Sometimes people say that water is removed from clothes in a spin drr e9*/lxep/ iayer by centrifugal force throwing the water outward.e 9axp/l *eri/ What is wrong with this statement?

Will the acceleration of a car be the same when the car travels around asbuz*lfdy gwi ) * ;eg8pklaas(nl952n6yu: 6 sharp curve at a constant 60 km/h as w uyykb8seulsw 6 p*g ;f2*9lian:56n z)(gldahen it travels around a gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Where does the cfu89t5lkn dhbo/ th+ z9 dlm,7-ccwl-ar exert the greatest and least forces on the road: (a) , t9mdh c n+7 zk5b9lll/-u -8hwdctfoat the top of a hill, (b) at a dip between two hills, (c) on a level stretch near the bottom of a hill?

Describe all the forces acting on a chiykni)(v)dmi)k-p9j7ej d (lcld riding a horse on a merry-go-round. Which o)-(cvkkpji( )m di) yel97djnf these forces provides the centripetal acceleration of the child?

A bucket of water can be whirled /-hwh8 e j+ rwrahb17win a vertical circle without the water spilling out, even at the top of the circle when the 1bh+ rhr -aw/e78jw whbucket is upside down. Explain.

How many “accelerators” do you have in your car? There aodz )1pke4mld xf*;,vre at least three controls in the car which can bd o *4lzvedm ;kfx,)1pe 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 hill,5pbya9r q+2 fnmuc4iza . 7x:p as shown in Fig. 5–31. His sled does not leave the ground (he does not achieve “air”), but he feels the normal force between his chest and the sled decrease as he goes over the hill. Explain this decrease usinym27: a+rf . ux45zcb nq9ipapg Newton’s second law.

Why do bicycle riders lean inward wg)sr 3juc:qgs +anhkls 4;/4chen rounding a curve at high speed?

Why do airplanes bank whi)z6fek p 5)x.xc5qk yen they turn? How would you compute the banking angle given its speed and 6qk.xzexpi5)) c fy5kradius of the turn?

A girl is whirling a ball on a stz b/jx)vbmw4f hi 3ve+br4g vp* tx.2n h7:,cxring around her head in a horizontal plane. She wants to let go at pr xbtgv*wvh/m:4 72i, vpc x)+f4jexz.r n3bhbecisely the right time so that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force o;w6 y:i4o ovpkn the Earth? If so, how large a force? Consider ak64;y :pwv ooin apple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were doublemr tnx( t+t3e+s;s+tfyjx thv)+r9i : what it is, in what ways would the Moon’s orbit be different?+ 9xtr:vh +;+fts(ije3t m t)rnysxt+

Which pulls harder gravitationally, the Earth on the Moon, or the Moon5ujz w01f5ks f on the Earth?s zuj 501f5kfw Which accelerates more?

The Sun's gravitational pull9:lqrsam i4)n, jr-ptl.rxb* 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 gravitational pull from one side of mx l,asr:4r9itjq l- b*.pr )nthe Earth to the other.]

Will an object weigh more at the equator or at the ye-i ahewk .60poles? What two effects are at work? Do te0 e.6ywha-ikhey oppose each other?

The gravitational force on the Moon due to the Earth is only about half 3fd x fx,xr2-o2gisj/9f no1g the force on the Moon due to the Sun. Why g/ xifdsnr92gf 3ox1x f2,-joisn’t the Moon pulled away from the Earth?

Is the centripetal acceleration of Mars in its orbit aroufmvlzsau8 +n(:00h vfcd/8 sck+3 vefnd the Sun larger or smaller than the vzsc3a 0fkffd/c 0(+v8+ mlvuse n: h8centripetal acceleration of the Earth?

Would it require less speesh-cgp anp;3 ,d to launch a satellite (a) toward the east or (b) toward the west? Consider the Earth’s rotation np-sa3gp;h,c direction.

