Question

A particle moves in the x-y plane under the influence of a force such that the

linear momentum Is P(t) = A [ î cos kt - ĵ sin kt ]

Where A and k are constants. The angle in degrees between force and

momentum is_________.​

Answer 1

Answer:

Then angle between force and momentum must be 90 degree.

Explanation:

As per Newton's 2nd law we know that rate of change in momentum is equal to the net force acting on it.

Here we know that the momentum of the object is given as

$\vec P = A(cos kt \hat i - sin kt \hat j)$

now we have

$\vec F = \frac{dP}{dt}$

here we have

$\vec F = A(- k sin kt \hat i - k cos kt \hat j)$

now in order to find the angle between them

$\vec F. \vec P = A^2(-k sin kt cos kt + k sin kt cos kt)$

$\vec F . \vec P = 0$

since scalar product of these two vectors is ZERO

so the two vectors must be perpendicular to each other

#Learn

Topic : Newton's 2nd Law

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