Heisenberg Uncertainty Principle - find minimum uncertainty in position

daleklama

1. The problem statement, all variables and given/known data

Assume speed of 435g football is known with 1mm/s uncertainty.
What is the minimum uncertainty in its position?

2. Relevant equations

I'm not quite sure... I know p=mv, and I know that Heisenberg's uncertainty principle states that certain parameters of quantum particles cannot be measured/known at the same time without uncertainty.

When I did a previous example, I used the formula:

dx ≥ h/(4∏mdu)
where dx = uncertainty in position
h = plancks constant
m = mass in kg
du = uncertainty in velocity


3. The attempt at a solution

Well I was trying to do it using the formula given above, but there are a couple of things I don't understand.
i) How do I find du?
I previously found du by multiplying the speed (given in question) by the uncertainty, which was in percentage form.
How do I find du now? I'm not actually GIVEN a speed, and I don't quite know what to make of "1mm/s uncertainty." Is that 0.001%, which would be 0.00001, or...?

Thanks :)

Steely Dan

The uncertainty appearing in the uncertainty principle is always a quantity with units of position or speed, not a dimensionless ratio (or percentage) of quantities. In this case, the uncertainty in the velocity is given to you directly in the problem. The actual velocity is irrelevant for the application of the uncertainty principle, in cases where you know the uncertainty directly. The actual velocity is only relevant when you use it to infer what the uncertainty in the velocity must be (e.g. if you are a given a problem that says "the velocity of the football is measured to be 10.000 m/s -- in which case you are being indirectly told the uncertainty in that measurement).

daleklama

Okay, I'm not sure if I'm doing this right, but in that case, would the following be a correct calculation?

dx ≥ h/(4∏mdu)
where dx = uncertainty in position
h = plancks constant
m = mass in kg
du = uncertainty in velocity

dx ≥ (6.626e-34)/(4∏(0.435)(0.001)
dx ≥ 1.21e-31 m


I used 0.001 as the uncertainty because it's given as 1 mm/s, and I felt I should convert that to metres?

Thanks very much for reply :)

Steely Dan

Yes, this is fine. Certainly you do want to have the velocity uncertainty in SI units if your other units will be too.

daleklama

Thank you :)