When will your apparent weight be the greatestyk); yi6-6wxj+gg fqi 1fo nd+b;z,mi, 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 leas6 oj;,+ig;x mgzdnbfkqyi6)w1-if +yt? 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 spashogs 3t9zuz-kifrz, u4d8c/; kt t: :ce 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 cziutoz:t :zk/hfgu3dk s;, 89s4 t-r force we feel on our feet, and (c) any other aspects of gravity you can think of.

Explain how a runner experiences “free 7f;bda*p1 cjc.n 3 9m h1hkmwffall” or “apparent weightlessness” between stepsmbj kcf1 .mdn;hw391* pach 7f.

The Earth moves faster in its orbit around the Sun in Janu o4juv3n+5 itdsb7a obo755apary 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 tiltu4nsb a3pbo7vj o ito 557d5a+ of the Earth’s axis relative to the plane of its orbit.]

The mass of Pluto was not known until it was discx i (l/umx wyibo3x,+3overed to have a moon. Explain how this discovery enabled an estwxu(mx l3+/yi , obx3iimate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is mv*:t-doepgeov;x m4z.h:- tvuch larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of the Earth to the other.]A child sitting 1.10 m from the -:.te x; tmovvzo-eg 4 :vhdp*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 1c8c4fbesv +-d 980 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 Earvgnsmr c,6:s7 :/ r7ldr;d4wsnjl b1fth in its orbit around the Sun, and the net force exerted on the Earth. What exerts this force on the Earth? Assume that tr 4sl1d, f7:n c /vl6dmsn:rb7gjwr;s he Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg dq,;4cm/ig5ges mhl+ 5dq t3eeiscus as it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. Calculate the speed of the discusqe;e t 5g5gl3 qcs/4dhm ,e+mi.   

  Suppose the space shuttle is xnb)a)m/odxzjy pl7 mqbe 1l3 +i b55)in orbit 400 km from the Earth's surface, and circles the Earth about once every 90 minutes. Find the cen 3lbb q5ja)ib )z yxp157dxn +m)e/lomtripetal 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 t9 nae e:+kg 0r+grki3ohe acceleration of a speck of clay on the edge of a potter’s wheel turning at 45 rpm (revolutions per minute) if the wheel’s da or+9 e 0kegnk3gir:+iameter is 32 cm?   

  A ball on the end ofl.th 3 *w+iou+ :t cv2o rqwe)+jhjy7v a string is revolved at a uniform rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its spjw+ 7h: 3)2uo*iv jchlyvewt q. o+rt+eed 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 whic(jhfp:(skj8d h a 1050-kg car can round a turn of radius 77 m on a flat road if the coefficient of static friction between tires and road is 0.80? Is this result independent jf( :js(k8d hpof the mass of the car?   

  How large must the coefficient of static friction be between the tires andjvfqzk. h: hi7,jgz66 the road if a car is to round a level curve of radius 85 m at a speed of 95km/h z7qj6fjg , :k6hihvz .?   

  A device for training astronauts and jet fighter p+, li+g*vadie ilots 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 weiid la+ive+* g,ght, 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 rotating turntab7n fddj9zqe1vf)*( r - 4zkeflle 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 7-e e 4ffv1njdkzzl*r9)dq (f 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 do9 -vhhkzu- 81 ) jhqysqo;,laxwn at the top of a)1v y8oa z9jkqqh- ,-hux lsh; 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 masssir ;8+v- ppgca+- yi8 u3tfhf,3gxwt 950 kg (including the driver) crosses the rounded top of a hill (radius p38ha --ufy+s;8g+3xwig ttrfv, ipc =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 Ferrisc cb3euzu/n d+3a57f9*owr nky 7tea( wheel need to make for the passengers to feel “weightlescawter9koun(ad7c 3 uyb* /+ ez n37f5s” at the topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.10 m. At tox0x1 q50p 0sa sjha1she50jaaq0xshxo1 s0 s1 p lowest point of its motion the tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a cenxdnql:n47 rd6 dxv*y +trifuge rotate if a particle 9.00 cm from the axis of rotation is to experience an accelelv4qn6ddx+xny7d r :* ration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically walled "r 9um(b 5dfhxjw/; 2rhioom." (See Fwb5 mf9u ir(;j2hh/ xdig. 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 ex jz( ,e(j:o 2xumg7cin a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connectede(o e(m7:j cuz ,j2xgx 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 ignop-+qh/1k*dk kek ze7bhj9- xb ring the weight of the ball which revolves on a string 0.600 m long. In particular, find the magnitude of x9jhk1e kq+*/-pzbde kb- k7 h$\overrightarrow{\mathbf{F}}_{\mathrm{T}}$ , 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 tra 2 qopniwy6,o,veling 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 r4wvhusi:3:ve)w v-*;6z im vup ki4r$ 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 m2t.xo*x*cf -h, ha, r udiw9):kutkz t 4o3jssaneuver by diving vertically at 310 $\mathrm{~m} / \mathrm{s}$ . If he can withstand an acceleration of 9.0 g 's without blacking out, at what altitude must he begin to pull out of the dive to avoid crashing into the sea?   

