Sometimes people say that water is removed ;4tox :mu*w hsfrom clothes in a spin dryer by centrifugal force throwing th :4wsux*m oht;e water outward. What is wrong with this statement?

Will the acceleration of a car be the same when the car travelvr(rk,4a / yrvs around a sharp curve a /k,r4ar v(rvyt a constant 60 km/h as when it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant spee/uu k(8,s3 nj0eizeou d along a 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 tuisu0uzj e ,en3/ok8( wo hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a child riding a hors(en;vjuzb-;i e on a merry-go-round. Which of these forces provides the centr;j(;iuvze-nb ipetal acceleration of the child?

A bucket of water can be whirled in53,7qh r;s ejx trly+z a vertical circle without the water spilling out, even at the top of the circle when the bucket is upside down.3ersz7lhy q,x j+rt5; Explain.

How many “accelerators” do you have in your car? There are at least tbug )3)ald b+hhree controls in the car which can be used to cause the car to accelerate. What are they? What acceleratioub)gahl) bd+3 ns do they produce?

A child on a sled comes flying over the crep1s: fzu8 vv-fst 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:u1f8zpv vsf - goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high smku2 / t+osc+vpeed?

Why do airplanes bank when they turn?w;h,w jn0 u9rv How would you compute the banking angle given its speed and radius of tvr0 hw;ujn9w ,he turn?

A girl is whirling a ball on a string around herchc n6)vk7 sktguw9 m0avwa2y ;ih+6/ head in a horizontal plane. She wants to let go at precisely the right time so that the ball will hit a target on the oth ck6hc2s0 vw) v/ 6th;y+wim7ka9agu ner 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 larktg4g+wm sv -mapkbt-0tbg*/b 5+k)rge a force? Consider an apple a+5mt vgb+)b-g0t bk4ktpkmgs/r*w -
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would thecmu ;7oftx(8 l Moon’s orbit beu;oc l7mt(8fx different?

Which pulls harder gravitationally, the Earth on the Moon, or41bv .ti * tl(yj6 ;yf ri-/ibgzha-as the Moon on the Earth? Which accelerates more?blyyt-f br -a*.i4ti v6s1; g /(hjiza

The Sun's gravitational pull on the Earth is mucx w u,wgt40l,uh 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 Eatwg4uu x l,w0,rth to the other.]

Will an object weigh more at the equator or at the poles? What two evfstg 0- ys)wgx5qa*6cre 1 / tcgie0-ffects are at work? Do they oppose each other-fte 5g1-c6qvstgc/wi)r 0sg0aey *x ?

The gravitational force on the Moon due to the Earth is only about half jao +(g2 7bl ob/di;uithe force on the Moon due to tjobgb ; uoili+(da/72he Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit around the Su2s 2bpuzt3cq):;/te x0gpdq c+ uf4g mn larger or smaller than the centripetal acceleratio+u3eqmb/: t)0 4 ;ug d2c x2pgcqfspztn of the Earth?

Would it require less speed to launch a satellite (a) toward the east or (bd.bz;9.m3p beh eid uxjl3i+9) toward the west? Consider the Earth’s rotation directi3;b.u99zem.i i pjedl 3h+dbxon.

When will your apparent weight be the grbt osh2dv( vq0hj3;.b eatest, as measured by a scale in a moving elevator: when the elevator (a) aohbq b s;( .vjhtv032dccelerates 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 could beluj: s c+a /nkp.*d e-q3nvh*f adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Expna* jkp- flnd /:cv+hu.3eq*slain 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 weigd n;pvd ttg ox:4n;4+ahtlessness” between steps:o4tn+4davgtd;n p; x.

The Earth moves faster in its orb, lyerki,1gha.,+vmw ec- p (wit around 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 tve-rh+e. clp y,ma ig,w(1k,whe Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to hu ( vip30m kikmz.e4a4ave a moon. Explain how this discovery enabled an estimate of Pluto’s mav4k.em 4zu0k3a(i pi mss.

