09-march-2015 Lab 4: Propagated Uncertainty in Measurements

Lab 4 

Purpose: The purpose of this lab is to find the relationship between density, volume and find out the how they will affect the density by changing and volume. Also, find the relationship between Mass, Angle and Force and find out the how they will affect the density by changing the Angle and Force.

Of course, to begin with this lab, we need to get all the material we need.

First experiment: Measuring the Density of Metal Cylinder. 

1. Find three cylinder with different materiel such as Ferrum, Copper, and Aluminum.

2. Measure their weight, height, radius.

We know the formula p=m/v

If we want to find how density will
change when volume changed, we should 

differential this equation by parts.

When we use AL, we get this.

We can see from our calculation.

So we can see from picture.
uncertainty of Al's density is 0.1169 g/ cm^3 
For this experiment uncertainty is 0.1169, so it's not acceptable depending on the density is 0.56g/cm^3 it's 0.1169/0.56 *100% =20.8%  it's little big for uncertainty.

When we use Cu, we get this.

We can see from our calculation.

Uncertainty of Cu's density is 0.07737 g/ cm^3 
For this experiment uncertainty is 0.07737, so it's acceptable depending on the density is 2.292/cm^3
it's 0.07737/2.292 *100% =3.38%, uncertainty for Cu is good values.

When we use Fe, we get this.

We can see from our calculation.

Uncertainty of Fe's density is 0.06587 g/ cm^3 

For this experiment uncertainty is 0.06587, so it's acceptable depending on the density is 1.71/cm^3
it's 0.06587/1.71 *100% =3.35%, uncertainty for Fe is good values.

Second experiment

To begin for this experiment, we need to set up the equipment and measure the force and angle with two different objects.

Now, we need to read the force and measure the angle for this two objects

As show in picture, we know the force and their uncertainty, and their angle and uncertainty. What we need to do is to calculate the range of the uncertainty and see if the range is acceptable. 

And then we use the function and differential equipment to get the range of the uncertainty by plugging all the data.

This is the function we use to calculate the mass and the change of mass

This is the first mass we calculate. and we plug the data we got the range of this mass should be in between 0.888kg to 1.09kg.

This is the second mass we calculate. and we plug the data we got the range of this mass should be in between 0.702kg to 0.8971kg.

Conclusion:

For every experiment, errors are very common things. Therefore, to avoid making error and to calculate the how big errors are should be the main thing we should do on experiment. This experiment just want to show you how to calculate the errors by using differential equipment by parts.