Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed from one form to another or transferred between objects. The total energy in a closed system remains constant ().
Gravitational Potential Energy () is the energy stored in an object due to its height above a reference point in a gravitational field: .
Kinetic Energy () is the energy possessed by an object due to its motion: .
Mechanical Energy () is the sum of kinetic and potential energy in a system: . In the absence of external forces like friction, .
Energy is often dissipated as thermal energy () due to friction or air resistance, which is frequently described as 'lost' energy, though it still exists in the environment.
Efficiency is a measure of how much of the total input energy is converted into useful output energy: .
Work () is the transfer of energy that occurs when a force () is applied over a displacement (): .
📐Formulae
💡Examples
Problem 1:
A ball is dropped from a height of . Calculate its velocity just before it hits the ground. (Assume and ignore air resistance).
Solution:
Using the conservation of energy: . \n \n \n \n \n \n .
Explanation:
At the top, the ball has maximum gravitational potential energy and zero kinetic energy. As it falls, is converted into . Just before impact, all has become .
Problem 2:
An electric motor uses of electrical energy to lift a mass to a height of . Calculate the efficiency of the motor. (Use )
Solution:
- Calculate useful energy output (Work done against gravity): . \n 2. Total input energy: . \n 3. .
Explanation:
The efficiency is the ratio of the energy that actually went into lifting the mass () compared to the total energy supplied by the motor. The remaining was likely dissipated as heat and sound.