Dimensional Formula of Potential Energy

Potential energy is a type of energy that has the capacity to conduct work but cannot now do so or exert force on someone. As a result, we say it’s the energy that things have as a result of their position rather than their motion. It is a type of mechanical energy. P.E. is derived from material and is an intrinsic part of all objects with mass. The potential energy equation is as follows:

Potential energy = m.g.h

Where m is the mass of any object

g is the acceleration due to gravity acting on the object

and h is the altitude or height at which an object is present

Dimensional formula:

A dimensional formula expresses a physical quantity in terms of fundamental quantities like mass length and time. We can identify how fundamental quantities are raised to different powers to produce a new physical quantity by creating dimensional formulas. Dimensions are the powers of fundamental physical quantities.

Example: Let’s take the formula of speed.

Speed = Distance / Time

The distance can be written in length [L]

Time can be written as [T]

The dimensional formula would be [M0 L1 T-1].

Hence, we can conclude that the speed is dependent on only length and time, not mass.

Derivation of dimensional formula of potential energy:

In order to find the dimensional formula of potential energy, break down the formula of potential energy in terms of mass [M], length [L], and time [T].

The formula of potential energy is:

P.E.= m.g.h 

Since m is mass, it can be written as [M1]

g is the acceleration and has a unit of m/s2, so it can be written as [L1T-2]

and h being height has a fundamental formula of [L1]

Substituting these quantities into the formula gives:

P.E.= [M1].[L1T-2].[L1]

Applying the exponent rule for the addition of powers,

P.E.= [M1L1+1T-2]

P.E.= [M1L2T-2]

So, the dimensional formula of potential energy is [M1L2T-2].

Potential energy:

The energy possessed by an object by its configuration, such as shape, size, and position, is known as potential energy. The potential energy depends on the force acting on any two things. The S.I. unit of potential energy is kg m2s-2.

For example:

• Electrical equipment until it is switched on.

• A stretched rubber band has potential energy stored in it by virtue of its shape.

• A stone kept on a table has potential energy due to its position.

There are other types of potential energy that exist. 

The energy trapped between the plates of a charged capacitor is known as electrical potential energy. Chemical energy, or a substance’s ability to produce work or emit heat by changing its composition, can also be thought of as potential energy coming from the mutual forces between its molecules and atoms. Nuclear energy is a type of potential energy as well.

Potential energy unit:

The units for gravitational potential energy are the same as those for kinetic energy: kg m² / s²

• All energy is measured in Joules and has the same units – kg m² / s² (J).

Potential energy formula:

The force acting on two objects determines the formula of potential energy formula. The formula for gravitational force is:

Where W = m×g×h = mgh

• The mass in kilograms is denoted by m.

• The acceleration owing to gravity is denoted by the letter g.

• The height in meters is denoted by h.

Conclusion:

The potential energy of an object is the energy an object can store and is a dot product of mass, acceleration due to gravity and height at which the object is present. There are various different types of potential energy, all of which are linked to different sorts of forces. Potential energy is the energy that an object has as a result of its position in relation to other objects. The dimensional formula of any quantity expresses it in terms of the basic fundamental quantities. So, the dimensional formula of potential energy is [M1L2T-2].