  Determine the tangential and centripetal compnlj hn2, a +gbc+6wku/onents of the net force exerted on the car (by the ground) in Example 5-, n6baw g+jcl+uk2n /h8 when its speed is 15$ \mathrm{~m} / \mathrm{s}$ . The car's mass is 1100 kg . F$_{tan}$ =    F$_R$ =   

  A car at the Indianapoljf 8azlyv i6oc*l09:jpw8b :ois 500 accelerates uniformly from the pit area, going from rest to 320km/h in a semicircular arc wpo8l689by*j jf0za:vil owc:ith a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static friction have to be between the tires and the road to provide this acceleration with no slipping or skidding? $\approx$   

  A particle revolves in a horizontal circle of radius 2.90 m . Atxf ,-dhf t.c9v a particular instant, its accele- d fxth9,.cfvration 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 gra( bt,egogv ts- w fjmxev3et ,1d6.9;pvity on a spacecraft 12,800 km (2 Earth radii) above the Earth’s surface if its mass is 1350,mxvt t3e-b g(1e,v et g6s.pdwfj;o9 kg.   

  At the surface of a certain planet, the gravitational acceleratiolvq3jc nj5r(zc42s7oc +y bg;n g has a magnit cjcc(24g +7njq lz3;sr5 ovybude 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 Mo)p)r8um4xstk fs;8y kon's radius is 1.74 pftu)y;8krx8s)s mk4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet he,4x 0nocy(r8p8la dhas a radius 1.5 times that of Earth, but has the same mass. What is the acya(e8o8hl x 4pd,cr0nceleration due to gravity near its surface?   

  A hypothetical planemmt0i:w ,0mtpt has a mass 1.66 times that of Earth, but the same radius. What is g near its surtpt00mm,:iwm face?   

  Two objects attract eakh.0 v o9;4ubzdi3rv9sdqq m8l 6,gcgch other 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 effective value of g , the acceleration of gravity, at (a) 3200 mta*z ddx3+kv58x .pl m +.dvkpmt5x x3zla8d *    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Earth’s center to s9;h(ol +s9xme lrl(ia point outside the Earth where thegravitational acceler9 li mh9s s+lrx(eo(l;ation 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 Sun ptls/+atd ;oe2ak02 s)y zxz*n acked into a sphere about 10 km in radius. Estimate the surface gravity on this monsterl ans0;tx*ky2+t z) odsa2 /ez.    $\times10^12$

  A typical white-dwarf star, which once was an avera,;qi :tckn/l mlsnabp -7.*o tge star like our Sun but is now in the last stage of its evolution, is the size of our Moon bm i;ska.tpcqn -lo,lt/ * nb:7ut has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astronauts feel 4qk-o8k mfua 4weightless while orbiting in the space shuttle. Your friends respond that they thought gravit -4oa8fkq4 umky 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 corners of a square ofm.uo u51m 2jzj side 0.60 m. Calculate the magnitude and direction of the total gravitat uojzu1 25mj.mional force exerted on one sphere by the other three.   $\times 10^{-1} \mathrm{~N} \text { at }$    $^{\circ}$

