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 the barge can carry without sinking, we need to consider the buoyancy force exerted by the fresh water on the barge and compare it with the weight of the barge and the coal.
First, let's calculate the volume of the barge:
Volume of barge = length * width * height
= 22 m * 40 m * 12 m
= 10,560 m^3
Now, let's calculate the volume of the steel plates covering the sides and bottom of the barge:
Volume of steel plates = 2 * (length * height) + 2 * (width * height) + (length * width)
= 2 * (22 m * 12 m) + 2 * (40 m * 12 m) + (22 m * 40 m)
= 1,872 m^3
To calculate the volume of coal the barge can carry without sinking, we need to subtract the volume of the steel plates from the volume of the barge:
Volume of coal = Volume of barge - Volume of steel plates
= 10,560 m^3 - 1,872 m^3
= 8,688 m^3
Now, let's calculate the mass of coal the barge can carry:
Mass of coal = Volume of coal * Density of coal
= 8,688 m^3 * 1500 kg/m^3
= 13,032,000 kg
Therefore, the barge can carry 13,032,000 kg of coal without sinking.
To determine whether there is enough room in the barge to hold this amount of coal, we compare it with the volume of coal:
Volume of coal = Mass of coal / Density of coal
= 13,032,000 kg / 1500 kg/m^3
= 8,688 m^3
Since the volume of coal (8,688 m^3) is equal to the volume of the barge (8,688 m^3), there is just enough room in the barge to hold the amount of coal calculated.
To determine the mass of coal the barge can carry without sinking, we need to consider the buoyant force acting on the barge and compare it with the weight of the coal.
First, let's calculate the volume of the barge:
V_barge = l * w * h
V_barge = 22 m * 40 m * 12 m
V_barge = 10560 m^3
Next, let's account for the volume occupied by the steel plates:
V_steel = (l * h * 4) + (w * h * 4) - (4 * 0.04 m * l * w)
V_steel = (22 m * 12 m * 4) + (40 m * 12 m * 4) - (4 * 0.04 m * 22 m * 40 m)
V_steel = 4224 m^3
Now, let's calculate the internal volume available for coal:
V_internal = V_barge - V_steel
V_internal = 10560 m^3 - 4224 m^3
V_internal = 6344 m^3
Finally, let's calculate the mass of coal the barge can carry without sinking:
m_coal = V_internal * density_coal
m_coal = 6344 m^3 * 1500 kg/m^3
m_coal = 9516000 kg
Therefore, the barge can carry a mass of 9,516,000 kg (or 9,516 metric tons) of coal without sinking.
To determine if there is enough room in the barge to hold this amount of coal, we need to compare the volume of the coal to the internal volume of the barge.
The volume of coal required:
V_coal = m_coal / density_coal
V_coal = 9516000 kg / 1500 kg/m^3
V_coal = 6344 m^3
We can see that the volume of coal is equal to the internal volume of the barge (V_internal), which means there is just enough room to hold the amount of coal calculated.
Figure the weight of the steel (volume*density of steel) .
Figure the displacement of the barge, and what that displacement would weigh in water. Subtract the weight of steel, and you have left the weight of coal.