A particle moves in the x-y plane under the influence of a force such that the linear momentum is p(t) = a [ cos kt - sin kt ] where a and k are constants. The angle in degrees between force and momentum is
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Answer:
90 degree
Explanation:
We know that, p(t)= a ( icoskt - jsinkt )
As F= dP/dt
= d[a (icoskt - jsinkt )] / dt
= ak (- isinkt - jcoskt)
Then dot product of F and P is: (where A is angle between F and P)
cos A= (F.P) / |F|.|P|
= {[ak (- isinkt - jcoskt )] . [a (icoskt - jsinkt )]} / (a*ak)
= {(a^2k) (-sinkt coskt + sinkt coskt)} / (a^2k)
= 0
= cos 90
Therefore angle between F and P is 90 degree
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Answer:
90 degree
Explanation:
We know that, p(t)= a ( icoskt - jsinkt )
As F= dP/dt
= d[a (icoskt - jsinkt )] / dt
= ak (- isinkt - jcoskt)
Then dot product of F and P is: (where A is angle between F and P)
cos A= (F.P) / |F|.|P|
= {[ak (- isinkt - jcoskt )] . [a (icoskt - jsinkt )]} / (a*ak)
= {(a^2k) (-sinkt coskt + sinkt coskt)} / (a^2k)
= 0
= cos 90
Therefore angle between F and P is 90 degree...................
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