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Force is one of the fundamental things to exist in nature. It can change the motion of an object. Technically, the force can be defined as a product of mass and acceleration(This is obtained by Newton’s second law). It is denoted by the letter F. Newton was the first-ever person to discover the force, and because of this, the SI unit of force is named after him, i.e. Newton. A few day-to-day examples are push and pull of a door, lifting objects.
Force
A force is defined as the push or pulls an object exerts on another. When two items come into contact with each other, they both exert a force on each other. Stretch and squeeze are other words that can be used to describe forces. What does it mean to have “force” in physics?
“Push or pull that alters the velocity at which anything with mass travels.”
You can find out how much force is at work by utilising a spring balance. Newton (N) is the SI unit of force.
Dimensional analysis
The dimensional analysis uses a set of units to determine the form of an equation or, more commonly, to ensure that the result of a computation is correct as a safeguard against many common errors.
Dimensions in units and measurements
The dimensions can be written as the powers of the fundamental units of length, mass, and time. It depicts their nature and does not show their magnitude.
Example of writing dimensions
Let’s take the formula of the area of the rectangle:
Area of the rectangle = length x breadth
= l x b
= [L1] X [L1]
= [L2]
Here, we can see the length to the power of 2, and we cannot find the dimension of mass and time. Hence, the dimension of the area of a rectangle is written as [M0 L2 T0]
Dimensional formula
The dimensional formula depicts the dependency of physical quantity with fundamental physical quantity and the powers.
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-1]
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.
Dimensional equation
To get the dimensional equation, the physical quantity is equated with the dimensional formula.
Example
Velocity = [ M0 L1 T-1]
Here, velocity is the physical quantity, which is equated to the dimensional formula.
Sr no | Physical quantity | Formula | Unit | Dimensions |
1 | Work | Force x distance | Joule – J | [M1 L2 T-2] |
2 | Force | Mass x acceleration | Newton – N | [M1 L1 T-2] |
3 | Energy | Work | Joule – J | [M1 L2 T-2] |
4 | Momentum | Mass x velocity | Kgms-1 | [M1 L1 T-2] |
5 | Pressure | Force/area | Nm-2 | [M1 L-1 T-2] |
Dimensional Formula of Force:
We know that:
Force = mass × acceleration (by Newton’s 2nd law)
Acceleration can be defined as the change in the velocity of an object to its time. To find the dimensional formula of force, we need to first find the dimensional formula for acceleration:
[a] = [velocity]/[time]
= [displacement]/[time×time]
= L/(T×T)
= L1T-2
Therefore, Force = mass × acceleration
= [M1] × [L1T-2]
= M1L1T-2
From the above derivation, it is pretty clear that M1L1T-2 gives the dimensional formula for force.
Dimensional formula of force importance:
- The Dimensional formula of force helps us understand the physical correctness of any equation involving force.
- It helps us to understand the relationship between different physical quantities involving force
- It helps us in converting units from one physical quantity to another
- In any relationship, the constant dimensions can be found using this analysis.
Uses of Dimensional Formula:
- It can be a helpful tool to check the consistency and coherency of your dimensional equation.
- The dimensional formula will be used to establish the correlation between the physical quantities of physical phenomena.
- These formulas can be used to change the units from one system to another.
There are some limitations of dimensional formulas:
- It is not concerned with the dimensional constant.
- The formula that contains functions like trigonometric, exponential, logarithmic, and the like cannot be derived.
- In the context of a physical quantity being a scalar or vector, it does not provide any information about whether the quantity is physical or not.
Conclusion
This article covers content related to the dimensional formula of force notes and includes basic definitions of force. Dimensional analysis helps us perform mathematical calculations that are easier, more precise, and quicker. It is the method used to manipulate dimensional formulae. The dimensional formula has several uses while calculating.
