Sometimes people say that water is reky 3lgq04 -uc;v6fuqh moved from clothes in a spin dryer by centrifugal force throwing the water outward. What is wrong with this statementkc f;3guvuh6y4q0l- q?

Will the acceleration of a car be the same when th2o-,20nxz6f3mhjc4h va v v yhe car travels around a sharp curve at a constant 60 km/h as wh3f zy06a2mhhvx2vo c4v ,nh-jen it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed alonz*, *8dhnhz8 gx q;r r5ffvqm(g a hilly road. Where does the car exert the greatest and least forces on the road: (a) at the top of af*qh;qgr8zzmhvn5(8 xd r*,f 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 child riding a horse on a m9b*1ef8)j54wd jst /j u(y ju.tvgfk qerry-go-round. Which of these forces provides the)kgut /*v.4s5jjjf9wd8qb1efu jy( t centripetal acceleration of the child?

A bucket of water can be whirled in a vekz04x e6auvx.rtical circle without the water spilling out, even at the top of the circle when the ax6evz4 .kx 0ubucket is upside down. Explain.

How many “accelerators” do you have in your car? There are se*3 sm t5jkjt 1ur(w6at least three controls in the c6 u(k1sjt3sm j5te wr*ar which can 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 oinbk4m9r2n 8t z-zqm2f 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 go29mntq42z-nk8m zbir es over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inward when rounding a curve at high gu ()wvwgr7.i)5 q 8yfcb;pqr speed?

Why do airplanes bank when they turn? How would you compute the banking angle 6;nrwcw.po/bt alh2j 6pz )p9k f h6:wgiven its speed and radius of th296ltkjza w pc6p h:fhwo6w.p) n; br/e turn?

A girl is whirling a ball on a string around her head in a hor 51j9( z g ohwool-2ius0cwny,izontal plane. She wants to let go at precisely the righ9-wz1,joo s cl ow2(y 0nh5igut 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 force on the Earv e(z7om,u0f :bhdw3 tth? If so, how large a force? Consif: ed 3m thb7u,(z0wovder an apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doubl 2oewo0u8y:y: u zbno:e what it is, in what ways would the Moon’s orbit be differenun:::yuwo yzo2bo8 0et?

Which pulls harder gravitationally, the Earth on the Moon, or tpk/fahqx*)rs5b *bwq(; t8ei-j ;gu che Moon on the Earth?;f * u*jsk- gqcxr(5hwet8pqiab;b)/ Which accelerates more?

The Sun's gravitational 5;izxh ql. 6oppull on 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 gr5h ixz;qopl6 .avitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator orewi l) of8-8op at the poles? What two effects are at work? Do they oppose eaceo8 li-)fw 8oph other?

The gravitational force on the Moon due to the Earw x60;8+uj 5 ikofbbyfth is only about half the forcf;8x o5b0 i+6kwbu yfje on the Moon due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal acceleration t5 5nyht (.9sug0tlhd )uggd3of Mars in its orbit around the Sun larger or smaller than the centripetal accelerd95 3 hg.0htug(lt dn5tg)sy uation of the Earth?

Would it require less speed to launch a satelrdt/k;ts:uj +lite (a) toward the east or (b) toward the west? Consider the Earth’s rotation dk r/:t+ts jdu;irection.

When will your apparent weight be the groe* r i+ .0(jr9 h:pu)jcddluyeatest, 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 weight be the least? Whenhi)0rd(+l *duo pr .c :9jueyj 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 o,3y.nfffrtbv6q mqm*s p0* k1uter space could be adversely affected by weightlessness. One way to simulate gravity is to shape the spaceship like a cylindrical shell that rotates, with the astronauts walking on the inside surface (Fig. 5–32). Explain how this simulates gravity. Consider (a) how objects fall, (b) the force we 3v,1mf*ysfm*q r. b0fntpk6q feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiendf.:mz:c t * 6*wqtxveces “free fall” or “apparent weightlessness” betweett cv fe.qxm :wd:*z6*n steps.

