 9*ph-x *mco/wsx he poles? What two effects are at wopqwm4ph-/c9s * xc* xork? Do they oppose each other?

The gravitational force on the Moon due to th+ha h9sfdjg p)4n,mt .e Earth is only about half the force onspj4)m n, t+hhda9f.g 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 theik0xx y)v b5z5 Sun larger or smaller than the cenzixxb5 5v)k y0tripetal acceleration of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (b) toz:ujg/ ae s)exb9;7d pwarda d9/j: pb)z sgx;7eeu the west? Consider the Earth’s rotation direction.

When will your apparent weight be th(ocxjyd l qt/1 cu4 .7bk.qpe7e 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 constant speed? In which case would your weigbjqk 7c.x( e/ 74l cdytuopq1.ht 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 uc 3onk9y k-1qo;s/a faffected by weightlessness. One way t3k/1af9s;q u- yoc kono simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runnersmm1 efm:nmtixmxqb58 02;nj nc; r67 experiences “free fall” or “apparent weightlessness” between st cir2em j0x81x6tmmm5f ;q b nn:nm7;seps.

The Earth moves faster in its orbit around the Sun i d1h60g2n+ adubq)ha 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 relativ1 a )u+ndh6g2a0ihbqde to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to have a moo htnr,uxx/:: .gu5hdnn. Explain how this discovery enabled ahh.t:/ nxud, r xngu:5n estimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the kl r nxjtq)76vg8b( m8Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the E)qmn8k(xtjl bv8g6r7 arth 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 19g m20 54ywuydn80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ pulls out of a dive by moving in an arc of radius 6.00 km . What is the plane's acceleration in $g^{\prime}$ 's?    g's

  Calculate the centripetal acceleration of the Earth in its orbit around tn 9mai1ta* (n-hvmwt+he Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1(1n vt-wh+m9ti nm*a a.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 rota3n;8jdbd :l cmtes uniformly in a horizontal circle (at arm’b8c: mjd d;3nls length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surfabv;2 j36v7 rcxv p/vface, and circles the Earth about once every 90 minutes. Find the centripetal accelerat/6vv pcv b7fr vx2a;3jion of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck of clay on u c4hx tuzb064the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s diameter isc04x tbu64 uzh 32 cm?   

  A ball on the end of am2;5xfqoe.fa string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown i mq.oaff25e;xn 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 wug;v4w44 y wiihich a 1050-kg car can round a turn of radius 77 m on a flat road if the coeffi;i4wi4g yu v4wcient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffic87vts8a y eckzgf7phx+)l8; nient of static friction be between the tires and the road if a car is to round a level curve of radius 85 m at a speed of 95k 7xk+f 8vnpsg7tc;8 la hyz)e8m/h ?   

  A device for training astronauts and jet fighter pilots is designed to rotba2 uoz)k/5sr. o +bgoate a trainee in a horizontal circle o2rgzk.o + buo/bsoa)5 f radius 12.0 m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rob+le:k y 0tuabih*3r+tating 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 thh0 k+:re bl+bu*3yi ate coin slides off. What is the coefficient of static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be travelnkyo mc+.m um 8,u4490xzojez ing when upside down at the top o90o4zu j+xmnz.c4 8ku ye,mmof 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 (in5w5ch4nqtj rd 4y 4maehmuu0 cv4 ;nx2-ll23fcluding the driver) crosses the rounded top of a hiljumc2r;um 5ya- 2 4t4h3xqnd hc4vl n0 lefw54l (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 whemi e pb5m.(y4x0u3 lu..2 p oyznkfog(el need to make for the passengers to feel y.(xukle5y o4 o(mn3 2.gzu0fm.p ibp “weightless” at the topmost point?    rpm

