Unit 3 Mastery: Work, Energy, and Power

Kinetic Energy (K)

The energy associated with the motion of an object, defined as K = 1/2 mv².

Scalar Quantity

A quantity that has magnitude only, with no direction; kinetic energy is a scalar.

Work-Energy Theorem

States that the net work done on an object equals the change in its kinetic energy (W_net = ΔK).

Conservative Force

A force where the work done is independent of the path taken between two points.

Non-Conservative Force

A force where the work done depends on the path taken, often converting mechanical energy to thermal energy.

Potential Energy (U)

Energy stored in a system due to the configuration or relative position of objects.

Gravitational Potential Energy (U_g)

The potential energy of an object due to its height in a gravitational field, defined as U_g = mgy.

Elastic Potential Energy (U_s)

Energy stored in a spring following Hooke's Law, defined as U_s = 1/2 kx².

Law of Conservation of Energy

The principle that total mechanical energy remains constant when only conservative forces are acting.

Net Work (W_net)

The total work done by all forces acting on an object.

Total Mechanical Energy (E_mech)

The sum of kinetic and potential energy in a system, E_mech = K + U.

Stable Equilibrium

A state where a small displacement from equilibrium results in a restoring force returning the object to its original position.

Unstable Equilibrium

A state where a small displacement results in a force that pushes the object further away from its original position.

Work Done by Conservative Forces (W_cons)

The work done by a conservative force, defined as W_cons = -ΔU.

Maximum Compression of Spring

The point at which the kinetic energy of an object transferred to a spring is entirely converted into elastic potential energy.

Newton's Second Law

The law stating that the net force acting on an object equals the mass of the object times its acceleration (F_net = ma).

Forces in Closed Path

If a force is conservative, the total work done around any closed path is zero ( ∮F_cons · dr = 0).

Hooke's Law

The principle stating that the force exerted by a spring is proportional to its displacement from its equilibrium position (F_s = -kx).

Change in Potential Energy (∆U)

The change in potential energy of a system is equal to the negative of the work done by conservative forces.

Work-Energy Principle

The principle that the work done by the net forces acting on an object equals the change in its kinetic energy.

Friction Force

A force that opposes motion, often classified as a non-conservative force.

Mechanical Energy Loss

A reduction in total mechanical energy due to the work done by non-conservative forces.

Example Problem - Spring Compression

Problem involving calculating the compression of a spring when an object falls from a height.

Reference Level in Potential Energy

A chosen height (y=0) from which other heights are measured for calculating gravitational potential energy.

Acceleration Due to Gravity (g)

The acceleration experienced by an object due to Earth's gravitational field, approximately 9.8 m/s².

Work Calculation Formula

Work can be calculated as W = ∫F · dx, representing the scalar product of force and distance.