  The Sun's gravitational pull on the Earth is much larger than the w v cb7 ztdv s;7jr2(svig1:*yMoon'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 othewjv y:sv 7*tzv2idr1(c7 sg;br.]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 traveling6 r2xp3jy0b- v a hhw3nlbf+m+ 1980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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-lzpne/qzjr aj:q7mf9 : i4r/ its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earpe:j l/qn r4 aqr9fi:m-jzz /7th? 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 iqr y, cil7.r*exerted on a 2.0-kg discus as it rotates uniformly in a horizontal cir iliy.c,*r7rq cle (at arm’s length) of radius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km frosh1 4tv4i(jyf jpr3ij kd5ay53:bat - m the Earth's surface, and circles th tjk4yda5jib(41 t3j s-y3:i p5vfarhe Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude of the acceleration of a speck 3;p ;0g mcfgh j-elam-of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel;me lp--3hg0;cgf jam’s diameter is 32 cm?   

  A ball on the end of a string is j2d is*: h(wem r os*:(ip4nufrevolved at a uniform rate in a vertical circle of radius 72.::ur d hpmws(2 i*4inse(ojf* 0 cm , as shown in Fig. 5-33. If its speed is 4.00 $\mathrm{~m} / \mathrm{s}$ and its mass is 0.300 kg , calculate the tension in the string when the ball is (a) at the top of its path   
(b) at the bottom of its path.   

  A 0.45$-\mathrm{kg}$ ball, attached to the end of a horizontal cord, is rotated in a circle of radius 1.3 m on a frictionless horizontal surface. If the cord will break when the tension in it exceeds 75 N , what is the maximum speed the ball can have?   

  What is the maximum speed with which a 1050-kg car can round a vt. n gud3imp*x hr hevnz25():i+g9sturn of radius 77 m on a flat road if the coefficient of static friction bi hng 9spdvv5g2 ehx .:nt3m*rzui) (+etween tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coeffmy u5fz(o u:d1s;rv5 kvnr:a,icient 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 95km/h ? u;myfn u:5o kz( a,:d1vsrr5v  

  A device for training astronauts 1 ;qvzemm7uem:78iq dt5; c+lc y0qd aand jet 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, edc tcq0mzyl8q 77ve i1qa+;m: u5m ;dhow fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntablp ,7 h(jvopejb3q0:cam 3z-a ue of variable speed. When the 3(0:7-bojezmja p ,u3 haqc vpspeed 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 static friction between the coin and the turntable?   

  At what minimum speed must a roller coaster be traveling when upside dog13nzgp( 6)m++y nh0cpnt pp nwn at the top of a circle png gnhm t1 cp+630ypn(+)pzn
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the driver) crosses ejc) ,ivn-9ygapx7e sm dk ;4(the rounded top of a hill (radiusgx ,7;vmpse9j4e cd)(akn yi- =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 15-7cypeq /7-j (tar9bs om-diameter Ferris wheel need to make for the passengers to feel “weigoe (ybsjq cpa7r/t-97htless” at the topmost point?    rpm

  A bucket of mass 2.00 kg is w-cpyqx, rckzy0 /1 x3 tb+3qlhhirled in a vertical circle of radius 1.10 m. At the lowest point of its motion the tension in thelrphk1z/y0 btcq x+cx-3 ,3yq 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 centrifuge86vqj3 u505upl teud p5t.qwi rotate if a particle 9.00 cm from the axis of rotation is to experience an acceleqi6lwuvp.q 8055 dp3uj 5teutration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a car2 sp5m(u(h h/vs gne/qnival, people are rotated in a cylindrically walled "room."(e2phgqsv u/sm/ (5hn (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 circle on a frictionifc;vc:,)n dqless air-hockey tabletop, and is held in thiv, f;c)qndc:is orbit by a light cord connected to a dangling block (mass m ) through a central hole as shown in Fig. 5-
36. Show that the speed of the puck is given by

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

  Redo Example 5-3 , precisely thi1i.lgqz* b1 ycc g.np:an(l mxw8-4dys time, by not ignoring the weight of the ball which revolves on a stricql *d ix- y1ab48.ycz(w.n :mpn gg1lng 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 perfe:/r 14frt42 k( b r,b)tyuptgrdfvpp1(x8mzz ctly 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 kh/jeno;z+hccd c/8 .$ m_{1}$ and $m_{2}$ , are connected to each other and to a central post by cords as shown in Fig. 5-37. They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances $r_{1}$ and $r_{2}$ from the post. Derive an algebraic expression for the tension in each segment of the cord.

