Module 6: Work, Potential Energy, and Conservative Force

Vocabulary flashcards on Work, Gravitational Potential Energy, Elastic Potential Energy, and Conservative Forces covering key definitions, mathematical formulas, and theoretical properties.

Work

The product of the force applied and the distance moved in the direction of the force; it is a scalar quantity.

Joule ($J$)

The SI unit for work, also called a newton-meter ($N \times m$); $1\text{ Joule } (J)$ of work is done when a force of $1\text{ newton } (N)$ moves a body through a distance of $1\text{ meter } (m)$.

Horizontal Component of Applied Force ($F_x$)

The component of applied force in the direction of the horizontal movement of an object, calculated as $F_x = F_{\text{applied}} \times \text{cos}(\theta)$, which performs work on the object.

Vertical Component of Applied Force ($F_y$)

The component of applied force perpendicular to displacement, calculated as $F_y = F_{\text{applied}} \times \text{sin}(\theta)$, which does no work on the object.

Work Done by Applied Force at an Angle Formula

The work done when an applied force acts at an angle $\theta$ relative to an object's displacement, expressed as $W = F d \text{cos}(\theta)$.

Graphical Analysis of Work

A technique where work done in a force-distance graph is calculated as the area under the graph.

Potential Energy

The energy of a system of particles or objects due to the position of those particles in the system; often referred to as stored energy.

Gravitational Potential Energy (GPE)

The energy that an object has due to its position relative to the Earth's surface, calculated using the formula $\text{GPE} = mgh$.

Variables Affecting GPE

The physical factors that affect Gravitational Potential Energy: height ($h$) and mass ($m$).

Elastic Potential Energy

Potential energy that is stored as a result of deforming an elastic material, such as a spring.

Hooke's Law

The law stating that the force required to extend a spring is equal to the negative product of the spring constant and the distance stretched, expressed as $F_s = -k x$.

Spring Constant ($k$)

A constant parameter of a spring that remains fixed regardless of the length of time the spring is stretched.

Elastic Potential Energy Formula

The formula describing the work done on a spring or potential energy stored within it: $W = \frac{1}{2} k x^2$.

Conservative Force

A force done in moving a particle from one point to another such that the work done is independent of the path taken and depends only on the initial and final position of the particle.

Closed Path Property of Conservative Forces

The property stating that the work done by a conservative force on any closed path (where the object returns to its initial position) is equal to zero.

Reversibility Property of Conservative Forces

The property stating that the energy transferred by a conservative force is reversible and can be completely recovered when an object returns to its original position (assuming no friction or air resistance).