An open barge has the dimensions l=22 m, w=40 m, and h=12m. If the barge is made out of 4.0 cm thick steel plate on each of its four sides and its bottom, what mass of coal can the barge carry in fresh water without sinking? Is there enough room in the barge to hold this amount of coal? ( the density of coal is about 1500 kg/m^3)
To calculate the mass of coal the barge can carry without sinking, we need to determine the volume of the barge and then calculate the mass of coal that can fit within that volume. Here's how you can do it:
1. Calculate the internal dimensions of the barge:
The internal length, width, and height of the barge can be calculated by subtracting twice the thickness of the steel plates from the external dimensions.
Internal length (L) = external length (l) - 2 * thickness
Internal width (W) = external width (w) - 2 * thickness
Internal height (H) = external height (h) - 2 * thickness
Given:
External dimensions: l = 22 m, w = 40 m, h = 12 m
Thickness of steel plates (t) = 4.0 cm = 0.04 m
Calculation:
L = 22 m - 2 * 0.04 m = 21.92 m
W = 40 m - 2 * 0.04 m = 39.92 m
H = 12 m - 2 * 0.04 m = 11.92 m
2. Calculate the volume of the barge:
The volume of the barge can be calculated using the formula:
Volume = Length * Width * Height
Calculation:
Volume = L * W * H
Volume = 21.92 m * 39.92 m * 11.92 m
3. Calculate the mass of coal:
The mass of coal that can be carried by the barge is equal to the volume of the barge multiplied by the density of coal.
Given:
Density of coal (ρ) = 1500 kg/m^3
Calculation:
Mass = Volume * Density
Mass = (21.92 m * 39.92 m * 11.92 m) * 1500 kg/m^3
4. Determine if there is enough room in the barge:
Compare the mass of coal with the maximum load capacity of the barge. If the mass of coal is less than or equal to the maximum load capacity, then there is enough room in the barge to hold that amount of coal. Otherwise, the barge cannot carry the entire amount of coal.
To determine the maximum load capacity of the barge, we need additional information about the barge's load-bearing capacity or displacement. This information is required to make a definitive conclusion.