Mechanical Energy

There are two main types of mechanical energy.

1. Potential Energy: It is the energy stored in an object due to its position. Gravitational potential energy due to Earth’s gravity is a common type of potential energy. It depends on the object’s height from the Earth’s surface. For example, an apple in an apple tree has the maximum potential energy. When it falls, its potential energy reduces and becomes zero upon reaching the surface.

Apart from gravitational potential energy, other forms are elastic potential energy, electric potential energy, magnetic potential energy, and nuclear potential energy.

2. Kinetic Energy: It is the energy possessed by an object due to its motion. The movement of an object is manifested by its speed. Consider the above example. When the apple is in the tree, it is at rest with zero kinetic energy. When it falls, it gains speed owing to acceleration due to gravity. The kinetic energy increases and reaches a maximum when the apple hits the ground.

The types of kinetic energy are electrical energy, thermal energy, radiant energy, and sound energy.

According to the law of conservation of energy, energy can neither be created nor destroyed. It transforms from one form to another. In the above example, the potential energy of the apple transforms into kinetic energy. Therefore, the sum of potential and kinetic energy remains constant throughout its path. This sum is known as the total mechanical energy. The initial total mechanical energy is the same as the final total mechanical energy.

Mechanical energy is conserved only when the force acting on an object is conservative. A conservative force does not depend on the path taken to do work. On the other hand, non-conservative and dissipative forces depend on the path taken. In the apple example, gravitational potential energy acts on it, which is a conservative force. If non-conservative forces like friction or air resistance are present, the mechanical energy will get converted into heat energy. In this way, although the mechanical energy is not conserved, the total energy is conserved.

• A book on a shelf has potential energy due to its height above the surface.

• A moving car possesses kinetic energy due to its motion.
• A baseball on its trajectory has potential energy due to its height and kinetic energy due to its speed.
• A weightlifter lifts a barbell above its head and gives it potential energy.
• A hammer gathers potential energy and transforms it into kinetic energy to hit a nail.
• A loaded dart gun has potential energy as the spring is compressed.
• A roller coaster moves on its track with kinetic energy. When it reaches its highest point, the kinetic energy is converted into potential energy. When it departs, the potential energy is converted back into kinetic energy.
• A swinging pendulum has both potential and kinetic energy. The potential energy is maximum when the pendulum is at two extreme points. The kinetic energy is maximum when it passes through the equilibrium point.
• A wrecking ball is a massive object with potential energy and kinetic energy. When it is swung to a high position, it has potential energy. When it is released, it gains kinetic energy.

How to Find Mechanical Energy

The total mechanical energy is defined as the sum of potential energy and kinetic energy.

1. Potential Energy

Suppose an object of mass m is at a height h above the surface of the Earth. Then, the potential energy can be found by the following equation.

P.E. = mgh

Where,

P.E. : Potential energy of the object

m : Mass of the object

g : The acceleration due to gravity

h : Height of the object

2. Kinetic Energy

Suppose the same object is moving with a velocity v. Then, the kinetic energy can be determined by the following equation.

K.E. = ½mv²

Where,

K.E. : Kinetic energy of the object

m : Mass of the object

v : Velocity of the object

Then, the formula for the total mechanical energy of the object is

Mechanical Energy = Potential Energy + Kinetic Energy

Or, M.E. = mgh + ½mv²

SI unit: J or Joule (1 J = 1 kg m²/s²)

Cgs unit: erg (10⁷ erg = 1 J)

Dimension: [ML²T^-2]

Many technical devices convert mechanical energy into other forms and vice versa.

• An electric motor converts electrical energy into mechanical energy (for example, a table fan).
• A generator converts mechanical energy into electrical energy (for example, a dynamo).
• A hydroelectric power station converts the mechanical energy of water stored in a dam into electrical energy, a phenomenon known as hydroelectricity.
• Gasoline burns to release chemical energy, which converts into mechanical energy to drive a car.
• Steam energy converts thermal (heat) energy into mechanical energy.
• A wind turbine converts the kinetic energy of wind into electrical energy.