Work, Energy and Power

Energy is one of the most fundamental concepts in physics. Unlike forces which act in specific directions and have complex interactions, energy gives us a powerful scalar approach to solving problems. The work-energy method often provides simpler solutions than Newton's second law, especially for problems involving changes in height or speed.

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Work Done

Work is the transfer of energy by a force. When a force moves an object through a displacement, it does work on that object.

Work done = Force x displacement x cos(theta)

W = Fs cos(theta)

where F is the force in newtons, s is the displacement in metres, and theta is the angle between the force and the displacement. Work is measured in joules (J).

Important cases:

• Force in the same direction as displacement (theta = 0°): W = Fs. Maximum work is done.
• Force perpendicular to displacement (theta = 90°): W = 0. No work is done (e.g. the normal force on a moving object on a horizontal surface).
• Force opposite to displacement (theta = 180°): W = -Fs. Negative work — the force removes energy (e.g. friction slowing an object).

Worked Example 1