A Level Physics Base Units Question

[hellarda]

Hi all,

Just come across a question asking me to show that the base units of intensity of X-rays are kgs^(-3) by using the equation I=P/(4(Pi)r^2)

I can't for the life of me work it out?

Any ideas?

Cheers

 

[AshD93]

For each variable, substitute the unit for each and then do the maths.

I don't know what your variables are but as a example, take Newtons second law, F = ma

Substituting variables, you get N = kg * ms^-2 (Which is the base units for Force)

Not the best example. But let's take area of a rectangle. You get A = l * w

In units, m^2 = m * m

Make sense?

 

[dirtychinchilla]

You could use this method, http://en.wikipedia.org/wiki/Buckingham_π_theorem but it may be a bit much for what you need.

 

[Elixir]

Ok, so most of this is in knowing the various base units for a few variables. I've separated each unit with a dot for clarity.

Power is measured in watts (W), which is another name for joules per second J.s^(-1).

A joule is a unit of energy or work, and is a function of force by distance, i.e. N.m. Substituting this into power you now have newton metres per second, N.m.s^(-1).

A newton is the unit of force, and from F=ma you can work out that the base units of force are kilogram metres per second per second, kg (from mass) and metres per second per second, m.s^(-2) (for acceleration), so kg.m.s^(-2).

So putting this into your power changes it from:
N.m.s^(-1)
to
kg.m(^2).s^(-3)

So you can now go back to your original equation using kg.m(^2).s^(-3) as your units for power, and the only variable with units on the denominator is the radius squared, so m^2.

Divide kg.m^2.s^(-3) by m^2 and it just removes the m^2 component, leaving you with kg.s^(-3) for I.

Hope that's clear, not that easy to follow!

 

[Judgeneo]

4pi is a constant, so ignore it.


Then you have I = P/r^2

1/r^2 has base units of m^(-2) so we now just need to work out the units of power.

Power is Energy/Time
E = Mc^2

c has units of m*s^(-1) so Mc^2 has units of Kg*m^(2)*s(-2)

Put it all together and you get:

Kg*m^(2)
------------
m^(2) * s^(3)

Which is equal to your answer.


Curses! Beaten!

 

[Elixir]

Curses! Beaten!

Slightly different approach though, I hadn't considered using E=mc^2 which is more straightforward!

 

[WKN]

4+4 = 8 etc etc

 

[Ricochet J]

4pi is a constant, so ignore it.

That's a dangerous statement to make. Many constants do have units (see Avogadro's constant, for example). It's better to say "4pi is dimensionless, so ignore it".

 

[Judgeneo]

That's a dangerous statement to make. Many constants do have units (see Avogadro's constant, for example). It's better to say "4pi is dimensionless, so ignore it".

I was using constant in the purely mathematical sense

Good point though

 

[Robosapien]

Put them in those cool square brackets: [kg][s^-2] etc.