A diver swims to a depth of 3.2 m in a freshwater lake. What is the increase in the force pushing in on her eardrum, compared to what it was at the lake surface? The area of the eardrum is 0.60 cm2.
The increased pressure is
(water density)*g*depth
Multiply that by the eardrum ares (in square meters) to get the increase in force.
To calculate the increase in the force pushing on the diver's eardrum, we need to consider the change in pressure as she swims to a depth of 3.2 m in a freshwater lake.
The pressure exerted by a fluid increases with depth and can be calculated using the equation:
Pressure = density * gravitational acceleration * depth
In this case, we are dealing with freshwater, which has a density of approximately 1000 kg/m^3.
Step 1: Convert the area of the eardrum from cm^2 to m^2.
Given: Area of the eardrum = 0.60 cm^2
To convert cm^2 to m^2, divide by 10,000:
Area of the eardrum = 0.60 cm^2 / 10,000 = 0.00006 m^2
Step 2: Calculate the increase in pressure.
Given: Depth = 3.2 m
Density of freshwater = 1000 kg/m^3
Gravitational acceleration = 9.8 m/s^2
Pressure = density * gravitational acceleration * depth
Increase in pressure = (density * gravitational acceleration * depth) - (density * gravitational acceleration * 0)
Increase in pressure = (1000 kg/m^3 * 9.8 m/s^2 * 3.2 m) - (1000 kg/m^3 * 9.8 m/s^2 * 0)
Increase in pressure = 31,360 Pa
Step 3: Calculate the force exerted on the eardrum.
Given: Increase in pressure = 31,360 Pa
Force = pressure * area of the eardrum
Force = 31,360 Pa * 0.00006 m^2
Force = 1.8816 N
Therefore, the increase in the force pushing on the diver's eardrum compared to what it was at the lake surface is approximately 1.8816 N.
To solve this question, we can use the concept of pressure. Pressure is defined as the force per unit area.
The formula for pressure is:
Pressure = Force / Area
In this case, we need to calculate the increase in pressure on the eardrum when the diver swims to a depth of 3.2 m.
Step 1: Calculate the increase in pressure due to the depth:
The pressure at a certain depth in a fluid can be calculated using the formula:
Pressure = Density x Gravity x Depth
For freshwater, the density is approximately 1000 kg/m^3 and the gravitational acceleration is approximately 9.8 m/s^2.
Pressure = (1000 kg/m^3) x (9.8 m/s^2) x (3.2 m)
= 31360 Pa (Pascals)
Step 2: Calculate the increase in force on the eardrum:
The increase in force can be calculated using the formula:
Force = Pressure x Area
Given that the area of the eardrum is 0.60 cm^2, we need to convert it to square meters (m^2):
Area = (0.60 cm^2) x (1 m / 100 cm)^2
= 0.006 m^2
Now we can calculate the increase in force:
Force = (31360 Pa) x (0.006 m^2)
= 188.16 N (Newtons)
Therefore, the increase in force pushing in on the eardrum, compared to what it was at the lake surface, is 188.16 N.