Sometimes people say that water is removed from clothes in,9 d o+dpyzlyl/j7f c0 a spin dryer by centri/z +dpc l,lyf 79jd0yofugal force throwing the water outward. What is wrong with this statement?

Will the acceleration of a carjw)yn7aw m6,k o+her, be the same when the car travels around a sharp curve at a constant 60 km/h as when it travels around a raye,woj7kwn6 )hm,+ gentle curve at the same speed? Explain.

Suppose a car moves at constant speed along a hilly road. Whk6fcqz3l xz/r71 uh n/ere does the car exert the greatest and least forces on the road: (a) at the top of a hill, (b) at a dip between two hilc6z/un7kzl hr qx3/f1 ls, (c) on a level stretch near the bottom of a hill?

Describe all the forces;s a,xan5m.b 7 ibua1ebi8 41bnlkw.k acting on a child riding a horse on a merry-go-round. Which of these forces providi a n1x7.k41mab kai5,.bb sblw8 uen;es the centripetal acceleration of the child?

A bucket of water can be wh+zdhqoc4xbf1 -pwg+ 4irled in a vertical circle without the water spilling out, even ofxq 41+bdgz 4-+pchwat the top of the circle when the bucket is upside down. Explain.

How many “accelerators” do you have in your car? Tjyy/l( s lz i3f6m.qp0here are at least three controls(lf 3z ls6imjyq0 .p/y in the car 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 qim.i kbw;5.e q;2yx7twzsb,over the crest 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 anbm5xtww i qz;. qe;7y,is2bk.d the sled decrease as he goes over the hill. Explain this decrease using Newton’s second law.

Why do bicycle riders lean inwa efn7t.b9o,) chlbusm6j 9ug ;rd when rounding a curve at high speed?

Why do airplanes bank when they turn? How would you compute the bthz+ 5ul5 x e 1gh4ba:x9 xp0:lvk2eouanking angle given its speed and2u0 z eo4xlk h+b5x:5hp9t :avxeugl1 radius of the turn?

A girl is whirling a ball on a string around her head in /q ug v,(v:nrlk vz/a6a horizontal plane. She wants to let go at precisely the right time s z :vnau6/v/(rqlkvg,o that the ball will hit a target on the other side of the yard. When should she let go of the string?

Does an apple exert a gravitational force on the Earth? If so, how law6)4qe 4s /s1npgsv+lxu uee3jn n24 mrge a force? Consider an ap wss24lx6eun4/e)3sen+ujn1 mv4gq pple
(a) attached to a tree, and (b) falling.

If the Earth’s mass were double what it is, in what ways would the Mooezhc o . 35b7nb/hhhtz y)k,e/n’s orbit be d7b .yz/3eeoh k ,hczthhn b5)/ifferent?

Which pulls harder gravitationally, thf1brg pcjq;l)d:l6 o88 .n.r9ufofz x e Earth on the Moon, or the Moon on the Earth? Which accelerates mor9pc6zf8xuq bdljrorn.;o f:g. f8)1l e?

The Sun's gravitational pul7 rany*; 2*j3futw ntel on the Earth is much larger than the Moon's. Yet the Moon's is mainly responsible for the tides. Explain. [Hint: Consider tt7aj* wt ru2*;nneyf3he difference in gravitational pull from one side of the Earth to the other.]

Will an object weigh more at the equator or s70e7q lz-ctiat the poles? What two effects are at workt-lq70 7zices ? Do they oppose each other?

The gravitational force on. r eo,qqu1r+b(rn py+0q)6imf ml8fz the Moon due to the Earth is only about half the force on the Moo y 086m r++pmqeiozrbnq1l,(r)uq.ffn due to the Sun. Why isn’t the Moon pulled away from the Earth?

