physics fluid question

Question

A river raft is square and has a specific mass of 25.65 grams. it also has a thickness of 0.9 cm

its dimensions are:

0.009m × L × L.

If we put the raft to float on a tray water that is soapy and has a specific density of 𝜌 = 1092 kg/m³. The most mass we can put on the raft before it sinks is 103.45 grams.

What is the length of the raft?

Answer 1

The buoyant force on the raft is equal to the weight of the water displaced by the raft. The weight of the water displaced by the raft is equal to the density of the water * the volume of the raft * the acceleration due to gravity.

The mass of the raft is equal to the specific mass of the raft * the volume of the raft.

The raft will float when the buoyant force is equal to the weight of the raft.

So, we can write the following equation:

density * volume * acceleration due to gravity = specific mass * volume

We can solve for the volume of the raft:

volume = specific mass * acceleration due to gravity / density

The length of the raft is equal to the square root of the volume of the raft.

length = sqrt(specific mass * acceleration due to gravity / density)

Plugging in the values that we were given, we get the following:

length = sqrt(25.65 * 9.8 / 1092) = 2.766852116551215 meters

Therefore, the length of the raft is 2.766852116551215 meters.