Understanding Units of Force (Newtons and Pascals)

[tomtomtom1]

Homework Statement

Understanding Units of Force (Newtons and Pascals)

Relevant Equations

1) Kg * m / s^2
2) kg/s^2

Hi all

I am trying to get my head around some units of force.

1) I have units of:-
Kg * m / s^2

Am I correct in thinking that these are units of Newtons.

So if I had 560Kg * m / s^2, then can I say 560 Newtons - would this be correct?

2) Secondly I have units of:-
kg/s^2

I have no idea what these units are they pascals or Newtons ?

Can someone shed any light?

Thank you.

 

[PeroK]

Homework Statement: Understanding Units Of Force (Newtons and Pascals)
Homework Equations: 1) Kg * m / s^2
2) kg/s^2

Hi all

I am trying to get my head around some units of force.

1) I have units of:-
Kg * m / s^2

Am I correct in thinking that these are units of Newtons.

So if I had 560Kg * m / s^2, then can I say 560 Newtons - would this be correct?

2) Secondly I have units of:-
kg/s^2

I have no idea what these units are they pascals or Newtons ?

Can someone shed any light?

Thank you.

Yes, Newtons are the SI unit for force $kg \cdot m/s^2$.

https://simple.wikipedia.org/wiki/Newton_(unit)

The pascal is a unit of pressure, which is $N/m^2 = kg/(m \cdot s^2)$

https://en.wikipedia.org/wiki/Pascal_(unit)

The units $kg/s^2$ would be the units of a spring constant, $k$. The force of an elastic medium may be proportional to the length it is stretched: $F = kx$.

 

[DEvens]

Often units of force don't get simplified the way you have done. So a Newton is a unit of force, yes. But you won't often see that as kg m / s^2, though of course you could.

Similarly, a spring's force constant won't usually be listed as kg/s^2. Rather it will be N/m, meaning Newtons per meter.

On the other hand, you should be thinking about these things when you do a calculation. If the units come out to kg/s^2, the context may help you figure out what that is supposed to be. If you are dealing with springs, you probably want a force per distance.

But the context is going to be important. Imagine you were dealing with a bridge across a span. You might need to work out the weight of the bridge per meter of bridge. Not the mass, but the weight. So that would be Newtons per meter. But if you simplify the units, that's kg/s^2. Which does not instantly *look* like a weight per meter. Then the context reminds you it's Newtons per meter.

 

[tomtomtom1]

Often units of force don't get simplified the way you have done. So a Newton is a unit of force, yes. But you won't often see that as kg m / s^2, though of course you could.

Similarly, a spring's force constant won't usually be listed as kg/s^2. Rather it will be N/m, meaning Newtons per meter.

On the other hand, you should be thinking about these things when you do a calculation. If the units come out to kg/s^2, the context may help you figure out what that is supposed to be. If you are dealing with springs, you probably want a force per distance.

But the context is going to be important. Imagine you were dealing with a bridge across a span. You might need to work out the weight of the bridge per meter of bridge. Not the mass, but the weight. So that would be Newtons per meter. But if you simplify the units, that's kg/s^2. Which does not instantly *look* like a weight per meter. Then the context reminds you it's Newtons per meter.

Thanks DEvens.

Your correct looking at the context does makes sense.

In fact i calculated kg/s^2 incorrectly, it should be kg *m/s^2 which is a measure of Newtons.

Thank you again.

 

[mfig]

When you have a combination of units that is not one of the standard combinations, it is hard to tell what is going on without a context because there are many ways to get the same resultant units from combining base and named combinations. I have seen all kinds of weird units working in industry. For example, one could make the units under consideration in many different ways:

Newtons per meter: $\frac{N}{m} = \left[\frac{kg m}{s^2}\right] \cdot \left[\frac{1}{m}\right]= \frac{kg}{s^2}$

Pascal meters: $Pa \cdot m = \left[\frac{kg}{m s^2}\right] \cdot \left[m\right] = \frac{kg}{s^2}$

Watt seconds per square meter = $\frac{W \cdot s}{m^2} = \left[\frac{kg m^2}{ s^3}\right] \cdot \left[s\right]\cdot \frac{1}{m^2} = \frac{kg}{s^2}$

So context is important in interpreting any combination. Even the standard combinations have different interpretations. As an example, it was a big "A-ha" moment for me when I realized that pressure can be interpreted as Force per Area or as Energy per Volume. Which is more useful depends on the application.