Density Lab

Density (Linearized plot)
TA: Blue
Rex rex
Group Members:
Billy and Mandy
Tuesday; 1200-1350

Abstract:
In this lab the density of hand-made clay balls were calculated to understand how scientists model physical effects and to understand logarithmic plots. The hand-made balls ranged from diameters of 2cm to 6cm and were measured with vernier calipers by each member of the group. A total of 6 independent measures of each diameter were taken to establish uncertainty. The clay balls were then weighed on a gram slider and then recorded. The first data set was graphed mass (kg) against diameter^3 (m^3).

ρ=6π(slope)

Yielding the linearized slope of density. The density, ρ ±Δρ was calculated to be 1747+/- 11 (kg/m^3)

Assuming
Lists the results of 6 different sets of diameter measurements: the spheres’ masses, the average diameters, the cubes of the average diameters, and the natural logarithms of average diameters and masses. These values were used to create two data plots.

Plot1.
The density of clay from the linearized plot of mass and the diameter cubed (m, D^3) data. Yielding a slope of 1.093 +/- 0.01749 m^3/g.

Since the density of an object is ρ=mV
And the formula for the volume of a sphere is V=π6D3
The density of a material shaped into a sphere would be equal to the volume of a sphere plugged into the density equation, which is:

ρ=mπ6D3
Solved for D3: D3= 6πρm
In the linear plot, it is expectable to say the slope=6πρ
Using the value of slope, density can be solved for ρ=6π(slope) ρ=1747kg/m^3 The error of ρ(Δρ) can be calculated from the error of the slope:
Δρ=|ρslope0+Δslope-ρslope0|
Δρ=11kg.m^3
The density of the modeling clay with error
Plot 2.
V=aDn, where ‘a’ is a constant. Ln(D) vs. ln(m) is plotted. The linear fit to this data provided a slope that could be used to calculate the power, n.
The slope of the linear fit was:

This was solved by taking: m=