Calculate the pressure on the top lid of a chest buried under 4.00 meters of mud with density 1.75*10 3 kg/m3 at the bottom of a 10.0-m-deep lake
Calculate the pressure on the top lid of a chest buried under 4.00 m of mud with density equal to 1.75 x 10^3 kg/m^3 at the bottom of a 10.0-m deep lake.
To calculate the pressure on the top lid of the chest, we will use the hydrostatic pressure formula:
Pressure = Density * Gravity * Height
First, let's calculate the pressure due to the water above the chest lid.
Density of water = 1000 kg/m³ (standard value)
Gravity = 9.8 m/s² (standard value)
Height = 10.0 m
Pressure of water = Density of water * Gravity * Height
= 1000 kg/m³ * 9.8 m/s² * 10.0 m
= 98,000 Pa (Pascal)
Now let's calculate the pressure due to the mud.
Density of mud = 1.75 * 10³ kg/m³
Height = 4.00 m
Pressure of mud = Density of mud * Gravity * Height
= 1.75 * 10³ kg/m³ * 9.8 m/s² * 4.00 m
= 68,600 Pa (Pascal)
To find the total pressure on the top lid, we need to sum up the pressure of water and mud:
Total pressure = Pressure of water + Pressure of mud
= 98,000 Pa + 68,600 Pa
= 166,600 Pa (Pascal)
Therefore, the pressure on the top lid of the chest buried under 4.00 meters of mud with a density of 1.75 * 10³ kg/m³ at the bottom of a 10.0 m deep lake is 166,600 Pa (Pascal).
To calculate the pressure on the top lid of the chest, we can use the concept of pressure due to a fluid column. The pressure at a particular depth in a fluid is given by the equation:
P = ρgh
Where:
P: Pressure
ρ: Density of fluid
g: Acceleration due to gravity
h: Depth
Given values:
Density of mud, ρ = 1.75 * 10^3 kg/m^3
Depth of mud, h = 4.00 m
Depth of lake, H = 10.0 m (not required for the calculation, but given for reference)
To solve the problem, we need to calculate the pressure at the bottom of the mud, and that will be the pressure on the top lid of the chest.
1. Calculate the pressure at the bottom of the mud (P_bottom):
P_bottom = ρ * g * h
P_bottom = (1.75 * 10^3 kg/m^3) * (9.8 m/s^2) * (4.00 m)
Now, we can calculate the pressure on the top lid of the chest using the pressure at the bottom of the mud:
2. Calculate the pressure on the top lid (P_top):
P_top = P_bottom
Therefore,
P_top = (1.75 * 10^3 kg/m^3) * (9.8 m/s^2) * (4.00 m)
Now, let's plug in the known values:
P_top = (1.75 * 10^3) * (9.8) * (4.00)
P_top = 68,600 Pa (Pascals)
So, the pressure on the top lid of the chest buried under 4.00 meters of mud is 68,600 Pascals.