8th Grade Unit 2, Module 2 - Mechanical Energy, Notes

Mechanical Energy

Definition: Kinetic energy (KE) is the energy of an object due to its motion.
Key Points:
- All moving objects have kinetic energy.
- The amount of kinetic energy depends on two key factors:
1. Mass: More mass results in more kinetic energy.
2. Speed: Higher speed results in more kinetic energy.
Example: When a baseball is thrown, it has kinetic energy related to its speed and mass.

Experiment: Dropping two balls of different masses from the same height demonstrates that the more massive ball creates a larger dent in the clay due to higher kinetic energy.
Conclusion: Kinetic energy increases as mass increases, represented by the equation:
KE ext{ (kinetic energy)} ext{ is proportional to } M ext{ (mass)}

Observation: Kinetic energy also increases with the speed of an object. As speed doubles, kinetic energy increases by a factor of four (quadratic increase).
Equation: This relationship can be represented mathematically as:
KE ext{ (kinetic energy)} ext{ is proportional to } V^2 ext{ (speed)}

Definition: Potential energy is the energy stored in an object at rest, based on its position or configuration.
Example: In a slingshot, energy is stored in the stretched rubber band. When released, that energy converts to kinetic energy allowing an object like a nickel to move.
Types of Potential Energy:
1. Elastic Potential Energy: Energy stored in objects like rubber bands or springs when they are stretched or compressed.
2. Gravitational Potential Energy: Energy due to the height of an object above the ground, dependent on mass and height.

Concept: When lifting an object, like a backpack, energy is added as gravitational potential energy increases with height. The potential energy can be calculated by considering gravitational interaction: PE = mgh where:
- m = mass
- g = acceleration due to gravity
- h = height

Concept: Energy cannot be created or destroyed; it can only be transformed from one form to another.
Example: In a pendulum swing, kinetic energy converts to potential energy and back without changing the total energy of the system.
Implication: The total mechanical energy of a system (ME = KE + PE) remains constant throughout the motion of the system.

Definition of Work: Work is the transfer of energy to an object via a force that causes it to move in the direction of the force.
Formula: Work can be defined mathematically as:
W = Fd
where:
- F = force applied
- d = distance moved in the direction of the force
Observation on Energy Transfer: When work is done (such as lifting a box), potential energy increases due to gravitational interaction, demonstrating the transfer and transformation of energy.