Question

a large square floating dock has sides with a length of 4.00 cm. if 10 people, each with an average mass 91.0 kg, step on the dock, how far down into the water would you expect the dock to sink? (you may assume the dock is solid so it displaces water over its entire area it sinks)

Answer 1

Let the dock sink by a length d , then the volume of water displaced = Ad where A is the area of the dock

Also the Archimedes principle states that the mass of a floating object is equal to the mass of water it displaces

So 91*10kg = Ad*1000kg/m^3

d = 910/(1000*16*10^-4) = 910/1.6 = 568.75m

But large square dock can't have dimensions of 4cm thus the value given in the problem is incorrect we have to take it as 4m

d = 910/(16*1000) = 0.0568 = 5.6875 cm which is a more practical value