Mass & Weight density Mass density (  ): It is defined as the mass of unit volume of an object or substance. 𝑀 𝑉 𝑔 𝐾𝑔⁄ Typical Unit: ⁄𝑐𝑚3 , 𝑚3 𝜌= Weight density (D): It is defined as the weight of unit volume of an object or substance. 𝐷= Typical Unit: 𝑁⁄𝑚3 , 𝑔𝑓⁄ 𝑐𝑚3 𝑊 𝑉 Since: W = M. g Therefore: 𝐷 = 𝜌 ∙ 𝑔 Where: “g” the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth is: g = 9.8 m/s2 Example 1: The mass density of steel is 7.8 gr/cm3. A solid chunk of steel has a volume of 141cm3. Determine (a) its mass in grams and (b) its weight density in N/m3. Solution: (a) Since ρ =M/V; M = ρV; M = (7.8gr/cm3) (141cm3); M = 1100 gr. Before going to Part (b), let's first convert (gr/cm3) to SI that means (kg/m3). Use horizontal fraction bars. 7.8gr/cm3 = 7.8 (0.001kg) / (0.01m) 3 = 7800 kg/m3. 1 kg is equal to 1000gr. This means that 1gr is 0.001kg as is used above. Also, 1m is 100cm. This means that 1cm is 0.01m. Cubing each, results in: 1cm3 = 0.000001m3 as is used above. Now, let's solve Part (b). (b) D = ρg ; D = [7800 kg /m3] [9.8 m/s2] = 76000 N/m3. Not only you should write Part (b) with horizontal fraction bars, but also check the correctness of the units as well.

Mass & Weight Density Notes

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