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Force Formula with solved questions

A force is an interaction in physics that can modify the velocity of an object. A force can cause a mass object to change its velocity (e.g., moving from a resting position), i.e., to accelerate.

Learn more about the Effect Of Force and Force is due to interaction

Intuitively, a force can be described as a push or a pull. A force is a vector quantity since it has both magnitude and direction. It is measured in newtons, i.e., the SI unit of force (N). The sign F represents force.

Let us now learn about the force formula along with the force formula triangle along with an example.

Force Formula

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

Force Formula

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 algebraic 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.

Force formula triangle
Force formula triangle

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.

  1. 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 \[a=\frac{F}{m}=F\div m\]
  2. 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 \[m=\frac{F}{a}=F\div a\]
  3. 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.

Also, visit Acceleration Formula with Mass and Force for more information.

How to find displacement in physics x
How to find displacement in physics

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.