The force exerted by the wind on a plane surface varies...

Name: Problem 40, Chapter 2: Algebra and Trigonometry
Uploaded: 2021-06-25T16:35:01-08:00
Duration: 2 min 8 s
Channel: Andrew Elmer
Description: The force exerted by the wind on a plane surface varies directly with the area of the surface and the square of the velocity of the wind. If the force on an area of 20 square feet is 11 pounds when the wind velocity is 22 miles per hour, find the force on a surface area of 47.125 square feet when the wind velocity is 36.5 miles per hour.

The force exerted by the wind on a plane surface varies directly with the area of the surface and the square of the velocity of the wind. If the force on an area of 20 square feet is 11 pounds when the wind velocity is 22 miles per hour, find the force on a surface area of 47.125 square feet when the wind velocity is 36.5 miles per hour.

Key Concepts

Direct Variation

Direct variation is a relationship between two variables where one variable is a constant multiple of the other. In problems involving direct variation, if one variable increases, the other increases proportionally, and this relationship can be expressed with a constant of proportionality. Understanding this concept is crucial when dealing with scenarios where changes in one physical quantity directly affect another.

Constant of Proportionality

The constant of proportionality is the fixed value that relates two directly varying quantities. It is determined using known values and then applied universally within the context of the problem. This concept allows for the translation of real-world measurements into mathematical models, ensuring that the proportional relationship holds true regardless of the specific values involved.

Square Relationship

A square relationship means that one variable is proportional to the square of another variable rather than just the variable itself. This type of relationship significantly amplifies the effect of changes in the independent variable. In many physical processes, such as those involving kinetic energy or fluid dynamics, understanding the square relationship is essential to accurately model and predict outcomes.

Scaling Laws in Physics

Scaling laws describe how physical quantities change as the dimensions of a system are altered. In problems where force depends on both area and the square of velocity, scaling laws help in understanding how enlarging a surface or increasing velocity can non-linearly affect the force. These laws are fundamental in bridging theoretical physics with practical applications, guiding design and analysis in various engineering contexts.

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