Is the centripetal arx2q )9n za8vnly-uo :cceleration of Mars in its orbit around the Sun larger or smaller than the centripetal acceleration of the Earth?:-8yxloz q unvnr) 2a9

Would it require less speed to launch a satellite (a) towardtn1pz -4 -g;m 5po yfhq;xvgg1g :(dbb the east or (b) toward the west? Consider the Earth’s rotation directiodqtvgpmzp:b1 xg ;f;h5 (ob1n-g-4ygn.

When will your apparent weight be the greatest, as measured by a scale in a mo0)k90 *yqxucm) dj gwzving elev 0) 0*g9uzcxkqy)wmjd ator: 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? 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 f2q+0 7:r/owej+ 4qdcj,mcjd gj 0ufrspace 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. Consiw ,fde4cf j00 rq 2++jqu/d:jor7jmgcder (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 weighteexw+y oia sm0vh1* i .2nyiijz*1) 6qlessness” between steps.y 6)ii+am jwi *0v*sqo in1yhxz e2.e1

The Earth moves faster in itsdcj3c;/p an j4 orbit 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 pcj ;ac3n 4d/j— 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 have a moon.q a45p75azcj w *sckk2 Explain how this discovery enabled an est q5a*c 7j4s2awpckz5k imate of Pluto’s mass.

  The Sun's gravitational pull on the Earth is much larger than the Moon's. Yet m2spldxb/si0 x:dj3z d3sl6- the Moon's is mainly responsible for the tides. Explain. [Hint: Consider the difference in gravitational pull from one side of :lbi dpmsxdd2 - 3s3sx/06 lzjthe 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 19 gpr- +5dokbn(c /)ml;;dce:dsbl7r g80 $\mathrm{~km} / \mathrm{h}(525 \mathrm{~m} / \mathrm{s})$ 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 centripets s;7kp 9m0zztal acceleration of the Earth in its orbit around the Sun, andpz;9 k0s7sztm the net force exerted on the Earth. What exerts this force on the Earth? Assume that the Earth's orbit is a circle of radius 1.50$ \times 10^{11} \mathrm{~m}$ . [Hint: see the Tables inside the front cover of this book.]    $\times10^{22}$

  A horizontal force of 210 N is exerted on a 2.0-kg discus ash1cq6)7 )ven jccp6fp (cq / bhvj-hm/ it rotates uniformly in a horizontal circle (at arm’s length) of radius 0.90 m. C1hvcv)qcpec6hj )fp(bnq/ m67/- jhcalculate the speed of the discus.   

  Suppose the space shuttle is in orbit 400 km from the Earth's surface, and ci 44n+eb us5cm9:d 1sejh3p skprcles the Earth about once sj5h4:4 u cbep3sd+mn9 ep1sk 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 accelera 4 yzo8r2)nzogw q0q(mtion of a speck of clay on the edge of a potter’s wheel turning 0 nroqz4 qw2)zg(o8ymat 45 rpm (revolutions per minute) if the wheel’s diameter is 32 cm?   

  A ball on the end of a string is revolved at a uniformek)wt vcmi9ux3(2ai ;g+ ay8b rate in a vertical circle of radius 72.0 cm , as shown in Fig. 5-33. If its sp;v2k8ug 9 )3aiaebxy( + twmcieed 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 r:2ut3+gbgl ov adius 77 m on a flat road if the coefficient of static frictiob gg:vu+lo2 3tn between tires and road is 0.80? Is this result independent of the mass of the car?   

  How large must the coefficient of static friction be between the tires and thed,xozvd sr;a(bvh3m cjlm0 t /d+- ;3r road if a car is to round a level curve;z s lha,j3md3+-r(0d /brtovcdv;mx of radius 85 m at a speed of 95km/h ?   

  A device for training astronismwgmy.khv:5.6v f)5 g1jz hauts and jet fighter pilots is designed to rotate a trainee in a horizontal circle of radius 12.0hwyz5g)kmg: mjv hvs5fi. 16. m . If the force felt by the trainee on her back is 7.85 times her own weight, how fast is she rotating?    rev/s    m/s
Express your answer in both $ \mathrm{m} / \mathrm{s}$ and $\mathrm{rev} / \mathrm{s}$ .