  Every few hundred yew s+5brp yu6p6ars most of the planets line up on the same side of the Sun. Calculate the total force on the Earth due p6s bp+5urw6y 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 0.38z0u/1p(5:ytb-l f sexwijk 4k of what it is on Earth, and that Mars’ radius is 3400 km, detwk /5i4lfyp :0k ezj1tx(su -bermine the mass of Mars.    $\times 10^{23}$

  Determine the mass of the Sun using the known value for thj zd8 m4tc:4bo vveb/qzy7w;7e period of the Earth and its distance from the Sun. [Note: Compare your answer to thjvq 4:8 y bz4zdt7cow;/bevm 7at obtained using Kepler’s laws, Example 5–16.]    $\times 10^{30}$

  Calculate the speed of a satellite moving in a stable circuz0t: 78 qhe-brg(tqaelar orbit about the Ea(qhe- re tbgt078:qzarth at a height of 3600 km.    $\times 10^3$

  The space shuttle releases a satellitek1u0,hltqasp*ag. 5p r 5r; dq into a circular orbit 650 km above the Earth. How fast must the q5 aapg1*,k5t0rs .ldh;purq shuttle be moving (relative to Earth) when the release occurs?    $\times 10^3$

  At what rate must a p*xszldq0 kl0;h,7cwl;(in v cylindrical spaceship rotate if occupants are to experience simulated gravity of 0.60 g? Assume the spaceship’s diameter is 32 m, and give your answer 0 cnp ql,sll;h*kx 7z0(i wd;vas the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it r6 a4e63w yzomtakes for a satellite to orbit the 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 depend on the mass of oa wm4e66zy r3the satellite?    s ~    min

  At what horizontal vel7i09xe svl m f,hl1s-nocity would a satellite have to be launched from the top of Mt. 9ls sv01h,i7xlfn m-e Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module con stxj1 mj-*.iq pzb(p;tinued to orbit the Moon at an altitude of about 100 km. How long did it take to go around ts1tzib.pp(q;mjj x *-he Moon once?    s

  The rings of Saturn are composed of chunks of ice t qlo/w8a3 jlwo+j3n: i(zp 7z xgbgm*/hat orbit the planet. The inner radius of the ring gi3 7 3lo(qz njao/bgj*/p:lwm+xzw 8s 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 ro 8y8 (nfpwai+mtates once every 15.5 s (see Fig. 5–9). What is the rationa+fp88y m( wi of a person’s apparent weight to her real weight (a) at the top, and (b) at the bottom?
(a)    (b)   

  What is the apparent weight of a 75-kg astronaut 4200 km from the center of ,nd6*eh; ktghp 8 6dmkthe Earth6 kd,p nemd*h ;kgt8h6's Moon in a space vehicle (a) moving at constant velocity,     ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-stdmunuf 6k;b99ar system consists of two stars of equal mass. They are observed to be separated by 360 million km and take 5.7 Earth years to o fnuk6;umb9d9 rbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the weight of a 55-kg woman in an elevator thalnpr c.(v -.e,:kkwtat movctk .vp lk:e,w.(ran- es
(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 ufc-fleqs,3 v1:sdzx z* 8y1asuspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. Wuvs,: exz-z 813ay* sf1ld fqchat was the elevator’s minimum acceleration (magnitude and direction)? a =   

Show that if a satellite orbitswt/:pkif 4wc+fe64q e very near the surface of a planet with period T , the density (mass/volume) of the planetp:f+t4 w46w /efi eqck 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 dhwzg djf*r9t i 6(4(nMoon (27.4 d) to determine the period of an artificial satellite orbiting very near the Earth’s (ntdfj9 (r gz4d* wih6surface.    s

  The asteroid Icarus, though only a few hundred meters gj(bq (s7d-5v/ hjsbzacross, orbits the Sun like the planets. Ig zsjj( bsh5vb/7q- (dts period is 410 d. What is its mean distance from the Sun?    $\times 10^{11}$

