Unit 3: Work, Energy, and Power

Translational Kinetic Energy (TKE)

The energy of motion an object has due to its movement from one place to another.

Kinetic Energy Equation

K = ½ mv², where K is kinetic energy, m is mass, and v is velocity.

Scalar Quantity

A quantity that has magnitude but no direction.

Work

The transfer of energy that occurs when a force is applied to an object and the object moves in the direction of the force.

Work Formula

W = F ⋅ d ⋅ cos θ, where W is work, F is force, d is displacement, and θ is the angle.

Angle θ in Work

The angle between the force vector and displacement vector; affects the amount of work done.

Gravitational Potential Energy (PE₉)

Energy stored due to height above a reference point, calculated as PE₉ = mgh.

Elastic Potential Energy (PEₑ)

Energy stored in a stretched or compressed spring, calculated as PEₑ = ½ kx².

Energy Transformation

The process of energy shifting between forms depending on the situation.

Law of Conservation of Energy

Energy cannot be created or destroyed, only transformed; total energy in a closed system remains constant.

Conservative Forces

Forces such as gravity or springs that conserve mechanical energy (kinetic + potential).

Non-Conservative Forces

Forces such as friction or air resistance that dissipate energy, often turning it into heat.

Power

The rate at which work is done or energy is transferred.

Instantaneous Power

Power at a specific moment in time.

Average Power

Total work divided by total time.

Units of Work

Measured in joules (J), where 1 J = 1 N·m.

Kinetic Energy Dependence on Mass

Kinetic energy has a direct relationship with mass: double the mass = double the kinetic energy.

Kinetic Energy Dependence on Velocity

Kinetic energy has an exponential relationship with velocity: double the velocity = four times the kinetic energy.

Positive Nature of Energy

Energy is always positive because velocity is squared in the kinetic energy formula.

Total Kinetic Energy in a System

To find total kinetic energy, simply add the individual kinetic energies of the objects.

Work Done by Variable Force

Calculated by finding the area under the force vs. displacement graph.