  A coin is placed 11.0 cm from the axis of a rotating turntable of var9 duipuh x(z3q,x9 -uaiable speed. When the speed of theiu9x9hu-up q, a(dzx 3 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 upskh7 4m1wss-a dy3e(v :bz2fz mide down at the top of m hs:ez zw( 32v1 bfakdyms7-4a circle
(Fig. 5-34) so that the passengers will not fall out? Assume a radius of curvature of 7.4 m .   

  (II) A sports car of mass 950 kg (including the drivetpl1m:6 p-e.xem.zy 3a gjf ,yr) crosses the rounded top o,zt1:gy efp.m6 am3e- ly. jpxf a hill (radius =95$ \mathrm{~m}$ ) at 22 $\mathrm{~m} / \mathrm{s}$ . Determine
(a) the normal force exerted by the road on the car,   
(b) the normal force exerted by the car on the 72-kg driver   
(c) the car speed at which the normal force on the driver equals zero.   

  How many revolutions per minute would a 15-m-diameteruj3:d2zqy jawx(xwu :7gi8o9 Ferris wheel need to make for the passengers to feel “weightless” at the (g 9jw83xi7z:u:dw2qojx uay topmost point?    rpm

  A bucket of mass 2.00 kg is whirled in a vertical circle of radius 1.1mr,sez w*2k9wld fz000 m. At the lowest point of its motion th ,fwmkzd 290rz*e 0wlse tension in the rope supporting the bucket is 25.0 N.
(a) Find the speed of the bucket. $\approx$   
(b) How fast must the bucket move at the top of the circle so that the rope does not go slack?   

  How fast (in rpm) must a centrifuge rotate if a partic,h :j vy v4o:uvn0)ycqle 9.00 cm from the axis of rotation is to experiencun,0vh:y)o: cvqv 4jye an acceleration of 115,000 $\mathrm{~g} $'s?    rpm

  In a "Rotor-ride" at a carnival, people are rotated in a cylindrically dwo gou 9rv*))walled "room." (See Fig.)o9)d *r ugwvo 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 roi vpb1:qkb. ,t2anc1x tated in a circle on a frictionless air-hockey tabletop, and :ncx 2p b1t kqbv1.,iais held in this 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 this time, by not ignorin) an)wf;ejbt / 6;tyt*9uqduug the weight of the ball which uftw/*;u njt dyb6;9eq )a ut)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;b r (z8 z37urr lbyh/z6+zzqt 88 m is perfectly 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 massesnxjg ) dvs0x29 $ 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 vertically at 310rw-e8f*m6 m;g4 .pch vmq.cj z $\mathrm{~m} / \mathrm{s}$ . 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 componerrne . zpt6i+.66dea vf3xsa* nts of the net force exerted on the car (by the ground) in Example 5-8 when its speed is 15+f6ie .xznte6s 3.r*rd a6 apv$ \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 area, go 0hbl1)p2u1t-r vx wgny;+eul 7 atqt9ing from rxb );+h1n 1 yvruqlugtp late0-27wt9est to 320km/h in a semicircular arc with a radius of 220 m. Determine the tangential and radial acceleration of the car when it is halfway through the turn, assuming constant tangential acceleration. If the curve were flat, what would the coefficient of static 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 . At a particular a3f/*52adpu ,u jshbhinstant, its acceleration is 1/ auua5 hs,* dhfjp2b3.05 $\mathrm{~m} / \mathrm{s}^{2}$ , 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 nf ;pmwo9o)j ct72z:con a spacecraft 12,800 km (2 Earth radii) above the Earth’c27m c)tf :w;op9nzoj s surface if its mass is 1350 kg.   