  Neptune is an average distdmnd),kz j a1;hw7 in+ance 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 everye81 z zm zwa jr1is-ym4o++ge;j,) h)xmbztn( 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 Solar System? What planet’s orbit is nearest when +e z-o, mmbzi;g)hjwt1z m4+)yna1 rxe8z( s jit 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 about0hk,1 +j ehcwp the 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 di(d8zwbdrc*k /stance for the four largest moons of Jupiter (those dirck*wbd8/d z (scovered 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 Eai*1lrzai, ;b1j bny s3pi5d 3hrth from the known period and distance of the Moon. 1 ,;1nbriza*j53yhid 3ibps l    $\times 10^{24}$

  Determine the mean dis9,lbtpy : d+ lcyhyl)x/;gf kx4-sl3utance from Jupiter for each of Jupiter’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Tabl,lhgy 4f/kxll); cb-3+yxltdpys:9 ue 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 ma:) 2qw4ctsp iuny fragments (which some space scientists 2s)up qcw4:i tthink came from a planet that once orbited the Sun but was destroyed).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an a t32vjfl/an 6 k2y/f ua1ajh/ortificial "planet" in the form of a band completely encircling a sun (Fig. 5-40). The inhabitants live on the inside surface (where it is always noon). Imagine that this sun is exactly like our own, that the distance to the band is the same as the Earth-Sun distance (to make the climate temperate), and that the ring rotates quickly enough to produce an apparent gravity of g as on Earth. What will be the period of a/aju1ljayn32 /k/fhv o6tf2revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging inhorh/bx 9nqmw:b;oj :nr1fj .88q,la qif 57d an arc from 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 poh:7 j.q8 w 95ornoafqqni1:b ,frhb mdxj/;l8int 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 gravi3yz+ )i(.xlhnpva,*kuktg d .rx+g0cty be half what i uk.k +nyhx 3 xv a*pg.rc)dz0(+tlgi,t is on the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutuau wtj *h,5/u0 tu d6es5kkxns1l 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 thek,steujn 5ktuw u*d56/hs10 xy pulling on one another?    $\times 10^2$

  Because the Earth rotates once k2d0; aj ) l.twn9ulqncuq- )utjc.(vper day, the apparent acceleration of gravity at the equator is slightly less than it would be if the Earth c)c. l - t;)kwu d.lqauvntj09 2u(qjndidn’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 traveling directly :xc:+hcg- 1eo pe3zr+lgyo3l p5n 1lifrom the Earth to the Moon expe lrylg +1pcp+o1h:3 elce:x- zni3o5grience zero net force because the Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, .xtuf8aiflx xyq1kns07u3 / .but when you stand on a bathroom scale in an elevator, it says your mass is 81ufx0kls. t n8axy/q i.xu37f 2 kg. What is the acceleration of the elevator, and in which direction?     ----待选择----upwartddown 

  A projected space station jqhqb8p1a .;r7**y + yghlfkdconsists of a circular tube that will rotate about its center (like a tubular bicycle tire) (Fig. 5–42). pf8*jl *;yk.q yahdqb1+ h 7grThe 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 (F 0-k)gvmnt it.ig. 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 r603m newufw/ 4xfc0 lv,0qc ,dp4dlitjj .g7planet in terms of its radius r, the acceleration due q3dd64uc0 ljrjnpl wfgwvxfc, t,e 4m70.0/ito gravity at its surface and the gravitational constant G.

A plumb bob (a mass m hanging on a string) is deflecte t2y qufu7. n7oo:hzz*d from the vertical by an angho7 f *:27ntzoy.uuzqle $\theta$ 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 bl g h mn(p*rlx )),6nx4+mnd7u kw9ujranked for a design speed of If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car sah6u97nl*(nxd m))rr,nxlk+ pj w g4mu fely handle the curve?

