Imagine that a log is completely submerged in water, its volume is 0.1 m3, and its density is 700 kg / m3. Calculate the Archimedean force acting on the log and find the mass of hares on it.
V = 0.1 m ^ 3 – the volume of a log completely submerged in water;
g = 10 m / s ^ 2 – acceleration of gravity;
ro1 = 700 kg / m ^ 3 – density of the log;
ro2 = 1000 kg / m ^ 3 is the density of water.
It is required to determine A – the Archimedean force acting on the log and the mass of hares sitting on the log, m1.
Archimedean force will be equal to:
A = ro2 * V * g = 1000 * 0.1 * 10 = 1000 Newton.
Since, according to the condition of the problem, the log is completely immersed in water, it means that the gravity of the log is balanced by the Archimedean force, that is:
F gravity = A;
(m + m1) * g = ro2 * V * g (where m is the mass of the log);
m + m1 = ro2 * V;
ro1 * V + m1 = ro2 * V;
m1 = ro2 * V – ro1 * V = V * (ro2 – ro1) = 0.1 * (1000 – 700) = 0.1 * 300 = 30 kilograms.
Answer: the Archimedean force is 1000 Newtons, the mass of hares on a log is 30 kilograms.