Saturday, November 15, 2008

Application of scalar product in mechanics to find the work done

Word done by a force is a scalar quantity. This can be calculated by finding the scalar product of force vector and displacement vector.

If the force vector is represented by OA and the displacement vector by OB and if the angle between them is θ work done is

W = OA.OB = |OA||OB|cos θ

|OB|cos θ represents the component of OB in the direction of OA

If a number of forces are acting on a particle, then the sum of works done by the separate forces is equal to the work done by the resultant force.

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