How to find the Density of some Ball Bearings

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Presentation transcript:

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