The Earth moves faster in its orbit around the q9x v;j8psg 6nSun in January than in July. Is the Earth closer to the Sun in Januaryv9jg6xn p;8sq , or in July? Explain. [Note: This is not much of a factor in producing the seasons — the main factor is the tilt of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discovered to h2sem5pqitsz n 32c:+a ave a moon. Explain how this discovery enab 3mtspn2e5qiac+zs2: led an estimate of Pluto’s mass.

  The Sun's gravitational pull on thetk th)(kkv 8e0 Earth is much larger than the Moon's. Yet the ( kkekt hv0)8tMoon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the center of a merry-go-round moves 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;:5(zwx)f8c ka heunx o3v*el 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 its orbi7pr:xrv 5+xc)hrf 8 ocju(m3x t around the Sun, and the net force exerted on the Earth. What exertsrx3x( m+pro c7)c hrj5u8xfv: this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force ogvai/qkw,27 n 8sye:bf 210 N is exerted on a 2.0-kg discus as it rotates uniformly in a horizontal circle (at arm’s length) of ra2e i/:,ns vbqa ygwk78dius 0.90 m. Calculate the speed of the discus.   

  Suppose the space shutn9z4t + o*mmzfm 2bnl4tle is in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Ex ob492zmtz lmf+m4nn*press your answer in terms of g , the gravitational acceleration at the Earth's surface. $\approx$    g

  What is the magnitude orndi5(4pzj8 cf the acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel8r( j5d icz4pn’s diameter is 32 cm?   

  A ball on the end of a string is revolv sly: el)c1c-wed at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its speewcl)1lsyc- : ed 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 turn of rad*pw*zr1b fr q+ius 77 m on a fl*q 1b+wfpzrr*at road if the coefficient of static friction between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static frict+ma h46() eknrun o2kqion be between the tires and the road if a car is to round a level curve o2+knuhe q4 ao()6 mrknf radius 85 m at a speed of 95km/h ?   

  A device for training astronauts and jet fighter pi : elre( 2jhlv:dvoeub-g .g13lots 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 tider v g :j2obegv-h:3.e ul(1lmes 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 ro,3pu sr4y;kka4c:j+z pb4 xu otating turntable of variable speed. When the speedabzy4pk44 j:xr3+, u; ups okc 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 do njasb0k*x4) ,sal1ukwn at the top of a ci0,bj ak au1s sk*n4)lxrcle
(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) p 1.vusy;8lk ecrosses the rounded top of a hill (radiu v.k p1luesy;8s =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 to makedy 15hiu txv;h8vvz(jw+ g9sv g:g7n9rjcw19 for the passengers to feel “weightless” a hg z91t dnv59;sjcv9xvuw8iw(y hg7g :1jrv+t the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertijy7 e. l6p:ppby,j q.gcal circle of radius 1.10 m. At the lowest point of its motion the tensipqe67p yy., :jjl.bgp on 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 o*y;r36jpw vm rotate if a particle 9.00 cm from the axis of rotation is to experience an ac*p 6 j;mo3vwyrceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people a/sb w;uh.sjaw(l5 ; yire rotated in a cylindrically walled "room." (See Fig. 5-35auy5h s.; w s;iw/jb(l.)
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 circp7 nplf4n ;.uwle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling.l4 un;n 7ppwf 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, bxa3z4 4 pha6yzy not ignoring the weight of the ball whic44aza yxp6z3hh 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 perfectly banked d k2f;3 r;zovtba+u(:xud(x x 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 u c+z: chqr,u5 o2qc/v$ 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 dypi, 89gy xp5dv6rj 9by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal components of the net mtdc1d u4ti)hio,r6j6tv 9 gfor73s0 force exerted on the car (by the ground) in Example 5-8 when its speed i gvo d4j)rdfc thui61oms,7t 03r6t9is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapolis 500 accelerates unif-dx nfa awv.o /05vyy fvy7(+oormly 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 a5wxv+yyavoff( y 7a0-v. d/nocceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal dw-a)0fe,yce aq /i/j circle of radius 2.90 m . At a particular instant, its accelefi,e/j 0qcay-/)a de wration 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 12,800 km (2 Earth radipt327wa+hdk b i) above the Ear3wa+ pt dhkb72th’s surface if its mass is 1350 kg.   

