June 11, 2026 - Calculus 2 - Physics Applications: Pumping, Hydrostatic Pressure, and Center of Mass

Vocabulary flashcards covering weight density, hydrostatic pressure, work in pumping liquids, and moments for calculating the center of mass based on the lecture transcript.

Weight Density

The amount of force needed to lift one unit of volume of water, measured as a constant depending on the units of volume used.

Metric Weight Density Constant

The constant value of $9800$ used when volume is measured in meters cubed.

Imperial Weight Density Constant

The constant value of $62.4$ used when volume is measured in feet cubed.

Joule

The unit of measurement for work, representing force times distance, specifically $\text{Newton} \times \text{meters}$.

Hydrostatic Pressure

The pressure exerted by water at a specific depth, which is equal to the weight of the water column above a submerged object.

Flat Plate Hydrostatic Pressure

The pressure on a surface submerged at a constant depth $s$, where the pressure is uniform across the entire area.

Vertical Plate Hydrostatic Force

The total force calculated by integrating pressure across a sideways plate where the depth varies between points $S_1$ and $S_2$.

First Moment of the System

The sum of each mass multiplied by its distance from the origin ($\bar{x}$), used to find the balance point of the system.

Total Mass

The sum of all individual masses in a system, serving as the denominator in the center of mass calculation.

Center of Mass ($\bar{x}$)

The exact middle point of a system where it would be balanced, calculated by dividing the first moment by the total mass.

Moment in the $y$-direction ($M_y$)

In a 2D plane, the sum of the masses multiplied by their $x$-coordinates, used to calculate the $x$-coordinate of the center of mass.

Moment in the $x$-direction ($M_x$)

In a 2D plane, the sum of the masses multiplied by their $y$-coordinates, used to calculate the $y$-coordinate of the center of mass.

Remon Sum (Riemann Sum)

The mathematical process of breaking a volume or area into thin slices or strips to set up an integral for work or force.

Pumping Work

The energy required to displace water from a tank, calculated by integrating the force needed to lift individual slices of water to the top edge.

Lamina

A thin, flat plate of material with a distributed mass, mentioned as a subject for finding center of mass using calculus.