Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Energy is the capacity to do work and is measured in Joules ().
The Law of Conservation of Energy states that energy cannot be created or destroyed; it can only be transformed from one form to another or transferred between objects.
The total energy in a closed system remains constant, expressed as .
Kinetic Energy () is the energy possessed by an object due to its motion, depending on mass () and velocity ().
Gravitational Potential Energy () is the energy stored in an object due to its height () above a reference point.
Energy transfers involve energy moving from one place to another (e.g., heat moving from a stove to a pan), while energy transformations involve changing forms (e.g., Chemical Energy in a battery changing to Electrical Energy).
In real-world systems, energy is often 'dissipated' (usually as heat, , or sound) due to friction, though the total energy still follows the law of conservation.
📐Formulae
💡Examples
Problem 1:
A ball is held at a height where it has of Gravitational Potential Energy (). If the ball is dropped, what is its Kinetic Energy () just before it hits the ground, assuming no air resistance?
Solution:
Explanation:
By the Law of Conservation of Energy, the initial energy at the top must equal the final energy at the bottom (). Since all is converted into during the fall, the Kinetic Energy at the bottom is equal to the Potential Energy at the top.
Problem 2:
An electric motor is supplied with of electrical energy. It performs of useful mechanical work. Calculate the amount of energy dissipated as heat ().
Solution:
Explanation:
Using the conservation formula , we substitute the known values: . Subtracting from both sides gives .
Problem 3:
A swinging pendulum has of at its highest point. At its lowest point, it has of . How much energy was transformed into thermal energy due to air resistance?
Solution:
Explanation:
The total energy at the start was . At the bottom, the measurable mechanical energy is . The 'missing' energy () has been transformed into heat () because energy must be conserved.