Final answer:
The net force exerted on a 0.50-cm² eardrum when snorkeling 2.4 meters under water is 1.176 Newtons, using the formula for pressure at a depth and considering the area of the eardrum.
Step-by-step explanation:
The question pertains to finding the net force exerted on an eardrum while snorkeling at a certain depth.
To calculate this, we need to find the pressure of the water at the depth given and apply the formula:
Pressure = Force/Area.
To calculate the water pressure at a depth, we use the formula Pressure = density * gravity * depth.
For freshwater, the density is approximately 1000 kg/m³ and the acceleration due to gravity is about 9.8 m/s². The depth underwater is 2.4 m.
First, convert the eardrum area from cm² to m² by dividing by 10,000 (since 1 m² is 10,000 cm²).
Therefore, the area is 0.50 cm² or 0.50 / 10,000 m² = 5.0 * 10⁻⁵ m².
The pressure at 2.4 m depth is: Pressure = 1000 kg/m³ * 9.8 m/s² * 2.4 m = 23,520 Pascals (Pa).
The net force on the eardrum is: Force = Pressure * Area = 23,520 Pa * 5.0 * 10⁻⁵ m² = 1.176 N.
This result indicates that the net force exerted on the eardrum when the student is 2.4 meters under water is 1.176 Newtons, assuming the pressure was equalized before the dive.