Question

A sample of air weighing 1.32 x 103N is confirmed in a room measuring 1.5cm x 5.0 x 2.0cm calculate the density of the sample

Answer 1

To calculate the density of the sample of air, we first need to calculate the volume of the air sample.

Given that:
Weight of air sample, W = 1.32 x 10^3 N
Dimensions of the room: 1.5 cm x 5.0 cm x 2.0 cm

Volume of the room, V = Length x Width x Height
V = 1.5 cm x 5.0 cm x 2.0 cm

V = 15 cm^3

Since the air sample is filling up the entire room, the volume of the air sample is also equal to 15 cm^3.

Now, we can calculate the density of the air sample using the formula:

Density = Mass / Volume

First, we need to convert the weight of the air sample into mass using the formula:
Weight = Mass x Acceleration due to gravity
Mass = Weight / Acceleration due to gravity

Mass = 1.32 x 10^3 N / 9.8 m/s^2 (acceleration due to gravity)

Now, we convert the volume from cm^3 to m^3:
1 cm^3 = 1 x 10^-6 m^3

Volume = 15 cm^3 x 1 x 10^-6 m^3/cm^3

Volume = 15 x 10^-6 m^3

Now we can calculate the density of the air sample:

Density = Mass / Volume
Density = (1.32 x 10^3 N / 9.8 m/s^2) / (15 x 10^-6 m^3)
Density = (1.346 x 10^2 kg) / (15 x 10^-6 m^3)
Density = 8.97 x 10^3 kg/m^3

Therefore, the density of the air sample is 8.97 x 10^3 kg/m^3.