A ferry boat is 6.1 m wide and 7.1 m long. When a truck pulls onto it, the boat sinks 7.59 cm in the water.
What is the weight of the truck? The acceleration of gravity is 9.81 m/s2 .
Answer in units of N
There are two forces acting on the boat without a truck: 1) Gravitational force F = g * m, where m is the mass of a boat 2) Archimedian force Fa = pho * g * V, where pho=1000kg/m^3 is the density of the water, and V is the volume of boat below the level of water.
Since the level of boat is fixed these forces are equal F = Fa
When the truck pulls on the boat then the forces will change by the same amount: dF = dFa, and dF = Mg, where M is the mass of a truck, dFa = pho g V1, where V1 is the displaced volume of water:
V1 = 6.1 * 7.1 * 0.0759 = 3.2872 m^3
Hence the mass of the truck is M = pho g V1 / g = pho * V1 = 1000 * 3.2872 = 3287.2 kg