Heisenberg Uncertainty Principle - find minimum uncertainty in position

[daleklama]

Homework Statement

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

Homework 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

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]

Homework Statement

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

Homework 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

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 :)

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 :)