  At the surface of a cecj4b z1fhy/j 7m/v9ffrtain planet, the gravitational acceleration g has a magnitude of 12 bfm hj9c7/zy14j /vf fm/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 grj i1 td y34cghosaq*17avity on the Moon. The Moon's radius is 1.73 ahd1i*s1 4yjc ogqt74 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a ra*qge.zk hrk89 xee,(hdius 1.5 times that of Earth, but has the same mass. What is the acceleration due to gra,e x89k* zhe(. grkeqhvity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Earth v ecr1:eue5f3, but the same radius. What is g neacru e5f v:e31er its surface?   

  Two objects attract each ot )-8lbtuzl ,f tu03itther gravitationally with a force of 2.5$ \times 10^{-10} \mathrm{~N}$ when they are 0.25 m apart.
Their total mass is 4.0 kg . Find their individual masses. m$_1$ =    m$_2$ =   

  Calculate the effectiq,*ja,sc*l. zfe ,,x zy u7kkcve value of g , the acceleration of gravity, at (a) 3200 mk*sqaluckz,j,z,. , yec7 x*f    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to a point outside tiz45+fscyd j /q)s )o)jtpl0vhe Earth where thegravitational acceleration duz)5 j sj/foliy)d 0ctq)vs+4p e to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times the mass of our Sun packed into a sphere+8rfyc :u6.pg ts*vs rhb8+k w0sa3de about 10 km id6y fbs+ avk8+8th r.3pus r0sc :*ewgn radius. Estimate the surface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once hwmeg60ynrke v4p,5 t12gk7g was an average star like our Sun but is now in the last stage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this stay n5g6 v,grheptge7k2w4 0m1 kr?    $\times 10^7$

  You are explaining why astronauts ff2 1l*.x klgafeel weightless while orbiting in the space shuttle. Your friends respond that they thought gravity was just a lot weake *l.k1fxa f2glr 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 corners ov*ny (c4x,;nxxx-xwj f6svf-t5vd1 wf a square of side 0.60 m. Calculate the magnitude and direction of the total gravitational forc vs cxnf5y-vnw*4wf(d 61;- ,x tvxxxje 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 y m) nt) : --8tetuiiix y1zcvgo/0l3lup on the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn, assuming all four planets a-t )luy tlyecmng-: )8 v3i/0i izot1xre 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 o 4 /-xg uiikdtls8r,)lf Mars is 0.38 of what it is on Earth, and thastxkr/4g i)i,l - udl8t Mars’ radius is 3400 km, determine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for the period of the Earth g,yl22 cv ecpq 48ijf8wpeh ;;and its distw8; peh,2ye l2;ccq gf4pvi8jance 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 movhb*c.qct; g6p:nmcx q1f a e 4*ok,ng4ing in a stable circular orbit about the Earth at a height of n 4*qg, ck: m*cgp1qohc6fn4e b ;xta.3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular orbit 6v xk /xw..l)dh kkc:5z50 km above the Earth. How fahlw: x5k/dk)xc.z .vkst must the shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a cylindrical spaceship rotate if1v1*g jjf2 vtb occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s v bftj1vjg 12*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 h 5zcarx .y7wjb(1 -plthe 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 the Earth. Does your result depenbj-ach(1 x5 lz rypw.7d on the mass of the satellite?    s ~    min

  At what horizontal velocity would a satellitew aj17 z l*b f-dsa9dzh:--cmi have to be launched from the top of Mt. Everest to be placed in a circw-da*:-m9d 7 hl1-fsb ziaj zcular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to oxr/m3e,cek0 hdc ;etsp9/ o8z rbit the Moon at an altitude of about 100 km./xcp 9t;zkm/80e decosh3er, How long did it take to go around the Moon once?    s