  At the surface of a certain planet, the gravitatty)p f*ab l q;;b*obz:ional acceleration g has a magnitu;*lbfboat : )p;*qzby de 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 graqb7kb2c8*k3fa juz e:* w3q fkvity on the Moon. The Moon's radius is 1.7f3b 8 ek wkcj7z*23qf:bu *qka4 $\times 10^{6} \mathrm{~m} $ and its mass is 7.35 $\times 10^{22} \mathrm{~kg}$ .   

  A hypothetical planet has a radiur0y9:2c;p ch0n htqcfs 1.5 times that of Earth, but has the same mass. What is the acceleration due to grav0y9 cqp rhh:2n;tccf 0ity near its surface?   

  A hypothetical planet has a mass 1.66 times that of Ef+ j:9qbx q5eearth, but the same radius. What is qb 95ejq +efx:g near its surface?   

  Two objects attract eacv *p/ggm ee1o 0flq+i-h 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 di8 iphwi82;ii - +ev7ogze i9gravity, at (a) 3200 m widzigo 9;ipv7i8i e2+ei h-8    , and (b) 3200 km    , above the Earth's surface.

  What is thedistance from the Ear p//ar1)9jws 2jpud2nc0r ;vo q2kzzx th’s center to a point outside the Earth where thegravitational acceleration d2vz/jqpucxsro knpz9 a)d 2wrj ;/120ue to the Earth is $\frac{1}{10}$ of its value atthe Earth’s surface?   $\times10^7$

  A certain neutron star has five times thqwln)dr k22grh1 boex.6w-c- /yiqj/e mass of our Sun packed into a sphere about 10 km in radius. Estimate the suqie2 -r c .k1wg/o6lr)q2j whnxbd/y-rface gravity on this monster.    $\times10^12$

  A typical white-dwarf star, which once was an average star like our Sun but is )r+ p78am7 iw 1b orh-wfy elvp0ck7-zh4my)onow in the last s k8 1cyioy0ebwhf-hw o) )7m-rr7 v pz7+lpma4tage of its evolution, is the size of our Moon but has the mass of our Sun. What is the surface gravity on this star?    $\times 10^7$

  You are explaining why astrs ;t3zh6 .d lem)cis7k(bksj7onauts feel weightless while orbiting in the space shuttle. Your friends respond that they 7ed.smsh 36st (; i)ck7blkjz thought 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 g48nb: p v4d5rzybe(wat the corners of a square of side 0.60 m. Calculat4 b(zgnb548dp:vye r we the magnitude 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 planets line up on3duq euy 1r *z2+a/) baxrl/sk the same side of the Sun. Calculate the total force on the Earth due to Venus, Jupiter, and Saturn,r*qz e yd3ka) ulr/x+1s/2 bau 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 what p3m(,qkdkoz0it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mqd(m0,ok z kp3ars.    $\times 10^{23}$

  Determine the mass of the Sun using the know5tq1qg(5eixh kfkk 1o)8,hav n value for the period of the Earth an x151qkf5oh) kvkei hqg(8a,td its distance 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 satellq-c ehk2 qo5,wwyb0x 9ko(6eaite moving in a stable circular orbit about the Earth at a height ox9acy,-qokwwke26h(b e oq 50f 3600 km.    $\times 10^3$

  The space shuttle releases a satellite into a circular okt u ,jn) ecu/e- gv)jbn-b7p*rbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when th/ np-juuc*en v)kb) -b7e gjt,e release occurs?    $\times 10^3$

  At what rate must a cylindrical (g yt 3w1iu leh vj5*bny3(o6gha/x;ospaceship rotate if occupants are to experience simulated gravity of 0bay51gjgo ivy hxen3uw*loh3/t;( 6(.60 g? Assume the spaceship’s diameter is 32 m, and give your answer as the time needed for one revolution. (See Question 21, Fig 5–32.)   

