## Force Formula

According to Newton’s Second Law of Motion, the formula of force is mass times acceleration. So,

Unit of force is \(Kg.m.s{-2}\) and is also known as \(Newton\) written in short as symbol \(N\). Force is a vector quantity. It has a magnitude as well as direction.

## Force Formula Triangle

Force formula \(F=m\times a\) is a simple algebriac expression and if we have information about any two of these quantities we can easily find the third unknown quantity using this force formula expression.

Let us explore the above statement using the force formula triangle. The figure given below shows a force formula triangle that can be used to easily memorize this force formula and how we can use this formula to find the third quantity if any two of force, mass and acceleration are given.

We can see from this triangle that we have three different possibilities i.e., we can get three different algebraic expressions using the relation between force, mass, and acceleration.

- In the first case If we have knowledge of force \(F\) and mass \(m\) then we can easily calculate the acceleration of the body. So, we have \[a=\frac{F}{m}=F\div m\]
- In our second case if we have knowledge of force \(F\) and acceleration \(a\) then we can easily calculate the mass of the object using our known values of \(F\) and \(a\). So, we have \[m=\frac{F}{a}=F\div a\]
- Our third case in this formula triangle is the case where we have knowledge of mass and acceleration and we can use these quantities to find the force applied to the body. So, we have \[F=m\times a\] this is nothing but our force formula.

## Solved Examples on Force Formula

**Question 1. **What force would be required to produce an acceleration of 2ms^{-2} in a ball of 8 Kg?**Solution:** Here it is given in the question that

Mass \(m=8Kg\)

Acceleration \(a=2m/s^2\)

Force \(F=?\) which is to be calculated.

From the relation \[F=ma\] we get \[F=8\times 2 \,\, N\]or, Force \[F=16\,\,N\] which is the required answer.