  A pilot performs an evasive maneuver by diving vertilc6g fa(..mh wcally 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 forceh8cl+o-0he tk la2ovoc+e2 j7 exerted on the car (by the grav0k- ho j+ 2ceoll2+otce8h7ound) 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 the pit a+w(i0u*ws8 tccohkk36h9ep yb2,cc irea, 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 tup*0cweyt8wk i93b c+,kh ( i2 occshu6rn, 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 horizont0l 8 s+;l0,hi ozmqgltal circle of radius 2.90 m . At a particular instant, lmo h+ql; zl 8i0s0tg,its acceleration is 1.05 $\mathrm{~m} / \mathrm{s}^{2}$ , in a direction that makes an angle of 32.0$^{\circ}$ to its direction of motion. Determine its speed (a) at this moment   
(b) 2.00 s later, assuming constant tangential acceleration.   

  Calculate the force of Earth’v 1oql:b4 hd vw3:bbs0s gravity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if:b 1w3bo0s4dqhv: lbv its mass is 1350 kg.   

  At the surface of a certain planet, the gravitational acceleratioox35gby,6: 90 xxg-fnsouqr an g has a magnitude of 12 m6xgf:-x,9 0b3y xrg unsqo5 oa/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 tj0 8c(ecckfxuu9+b i63rp0vto gravity on the Moon. The Moon's radius is 1.7u6rkf tj9xccb +pc3 0evu0(8i4 $\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, buto z-z5x1i tl4u has the same mass. What is the acceleration due li-u z14xt5ozto gravity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth, but z/tkmsc7( g( nthe same radius. (n7 smc (kzg/tWhat is g near its surface?   

  Two objects attract each other graviz,6 ,/7xogn,)bk qlrl obiuy.tationally 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 q3v4vq+ d mv4.o)- l pvqbrlj/ g , the acceleration of gravity, at (a) 3200 mmv+l ob rvl/qd4 q3v)4-jqpv.    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s+mqx 2uvo (nf, center to a point outside the Earth where thegravitational acceleration d fo(uxq2vn+ m,ue to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sph5dul4y4wdv i*dsry83 ere about 10 km in radius. Estimsl uy* vd3idyrw5d844 ate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is /dvc70c g icf7now in the last stage of its evolution, is the size dvf cgci77c0 /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 orbiting in the d8mk n:h2g nm7space shuttle. Your friends respond that they thought:nkm h72g m8nd gravity was just a lot weaker up there. Convince them and yourself that it isn’t so by calculating the acceleration of gravity 250 km above the Earth’s surface in terms of g.   

  Four 9.5-kg spheres are located at the corner0cejy6 6+o h.pg 0uojjs of a square of side 0.60 m. Calculate the magnit+60 jyjuge .ojo ch0p6ude 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 plak2 97w9bd 7cel)bovb+* dgzitnets line up on the same side of the Sun. Calculate the total force on the Eartd*t 2d9lg7b b+ze9oc vi)kbw 7h 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 surface of Mars is 0.38 of lfst - /6ytnw/.z hb;hwhat it is on Earth, and that Mars’ radius h-szhy n t/lt6.wf/b; is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period ojojx04n 9y.liicm; 0ef the Earth and its distance from the Sun. [Note: Compare your answer to that obtained using Kepler’s ly0ij o emic4n9;l0xj .aws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moe9ihilmc0b 8(ving in a stable circular orbit about the Earth at a height of 3 hb9li(mc8i0 e600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 650 zt.kl/ fuac g q5m:qgc+9 aq7cq,r2 v:km above the Earth. How fast must the shuttle be moving (relative to Earth) wh uqaq7m.+gcrga5l:t , :q /cqc2kvf9zen the release occurs?    $\times 10^3$

  At what rate must a cylindrical spacesf)as g /zgm;.znae)8whip rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’zme wg.g/a nafz );8s)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 a satellite to orbit thenu4z*) b +e7/cfej:zq dro;tr Earth in a circular “near-Earth” 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 ttrcz4o */u+:bn d7fee; )q zrjhe Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellite have to be launched from i.w-y+x94 m )f4xymvju6t rrlthe top of Mt. Everest to blmrwyyr9+ix jmu x6- v4t4f).e placed in a circular orbit around the Earth?   