  Determine the time it takes2lebxx fwwy83 agqrhy-(7 .w2 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 8(-wlga 72w.3hew2yqr bxxyf the Earth which is very small compared to the radius of the Earth. Does your result depend on the mass of the satellite?    s ~    min

  At what horizontal velocity woul:92zdp 0o55vwqjsi( vjt2u ukd a satellite have to be launched from the top ofdij:25(juos9pzu ktw520 v q v Mt. Everest to be placed in a circular orbit around the Earth?   

  During an Apollo lunar landing mission, the command module continued to ov jm(0 08auj8upk2j izhv;pm5 qg1ze7rbit the Moon at an altitude of about 100 km. How long did it takek1 pvm7qehi0jmu j ja 0p8z(gv5uz; 28 to go around the Moon once?    s

  The rings of Saturn are composed of chunks of ice that orbit the planet. t17yy d e, ypl8u.-xucThe inner radeudcyp t y l.u1x7,y8-ius 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 k 1kcql d5v(5x;-o9 c0yxhyhg(see Fig. 5–9). What is the ratio of a ph 05od -k(yclxhx91kcy 5gvq;erson’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 lnhp ipu:e*zys-8*w6h )l i8n+0nfsa 75-kg astronaut 4200 km from the center of the Earth's Moon in a space vehicle (a) moving at constant velocity, 0uh6s8) n-+p 8iw*e:z lyf i*snnpl ha    ----待选择----towards the Moonaway from the Moon 
(b) accelerating toward the Moon at 2.9 $\mathrm{~m} / \mathrm{s}^{2}$ ?     ----待选择----towards the Moonaway from the Moon 

State the "direction" in each case.

  Suppose that a binary-star system consists of two stars of equal mass. They ary 5p,obt(f.ncp ; 4juse observed to 5(notys,.u pbp c ;4jfbe separated by 360 million km and take 5.7 Earth years to orbit about a point midway between them. What is the mass of each?    $\times 10^{29}$

  What will a spring scale read for the w-6us )-wv 5qt(t1epbgrw o1 nieight of a 55-kg woman in an elevator thasiwtb5t6 upqw(o 1)v-e 1- nrgt 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 ceiling of ac) b-xi gzq 1zo68:tjdn elevator. The cord can withstand a tension of 220 N andio-td16 bjc )gx:z qz8 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 with pej-q/xc:uhf(mkwq ( d0ljj4n3riod T , tf(43hj(cdu -:q w jmk/ njxlq0he density (mass/volume) 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 Moon (27.4 dvpg 0aq /8lx:w5c n tj+v3.dnw) to determine the period of an artificial satellite orbiting vergv+t wawq/3 v5n lj:p .x0cnd8y near the Earth’s surface.    s

  The asteroid Icarus, though only a few hundred meters across, orbits the Sb 7t:hpa*muh6c /,zb aun like the planets. Its period is 410 d. What is its me a7m: ,bzbhh cta6p/u*an distance from the Sun?    $\times 10^{11}$

  Neptune is an average distance of 4im pj,ab2d5 zzw. x+hz)qff .8.5 $\times 10^{9} \mathrm{~km}$ 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 o ,xbl9.qx fmw/t40jcq3 nx4ky nce 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 3x/4l nctqk0m wbjf4 ,xy9xq. 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 the Galax40+we , kyd7dtlfts 7wy $\left(M_{G} \approx 4 \times 10^{41} \mathrm{~kg}\right)$ 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, +h2u-+9:fg;f4g-o+pui wqf rodpwl+a 9u jon and mean distance for the four largest moons of Jupiter (those discph o+-gff-++on 4+9 w:uw9qudao ;ilup jrf 2govered 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 distanceb 92yap-9vlaa of the Moon. ay al9abv2p9-    $\times 10^{24}$

  Determine the mean distance from Jupiter for each of Jupiteawy*i n41r.- f fh- rex;(uuxwr’s moons, using Kepler’s third law. Use the distance of Io and the periods given in Table 5–3. Compare to tn1 wu whr-( fiea; u-f4r*y.xxhe 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.+ b4jeih x2 tr6k*hwtq bkp8: consists of many fragments (which some space scientists think came from a planet that once orbited the Sun but was destroyehrx8p:ht+2 t4webk i *bq. j6kd).
(a) If the center of mass of the asteroid belt (where the planet would have been) is about three times farther from the Sun than the Earth is, how long would it have taken this hypothetical planet to orbit the Sun?$\approx$    y
(b) Can we use these data to deduce the mass of this planet?

