Weight Formula

This article deals with weight formula and its derivation. Weight refers to the force which acts on a body or object due to the effect of gravity. So, when an individual stands on a scale, the reading that appears is the weight. The more an individual weighs consequently means a higher reading on the scale. When an individual loses weight, he should think of it as lessening one’s force on the Earth due to gravity.

What is Weight?

Simply speaking, weight refers to the force of gravity. Weight is certainly a force that acts on all bodies or objects at all times near a heavenly body such as the Earth. The Earth pulls all objects downward towards the center with a force of gravity. One can find the magnitude of the force of gravity by multiplying the magnitude of the acceleration due to gravity by the mass of the particular object.

Some books describe weight as a scalar quantity, the magnitude of the gravitational force. In contrast, some books refer to weight as a vector quantity, the gravitational force which acts on the object. Moreover, some experts explain weight as referring to the magnitude of the reaction force which is exerted on a body by various mechanisms. Also, these mechanisms keep the body in place.

The unit of measurement for weight is certainly that of force. This unit in the International System of Unit (SI) is the newton. The object with a mass of 1 kilogram would weigh about 9.8 Newtons on the Earth’s surface. Furthermore, it would weigh about one-sixth as much on the moon.

Weight Formula

The weight of an object or body certainly depends on the mass of the object and the gravity acting on it. This is why, the weight is different from mass. The mass of an object would be same whether on the Earth or on the Moon. The weight of an object due to the influence of gravity would be different on the Earth than on the Moon. The weight formula can be explained as follows:

Weight = mass × gravity

The formula for this is:

w = mg
Here we have,
w = weight
m = mass
g = gravity

Weight Formula Derivation

A fact that is well known by experiment is that a freely falling body irrespective of the mass would experience acceleration. This acceleration is due to the influence of gravity and its denotation is by ‘g’. Furthermore, this acceleration acts towards the center of the Earth. Therefore, from the Second Law of Motion we certainly have:

F = ma

Here, F = force, m = mass, and a = acceleration.

Now for freely falling bodies

a = g
F = w

Here, g = gravity and w = weight
Hence, w = mg

Solved Examples on Weight Formula

Q1. A person’s mass happens to be 70 kg, while the gravity on Earth is 9.8 m/s². Find out the weight of this person?

A1 In order to determine the formula of weight, one has to apply the weight formula.
Here m = 70 kg and g = 9.8 m/s²

W = mg
W = 70 × 9.8
W = 637 Nw

Hence, the weight of the person is 637 Nw.

Q2. An individual weighs 250 Nw on the moon. Calculate the mass of the individual considering the gravity on the mass as 1.6 m/s²?

A2 Here, w = 250 Nw and g = 1.6 m/s²

W = mg
m = w/g
m = 250Nw/ 1.6m/s²
m = 156.25kg.

Hence, the mass of the individual is 156.25 kg.