If the force on the tympanic membrane (eardrum) increases by about 1.50 N above the force from atmospheric pressure, the membrane can be damaged.
When you go scuba diving in the ocean, below what depth could damage to your eardrum start to occur? The eardrum is typically 8.20 mm *.0082m* in diameter. Take the density of seawater to be equal 1.03)10^3 kg/m^3.
To determine the depth below which damage to the eardrum could start to occur during scuba diving, we need to calculate the pressure on the eardrum.
1. First, we need to convert the diameter of the eardrum from millimeters to meters:
diameter = 8.20 mm = 8.20 × 10^-3 m
2. Since the force on the eardrum is given by the pressure difference across it multiplied by its area, we need to calculate the area of the eardrum:
radius = diameter/2 = 4.10 × 10^-3 m
area = π × radius^2 = 3.14 × (4.10 × 10^-3 m)^2
3. Next, we need to calculate the pressure exerted by the seawater at a specific depth using the hydrostatic pressure formula:
pressure = density × gravity × depth
where:
density = 1.03 × 10^3 kg/m^3 (density of seawater)
gravity = 9.8 m/s^2
depth is what we need to find.
4. Rearrange the formula to solve for the depth:
depth = pressure / (density × gravity)
5. Finally, we plug in the given values and calculate the depth:
depth = (1.50 N) / (3.14 × (4.10 × 10^-3 m)^2 × (1.03 × 10^3 kg/m^3) × (9.8 m/s^2))
After performing the necessary calculations, we can find the depth at which damage to the eardrum could start to occur during scuba diving.