The dimensions of a wooden raft (density = 150 kg/m³)are 3.0 m x 3.0 m x1.0 m.What maximum load can it carry in sea water (density =1020 kg/m³)?

Question

Quizplus · Accepted Answer

First, we need to find the volume of the raft:
V_raft = L x W x H = 3.0 m x 3.0 m x 1.0 m = 9.0 m^3

Next, we need to calculate the buoyant force that the water will provide to the raft:
F_buoyant = V_displaced x density_water x g

where V_displaced is the volume of water that the raft displaces, which is equal to the volume of the raft itself:

V_displaced = V_raft = 9.0 m^3

Substituting the values, we get:

F_buoyant = 9.0 m^3 x 1020 kg/m^3 x 9.81 m/s^2 = 88554.6 N

Finally, we need to find the maximum load that the raft can carry without sinking:

F_load ≤ F_buoyant - F_raft

where F_raft is the weight of the raft, which is equal to:

F_raft = V_raft x density_wood x g = 9.0 m^3 x 150 kg/m^3 x 9.81 m/s^2 = 13229.5 N

Substituting the values, we get:

F_load ≤ 88554.6 N - 13229.5 N = 75325.1 N

Converting to kilograms, we get:

F_load ≤ 75325.1 N ÷ 9.81 m/s^2 ÷ 1000 kg/m^3 = 7.68 kg

Therefore, the maximum load the raft can carry is 7800 kg.

The Dimensions of a Wooden Raft (Density = 150 Kg/m3)are