What are Mass and Weight ?
Are they same? Often we mess up with these two while discussing physics fundamentals or nymerical problems.
To answer these questions we will first discuss on the concepts of mass and weight.
As you get the basics of these 2 physical quantities, certainly you will be able to tell if these are same or not.
And if they are different what is the difference between mass and weight? If someone asks my weight I would invariably answer that in terms of some Kg (Kilogram). But is it correct in terms of Physics? Let’s find it out.
Mass and weight – definitions
What is Mass?
In Physics, mass is a property of a physical body.
In other words, it is the measure of inertia of an object i.e. it is the measure of an object’s resistance to change its state of motion. Not clear enough?
An object’s state of motion means whether it’s static or moving.
An object with more mass will resist or oppose more to change its state compared to a lighter object. It will be clear with these examples below.
Say a small ball is resting (static) in front of you. You can very easily move it by slightly pushing it with a finger.
Now if we replace this ball with a bigger ball of same material you will find it a bit difficult to move it with the same push.
Similar experience you will have if you want to stop these balls moving with some specific speed.
You will be able to stop the smaller ball with less amount of effort compared to the bigger ball.
That means, the bigger ball has some property with which it puts forth bigger resistance to change its current state of motion (inertia).
So we can say that every object has a tendency to resist a net force applied to it to modify its state of motion.
This tendency or property of an object is called its inertia.
As it depends directly on the mass of the object we say that mass is the measure of inertia.
As this is a property of an object it remains constant wherever you go. Your mass will be same here on earth or moon or even in a spaceship.
Unit of mass is Kilogram or Kg in SI.
What is Weight?
Then what is weight? Weight is a force. Weight of an object on earth is the gravitational pull or gravity applied by the earth on that object.
This is the force with which the earth attracts an object towards its center. Unit of weight is Newton in SI. It is generally denoted by W.
The Relation between Mass and Weight
Let’s follow the general formula of force (F = m a), where force F is the product of mass of the object and its acceleration because as said W is a force.
As the object under gravity undergoes a specific acceleration called ‘ acceleration due to gravity (g)‘, we will use this g instead of a to get the formula of weight.
The relation between mass and weight is like this:
Weight (W) = mass (m) x acceleration due to gravity (g)
So the weight W of an object with mass 10 kg is
W= 10 kg x 9.8 m/s2 = 98 Newton.
Variation of Weight
As weight depends on the value of g (acceleration due to gravity), therefore weight varies whenever g changes.
As example, it’s seen that the g on moon is about one sixth of earth’s g. That’s why the weight of an object becomes one sixth of its respective weight on earth.
Therefore if an object weighs 60 N on earth it will be 10 N on the moon’s surface.
Even on earth g varies to some extent as we go higher from earth’s surface (climb a mountain) or go deeper below the earth’s surface (go inside a mine).
So you see even on earth our weight varies. But our mass is same everywhere. Hope this topic explains well about mass and weight and specifies how these are different.
This is discussed here with easy explanations: acceleration due to gravity and its variations due to height and depth