  The rings of Saturn are composed of ch*pjd xe x))jz+unks of ice that orbit the planet. The inner j + xez*xp)d)jradius 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 every 15.5 s (see Fig. 5–9). 7g qsw j:+tr9kp. pfw2What is the ratio of a pe :2qt7pw.sfrpg9k+ w jrson’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 75dwpg:o(*+0sl hu*kh h-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) modgk:0*+hu(p * ohlwhs ving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars okgxa.rsl6dmd59n1,e qf41 e kf equal mass. They are observed to be separated by 360 million km and take 5.7 Eam9,fdg.4er1xeq sdk 6lk51 narth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale r,ina z8bs6 amcd) s/qqv,/w;read for the weight of a 55-kg woman in an elevator that mod 68,; wr)b/av q ,zis/nqmcasves
(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 cor 0tzqymk*v61fd suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator’s minimum acceleration (magnitude and fy6kt q1 0z*mvdirection)? a =   

Show that if a satellite orbits very near the surface of a planet with periqxz; yk5gm mw 4oyt59eiv:3r6od T , the density (mass/volume) vt9yr5 w:oq6m 4ymzei3xk;g5 of the planet is $\rho=m / V=3 \pi / G T^{2}$ .
(b) Estimate the density of the Earth, given that a satellite near the surface orbits with a period of about 85 min .

  Use Kepler’s laws and the period of the* rn o.an5t*i2ef q6dfm4 nc1k Moon (27.4 d) to determine the period of r. n2 4n eiqmdoffk*1t5n* 6acan artificial satellite orbiting very near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sun spllz(q -yr2 2g2)mc slike the planets. Its period is 410q2 -llpc2 )ysrz(m sg2 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4.ih/h1(3 ftjfl5 $\times 10^{9} \mathrm{~km}$ 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 on7 4/: gxldsymbce every 76 years. It comes 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 Solasbyx 7l:g/4 mdr 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 c c074qgah vuws2gctd/1 x7 ;nqenter 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 2 lb,b ,gdtsb4xym5cz9j- a 1jmass, period, and mean distance for the four largest moons of Jup5s1j- 2,c,t gmb yjld9xbba 4ziter (those discovered by Galileo in 1609).
(a) Determine the mass of Jupiter using the data for Io.$M_{\substack{\text { Jupiter- } \\ \text { Io }}}$ =    $\times 10^{27}$
(b) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?
$M_{\substack{\text { Jupiter- } \\ \text { Europa }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Ganymede }}}$ =    $\times 10^{27}$
$M_{\substack{\text { Jupiter- } \\ \text { Callisto }}}$ =    $\times 10^{27}$

  Determine the mass of the Earth from the known period and distance of the Motg.znbsh6y-h dvyyu +)1)l : ton. z)tv -y.h:)tysuy6 ld gn1hb +   $\times 10^{24}$

  Determine the mean distance from Jupiter for e 2gs1h /v4zghiach of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Com1gh4 v 2higzs/pare 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 m1f3 ;pwax8dnqj5c(fdx ck i44any fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyed).iwf4 dxq3;1cx(apdk5n8jc 4 f
(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 des /p b/ 6b udokgnqm371vtr)0dfcribes an artificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is alwam v kdqrtb0 fd ng7pu/1o63b)/ys 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 (Fi 23lpipv;rf dr9q2z (zg. 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 the9rlpp z fqv(32ir;2zd 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 will the acceleration of gravity be half whl5pdecpm he ) 3t0vf7(at it is on the sle)pfpdev c503h t7( murface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutua /v01sraq8qr tl circle once every 2.5 s. If we assume their arms are each 0.80 m long and their in0 at1/rqvs q8rdividual masses are 60.0 kg, how hard are they pulling on one another?    $\times 10^2$

  Because the Earth rotates onc: 2 q/(r(fz9rxgj xqh+z8b v+hl6hug pe 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 fracl:uf6g bp2/8gr +xvh(zrq+9zj q xh h(tion of g is this?    $\times 10^{-1}$

