Final answer:
The maximum depth you could dive without rupturing your eardrum is approximately 10 meters. This is calculated based on the pressure your eardrum can withstand, which is 100 kPa, and considering that underwater pressure increases by about 9.8 kPa for each meter of depth.
Step-by-step explanation:
The question relates to the concept of pressure underwater and the effects on the human eardrum. To find the maximum depth you could dive without rupturing your eardrum, we need to calculate the pressure that a force of 7 N would exert on an eardrum with an area of 70 mm2 and compare it with the water pressure increase per meter of depth.
Pressure (P) is defined as the force (F) divided by the area (A) over which the force is distributed. Hence, P = F / A. Let's convert the area into meters squared for coherence: 70 mm2 = 70 × 10-6 m2.
Now, we calculate the pressure the eardrum can sustain: P = 7 N / (70 × 10-6 m2) = 100,000 N/m2 or 100 kPa (since 1 Pa = 1 N/m2). This is the gauge pressure that can be withstood without injury.
Underwater, pressure increases by approximately 9.8 kPa for every meter of depth due to the weight of the water. Therefore, the maximum depth before the pressure exceeds 100 kPa would be 100 kPa / 9.8 kPa/m ≈ 10.2 meters, which rounds down to 10 meters as the maximum safe depth.