PHYS 1003 Lecture Notes - Lecture 11: Volume Integral
26 Dec 2017
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Document Summary
Density is defined as the mass per unit volume p (density)= m(mass)/v(volume) =kg/m3. If object is composed of more than one material, the average density can be calculated through pav = (sum of masses)/(sum of volumes) o. Example: ship with total volume has steel inside (total volume and mass of steel given and air/steel density). Calculate mass of air by subtracting total volume by volume of steel. The volume integral is nested triple integral over space object occupies o o o. Add all increments along one side through integral to get result, another side of result and another side for a nested integral. For cube (1): since a=b=c then v= l3. For a cylinder: it can be simplified to 1 d integral because of radial symmetry of the cylindrical stack, = 2 x dx (slice) Total mass with variable density o o o. Densities can change such as foam so we assumed that a thin slice has constant density/mass.
