User's Manual

012–07192A Discover Density Set
21
Finding the equation that describes the experimental data
(spheres)
From the experimental data, the following relationships are shown to
exist:
mass is proportional the diameter cubed
therefore:
mass = C * diameter
3
where “C” is some constant
Solving for “C”:
C = mass / diameter
3
Substituting values for smallest sphere:
C = 2.48 g / (1.59 cm)
3
= 0.617 g/cm
3
Rechecking with values from the next to largest sphere:
C = 4.81 g / (2.22 cm)
3
= 0.622 g/cm
3
Calculating the theoretical value using known equations
(spheres)
mass = density * volume; volume = 4/3 πr
2
density of acrylic = 1.18 g/cm
3
; radius = diameter/2
then, mass = 1.18 g/cm
3
* 4/3 * π * (diameter
3
)/8
mass = 0.618 g/cm
3
* diameter
3
This result is in agreement with the experimentally determined equations,
considering uncertainty.
Spheres
Teacher’s Notes