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 isa bout 1500 kg/m^3)
To calculate the mass of coal that the barge can carry without sinking, we need to calculate the buoyant force acting on the barge and compare it with the weight of the barge and the coal.
1. Calculate the volume of the barge:
The volume can be calculated by multiplying the length, width, and height of the barge:
Volume = l × w × h
2. Calculate the volume of the steel plates:
The steel plates cover the bottom and four sides of the barge. Since the plates are 4.0 cm thick, the volume of the steel plates can be calculated as:
Volume of steel plates = (l × w × 4) + (l × h × 2) + (w × h × 2)
3. Calculate the volume of the empty space inside the barge:
The volume of empty space inside the barge can be calculated as:
Empty space volume = Volume of the barge - Volume of steel plates
4. Calculate the weight of the barge:
The weight of the barge can be calculated using the density of steel and the volume of the steel plates:
Weight of barge = Density of steel × Volume of steel plates
5. Calculate the maximum buoyant force:
The maximum buoyant force on the barge can be calculated using Archimedes' principle. The buoyant force is equal to the weight of the water displaced by the barge:
Buoyant force = Weight of water displaced = Volume of the barge × Density of water × g
6. Calculate the maximum mass of coal the barge can carry:
The maximum mass of coal the barge can carry without sinking is equal to the difference between the maximum buoyant force and the weight of the barge:
Maximum mass of coal = (Buoyant force - Weight of barge) / Density of coal
7. Check if there is enough room in the barge:
Compare the maximum volume of coal calculated from the maximum mass of coal with the empty space volume. If the maximum volume of coal is less than or equal to the empty space volume, then there is enough room in the barge to hold the amount of coal.
Please provide the density of steel and water so that the calculations can be completed.