measure density of metal

In this lab, our goal is figuring out the uncertainty of values.
In the first part, we were going to measure 3 different metals' length, diameter, and mass in order to get the density with its uncertainty.

And then, we get:

    metal         length        diameter         mass            density

1. steel      5.00+-0.01 cm  1.26+-0.01 cm  48.9+=0.1 g      7.6 g/cm^3
2. copper     5.14+-0.01 cm  1.28+-0.01 cm  58.4+=0.1 g      8.8 g/cm^3
3. brass      4.80+-0.01 cm  1.60+-0.01 cm   80.0+=0.1 g     8.3 g/cm^3

From the equation for density:

And then, we take the natural logarithm of each side we get:

=>

1. steel 
   
2. copper
   
3. brass
   

This,we can get those metals' density with their uncertainty:

1. steel:  7.6+-0.15 g/cm^3
2. copper: 8.8+-0.16 g/cm^3
3. brass:  8.3+-0.12 g/cm^3

And, there is next lab to determine the mass of object by measuring two angles and those forces of two strings.

All of first, we focus on the y size of the object.

and then, we focus on the x size of the object.

The data we measure about force on strings and angles:

F1=7.5+-0.5N

F2=7.0+-0.5N

a1=46degree+-1degree

a2=50degree+-1degree

plug those data to equation.

And we can get the force from equation

is 1.0976+-0.015N