Percentage Uncertainties Question

[Benge]

Homework Statement

Been given a problem where a force (F) is applied on a circular area (m²). If the percentage uncertainty of the force is 8% and the percentage uncertainty of the radius is 3%, what is the percentage uncertainty of the obtained value pressure?

Homework Equations

I know that pressure equals force over area and to find the area it is πr². Anyway to work the percentage out?

The Attempt at a Solution

I assume you don't just 'add' the percentage uncertainties in this case. So far see that 8% over π3%² would be the equation to work this out.

 

[PeroK]

Homework Statement

Been given a problem where a force (F) is applied on a circular area (m²). If the percentage uncertainty of the force is 8% and the percentage uncertainty of the radius is 3%, what is the percentage uncertainty of the obtained value pressure?

Homework Equations

I know that pressure equals force over area and to find the area it is πr². Anyway to work the percentage out?

The Attempt at a Solution

I assume you don't just 'add' the percentage uncertainties in this case. So far see that 8% over π3%² would be the equation to work this out.

What does a percentage uncertainty actually mean?

 

[Benge]

It's the absolute uncertainty expressed as a percentage. So how 'large' the uncertainty of a measurement. If it is just the measurements would it be 11%? As that is what's being 'measured' and not calculated?

 

[PeroK]

It's the absolute uncertainty expressed as a percentage. So how 'large' the uncertainty of a measurement. If it is just the measurements would it be 11%? As that is what's being 'measured' and not calculated?

You're still not thinking about what it actually means. For example, if a force is 100N with a percentage uncertainty of 8%, could that force be, say, 150N? Or, 62N?

 

[Benge]

That force could be 92N or 108N...
Force = 100 +- 8% N

 

[PeroK]

That force could be 92N or 108N...
Force = 100 +- 8% N

So, you're saying the force could have a maximum value of 108N and a minimum value of 92N.

And, the radius?

 

[Benge]

I understand that there is a range of values that the area 'could' be, ranging from the area -8% to area +8%...

 

[PeroK]

I understand that there is a range of values that the area 'could' be, ranging from the area -8% to area +8%...

It's getting difficult to thing of a hint without actually telling you the answer! But, let's try:

If the force is 100N (with 8% uncertainty) and the radius is 1m (with 3% uncertainty), could the pressure be 50N/m^2?

 

[Benge]

Well from your example, the answer to the equation would be 100 over pi x 1²? Then +- the percentage uncertainties added. So 31.8 +- 11% which means the answer is ranging between 28 and 35 Pa. Or would it be like considering bounds in maths, the maximum and minimum possible values for pressure with the equation?

Sorry if I'm not understanding this as easily as most would.

 

[PeroK]

Well from your example, the answer to the equation would be 100 over pi x 1²? Then +- the percentage uncertainties added. So 31.8 +- 11% which means the answer is ranging between 28 and 35 Pa. Or would it be like considering bounds in maths, the maximum and minimum possible values for pressure with the equation?

Sorry if I'm not understanding this as easily as most would.

Why would the uncertainties add? Why not do a calculation with the maximum possible force and minimum possible area? And vice versa.

 

[Benge]

So to answer that question it is like considering bounds then. Thanks.

 

[PeroK]

So to answer that question it is like considering bounds then. Thanks.

The answer to the question lies in calculations. And, yes, the maximun possible pressure must be the maximum possible force divided by the minimum possible area.