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Ask iit jee aieee pet cbse icse state board experts Expert Question: THE POSITION OF A PARTICLE IS GIVEN BY r = acos(wt)i + asin(wt)j+ btk.THE DISTANCE MOVED
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[Post New]17 Nov 2007 00:16:45 IST
    Subject: THE POSITION OF A PARTICLE IS GIVEN BY r = acos(wt)i + asin(wt)j+ btk.THE DISTANCE MOVED
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BALGANESH (677)

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THE POSITION OF A PARTICLE IS GIVEN BY  r = acos(wt)i + asin(wt)j+ btk.THE DISTANCE MOVED BY THE PARTCLE IN ONE FULL TURN OF HELIX IS ? ( w =OMEGA)
    
[Post New]17 Nov 2007 00:43:38 IST
    Subject: Re:THE POSITION OF A PARTICLE IS GIVEN BY r = acos(wt)i + asin(wt)j+ btk.THE DISTANCE MOVED
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aditya_arora04 (1077)

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Hi,
 
Look,
 
r = acos(wt)i + asin(wt)j+ btk
 
v = dr/dt = -iawsinwt  + jawcoswt + kb
 
Now, speed = Mod of velocity
 
So, speed, s = |v| = (a2w2 + b2)0.5   
 
So, Distance travelled = s*t = s*T = 2(pie)s/w
 
So,
 
Distance trvelled = 2(pie)(a2w2 + b2)0.5   / w
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[Post New]17 Nov 2007 00:54:33 IST
    Subject: Re:THE POSITION OF A PARTICLE IS GIVEN BY r = acos(wt)i + asin(wt)j+ btk.THE DISTANCE MOV
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iitkgp_bipin (6144)

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Total distance = (dx)2+(dy)2+(dz)2

= [t=0][t=2pi/w] (d(a.coswt))2+(d(a.sinwt))2+(d(bt))2

= [t=0][t=2pi/w] dt.(a2w2(sin2wt+cos2wt)+b2)

= [t=0][t=2pi/w] dt.(a2w2+b2)

= (2/w).(a2w2+b2)



Bipin Kumar Dubey
Chemical Dept.
IIT Kharagpur

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[Post New]17 Nov 2007 00:57:03 IST
    Subject: THE POSITION OF A PARTICLE IS GIVEN BY r = acos(wt)i + asin(wt)j+ btk.THE DISTANCE MOVED
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BALGANESH (677)

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thanks to both
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