# — What exactly does kilograms times metres per second squared mean?

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I understand that F=ma, mass is in kilograms and acceleration is metres per second squared so Newtons are just kilograms metres per second squared, but what does that mean? I can’t seem to comprehend it/really understand it intuitively. Why are we adding kilograms, metres per second squared times (or vice-versa)? I understand stuff with division, like density, because it makes sense, like with density, you’re dividing the mass over the volume occupied to see how many kilograms you have per cubic metre of the substance in question, so kg/m^3 , but I seem to have trouble understanding the multiplied quantities, like Newtons.

In: 6 Personally I never found it useful to think of force in terms of kilograms per meter per second squared. Almost all units can be broken down/described in terms of other units, and until you’re at the highest levels of science it’s usually not useful to think of them this was.

Jist remember that f=ma, and that a force being exerted on a body results in a change in ACCELERATION, not just a change in velocity. The big takeaway is the relationship between acceleration and force, focusing on the units can just complicate things [deleted] Meters per second squared is meters per second per second.

So if acceleration is (like the gravitational constant) 9.8 meters per second squared, in one second an object would (ignoring other details like air resistance) be falling at 9.8 meters per second, and and two seconds it would be falling at 19.6 meters per second, and at 3 second it would be falling at 29.4 meters per second…

It is going 9.8 meters per second faster, per second.

Does that make sense? Lets break it down, velocity is the change of distance over time so m/s, then acceleration is the change of velocity over time or (m/s)/s or m/s^2.

Now we know that it doesn’t take any force to move something it only takes a force to accelerate something.

And the mass times the acceleration is equal to the force needed. So the dimensions of force are kg*m/s^2

What’s more, kinetic energy takes the form of kg*v^2 or kg*(m/s)^2 and the energy consumed is equal to the force over a distance so (kg*m/s^2 ) *m which is equal to the dimensions of kinetic energy. The kilogram is being accelerated at a rate of one meter per second each second.

So, every second, that kilogram’s velocity is increasing by one meter per second.

It’s all multiplied together, so if you have twice the mass, you’d have half the acceleration. If the mass is the same, but the velocity increases by twice as much then it will take twice as long.

If you want to convert to different units… say tons kilometers per square hour. then you have to convert each individual element (kg to ton, meters to kilometers, seconds to hours (twice)). Imagine an object moving at some velocity with no other forces actin upon it. If we apply a force such that it slows down it will slow down based on a couple of factors first how heavy is it (the kg part) and it will slow down at a certain number of meters per second every second. (The meter per second per second.)

The problem you might be having it what about the force you apply when pushing on a wall, it doesn’t slow down or change its velocity so what does it mean? The answer is there is no force you push on the wall and it pushes back equally and so nothing happens. For there to be a force there has to be a change in momentum (typically this is a mass accelerating but there is more to the equation than f=ma it just cancels out for object with mass) You can think of it a few different ways. The way I find most helpful is to think of it as (kg * m/s) / s, in which case it’s the rate at which momentum (which is mass times velocity, units of kg m/s) is changing per second. It’s hard to explain because when it ‘clicks’ the difficulty becomes forgotten.

In your case I think you are overthinking rather than under thinking.

Look at the first equation: F=ma.

Force is what we call matter (mass) as it is accelerated. Does that make sense? If so hang on tight to that. We are going to add the rest to it.

So we need a way to describe mass. Si is pretty set on grams and kilograms so let’s just go with them. In fact, we are building machines for ants so we are going to just stick with kilograms.

Next part is where it gets a little tricky. Acceleration is a change in velocity. Let’s say how much it changed in a second. So acceleration is (change in velocity) ‘per’ second also written as (change in velocity)/second. But velocity also has a term. We list it in meters per second. So acceleration is really (meters per second per second) Or switching that to our more mathy view, meters/sec/sec. And since that’s a lot to write, let’s just say meters/sec^2. The velocity and change in velocity are in the same second so it is logical to square up.

So now that we built the ‘m’ and ‘a’ parts, let’s put them together.

Force is mass times acceleration. Force is (kilograms, a measurement of mass) times (m/s2, a measurement of acceleration).

Force is kg • m/s2

Just walking through the steps and ideas demonstrates how we arrive at the kg•m/s^2. We just put in base units from velocity to acceleration to time up to Force, which a derived unit. We get a somewhat unwieldy term. So someone created Newton.

My hardest concept (still) is ‘how is there no force if there’s no change in velocity. I mean, I’m pushing pretty hard on this building, how are you telling me there’s no force?

Anyway I probably put too high an expectation on five year olds and someone probably did a better job by now. Good luck. We start with one kilogram. That is a unit of mass. It is stuff.

We want to move it. Which means speeding it up.

To speed it up we have to change how fast it is going.

To know how fast something is going we have to measure how far it has gone in a particular time.

We measure distance in metres, and time in seconds. So how fast something is going is measured in metres per second – how many metres every second. So how quickly we speed up will be how many metres per second our speed is increasing by every second, so metres per second per second, or metres per second-squared.

Putting this all together, 1 kg m s^(-2) means that we are taking one kilogram of mass and every second we are increasing how fast it is going so that at the end of that period it will be travelling one more metre every second than it was at the start of that period.

If you want to understand intuitively why the kg and m are multiplied together, if we have more mass we need to push harder to get it to speed up. If we want it to start going an extra 2m every second for each second we push it, rather than just 1m, we need to push harder. Basically if you push something 4 kg at 1 m/sec^2 and someone else is pushing something 1 kg at 4m / sec ^2. Then you two are exerting exactly the same strength and if you are pushing each thing over the same distance. Then you two expanded exactly the same energy Weight is the easiest way to conceptualize it. Your mass is the same no matter where you are in the universe. But the force your mass applies on the ground would be different on the Earth, the Moon, Mars, etc. due to the differences in mass of those bodies. Thus, if the force you apply in leaping from each body stays the same, your jumping height will change because the force keeping you “grounded” is different. If I threw a brick at you, that shit would hurt. If I threw a bigger brick at you chucking it just as hard, it would hurt more. If I shot a bigger brick out a freaking potato cannon. I reckon that would knock you back a few meters more.

Mass is the size of the brick. Meters per second squares is how hard I throw it at you. How bad it hurts is force. Just think of using a hammer. It takes a certain amount of force to drive the nail. How many swings it takes will depend on 2 things: the weight of the hammer (kilograms) and how fast you accelerate it (meters per second ^2).