  How long would a day be if the Ear1mnnw;.k)7:zg m ; 4ahlsjitjn4 h :czth were rotating so fast that objects at the equator were apparently weightlesmm4z1isg)n 7jlwhc nj tn;;:.:4ahz ks?    $\times 10^3$s

  Two equal-mass stars maintain a constant distance apart of 8igab-4 ,tgm0 z.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 convx0v els6j irf nz,y,.v:-c p*stant speed rounds a curve of radius 235 m. A lamp suspended from the ceiling swi:is0pezv-,v*yv jc . l n6fx,rngs out to an angle of 17.5$^{\circ}$ throughout the curve. What is the speed of the train?   

  Jupiter is about 320 times as massive as the Earth. Thus, ilo k, g11ii/qc*fb(eet has been claimed that a person would be crushed by /likb(i1c* e,fg 1qe othe force of gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the;de: wk s6oxj8t7qcq4 Hubble Space Telescope deduced the presence of an extremely massive core in the distant galaxy M87, so dense that it could be a black hole (from which no light escapes). They did this by measuring the speed of gas clouds orbit;se7c:4ktw 6o8xd qqjing 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 valleyv nvg o/,rp:e.r i,keq-42upe shown in Fig. 5–45. Both the hill and valley have a radius of curvatu poverp.q4-n2veu ,i ,:k/egrre R. (a) How do the normal forces acting on the car at A, B, and C compare? (Which is largest? Smallest?) Explain. (b) Where would the driver feel heaviest? Lightest? Explain. (c) How fast can the car go without losing contact with the road at A?

  The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites oda/jet n 26ia7 nnrgh +bfl)52rbiting 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 orbitsjb6hi nn lt2fed) a/7rga 5+2n, 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 Rendeka.tth24lk 7l zvous (NEAR), after traveling 2.1 billion km, is meant to orbit the a24kll t.7ka htsteroid 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 .rkw/2vsil: fc xugtw*og-5*qr 32gpshuttle pursuing a satellite in need of repair. Yovwi5 pr*.t x:c3*k / lg2rgug 2f-soqwu are in a circular orbit of the same radius as the satellite (400 km above the Earth), but 25 km behind it.
(a) How long will it take to overtake the satellite if you reduce your orbital radius by 1.0 km?$\approx$    h
(b) By how much must you reduce your orbital radius to catch up in 7.0 hours?$\approx$    $\times 10^3$

  The comet Hale-Bopp has a period of 3000 years. (a) What is its mean dista2 u6f:jx:br) clrvj)ince from the Sur6cjbf:uv rxi ):j l)2n?   
(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 vale 9n:07ttryj,v df mzbp8.;ylue of G would need to be if you could actually "feel" yourself gravitationany j9;:dbr8tvf7pt.e, l0ym zlly attracted to someone near you. Make reasonable assumptions, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of ttq af u4p:.qs2he Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the cente q4spuqfa .t:2r $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on eebj+ d9wm ./mbach side. Find the m jb mbm/e+d.w9agnitude and direction of the gravitational force on a fifth 1.0-kg mass placed at the midpoint of the bottom side of the square.    $\times 10^{-10}$  ----待选择----downupward 

  A satellite of mass 5500 kg orbits the Earthq(j q a o+8*y9 ahalkgfjl51f03etre3 $ \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 sw4zze-d:j dp2 eeep second hand on your wris d2:j4dz-pezet watch?    $\times 10^{-4}$

  While fishing, you get bored and start to swing a sinker weight around* f i 5,bmbcdhf)aj+;f 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 ib b*a d+h, ;fjimff)5cs the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of ro2c ud65p5ibqf -u,zbzsh-axvj/ zu:p r1( b*adius R in a new highway is designed so that a car traveling at szu 1 v2q u*j 6dzx-sbb5zh5-u(ifrocpba:/p,peed $ 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 the cars when neb8w l zt*obuo8o:pr:oz5 2lr9gotiating 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 (approximately ). (a) Calculate the friction force needed on a train passenger of mass 75 kg if the track is n l928z*tz brob:o :8wpoo5lru ot 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.$\approx$    $\times 10^2$