What is the Difference Between Mass and Weight

One of the most basic concepts you need to grasp in science are 'Mass' and 'Weight' of the object. Although these two different concepts are often referred to be the same, they are entirely different physical parameters. The difference must be tackled right at the start, when you learn about the concept of force, in your basic physics courses. I assume that you have basic knowledge of what is a force and are familiar with Newton's laws of motion, which define it.

How are Mass and Weight Different?

If you plan to go for a career in pure science or physics, it's essential that your basic concepts are clarified. You need to have a precise definition of what each physical concept means, if you hope to understand other concepts of a greater complexity. Let us see what is the relationship between mass and weight and how two objects with the same mass may have different weights.

Right at the outset, let us clearly define mass and weight. Mass is the total 'matter' content in an object, which is made up of atoms and molecules. It could also be defined as the property which causes gravitational force to be exerted on an object. Any object that can feel the attractive gravitational force has mass. It is measured in Kilograms according to SI units. Almost every physical object has mass, except entities like photons of light, which have zero mass and hence are unaffected by gravitational force.

The general theory of relativity proves that every object with mass, warps space time around it. This warping of space time gives the illusion of a gravitational force acting between objects, causing them to move. Actually, it's the curvature of space time that's responsible for this movement of objects. Still, Newton's law of gravitation, although proved to be wrong, predicts the movement of objects in a gravitational field quite accurately, within a certain range of approximation.

So now that you know what is mass of an object, it will be easier to understand how weight is different from it. The general theory of relativity describes gravity, as a result of the curvature of space time and the natural motion for any object in a gravitational field is 'free fall'. Whenever an object is at rest in the gravitational field, it is obstructed by other objects to be stationary, which gives rise to weight.

Ergo, the weight of any object is actually the repulsive and obstructive force acting on it, which prevents its free fall motion. Thus weight is this obstructive repulsive force acting on an object, which is equal and opposite to the gravitational force acting on it. Here is one more addition to the long physics formulas list, you will eventually create. This formula provides the magnitude of weight acting on an object.

Weight (W) = Mass (m) x Acceleration (a)

Thus the magnitude of the weight of an object is its mass, multiplied by the local gravitational acceleration in the vicinity of that object. This physics formula clarifies the relation between mass and weight. The local gravitational acceleration on Earth's surface is 9.80665 m/s². That's only the average value, as the acceleration varies with altitude and location on Earth's surface. Since weight is directly proportional to the value of acceleration, which in turn is directly proportional on the mass of the object creating the massive gravitational field, it's perfectly possible for objects to have the same mass but different weight. The unit of weight is same as that of force, which is Newton.

So how does a weighing balance work and help us measure the mass of an object? If we assume that the local gravitational acceleration remains the same for both pans of a weighing balance, then it can be used to accurately measure the mass of an object. When the pans balance themselves, we can assume that the gravitational force acting on the two objects is equal. We can then safely assume that they have the same mass. Why it is so, can be understood when you look at the weight formula above. When force acting on both objects is the same, the acceleration part of the formula cancels out and we can say that both objects have equal masses.

Mass of an object may remain constant, but its weight is entirely dependent on the amount of gravitational force exerted on it by Earth's mass. That's why your mass on the Moon will be the same as that on Earth, but your weight on Moon will be different, as it exerts a lesser magnitude of gravitational force compared to Earth.