How to find the Density of some Ball Bearings

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How to find the Density of some Ball Bearings

• By David Hewitt

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Apparatus Needed

• Displacement can
• Measuring cylinder
• Mass balance
• At least four ball bearings of the same size
  (more is better)

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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.

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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 0.1/164.1100 0.060938
• Mass of 1 ball bearing 164.1/10 16.41g
• (16.41g 0.060938)

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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 0.1/6.2100 1.612903
• Volume of 1 ball bearing 6.2/3 2.067cm3
• (2.067cm3 1.621903)

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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