7.5) If the maximum force that an eardrum can withstand without breaking is 3.0 N and the area of the eardrum is 1.0 cm^2.
A. Calculate the maximum tolerable pressure in the middle ear in N/m^2 and convert this to mm Hg. When might the pressure in the middle ear become greater than the air pressure outside the ear
B. To what maximum depth could a person dive in fresh water without bursting an eardrum?
Note: Guys help me, provide me an answer with solution/formula. Thanks!!!?
A. To calculate the maximum tolerable pressure in the middle ear, we can use the formula:
Pressure = Force / Area
Given:
Maximum force (F) = 3.0 N
Area (A) = 1.0 cm^2
First, let's convert the area from cm^2 to m^2:
1 cm^2 = 0.0001 m^2
Substituting the values into the formula:
Pressure = 3.0 N / (0.0001 m^2)
Calculating:
Pressure = 3.0 N / 0.0001 m^2
Pressure = 30,000 N/m^2
To convert this pressure to mm Hg, we can use the conversion factor:
1 mm Hg = 133.32 N/m^2
Converting:
Pressure = 30,000 N/m^2 * (1 mm Hg / 133.32 N/m^2)
Calculating:
Pressure = 0.225 mm Hg (rounded to three decimal places)
The pressure in the middle ear might become greater than the air pressure outside the ear when there is a significant change in altitude, such as during flights or scuba diving. In these situations, the air pressure outside the ear decreases, causing an imbalance with the pressure in the middle ear, which could result in discomfort or pain.
B. To calculate the maximum depth a person can dive in fresh water without bursting an eardrum, we can use the concept of hydrostatic pressure. The formula for hydrostatic pressure is:
Pressure = Density * g * Depth
Given that we want to find the maximum depth, we rearrange the formula:
Depth = Pressure / (Density * g)
The density of fresh water (ρ) is approximately 1000 kg/m^3, and the acceleration due to gravity (g) is approximately 9.8 m/s^2.
Using the maximum tolerable pressure calculated in part A, which is 30,000 N/m^2, we can now calculate the maximum depth:
Depth = 30,000 N/m^2 / (1000 kg/m^3 * 9.8 m/s^2)
Calculating:
Depth = 3.06 meters (rounded to two decimal places)
Therefore, a person can safely dive to a maximum depth of approximately 3.06 meters in fresh water without the risk of bursting an eardrum.
Where are your attempts to do this work?
We are tutors, not a force = pressure times area algorithm.