Mass Formula

Mass refers to the amount of matter that makes up an object. Consider an example where a bowling ball, a tennis ball, and a marble sitting on three separate scales. Among these three, the bowling ball certainly would have the largest reading on the scale. This is because a bowling ball is definitely heavier than both a tennis ball and the marble. Most noteworthy, the quantity that the scale is reading is the mass. Learn the mass formula here.

What is Mass?

Mass refers to the property of a body. Furthermore, it is a measure of the resistance to acceleration when the application of a net force takes place. It is a dimensionless quantity that is representative of the amount of matter in a particle or object. When it comes to the International System (SI) the standard unit of mass is the kilogram(kg).

Mass is certainly not the same as weight. This is true despite the fact that the determination of an object’s mass usually takes place by measuring its weight by making use of a spring scale. For example, an individual on the moon would definitely weigh less in comparison to his weight on Earth. However, the mass of such an individual would remain the same whether on the moon or on the Earth.

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Mass Formula

In the field of physics, many formulas of mass are present. However, the most primary formula of mass is as follows:

F = ma or m = F/m

This formula represents the relationship between force and mass. Here,

F = force,

m = mass,

and a = acceleration.

Mass Formula Derivation

If the net force which acts on an object is such that it equals the rate of change of its momentum, then
F_{net} = change in momentum/ change in time = \(\frac{\Delta p}{\Delta t}\)

Furthermore, the rate of change of momentum happens to be the derivative of the momentum in relation to time. Moreover, on requires calculus to manipulate the particular equation.

\(F_{net}\) = \(\frac{dp}{dt}\) = \(\frac{d}{dt}mv\) = \(m\frac{dv}{dt} + v\frac{dm}{dt}\) = \(ma + v\frac{dm}{dt}\)

Here both the m and v are certainly variable quantities. The treatment of the derivative must be as the derivative of a product. The quantity dv/dt refers to the rate of the object’s velocity changes, which is definitely the acceleration. Also, the quantity dm/dt represents the rate at which the object’s mass changes.

Solved Examples Mass Formula 

Q1. An object accelerated at a constant 5 m/s² under a force of 5 Newton. Calculate the mass of the object involved?

Answer: Acceleration(a) of the object = 5 m/s²
Force on the object = 5 newton
Therefore, one must apply the formula of mass here,

F = ma
5 = 5 × m
m = 5/5 = 1

Hence, the weight of the object is 1 kg.

Q2. The mass of an object happens to be 1 kg. Furthermore, a force of 2 Newton is applied on it. Find out the magnitude an direction of the object’s acceleration…

Answer: Here, mass(m) = 1 kg
Net force(∑F) = 2 Newton
Also, a = ∑F / m

a = 2/1 = 2

Hence, the acceleration happens to be 2 m/s².

Hence, the direction of the acceleration = the direction of the net force (∑F)