What Exactly is Mass?

You know when a kid asks you, "What is a color?", and you realise that you don't really understand what color actually is but can only give this kid a memorized answer or have to resort to an example like "it's what you see in a rainbow".

This happened to me yesterday. On my way home from the gym, I randomly wondered (I love it when our brain does this) — "What actually is mass?"

While a kid, I didn't really question this, I knew that we were able to calculate atomic mass of elements since we studied it in our highschool physics class and I just thought maybe total mass of an object is just product of this atomic mass and the total number of atoms in that object.

And it hit me yesterday, there's no way in hell we know how many atoms there are in any object (I seriously don't know how I thought this in the past). So what exactly is mass, I questioned.

Then, obviously, I had to run to my room and look this up. That's when I experienced the thing I live for — the 'aha moment.'

Now, hopefully I can simulate that aha moment through this blog.

What Exactly is Mass?

Mass of an object is its resistance to be accelerated.

Intuitively, we all know this — A big boulder has higher mass than a small stone. But what does this mean? — What does it mean when we say the big boulder has a higher mass? It is essentially this — when we push/pull a big boulder, it is harder for us to accelerate it than it is if we push/pull a small stone — i.e we can accelerate a small stone much easily than a big boulder.

This right here is the main idea of what mass actually is.

Mass characterizes the object's inertia.

But then...

What does this statement mean — "The stone has a mass of 30kg."

How do we even calculate how "hard" is it to move an object — The thing is — we don't.

We actually considered the "International Prototype of the Kilogram (IPK)" or "Le Grand K" — mass of a chunk of platinum-iridium as a unit of mass — 1 kg. So those object that weighed the same as this mass was also 1 kg, that weighed double this mass was 2kg and so on. However, we no longer define units by material objects and instead define them by abstract constants of nature (a formula using Planck's constant in this case) since physical objects could be scratched or lose mass with passage of time.

Ways to Measure Mass

Measuring mass is essentially comparing the masses. For example, when we say a 30 kg stone — we are essentially comparing it to a unit kg (1kg), to take International Prototype of the Kilogram (IPK) for context, the stone is 30 times heavier than IPK.

Inertial Balance

Visualize this:

Two objects with unequal masses (m₁ and m₂) are attached to the ends of a straight, rigid rod. A rope is tied at the very centre of this rod, now wonder — if you pull this rope, what would the motion of the rod be like?

The answer is that the rod will move forward rotating.

Remember there are 2 unequal mass, and we would require greater effort to move the heavier object, so when we pull the rod, the object with heavier mass will accelerate less and the rod will rotate when it moves forward.

And if the objects were of equal mass, the rod would move forward without rotating.

The interesting thing about inertial balance is that it gives us a method to measure mass by using the very notion of the mass as its resistance to being accelerated.

Gravitational Balance

Using inertial balance to measure mass is impractical for the most part. There is another way to measure mass, which is also the most common way — gravitational balance.

You weigh yourself on a bathroom scale — this is one example of gravitational balance.

Gravitational balance works on this concept — Mass of the body is exactly proportional to the weight of the body.

w = m * g

It is based on Galileo's observation that objects are accelerated at the same rate by gravity (g ≈ 9.8 m/s²). So, when we weigh ourselves, we're actually measuring the force of gravity on our mass, not the mass itself.

This is also why we weigh different in different planets (g is different in different planet), but it is essential to remember that our mass always remains the same no matter where we are.

Wrapping It Up

Mass is more than just a number we slap onto objects. It's a fundamental property of matter, tied to how resistant objects are to changes in motion. It's measured by comparing against standards, whether through balancing forces or using nature's constants.

It's fascinating how something we take for granted, like standing on a scale, connects to deep, universal truths.

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❤️ SUPRIYA