Energy is an important idea in physics. It means the ability to do work.

In simple terms, work happens when a force moves something over a distance. Here's a formula that explains how energy and work relate:

$W = F \cdot d \cdot \cos(\theta)$

In this formula:

• W is the work done (measured in joules, J),
• F is the force applied (in newtons, N),
• d is the distance moved (in meters, m),
• θ is the angle between the force and the direction the object is moving.

How Energy Works in Mechanical Work:

1. Changing Energy: When we do mechanical work, we change stored energy (like potential or kinetic energy) into other types of energy. For example, when we lift something, it gains gravitational potential energy.

2. Efficiency: Machines are often rated on how well they turn input energy into mechanical work. Usually, machines work at efficiencies of about 30% to 90%.

3. Kinetic Energy Connection: The work-energy theorem tells us that the work done on an object is equal to how much its kinetic energy changes:

$W = \Delta KE = KE_{final} - KE_{initial}$

Kinetic energy can be calculated like this:

$KE = \frac{1}{2} mv^2$

In this equation, m is mass (in kilograms, kg) and v is velocity (in meters per second, m/s).

Overall, energy is key to understanding how mechanical work happens and how it affects different systems in physics.