  During an Apollo lunar landingtevsuk(0)i6q( arzo) q 8,rtf mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around the M(rtt qeu(6fiqs) 0zk)a8 v ro,oon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet.29cih(m go.zs The inner radius of the rings i.2zg9is chom (s 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 every 15.5 s (see Fig. 5–9). W2yon;+9ucqqm ji xmw gk(/ (i.hat is the ratio of a person’s apparent weight to her real w (92jx;g(qkimc.o wq i/muy n+eight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km fr ssb jvi/,y+r;om the center of the Earth's Moon in a space vehicle (a) moving at constant velocity,,bs r+/ y;vijs     ----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 w1mcfj 6jsk zhi:z3(* stars of 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. What is thj*f1smzic6w:z3khj (e mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg x4 x4f sfd+q,2*sul ykgo oh14woman in an elevator that*f+oyxldh q1o4x4ks42sgf u , moves
(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 c w2s 00 .lwn2k*cjt6rsihs e2neiling of an elevator. The cord can withstand a tennnes6200 l sc2. 2jshw*itrkwsion of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbits very near the surface of a planet walx7f2*39z gddedp/with period T , the density (mass/volume) of thedd7 zlw29/epdg a*xf3 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 off mx/1 ae)ecm(3h oxk8 an artificial satellite orbiting ver3kcof h /8 mm1x)(eeaxy near the Earth’s surface.    s

  The asteroid Icarus, though pqckd a-x/8 +bonly a few hundred meters across, orbits the Sun like theaxbq pck/+-8d planets. Its period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.5 ad*w5ab lv6ix4 a0yr2$\times 10^{9} \mathrm{~km}$ 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 h-+uppida s;g/96v)ah5mc4 rgp)vdrthe Sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach guh))d+p9v6 pcsr ih5gmda rpv4 a /;-(Fig. 5–39). Estimate the greatest distance of the comet from the Sun. Is it still “in” the Solar System? What planet’s orbit is nearest when it is out there? [Hint: The mean distance s in Kepler’s third law is half the sum of the nearest and farthest distance from the Sun.]    $\times 10^6$

  Our Sun rotates about the center of o(f uwo npk pcqo,s:c7 h4/e*: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 masst2a:f9c(acj6y0 cn tq, period, and mean distance for the four largest moons of Jupiter (those discovered by Galileo in 162 cjt n69ac(:cqtf0ay09).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period 1 jys3+66soah7e2 vfvtwzigw)r *6cq and distance of the Moon. w2j*s w+ 6qcz)7v6 ste v3y6orihf1ag   $\times 10^{24}$

  Determine the mean distance from Jupiter for eachh-m(i p +eep2 nam5 t)h+vcp(f of Jupiter’s moons, using Kepler th-fpapn+2( ece )5 h(mmipv+’s 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 Jupiter consists of many fragments (wts vcdom ()**dhich some space scientists think came from a plao)s(d*t dm* vcnet 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 ar4f*o 3w vnk fd5zhf2-vtificial "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 5w3 odvznfv f*f2h-k4 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 6k15: unlf1pwswi7 3r yx7uxrhanging vine (Fig. 5–41). If his arms u rnrp 37w1lwk:fsix567xu1y are capable of exerting a force of 1400 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 80 kg, and the vine is 5.5 m long.   

  How far above the Earth’s surfjb 5e qd2,z lho/szv85ace will the acceleration of gravity be half what it is on d5 zsej25 8qz/ hb,ovlthe surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and w:yn5 yp+ al7xspin in a mutual circle once every 2.5 s. If wewlxn ya5:y7 +p assume 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 per day, t.a9 :w qpcql0oi((zht he 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( qqoaizw lpt(c09h.:. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling dhoj*sq ,e0 jlp*/x6ej irectly from the Earth to the Moon experience zero net force bejx* lh0 e/e oj*p6q,jscause the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you8e 0* *l nnr;tni rv1l(u;ken4v6xehx stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the acceleration of v;inl 6xr*n8(en1ukv xne 0lr h e;*t4the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consists of a circular tube that will rotatb( 7ae66:yslo63gj u- jld xpve 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 eqx -6a3 j ej7gbyld6o:(6 usvlpual 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 h, w w. 6p)l1rfykgi;uin a vertical loop (Fig. 5–43).
(a) If the jet is moving at a speed of at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g’s.    $\times 10^3$
(b) Calculate the 78-kg pilot’s effective weight (the force with which the seat pushes up on him) at the bottom of the circle    $\times 10^3$
(c) at the top of the circle (assume the same speed).
   $\times 10^3$

