User's Manual

Discover Density Set 012–07192A
22
Finding the equation that describes the experimental data
From the experimental data, the following relationships are shown to
exist:
mass is proportional to the diameter squared
mass is proportional to the length
therefore:
mass is proportional to the (diameter squared * length)
this means:
mass = C * diameter squared * length
where “C” is some constant
Example:
Calculating “C” for the item in A4:
C = mass / (diameter squared * length) = 11.38 g/ (19.1 cm
2
* 2.86 cm)
= 1.09 g/cm
3
Example:
Calculating “C” for the item in B6
C = 13.81 g / 2.22 cm
2
* 2.54) = 1.10 g/cm
3
Final Equation for the cylinders:
mass = 1.095 g/cm
3
* diameter
2
* length (l)
Calculating the theoretical value using known equations
mass = density * volume
substituting the formula for volume of a cylinder (volume =
ππ
ππ
πr
2
* l ):
mass = density * π r
2 *
l
substituting an equation that relates radius and diameter (r = d / 2):
mass = density * π ∗ (diameter / 2)
2
* l
Substitute the value for the density of the plastic, and gathering numerical
factors:
mass = 1.42 g/cm
3
* π * 0.25 * diameter
2
* l
mass = 1.12 g/cm
3
* diameter
2
* l
This result is essentially the same as the experimentally determined value,
except for the slight difference in the constant, due to measurement error.
Cylinders