Percentage Uncertainties Question

Benge

1. 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?

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

3. 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.

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PeroK

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1. 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?

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

3. 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

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2018 Award
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

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2018 Award
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.

Benge

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

PeroK

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2018 Award
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

Homework Helper
Gold Member
2018 Award
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.