Derive a formula for the mass of a8ttg dq.p/ zmbg+t;,n planet in terms of its radius r, the acceleration due to gravity at its surface and the+.g/ tgtpdqbtm,n 8z; gravitational constant G.

A plumb bob (a mass m hangd g84 zdl;vq/hing on a string) is deflected from the vertical by an anglzlqg;4d h v/d8e $\theta$ 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 -1pt0durr l g9coefficient of static friction is 0.30 (wet pavement), tdr-pl9r1 gu0 at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were ro6 tbl hz /*nlyzqi1eap1- ;e9/xjhy)w tating so fast that objects at the equator were apparently weightix)/hleley1wa h-jq9tz6 n* b/y;z1pless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of gpq9 d ii0+qs7/b olh2- wjmi;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 rounn (dqga,; ef1uds a curve of radius 235 m. A lamp suspended from the ceiling swings out to and(; nf e,gu1qa angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as mas3 ep /5j58*wd bt/8 fegmnmmxxsive 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' d3etp8menxj/mx 58g 5wfbm/ *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 mfhew;mf5(2g deduced the presence of an extremelymm;f52f weh g( 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 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 8vkh q0ge+,4sy l3g x(stys )pit traverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast csvhg4()t8 es0p, q l+gyxysk3an the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of h .mgo-3myc(1op u 4uc24 satellites orbiting the Earth. Using “triangulation” anpo3o.1 ucc4mm(u - hygd 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), afte p1im d-eisr21r traveling 2.1 billion km, is meant to orbit thdr1 -me ipi21se asteroid Eros at a height of about 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing ab z8p3aae9quzbt*ya 2p 33ou, satellite in need of repair. You are in a circular orbit of the same radius as the satellite (400 km above the Eaaeo3y tpa8q*apb23 uz,9b uz3 rth), 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) r2-0ef suei +xhr/jh8What is its mean distance from threfs+ r jxhi0h/2 8-uee 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 act1a9j5si:r e,bw1 wx9dw ycyw0ually "feel" yourself grayb0 9wyxe9:was 1w dcwi,r15jvitationally attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the c8 ((1zey2 yej. iq*y;bjraspk enter of the Milky Way Galaxy (Fig. 5-46) at a distance of about 301p8birk jey2 *e.q(ayys;zj(,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.aukhv4 y.)twx sk20i -50 m on each side. Find the magnitude and direction of the gravitational force onv -y0a)w khu4ktx.si2 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 th67x l2mx.omgqe Earth $ \left(\operatorname{mass}=6.0 \times 10^{24} \mathrm{~kg}\right)$ and has a period of 6200 s . Find (a) the magnitude of the Earth's gravitational force on the satellite, $\approx$    $\times 10^4$
(b) the altitude of the satellite.    $\times 10^5$

  What is the acceleration experienced by the tip of the 1.5-cm-long sweep s6b.v mjk tf*e6(-7uh ilqp4) f*nytlsecond hand on your wris( n* ljt umkfp.ile4 f 667bshy*-tv)qt watch?    $\times 10^{-4}$

  While fishing, you ger5)w;gxxto 7)o 1 kcumt bored 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 0.5cxt7g5;u ork )m)o 1wx0 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 desig)*mz75a f cdpd*ps8rpvl8 3qdned so that a car traveling at dv5paps3dm7 p) **c dr8 fzq8lspeed $ 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, utilizesv.,2lxda vwy9 o3eu b6 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 force. The passengers experience less friction force against the seat, thus feeling more comfortable. Consider an Acela train that rounds a curve with a radius of 620 m at a speed of (approximate.d uvwe9x,oly vb2a3 6ly ). (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.$\approx$    $\times 10^2$