Percentage Uncertainties Question

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SUMMARY

The discussion focuses on calculating the percentage uncertainty of pressure derived from a force applied over a circular area. Given a force with an 8% uncertainty and a radius with a 3% uncertainty, the correct approach involves understanding that uncertainties do not simply add together. Instead, the maximum possible pressure is determined by dividing the maximum force by the minimum area, while the minimum pressure is calculated by dividing the minimum force by the maximum area. This method ensures accurate representation of the uncertainties involved in the measurements.

PREREQUISITES
  • Understanding of basic physics concepts, specifically pressure and force.
  • Familiarity with the formula for area of a circle, A = πr².
  • Knowledge of percentage uncertainty and its implications in measurements.
  • Ability to perform calculations involving maximum and minimum values based on uncertainties.
NEXT STEPS
  • Study the concept of propagation of uncertainty in measurements.
  • Learn how to apply the formula for percentage uncertainty in complex calculations.
  • Explore examples of pressure calculations involving varying uncertainties.
  • Investigate the implications of uncertainty in experimental physics and engineering.
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This discussion is beneficial for students in physics, engineering, and anyone involved in experimental measurements who seeks to understand the impact of uncertainties on calculated values.

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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.
 
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Benge said:

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?
 
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?
 
Benge said:
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?
 
That force could be 92N or 108N...
Force = 100 +- 8% N
 
Benge said:
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?
 
I understand that there is a range of values that the area 'could' be, ranging from the area -8% to area +8%...
 
Benge said:
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?
 
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.
 
  • #10
Benge said:
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.
 
  • #11
So to answer that question it is like considering bounds then. Thanks.
 
  • #12
Benge said:
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.
 

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