  A science-fiction tale describes an artificial "planet" in thl2 c cvfmg*p./e 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 Earfm p lv*cc/.g2th. What will be the period of revolution, this planet's year, in Earth days?   

  Tarzan plans to cross a gorge by swinging in abm +mhn;g ty65n arc from a hanging vine (Fig. 5–41). If his arms arebh 56m;m +tgny 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 surface will the acceleration of gravnqyk5ei u 7)2mo f64zlity be half what it is o oiz)f7m4q5eny6 u2kl n the surface?    $\times 10^6$

  On an ice rink, two skaters of equal mass grab hands and spin in a mutual circle6qagtg21 ye2s vi*0un once every 2.5 s. If we assume their arms are each 0.80 m long ang2 a1q v6iuteg2yn 0s*d 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, the apparent acceleration of gravi. f d5avw7,cctty at the equator is slightly less than it would be if the Earth didn’t rotate. Estimate the magnitude off5cv awc,d7t . this effect. What fraction of g is this?    $\times 10^{-1}$

  At what distance from the Earte0s)knab((oj3ixab9h g c f5,h will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the,b9x g (n)cfs b(5kaa0 oh3eji Earth and Moon pull with equal and opposite forces?    $\times 10^8$

  You know your mass is 65 kg, but when you stand on a bame062qi lmn2q throom scale in an elevator, it says your mass is 82 kg. What is the acceleration of the elevator, and in wmmq 2iq26enl0hich direction?     ----待选择----upwartddown 

  A projected space stat azqk d/4/k.gkion consists 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 (revz. dqkgk4//a kolutions 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 a/akj)/3c9l, i fldn fei-6xajircraft in 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 a pltt /wey4:,sjxanet in terms of its radius r, the acceleration due to gravity at t/ e,s4y j:wtxits surface and the gravitational constant G.

A plumb bob (a mass m hanging on a strtne/p0 h2jb,wing) is deflected from the vertical by an angle tbj02e w/hp, n$\theta$ 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 coefficieu og4orfyp ua 16ruq0mi,;1/h nt of static friction is 0.30 (wet pavement), 1ouu6 ;rg fiap0/mou4yr,qh1at what range of speeds can a car safely handle the curve?

  How long would a day be if the Earth were rotating so fast that objects at theua 1j91l lbi0r equator were a1bl l 0i1jr9uapparently weightless?    $\times 10^3$s

  Two equal-mass stars maintain a constant distansuigxi r 3xn fl.xz( fk1,1,n(ce 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.p/zpj900t/ yxtswm,o A lamp suspended fromsz ox/pty/ ,jt090wm p the ceiling swings 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, it has been claimedn+ (cgda( qydr+cvxr 93 *gk/mc4bt 7y that a person would be crushed by the force ofx+3yb dyc 9qn ( g*vm74adkc(rrctg/+ gravity on a planet the size of Jupiter since people can't survive more than a few g 's. Calculate the number of g 's a person would experience at the equator of such a planet. Use the following data for Jupiter: mass =1.9 $\times 10^{27} \mathrm{~kg}$ , equatorial radius =7.1$ \times 10^{4} \mathrm{~km}$ , rotation period =9 $\mathrm{hr} 55 \mathrm{~min}$ . Take the centripetal acceleration into account.    g's

