Energy

Principle

Energy is a scalar quantity used to track the ability of a system to produce changes such as motion, deformation, or heating. In particle mechanics, kinetic energy depends on speed, while potential energy is associated with position in a conservative force field.

Mechanical energy is the sum of kinetic and potential energy. Under conservative forces and no dissipative work, mechanical energy is constant.

Notation

Method

Step 1: Compute kinetic energy from speed

Kinetic energy uses speed squared, not velocity direction:

Step 2: Add potential energy when it is defined

If a conservative model assigns a potential energy \(U\), combine it with kinetic energy:

Step 3: Apply conservation only when justified

If no non-conservative work changes the system energy, the mechanical energy does not change:

Rules

• Energy is scalar, so it has no direction.
• Kinetic energy is always non-negative when mass is positive.
• Potential energy can be shifted by an arbitrary constant; potential-energy differences matter physically.
• Conservation of mechanical energy is a modelling statement, not an automatic rule for every system.

Examples

Checks

• Do not attach a direction to energy; energy is scalar.
• Use speed magnitude in kinetic energy, not a signed velocity component unless the motion is one-dimensional and speed is its absolute value.
• State the conservation assumption before setting \(E_1=E_2\).
• Keep joules consistent: \(J=N\,m=kg\,m^2\,s^{-2}\).