Ch. 13 - Fluids

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 13 - Fluids

Problem 85

Chapter 13, Problem 85

When you ascend or descend a great deal when driving in a car, your ears “pop,” which means that the pressure behind the eardrum is being equalized to that outside. If this did not happen, what would be the approximate force on an eardrum of area 0.20cm² if a change in altitude of 1120 m takes place?

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Convert the area of the eardrum from cm² to m². Use the conversion factor: 1 cm² = 1 × 10⁻⁴ m². Thus, the area in m² is A = 0.20 × 10⁻⁴ m².

Determine the change in atmospheric pressure due to the change in altitude. Use the approximate relationship for atmospheric pressure change: ΔP = ρgh, where ρ is the density of air (approximately 1.225 kg/m³ at sea level), g is the acceleration due to gravity (9.8 m/s²), and h is the change in altitude (1120 m).

Substitute the values into the formula ΔP = ρgh to calculate the pressure difference. This gives ΔP = (1.225)(9.8)(1120).

Calculate the force exerted on the eardrum using the formula F = ΔP × A, where F is the force, ΔP is the pressure difference, and A is the area of the eardrum in m².

Substitute the values of ΔP and A into the formula F = ΔP × A to find the approximate force on the eardrum. Ensure the units are consistent throughout the calculation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Pressure Change

Pressure is defined as force per unit area. When there is a change in altitude, the atmospheric pressure changes, which can exert a force on surfaces, such as the eardrum. Understanding how pressure varies with altitude is crucial for calculating the force acting on the eardrum during ascent or descent.

Atmospheric Pressure

Atmospheric pressure decreases with increasing altitude due to the reduction in the weight of the air above. At sea level, the standard atmospheric pressure is approximately 101,325 Pa. As one ascends, this pressure drops, and the difference between the internal ear pressure and external atmospheric pressure can lead to the sensation of 'popping' as the eardrum equalizes.

Force Calculation

The force exerted on an area can be calculated using the formula F = P × A, where F is the force, P is the pressure difference, and A is the area. In this scenario, knowing the change in atmospheric pressure due to altitude change allows us to compute the force acting on the eardrum, which has a specific area of 0.20 cm².

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