Work-Energy Principle

The work-energy principle states that the net work done on a particle equals the change in its kinetic energy. This provides a powerful alternative to using Newton's Second Law directly, especially when forces vary or when you need to find speeds without knowing the time.

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1 Work Done by a Constant Force

W = F d cos theta

where F is the magnitude of the force, d is the displacement, and theta is the angle between the force and the direction of motion.

• If theta = 0 (force in direction of motion): W = Fd.
• If theta = 90 degrees (force perpendicular to motion): W = 0.
• If theta = 180 degrees (force opposing motion): W = -Fd.

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2 The Work-Energy Theorem

Net work done = Change in kinetic energy

W_net = (1/2)mv^2 - (1/2)mu^2

If multiple forces act, the net work is the sum of the work done by each force.

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3 Worked Example 1

A 5 kg box is pushed 4 m along a smooth horizontal surface by a force of 20 N. It starts at rest. Find the final speed.

Solution: