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 in diameter. Take the density of seawater to be equal 1.03*10^3.

I have no idea how these two section corrolate to eachother...and no idea where to start even thinking about the problem! help!! :(

To determine the depth at which damage to the eardrum could start to occur during scuba diving, we need to calculate the pressure exerted on the eardrum and compare it to the force that can cause damage.

We can start by finding the area of the eardrum using the given diameter. The formula for the area of a circle is A = πr^2, where r is the radius. Since the diameter is given, we can calculate the radius as 8.20 mm / 2 = 4.10 mm = 0.0041 m.

Next, we need to calculate the pressure difference that would cause damage to the eardrum. The force that causes damage is given as 1.50 N, and this force is due to the pressure difference. We can use the formula P = F/A, where P is the pressure, F is the force, and A is the area.

Now, we can substitute the given values into the formula P = F/A. The force F is 1.50 N, and the area A is π(0.0041 m)^2.

Finally, to determine the depth at which the pressure becomes high enough to potentially damage the eardrum, we need to relate the pressure to the depth in a fluid. The pressure in a fluid is given by P = ρgh, where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth.

The density of seawater is given as 1.03*10^3 kg/m^3, and the acceleration due to gravity is approximately 9.8 m/s^2.

Equating the pressure difference on the eardrum to the pressure at a certain depth, we can solve for the depth h:

1.50 N / [π(0.0041 m)^2] = (1.03*10^3 kg/m^3) * (9.8 m/s^2) * h

Solving for h will give us the depth in meters at which damage to the eardrum may start to occur during scuba diving.

To determine the depth at which damage to your eardrum could start to occur while scuba diving, we need to calculate the pressure exerted on the eardrum at that depth.

The pressure exerted on an object in a fluid is given by the formula:

Pressure = Density * gravity * depth

In this case, the fluid is seawater, and the pressure is equal to the force on the eardrum.

Given:
Force on eardrum = 1.50 N
Diameter of eardrum = 8.20 mm = 0.0082 m
Density of seawater = 1.03 * 10^3 kg/m^3
Acceleration due to gravity = 9.8 m/s^2

Now, we can calculate the surface area of the eardrum using the formula:

Area = π * (radius)^2

radius = diameter / 2

Plugging in the values:

radius = 0.0082 m / 2 = 0.0041 m

Area = π * (0.0041 m)^2 = 5.31 * 10^-5 m^2

Next, let's calculate the depth at which the force on the eardrum reaches the critical value of 1.50 N. Rearranging the formula for pressure:

depth = Force / (Density * gravity * area)

Plugging in the values:

depth = 1.50 N / (1.03 * 10^3 kg/m^3 * 9.8 m/s^2 * 5.31 * 10^-5 m^2)

After performing the calculation, the depth at which damage to the eardrum could start to occur is approximately 28.9 meters.

Figure the weight of a colume of water of area A.

force= mass*g= density*A*h*g

Pressure= force/area, then figure the height h.