There is a zinc cube on the floor with a cavity inside. The length of the edge of the cube is a = 50 cm.
There is a zinc cube on the floor with a cavity inside. The length of the edge of the cube is a = 50 cm. The pressure exerted by the cube on the floor is p = 600 Pa. The density of zinc is ρ = 7100 kg / m3. What part of the volume of the cube is occupied by the cavity? Disregard atmospheric pressure.
Given:
a = 50 centimeters = 0.5 meters – the length of the edge of the zinc cube with a cavity inside;
P = 600 Pascal – the pressure exerted by the cube on the floor;
ro = 7100 kg / m3 (kilogram per cubic meter) – zinc density;
g = 10 Newton / kilogram – acceleration due to gravity (rounded off value).
It is required to determine n – what part of the volume of the cube the cavity occupies.
Find the surface area on which the cube rests:
s = a ^ 2 = 0.5 ^ 2 = 0.25 m2.
The force of gravity acting on the cube will be equal to:
F = P * s = 600 * 0.25 = 150 Newtons.
The mass of the cube is:
m = F / g = 150/10 = 15 kilograms.
If there was no cavity in the cube, its volume would be equal to:
V = m / ro = 15/7100 = 0.0021 m3.
The actual volume of the cube is:
Vact = a3 = 0.53 = 0.125 m3.
Then the volume of the cavity is equal to:
Vcavity = V – Vact = 0.125 – 0.0021 = 0.123.
That is, the volume of the cavity occupies a part of the total volume:
n = Vcavity / Vact = 0.123 / 0.125 = 0.984 or 98.4%.
Answer: the volume of the cavity occupies 98.4% of the volume of the cube.