  A bucket of mass 2.00 kg y k9cin:sy5az, 0d8/fryi,xyis whirled in a vertical circle of radius 1.10 m. At the lowest point ofdyizk 8y5:srya,yn,ic/0 fx 9 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 centrifuge2 4czqlysysp j9nv8fxclab .:(8m s;6 rotate if a particle 9.00 cm from the axis of rotation is ab 4qllny (vc c8:9pjx8fms6s2s.y; zto experience an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindricaie+ xl kkz d 8qu:22rn;r)ol6vlly walled "room." 6rlk +8 dkx q v)ue2;ozlirn:2(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 inbqdq6b y6 u;8 *0kruaiba8,sf a circle on a frictionless air-hockey tabletop, and is held in this orbita0f6;da s* 6b u8bqk8q, rbuiy by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely this time, by not fy sm6:0nib dwg3+.ancf )/uiignoring the weight of the ball which revolves on a string 0.600 m long. In pan6)fs/nab3 fgc:y.iw +iu0 dmrticular, 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 car tr7 xo;jcng j0l1aveling 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 83dz2fv 7 rvmt$ 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 evas- 3grmacxf-l 1;c i qc(p:zl,hive maneuver 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 r aqc0f19x)xz and centripetal components of the net force exerted on the car (by the ground) in Example 5-8 01r) zxcf9q xa 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 dm,/n, hk8ua 9iwz : e(b(6 gvpgyrfw1500 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 in(v( wm1da wh gf8:ezb,up6,9 /kygrwould the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . Atdcfjk7:fl;iy ha0b, e/d zf /r 0dg1p) a particular instant, its a)/ki0d dfg7e;y f/1 0dr :z,fpalcjb hcceleration 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+ mrohq*4+tjq q5r di: 12,800 km (2 Earth radii) above the Earth’s surface if its mass is hirmo5r +q*t :+q4qjd 1350 kg.   

  At the surface of a certain planet, al.qk tyua34.j 8wy0ethe gravitational acceleration g has a magnitude ty0jk.a lae .q83uwy4 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 due to gravity on the Moon. The Moon's rejv )ns)rb cr4kaq,p rufp ar,71 15.uadius is 1.74 cu5s)pfa)rer., rvjpr7ab1 uk,1n 4q $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radius 1.5 times that of Earth, but9wl (uc7c p47f ujv*hx has the same mass. What is the acceleration due to gravity ne c7uxpf 7*hcjw9u 4lv(ar its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but 6g4l cx-+zh*ets :gfht+o 9rn the same radius. Whats- 4roe9 h+nczx+*ftgh 6 ltg: is g near its surface?   

  Two objects attract each other gravitationally with a for0 bcu .stxsv+ba5bo77ce 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 j y52iq j5fq3pacceleration of gravity, at (a) 3200 m2p y5jfqjq35 i    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the+ky tgt)u9he * Earth’s center to a point outside the Earth where thegravitational h +t)y9g*tu ekacceleration 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 1zzg2z 9lru7e::kn 5atxn (ooSun packed into a sphere about9 (atnuko7 l:n:zz1 5 ezg2rox 10 km in radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf stabvrk /64yhhk r*-4o/oc, s qcur, which once was an average star like our Sun but is now in the last stagb,vrh c/usc r64y* -o /qkk4ohe of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel weightless while org njmbw( e.8)lbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weaker up there. Cw. n(l8bj )gemonvince 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 oo.dgfd3 5fybb5n ij 5gc /i,:s7 bzlf/f a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational force exerted on one sphere bb5y zdd: bnf fib,7f3go/ g55lc/. jsiy 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 a 0kg+;ztpx+adl2c b2 of the Sun. p ++a k txzd;ag2c2l0bCalculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets are in a line (Fig. 5-38). The masses are $M_{\mathrm{V}}=0.815 M_{\mathrm{E}}, M_{\mathrm{J}}=318 M_{\mathrm{E}}, \quad M_{\mathrm{S}}=95.1 M_{\mathrm{E}}$ , and their mean distances from the Sun are 108,150,778 , and 1430 million km , respectively. What fraction of the Sun's force on the Earth is this? $F_{Earth-planets}$ =   $\times 10^{17}$ ${F_{Earth-plantes}}$ \ ${F_{Earth-sun}}$=    $\times 10^{-5}$

