A loaded vessel, being in fresh water at the waterline, displaces 15,000 m3 of water.

A loaded vessel, being in fresh water at the waterline, displaces 15,000 m3 of water. The weight of the vessel is 5 * 10 to the 7th power of a newton. What is the weight of the load?

Given:
V = 15000m ^ 3,
P1 = 5 * 10 ^ 7 N,
Find: P2 -?
The weight of the cargo and the weight of the vessel are balanced by the force of Archimedes:
F_A = P1 + P2;
The force of Archimedes is equal to the weight of the water displaced by the vessel:
F_A = ρ * g * V,
where
ρ = 1000kg / m ^ 3 is the density of fresh water;
g = 10m / s ^ 2 – free fall acceleration;
Substituting the values of the quantities, we find the weight of the cargo:
P2 = F_A – P1 = 1000 * 10 * 15000 – 5 * 10 ^ 7 = 15 * 10 ^ 7 – 5 * 10 ^ 7 = 10 ^ 8 N.