Module 3: Fundamentals of Mechanical Energy

Work (W)

The transfer of energy that occurs when a force exerts an influence on an object while moving it over a given distance.

Scalar Quantity

A quantity that has magnitude but no direction; work is a scalar quantity.

Force (F)

A push or pull on an object, measured in Newtons (N).

Displacement (d)

The change in position of an object, measured in meters (m).

Angle (θ)

The angle between the force vector and the displacement vector.

Positive Work

Occurs when the force points in the direction of motion (0° ≤ θ < 90°).

Negative Work

Occurs when the force opposes the direction of motion (90° < θ ≤ 180°).

Zero Work

Occurs when the force is perpendicular to the displacement (θ = 90°).

Joule (J)

The unit of work; 1 J = 1 N·m.

Force vs. Displacement Graph

A graph where the area under the curve represents the work done.

Translational Kinetic Energy (K)

The energy an object possesses due to its motion through space.

Kinetic Energy Formula

K = (1/2)mv², where m is mass and v is speed.

Positive Kinetic Energy

Kinetic energy is always positive or zero; it cannot be negative.

Velocity Dependence

Because velocity is squared in K = (1/2)mv², small changes in speed lead to large changes in energy.

Gravitational Potential Energy (U_g)

The energy associated with the position of an object relative to the Earth's gravitational field.

Potential Energy Formula

U_g = mgh, where m is mass, g is gravitational acceleration, and h is height.

Elastic Potential Energy (U_s)

Energy stored in an elastic object like a spring when it is deformed.

Hooke's Law

The force required to deform a spring, denoted F_s = -kx.

Elastic Potential Energy Formula

U_s = (1/2)kx², where k is the spring constant and x is displacement.

Constant Force

Force that does not change in magnitude or direction while it acts on an object.

Work Done by Perpendicular Force

Work is zero when the applied force is perpendicular to the direction of motion.

Energy Transfer

The movement of energy from one system to another, which can be positive or negative work.

Area under Force-Displacement Curve

Represents the net work done on an object.

System Definition

A set of interacting components, where energy can be analyzed relative to internal and external forces.

Double Counting Gravity

Avoiding counting gravitational work when defining systems; consider gravitational potential energy instead.

Kinetic Energy Mistake

Forgetting to square the velocity in the kinetic energy formula K = (1/2)mv².

Energy Conservation

The principle that total energy remains constant in an isolated system.