  Given that the acceleration of gravity at the surfa hm8+ 6we7wpve pw)ko h+z:jhq ztq621ce of Mars is 0.38 of what it is on Earth, and that Mars’ radiusqw:z+khpw wo h m)+t26h8v jeqe7zp61 is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the kc3 .))6qrthm6rd1satm(ep e enown value for the period of the Earth and its distance from the Sun. [Note: Compare your answer to ts66p ) deqtmr.ece(3)mr1hathat obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in g6-8*eww-kl2sv kw seu)9y xda stable circular orbit about the Earth at ae e6wvk92*ss xg)k-8-yul wwd height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 km as:oh+v-qdyhn8k.hj z 12wyf(bove the Earth. How fast must the shuttle be movinghkn1-w+q dyys8.z f2vh j :o(h (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rot2psoy.4lxu:p-qij* o c g3q .hate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s d34uohs xpy.:gj-q c. *pl2oiqiameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes for a satellite to orbit the Earth in a circular “ g eaf,*;;rlh t/,pkninear-Earth” orbit. A “near-Earth” orbit is one at a height above the surface of the Earth fk*/ignpta ,hler;, ; 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 velocx 73 r*h6/d8mrgiuxch;hnvm) ity would a satellite have to be launched from the top of Mt. Emir3x7hcv guh8dmx6rn/h ); *verest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing missionssm1o18 r lm2a, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the Moon once?a 82 sms11molr    s

  The rings of Saturn are composed of chunks of ice that orbit the planeth2..gglr ,bmc,i grh+. The inner radius h2.r ,h+cl,g big.m grof 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 o7t2ch/a3h o.w 7,oqsv6 teimtnce every 15.5 s (see Fig. 5–9). What is the ratio of a person’s apparent , ihot7/ a6v3s ec7toq.ht 2wmweight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent wsrmu++t6f - ikeight of a 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at m6t+-f+ risukconstant 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 ofp(1ds/ bv+ymh8s5l++sdgs gj equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them.p s(v8y1g+gs +dss +d jlbm/5h What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elegeb63:rw hn,e/z tk.kvator that moves be kw:6 zg/ .th3nr,ke
(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 drf1* ktnk7g5 v4*b hhsuspended 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 acceleration (magnitude and direction)? ab*14fkvkr t7hg n*5d h =   

Show that if a satellite orbits very near the surface of a planet with perioejs kq*m ,nw9 t5jvs91dft,t1x3aa-p d T , the density (mass/volume) of the planet is3t t qpv,9js9a *sfwje-a5 mtn1xk d,1 $\rho=m / V=3 \pi / G T^{2}$ .
(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 t 1cmf+ 9*he8pc u/lhx3itfn 5fhe period of an artificial satellitm8 +fn heip35 xfh/fcu*9 1ctle orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though21i39tf74ht vcnno f i only a few hundred meters across, orbits the Sun like the planets. Its period is 4h49f 7n fnic213 itovt10 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average d dvd8, t iu w-iygl7r;t0d/qd*(inxn, istance 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 co6l*9b/7pr 9ww7 anz7rvz mowdmes very close to the surface of the Sun on its closest approach (Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? Whatz7w7w 9*bvm rndr pz7w/ oal96 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 ph+8of6co kj4aq.lwsdt*- p 6xlh/2 athe 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+ji6 ed(l +u8p71jc6 gsbkz y)ui 3xzg for the four largest moons of Jupiter (those discovered by Galileo in 1609 z eb 1kglu6 p(7)+ 8dy+igxuijj63csz).
(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 fre0-dx0 dff7feom the known period and distance of the Moon. ef-f07fx ded 0   $\times 10^{24}$

  Determine the mean dista:m124 ;sfdrmysh l3 lance from Jupiter for each of Jupiter’s moons, using Kepler’a:l2rdmys f slmh;341s third law. Use the distance of Io and the periods given in Table 5–3. Compare to the values in the Table.
$r_{\text {Farip }}^{r}$ =    $\times 10^3$
$r_{\text {Guarymale }}$ =    $\times 10^3$
$r_{\text {Culimio }}$ =    $\times 10^3$

  The asteroid belt between Mars and 4cw4mrzq iz.81 dvi.wd/r l5 bJupiter consists of many fragments (which some space scientists think came from a planet that o54l4rqzmw.v. /wddriib1z 8 cnce 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 ta0 o0xnos)sdb1le describes an artificial "planet" in the form of a band completely enco 0s0dosb 1nx)ircling 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 days?   

