Determine the weight of the cargo that can take a wooden raft with a volume of 5m3.

Determine the weight of the cargo that can take a wooden raft with a volume of 5m3. The density of the tree is 600kg / m3.

Given:

V = 5 cubic meters – the volume of the wooden raft;

ro = 600 kilograms per cubic meter – the density of the tree;

ro1 = 1000 kilograms per cubic meter – the density of water;

g = 10 N / kg – acceleration of gravity.

It is required to determine the mass of the cargo m (kilogram) that the raft can carry.

The raft is influenced by gravity, tending to flood it, as well as a buoyant force (Archimedean force), which lifts the raft up. Then, the maximum load that the raft can lift without drowning can be found from the equality:

F gravity = Farkhimedov;

(m + m1) * g = ro1 * V * g, where m1 is the mass of the raft itself without cargo.

(m + V * ro) * g = ro1 * V * g;

m + V * ro = ro1 * V;

m = ro1 * V – ro * V = V * (ro1 – ro) = 5 * (1000 – 600) = 4 * 400 = 2000 kilograms.

Answer: the raft can carry a load equal to 2000 kilograms (2 tons).