Difference Between Mass and Weight

Main Difference – Mass vs. Weight

In everyday usage, we use the terms mass and weight interchangeably. However, there is a technical difference between the two. The main difference between mass and weight is that mass is a measurement of the amount of matter in a body, whereas weight is a measurement of force felt by a body in a gravitational field.

What is Mass

Mass is a measurement of the amount of matter in a body. There are two separate contexts in which mass becomes important. Firstly, the mass of a body attempts to resist acceleration whenever a force is applied on a body. This reluctance by an object to resist acceleration is called inertia and so in this context, the mass is referred to as inertial mass ( $m_i$ ). If a resultant force $\sum F$ acts on the body, the acceleration $a$ that can be produced is inversely proportional to the object’s mass, such that:

$m_i=\frac{\sum F}{a}$

Secondly, mass is also the property that determines the gravitational force between two objects. In this context, mass is referred to as gravitational mass ( $m_g$ ). The gravitational force of attraction between two objects with masses $M_g$ and $m_g$ , separated by a distance $r$ can be given by,

$F=\frac{GM_gm_g}{r^2}$

where $G$ is called the universal gravitational constant, with $G=$ 6.67×10^-11 m³ kg^-1 s^-2. (Note: gravitational mass can be further subdivided into active gravitational mass and passive gravitational mass, but that is a distinction we will not go into).

Inertia and gravitational attraction are two separate things, and there is no reason for the inertial mass of an object to be equal to the gravitational mass. However, no experiment has demonstrated that the two are unequal. Mass is one of the base physical quantities, and in the SI system of units mass is expressed in kilograms. A set of traditional balancing scales measures the mass. Since objects are added to both sides of the scale, the gravitational force gets “canceled out” and the measurement you make ends up becoming a comparison of masses.

What is Weight

Weight is the gravitational force experienced by a body in a gravitational field. If the weight of the body is given by $W$ , then it is given by

$W=m_gg$

where $g$ is the gravitational field strength. Comparing with the equation we had for gravitational mass, we then have $g=\frac{GM_g}{r^2}$ where $M_g$ is the gravitational mass of the body that forms the gravitational field that the mass $m_g$ is in.

Weight is a force, and it is measured in newtons (N). Since weight depends not only on an object’s own mass but also on the masses of bodies surrounding it and distances to these other bodies, the weight can change from place to place. For instance, the gravitational field strength on the surface of the Moon is about a sixth of the gravitational field strength at the Earth’s surface. Therefore, two objects having same masses will still experience different weights if one of them is on the Earth and the other is in the Moon. The object in the Moon will “weigh” about a six times less! A bathroom scale measures your weight because it records how much force you are being pulled down.

A set of bathroom scales measures weight. You’d notice a 16% “weight loss” if you were to take these scales to the Moon and weigh yourself there (however, your mass would still be the same)!