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 Joules ().
Work Done () occurs when a force results in a displacement in the direction of the force.
Kinetic Energy () is the energy of an object due to its motion, depending on mass and velocity .
Gravitational Potential Energy () is the energy stored by an object due to its position in a gravitational field.
The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another; thus, .
Power () is the rate at which work is done or the rate of energy transfer, measured in Watts (), where .
Efficiency is a ratio (often expressed as a percentage) of the useful energy output to the total energy input, accounting for energy dissipated as heat or sound.
📐Formulae
balance
💡Examples
Problem 1:
A roller coaster car of mass starts from rest at the top of a hill high. Calculate its speed at the bottom of the hill, assuming no friction. Use .
Solution:
Explanation:
According to the Law of Conservation of Energy, the initial gravitational potential energy at the top is converted entirely into kinetic energy at the bottom in the absence of resistive forces.
Problem 2:
An electric crane lifts a load to a height of in . If the motor has an efficiency of , calculate the total electrical power input required.
Solution:
Explanation:
First, calculate the useful work (potential energy gain) and power output. Then, adjust for efficiency to find the total power the motor must consume from the electrical source.