A raft measuring 3m BY 3m by 0.16 m is made of wood with a density of 600kg/m3. For what uniformly distributed load (in kilograms) the raft will be submerged 80% in water

 

uniformly distributed load is equal to 288 kg

Step-by-step explanation

Let w be the uniformly distributed load (in kg)

   m be the weight of raft

   v be the volume = 0.3(0.3)(0.16) = 1.44 cubic meter

   p be the density = 600kg/m3

   Mw be the mass of displaced water

Solution:

  1. Solve for the mass of the raft

p = m/v ; m = pv

m = (600 kg/m3) x (1.44 m3) = 864 kg

  2. Solve for mass of displaced water

Mw = pv = (1.44 m3) x (1000 kg/m3) = 1440 kg

density of water is constant 1000kg/m3

  3. Solve for w with only 80% submerged in water

    By condition of floating vessels, w and m is equal to Mw

m + w = Mw (80%)

864 + w = 1440 x 0.80

w = (1440x0.80) - 864

w = 288 kg