Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Energy is defined as the capacity to do work and is measured in the SI unit Joules ().
Kinetic Energy () is the energy possessed by an object due to its motion. It depends on the object's mass () and the square of its velocity ().
Gravitational Potential Energy () is the energy stored in an object because of its vertical position or height () above a reference point.
The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another. Therefore, in a closed system, the total energy () remains constant.
Energy Transfer occurs when energy moves from one object to another (e.g., a bat hitting a ball), while Energy Transformation occurs when energy changes from one type to another (e.g., turning into as an object falls).
Mechanical Energy is the sum of the potential and kinetic energy in a system: .
📐Formulae
💡Examples
Problem 1:
A soccer ball with a mass of is kicked and travels at a velocity of . Calculate its kinetic energy ().
Solution:
Explanation:
We use the kinetic energy formula by substituting the mass () and velocity (). Squaring the velocity gives , which is then multiplied by half the mass.
Problem 2:
A textbook is lifted from the floor to a shelf that is high. Calculate the Gravitational Potential Energy () gained by the book. (Use )
Solution:
Explanation:
The potential energy is found by multiplying the mass of the book, the acceleration due to gravity, and the height of the shelf.
Problem 3:
A roller coaster car has of potential energy at the top of a hill and of kinetic energy. If it slides down to a point where its potential energy is , how much kinetic energy does it have? (Assume no friction)
Solution:
. At the new point: . Therefore, .
Explanation:
According to the Law of Conservation of Energy, the total mechanical energy must remain constant (). As potential energy decreases, it is transformed into kinetic energy.