  Tarzan plans to cross a gorge by swinging in an arc frm 8 +tkt5+a+( rfpj(djlli+nziom(p:om 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 sw+i ml+j+p (ma:nj8lzi+fr( ktdp(5 toing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surface will the acceleration o pfrus-w. :i5rf gravity be half what it is on thsrpui r.:-wf 5e surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spib,p z :xx3xdvos;l.0ln in a mutual circle once every 2.5 s. If we assume their arms are each 0.80 m long and their individual masses are 60.0 kg, how hard are they pulling on onex:zv.b l,;osxx0d3p l another?    $\times 10^2$

  Because the Earth rotates once per day, the aye he81f*b7z lpparent acceleration of gravity at the equator is slightly less thehzlbefy18 7* an it would be if the Earth didn’t rotate. Estimate the magnitude of this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft trkcwx:+vp6;v x9gj ,uoaveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equalvo x:9cw;, +jgv pk6xu and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bathroom sco ir5*y/lqktgd 2xg30ale in an elevator, it says yoqg 5xkd/rtilg y3o2 *0ur mass is 82 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circulqpyb t** ;.2+4que xu1fc 1xa xl/xpmrar tube that will rotate about its center (like a tub*yet+; ubu 1./ 1fm4xxc2 *lqppqarxx ular 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) is to be felt?$\approx$    $\times 10^3$

  A jet pilot takes his aircraft in a vertical loop 8q5w lcu -p5es(Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a planet in terms of its radius r, the accele495b2gj oehqeration due to gravity at its su9g 4jobhe q52erface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from the ve 223rcm28xds.zmzgx lrtical by an angle 2s 3zd8m22 c x.lgrxmz$\theta$ 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 coefficient oarw7fsr 37de;qj sw+ 4f static friction is 0.30 (wet pavement), at what range of speeds can a car sawsrw7s;r43de af 7+jq fely handle the curve?

  How long would a day be if the Earthdl*t3zf,j 0yh n8db-tf7l*aq were rotating so fast that objects at the eqh -3,ln8d yfa7j*zt0dqt fbl*uator were apparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant diy/)9/n kfl7cpog vb e0stance apart of 8.0 $\times 10^{10} \mathrm{~m} $ and rotate about a point midway between them at a rate of one revolution every 12.6 yr . (a) Why don't the two stars crash into one another due to the gravitational force between them?
(b) What must be the mass of each star?    $\times 10^{26}$

  A train traveling at a constant speed rounds a curve of radius 235 m. A lamp sus -5d,so;*e.pro zt zxfgl 2;ikpended from the ceiling swings out to anz;52zeg, ksx *df;lporio .t- angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, ixk.o rd49s.ss- +e lzxt 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 following data for Jupiter: m ..s-rdk+4esz9sx xl oass =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 dea6ht .*s9 epfwduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the s6eatw9. *ph fspeed 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 valleott 9y /gv.u)wy shown in Fig. 5–45. Both the hill and valley have a radius of curvatvygw). tt9uo/ ure 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) vzrg3mpqyq/6 nt 6r-+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, allowinmrv 6qpq/ yn6t zr3+-gg 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 Renrt - p6rj6y5eseh,lz /dezvous (NEAR), after traveling 2.1 billion km, is meant to orbit the asteroid Eros at a height of ,jptsr6l z / eh5-eyr6about 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 needssr3s+ge f cqj9h 6/i/(.ydxh of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 kmqf+3/g y/s esxd (s.9h6cjr hi 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 distancevq 0yjlbo29g 3;7dh hs from the ov3l ;j ydsgh2h0 bq79Sun?   
(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 actuall mkf7:8b h:)adzill1 xy "feel" yourself gravitationally attracted to someone near you. Make reasonable assumptions, hk7m ibd:8:)lf1zx la like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the ce r;l73kh0 xfgwnter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,00 lxkh ;73gr0wf0 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 squareulxzmig9k if t)/ ,dyhq0 b7a.xg5i 21 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placb9 hy7f gdxzk5mgqx2t,1.)i uli0ai/ ed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kq1kxc8pt7t, hg orbits the Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the 3bhopmu* qclg (x, : 40kwxk8wtip of the 1.5-cm-long sweep second hand on youk,4 :p3hx0 wco8q(bl*w mgxkur wrist watch?    $\times 10^{-4}$

  While fishing, you get borcugh:cgy9 8t y/c6dg.ed and start to swing a sinker weight around in a circle 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 vertig89u6g h cc/cgy: yd.tcal? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a n d +3zd.+f9ckzfd4, kqpzp)6ak d+van v7vr;few highway is designed so that a car travel+9+nac qv)ddz4ff.p,dv kp 36dzkzvk +far;7ing 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 thh:teb ) (8g::6wjrtz ld(zgvw e cars when negotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal acceleration, is the normal force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider tgrw8g:tj(6)b zeh :(l vz:wdan 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.$\approx$    $\times 10^2$