A container of area 0.02 m2 is filled with water up to a height of 1m. Find the pressure at the bottom if a 10 kg mass is placed at the top of covering piston .
Answers
Explanation:
The net force acting on the base = (ρgh)A + mg
F = 1000 x 9.8 x 1 x 0.02 + 1 x 9.8
= 2 x 9.8 x +9.8 = 29.4 N
Pressure = thrust / Area = 29.4 / 0.02 = 1470 Pa
The pressure at the bottom of the container with the 10 kg mass on top is 14,715 Pa
To find the pressure at the bottom of the container, we can use the formula:
P = ρgh
where P is the pressure, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the height of the liquid.
In this case, the container is filled with water, which has a density of 1000 kg/m³. The height of the water is given as 1 m. So, substituting these values in the formula, we get:
P = 1000 * 9.81 * 1
P = 9810 Pa
This is the pressure at the bottom of the container without the 10 kg mass on top.
Now, if we place a 10 kg mass on top of the container, the pressure at the bottom will increase due to the additional weight. The mass exerts a force on the liquid, which is transmitted equally in all directions. So, the pressure at the bottom will increase by:
ΔP = (m*g) / A
where m is the mass, g is the acceleration due to gravity, and A is the area of the container.
Substituting the given values, we get:
ΔP = (10 kg * 9.81 m/s²) / 0.02 m²
ΔP = 4905 Pa
So, the total pressure at the bottom of the container with the mass on top is:
P_total = P + ΔP
P_total = 9810 Pa + 4905 Pa
P_total = 14715 Pa
Therefore, the pressure at the bottom of the container with the 10 kg mass on top is 14,715 Pa.
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