Answer :
The pressure exerted by the gasoline on the bottom of the tank is 532.39 Pa
To determine the pressure exerted by the gasoline on the bottom of the tank, we need to know the depth of the gasoline in the tank. Assuming that the gasoline fills the tank to a depth of h meters, its volume can be calculated as follows:
Volume of gasoline = length x width x depth
V_gas = 0.874 m x 0.621 m x h
V_gas = 0.541 m^3 x h
The density of gasoline varies with temperature, but a reasonable approximation for gasoline at room temperature is 720 kg/m^3. Therefore, the mass of the gasoline in the tank can be calculated as:
Mass of gasoline = density x volume
m_gas = 720 kg/m^3 x 0.541 m^3 x h
m_gas = 390.12 h kg
We know that the tank can hold 51.7 kg of gasoline when full, so we can set up an equation:
390.12 h = 51.7 kg
Solving for h, we get:
h = 7.54 m
Now we can calculate the pressure exerted by the gasoline on the bottom of the tank using the formula:
Pressure = weight / area
The weight of the gasoline can be calculated as:
Weight of gasoline = mass x gravity
W_gas = m_gas x g
W_gas = 390.12 x 7.54 x 9.81
W_gas = 288.56 N
The area of the bottom of the tank is:
Area = length x width
A = 0.874 m x 0.621 m
A = 0.542 m^2
Therefore, the pressure exerted by the gasoline on the bottom of the tank is:
Pressure = W_gas / A
P = 504.2 N / 0.542 m^2
P = 532.39 Pa
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