  Astronomers using the Hubble Space Telescope deduced the presence of an extrl4d4oc( mix day v.;z)emely 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 coliv)4(yz;odaxdcm . 4re 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 trawal.g m*u 2e+uverses the hill and valley shown in Fig. 5–45. Both the hill and valley have a radius of curvature R. (a) How do the ma2. l+guuew* 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 2ia1/jbb; 0 fq 1n(jwhh p54iwh4 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy j/ah01j ibpf5whnbw4hi;1( q 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), after traveling 2.1 billion km5zb xoi8 c r((w6kfq*g, is meant to orbit the asteroid Eros at a height of abouf(k5c(zq bogwr *8 6ixt 15 km . Eros is roughly 40 $\mathrm{~km} \times 6 \mathrm{~km} \times 6 \mathrm{~km}$ . Assume Eros has a density (mass/volume) of about 2.3 $\times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ . (a) What will be the period of NEAR as it orbits Eros? $\approx$    $\times 10^4$sec
(b) If Eros were a sphere with the same mass and density, what would its radius be? $\approx$    $\times 10^3$
(c) What would g be at the surface of this spherical Eros?$\approx$    $\times 10^{-3}$

  You are an astronaut in the space shuttle pursuing a satellitd3icb )dz; -,)eft xgde in need of repair. You are in a circular orbit of 3t excz)d ;) ,bdd-gfithe 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 distance f kc absk9. xrbtvufo m2vc19us0v5623rok ar cmkvuu93vxfv t2165bsbc290s. om the Sun?   
(b) At its closest approach, the comet is about 1 A.U. from the Sun ( from Earth to the Sun). What is the farthest distance?   
(c) What is the ratio of the speed at the closest point to the speed at the farthest point? [Hint: Use Kepler’s second law and estimate areas by a triangle (as in Fig. 5–29, but smaller distance travelled; see also Hint for Problem 59).]   

  Estimate what the value of G would need to be if you could actually "feel" youb z7nfyto4wwl9j e xk422oc4js+:9m wrself gravitationally attracted to someone near you. Make reasonable assumpti4 zcwt7:9 jj o2bmo4xk+9w2nw leyfs4 ons, like F $\approx 1 \mathrm{~N}$ .    $\times 10^{-5}$

  The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a distaf s(h fsar1x8 ,nmh:o5nce of about 30,000 light-years sonxh m(:af5rf 8h1s ,from the center $ \left(1 \mathrm{ly}=9.5 \times 10^{15} \mathrm{~m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left(2 \times 10^{30} \mathrm{~kg}\right)$ , how many stars would there be in our Galaxy?$\approx$    $\times 10^{11}$

  Four 1.0-kg masses are located at the corners of a square 0.50 m on each si5d3inn seyw6e3 : y p+j w/wrukkqa/;:de. Find the magnitude and direction of the gravitational force o + sj:3qd/yk3np6urw5ee/ wwnika; :yn 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 Eartbql-j*vwvl ilxn-so usosd0 6f+(la45.h y9 ;h $ \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 sec( an mru,9f;g:f pwhsg+ys08wond hand on your wrist watch? fp8fws; hnau:+ 0swg9r ,(gym    $\times 10^{-4}$

  While fishing, you get bored and start to swingzo68 ngs 02 .fl7acqpr a sinker weight around in a circle below ycrgo.7n 8z20qas pfl6ou on a 0.25-m piece of fishing line. The weight makes a complete circle every 0.50 s. What is the angle that the fishing line makes with the vertical? [Hint: See Fig. 5–10.]    $^{\circ}$

A circular curve of radius R in a new highway is designed so thnrq0y)9v os b o0jl2a+0z-zkaat a car travelingl ka- bnzos0r)2+qy90az0ovj 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 the cars when powjksug/10e67byq( v y+ i*inegotiating curves. The angle of tilt is adjusted so that the main force exerted on the passengers, to provide the centripetal accelerati wvu+bp06i7(qji s oy g*yek1/on, 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 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.$\approx$    $\times 10^2$