lab 6- Propagated Uncertainty in Measurements

Propagated Uncertainty in Measurements

Purpose

Learn how to calculate propagated uncertainty in density measurements with different metal material cylinders.

Process

First, we need to measure the density of two cylinders made of different materials. To measure the density we should measure its mass m, diameter d and height h.

Mass(g)	Diameter(cm)	Height(cm)
69.4	1.55	5.01
27.6	1.59	4.98

So the density of the first material is about 7.31 g/cm^3, which may be zine. The density of the second material is about 2.80 g/cm^3, which may be aluminum.

Then we should calculate the propagated uncertainty of the density. For a cylinder, its density can be calculate with the equation p=(4/∏)* [m/(d2*h)]. The differential form of this equation is dp= (∂p/∂m)*dm + (∂p/∂d)*dd + (∂p/∂h)dh, which equals to

The calculation is attached below.

Conclusion

In this lab, we learnt how to calculate the density and uncertainty of metal cylinders. To calculate the propagated equation, we should derive an equation. Then we should calculate the derivative of the equation and plug in our measured values.