Determine how much the pressure force acting on the eardrum of a diver with an area of 0.6 cm2
Determine how much the pressure force acting on the eardrum of a diver with an area of 0.6 cm2, located at a depth of 40 meters in sea water (), is greater than the pressure force acting on the same membrane, at the same depth, only in fresh water ().
S = 0.6 cm2 = 0.00006 m2.
g = 9.8 m / s2.
h = 40 m.
ρm = 1030 kg / m3.
ρw = 1000 kg / m3.
ΔF -?
Pressure P is a scalar physical quantity equal to the ratio of the force F to the area S on which this force acts: P = F / S.
F = P * S.
The hydrostatic pressure of the liquid at the bottom is determined by the formula: P = ρ * g * h. Where ρ is the density of the liquid, g is the acceleration of gravity, h is the height of the liquid, in our case the depth.
Fв = ρв * g * h * S.
Fm = ρm * g * h * S.
ΔF = Fm – Fw = g * h * S * (ρm – ρw).
ΔF = 9.8 m / s2 * 40 m * 0.00006 m2 * (1030 kg / m3 -1000 kg / m3) = 0.7056 N.
Answer: the force of pressure on the tympanic membrane is ΔF = 0.7056 N in sea water more than in fresh water.