Mechanical energy is the sum of kinetic and potential energy in an object that is used to do work.
It is a conserved quantity, meaning the total mechanical energy in a closed system remains constant if the only forces acting are conservative forces.
Types of Mechanical Energy
Kinetic Energy
The energy an object possesses due to its motion.
Formula: ( KE = \frac{1}{2}mv^2 )
Where ( m ) is mass and ( v ) is velocity.
Potential Energy
The stored energy in an object due to its position or configuration.
Types of potential energy include:
Gravitational Potential Energy
Depends on the height and mass of an object and gravity.
Formula: ( PE_{grav} = mgh )
Where ( m ) is mass, ( g ) is acceleration due to gravity, and ( h ) is height.
Elastic Potential Energy
Associated with objects that can be stretched or compressed, like springs.
Formula: ( PE_{elastic} = \frac{1}{2}kx^2 )
Where ( k ) is the spring constant and ( x ) is the displacement from the equilibrium position.
Conservation of Mechanical Energy
In a conservative system, the total mechanical energy (TME) is constant:
[ TME = KE + PE = \text{constant} ]
This principle allows the prediction of the velocity or height of objects in motion under conservative forces.
Application
Understanding mechanical energy is crucial in fields like engineering, physics, and various applied sciences. It helps in solving problems related to energy conservation and transfer.
Practical Example
Consider a pendulum:
At its highest point, it has maximum potential energy and zero kinetic energy.
At its lowest point, it has maximum kinetic energy and zero potential energy.
Throughout its swing, the total mechanical energy remains constant if air resistance and friction are negligible.
Summary
Mechanical energy involves both kinetic and potential forms.
It is a fundamental concept in physics that explains how objects move and interact in a conservative system.
The conservation of mechanical energy principle is a powerful tool for solving dynamics problems.