  At what distance from the Earth will a spacecraft traveling directly froxk;ufw7qy8ju j wq/- 1m the Earth to wqx-w;8/jk y7u uf1qjthe Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but wi.lh mu;i72b /icty5jhen you stand on a bathroom scale in an elevator, it says your mass is 82 kg. What is the accel5 2cbijhltuim ;/iy.7eration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station consf+iwqzor. 1 i. ;rx)iuists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). The circle formed by the tube has a diameter of about 1.1 km. What must be the rotation speed (revolutions per day) if an eo .xwizrq ;f.ii+u)1r ffect 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 loopwsl(rn* jnt *t rq) /2v0qwbq5ie wn66 (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 radn6;igc3kp izgz/ bs: )ius r, the acceleration due to gravity atcbz: ;si3n 6kzp i)g/g its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflected from th85i9ies 10umfsh i h:ve vertical by an 9vh5s ue 0ifiim8sh:1 angle $\theta$ due to a massive mountain nearby (Fig. 5-44). (a) Find an approximate formula for $\theta$ in terms of the mass of the mountain, $m_{\mathrm{M}}$ , the distance to its center, $D_{\mathrm{M}}$ , and the radius and mass of the Earth. (b) Make a rough estimate of the mass of Mt. Everest, assuming it has the shape of a cone 4000 m high and base of diameter 4000 m . Assume its mass per unit volume is 3000 kg per $ \mathrm{m}^{3}$ . (c) Estimate the angle $\theta$ of the plumb bob if it is 5 km from the center of Mt . Everest.

A curve of radius 67 m is banked for a design speed of Ianc8:0j q qs1nf the coefficient of static friction is 0.30 (wet pavement), 0jqnns a8c q1:at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating soi0 k;uuz;-vo v fast that objects at the equator were apparently weightz-0; kviu;vuo less?    $\times 10^3$s

  Two equal-mass stars maintaiozu*tk6n5rp--1el2 e 2 c dxqqn a constant 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 speed rounds a curve of radius 235 m. A lampc8ppqcf5 .nh mt1)yx2fn*;:zob3f5xpbqi h 8 suspended from the ceiling swings out to an anglec8)p 3mcfp pxf; i5*yn 8h :5ozb1q2xfqnt.hb of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the086h p/ivygrn Earth. Thus, it has been claimed that a person would be crushed by the force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a pgi8 hp 6nv0y/rerson 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 the prw7a 9ek (flvc0esence of an extremely massive core i e(lackw9f7v0n 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 4tarl( j(b9fsh0vzxbq1n:v.it 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? Lightestt(v (zbx: aj4h9fbnqrl.1sv0? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellitex5y) unbn0qdkk+m3n6s 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 satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical ]n6bk)n+qu 53x knm0y d. (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 2.1kuiu4u- q5u3 oqwshr 9yx6v;2 billion km, is meant to orbit the asteroid Eros at a u9qq3uxosuk; -2 6 vy wui45hrheight 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 igbkg:oq*sbc1gi0 )i 1n the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the sac)bib *0g1s1q gik :ogtellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean dlbf tr8nnqf+u+-4f8z istance from th+f88fq-rfzn lt4bnu+ e 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 nsd 473ps i,m/eosw ,rG would need to be if you could actually "feel" yourself gravitationally attracted to someone nis/pos,emn, r 743wd sear you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around te6 7j j)p3 q8gat8dk2.;f:ueqqbonlhhe center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-aeq 8p 3ju6g ;h2n.dote8lj bqq)7 :fkyears 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 aqjb;*7ke p 7va square 0.50 m on each side. Find the magnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the miq v7j*ak 7;bpedpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 4y6 vybl)*8nafekc2:4s s pqc kg 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 tip of the 1.5-cz:w) l/teed+ d: g vp4yqu7w.am-long sweep second han.:zeqe p al g7t+uww 4y/d)v:dd on your wrist watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weighmrsdjvegk zw9 9,nurp61h) 86t 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 vertical? [Hint: See Fig. 5689 jhgu6e,nkzwsp 1r )dmrv9–10.]    $^{\circ}$

A circular curve of radius R in 1ilk dn)7ags18c;ek 5wq0hama new highway is designed so that a car traveli0m1s l;wi)c hk78aengda1 5q kng 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 thkley)vd:cc u d do r11vy55e04e 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 curve5 dly v11rk vcc0oy4)e:ud d5e 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.$\approx$    $\times 10^2$