How to use Heisenberg Uncertainty Equation/Principle?

[cam224]

I'm working on a few problems involving the Heisenberg Uncertainty Principle and I'm a little confused as to how the equation works and what to plug into the equation. The equation I'm using is: (delta(x)*m*delta(v) = h/(4pi).

In one of the problems I'm working on, I'm given the mass of a bacterium, its velocity, its % uncertainly in velocity, and its length.

For the delta x and delta v, are you supposed to plug in the uncertainties? E.g. the velocity in this problem is 2.00 micrometers with 5% uncertainty...should I plug in .2 micrometers for delta v, as 2*1.05 = 2.1 and 2*.95 = 1.9, and the difference between then is .2? And if so, why would it be important to even know the length of the bacterium, if we just need to know its uncertainty, or is this just extraneous information?

I've tried researching the equation a bit but I can't get any clear explanation of it. Any clarification would be appreciated!

Thanks :)

 

[jbsteele]

Yes, you should plug in the uncertainties for delta x and delta v. For delta x, you would use the uncertainty in the length of the bacterium, since that is what you are trying to measure. The length of the bacterium is important, as it helps to determine the uncertainty of the measurement. In this case, if you know the exact length of the bacterium, then you can calculate the uncertainty of the measurement more accurately.