Work, Energy & Power

In physics, work has a very specific meaning -- and understanding it leads to one of the most powerful ideas in science: the conservation of energy.

Work Done

Work = Force x Distance x cos(theta)

Work is done only when a force causes displacement in the direction of the force. Unit: Joule (J).

Example: Push a box with 50 N across 4 m: Work = 50 x 4 = 200 J

Zero work example: Carrying a bag and walking horizontally. Force is upward, displacement is horizontal, so work = 0.

Kinetic Energy (KE)

KE = (1/2) x m x v^2 -- energy due to motion

Example: A cricket ball (0.16 kg) at 30 m/s has KE = (1/2)(0.16)(900) = 72 J

Potential Energy (PE)

Gravitational PE = m x g x h -- energy due to position

Example: A 2 kg book 3 m high has PE = 2 x 10 x 3 = 60 J (using g = 10 m/s^2)

Conservation of Energy

Energy cannot be created or destroyed -- only transformed. Total energy remains constant.

When a ball falls: at the top PE is maximum (KE = 0), at the bottom KE is maximum (PE = 0). At any point: PE + KE = constant.

Power

Power = Work / Time. Unit: Watt (W) where 1 W = 1 J/s

Example: A motor lifts 100 kg to 10 m height in 20 s. Work = 100 x 10 x 10 = 10,000 J. Power = 10,000/20 = 500 W

Nepal Connection: Nepal generates most electricity from hydropower. Water at height (PE) flows through turbines (KE), which converts to electrical energy. The Upper Tamakoshi project (456 MW) is a massive example of energy transformation.

Key Takeaways

• Work = Force x Distance (in direction of force)
• KE depends on mass and velocity squared; PE depends on mass, gravity, and height
• Energy is always conserved -- it transforms between forms
• Power is the rate of doing work, measured in Watts