How to find the Density of some Ball

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. 1 g – Resolution to 0. 1 g – Thus % uncertainty = 0. 1/164. 1*100 = 0. 060938% – Mass of 1 ball bearing = 164. 1/10 = 16. 41 g (16. 41 g ± 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. 2 cm 3 – Resolution to 0. 1 cm 3 – Thus % uncertainty = 0. 1/6. 2*100 = 1. 612903% – Volume of 1 ball bearing = 6. 2/3 = 2. 067 cm 3 (2. 067 cm 3 ± 1. 621903%)

Step 3: Some Final Calculations • Density = 16. 41/2. 067 = 7. 940323 g/cm 3 • % 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/cm 3