PDA

View Full Version : Physics, uncertanty propagation (silly) question



Adin
2005-May-03, 09:29 AM
Hi all

I am writing up a physics prac at the moment and have come into some trouble.

The physics report is on fluids and viscocity.

Basically we were testing how fast certain diameter steel balls fall though oil.



V(corrected) = v (1 + ((2.4*r)/R) )

where
V(corrected) = Corrected velocity
v = velocity
r = radius of sphere
R = radius of cylinder

What would be the uncertainty in V(corrected) if the uncertanty in
r is 0.0001m (0.1mm)
R is 0.005m (5mm)
v is (Δdistance / Δtime)
Δd = 0.005m (5mm)
Δt = 0.1s (roughly the reaction time for a human)

Sorry about the silly question, I calculated an uncertanty of 0.07m/s.... the only problem with this is that the small spheres themselves move through the oil at a much lower value than the uncertanty.

In other words the uncertanty that I calculated is greater than the actual corrected velocity itself!

Thanks in advance. :)

swansont
2005-May-03, 01:07 PM
Hi all

I am writing up a physics prac at the moment and have come into some trouble.

The physics report is on fluids and viscocity.

Basically we were testing how fast certain diameter steel balls fall though oil.



V(corrected) = v (1 + ((2.4*r)/R) )

where
V(corrected) = Corrected velocity
v = velocity
r = radius of sphere
R = radius of cylinder

What would be the uncertainty in V(corrected) if the uncertanty in
r is 0.0001m (0.1mm)
R is 0.005m (5mm)
v is (?distance / ?time)
?d = 0.005m (5mm)
?t = 0.1s (roughly the reaction time for a human)

Sorry about the silly question, I calculated an uncertanty of 0.07m/s.... the only problem with this is that the small spheres themselves move through the oil at a much lower value than the uncertanty.

In other words the uncertanty that I calculated is greater than the actual corrected velocity itself!

Thanks in advance. :)

It's certainly possible to get errors larger than the value (try measuring zero), but...

IIRC When multiplying or dividing, you combine fractional uncertainties. If you are finding v=d/t, calculate deltad/d and deltat/t, then add them in quadrature (as long as the errors are independent). e.g. if they are each 1%, then your error in v is 1.4%

edit:typo