# Physics - Classical mechanics - Mass and Newton's second law Hello it's a me drifter1! Today we continue with Physics by getting into Newton's second law and by also describing what mass is! This post will cover everything that you need to know about those two things and so without further do, let's get straight into it!

## Getting into the second law

The first law that we covered last time in Physics covered motions where the forces applied to an object where zero or the total force was zero. That way the object had zero acceleration and stayed at rest or moved with constant velocity.

But, what happens if the total force is not zero?

Well, if the object is at rest then it will start moving. If it had a velocity then it can go faster, slower, change direction etc. So, in all those cases the object has acceleration! That's exactly what the 2nd law is all about.

Depending on the mass of an object and the force direction the result varies.

If the force is constant then we will have a constant acceleration and if the force is variable then we will also have a variable acceleration.

But what about the mass? Well if the mass is high then we have to push an object harder (more force) so that it moves. If the mass is low then we don't need a lot of force.

## What is Mass?

Mass or Intertial Mass is exactly that. It's the resistance of an object to changes of it's motion state. The more the mass the higher the inertia of an object. The less mass we have the easier (less force) it's to move that object. It's the actual quantity of matter an object has and is the most essential way of representing it's inertia.

We calculate mass in grams. If 1kg of mass gets pushed by a force of 1N then the object will have an acceleration of 1 m/s^2

You can get the mass by using:

m = F / a

where F is the force and a the acceleration.

You can see that mass and acceleration are inversely proportional and mass and force are directly proportional.

## Νewton's second law

This exact equation is Newton's second law.

ΣF = m*a

The total force applied is equal to mass times acceleration.

With that type of writing you can see that:

1 N = 1 kg * 1 m/s^2

The equation contains vectors and so we can use it in form of components like that:

ΣFx = m*ax,      ΣFy = m*ay,      ΣFz = m*az

Of course all those equations are true only when the mass is constant!

## Calculating the mass of another object

By knowing the mass of one object, applying the same force on another and having a way to calculate the acceleration, we can use the 2nd law to find the mass of a second object.

The force for the first object is:

F1 = m1*a1

For the second object:

F2 = m2*a2

Because F1 = F2 = F we have:

m1*a1 = m2*a2 =>

m2 = m2*a2 / a1

You can see that we now calculated the mass of the second object!

## Combining objects

It's pretty important too. Remember that if two masses get combined to a single mass, then the total mass will always be m1 + m2

So, if F = m1*a1 and F = m2*a2 and F = (m1+m2)*a3 we will see m1+m2 act as one object with mass m3 = m1+m2. This means that the acceleration of the combined object will be: a3 < a1 and a2.

By knowing the mass and acceleration of one of them (and the mass of the other), we can calculate the force applied and then we can use the equation below to calculate the acceleration of the combined one when the same force is applied.

F = m1*a1        (getting force value)

F = (m1+m2) * a3 => a3 = F / (m1+m2) ### Image Sources:   And this is actually it! I hope that you enjoyed it!

Next time we will cover Newton's 3rd law!

Bye!

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