How to find the Density of some
Ball Bearings
By David Hewitt
Apparatus Needed
•
•
•
•
Displacement can
Measuring cylinder
Mass balance
At least four ball bearings of the same size
(more is better)
Outline of the Experiment
• To find density:
Density =
Mass
Volume
• Mass will be measured using a mass balance.
• Volume will be found using a displacement
cylinder.
• Uncertainties will be then be calculated to find
an uncertainty for the final value.
Step 1: Finding the Mass
• Weighing 10 ball bearings and dividing by 10
gives a lower uncertainty than just weighing
one, as shown:
– Mass of 10 ball bearings: 164.1g
– Resolution to 0.1g
– Thus % uncertainty = 0.1/164.1*100 = 0.060938%
– Mass of 1 ball bearing = 164.1/10 = 16.41g
(16.41g ± 0.060938%)
Step 2: Finding the Volume
• Finding the volume of 3 ball bearings (more
would displace too much water) and dividing
by 3 works exactly like when finding mass:
– Volume of 3 ball bearings: 6.2cm3
– Resolution to 0.1cm3
– Thus % uncertainty = 0.1/6.2*100 = 1.612903%
– Volume of 1 ball bearing = 6.2/3 = 2.067cm3
(2.067cm3 ± 1.621903%)
Step 3: Some Final Calculations
• Density = 16.41/2.067 = 7.940323g/cm3
• % uncertainty = %u of mass + %u of volume
(dividing values means ADD % uncertainties).
= 0.060938 + 1.612903 = 1.673841%
• Uncertainty = value*(%uncertainty/100)
= 7.940323 * 0.01673841 = 0.1329
• Quote final value with uncertainty to 1 s.f.:
(7.9 ± 0.1) g/cm3