The density of the liquid is equal to the slope of the graph when plotting weight versus the volume of the displaced fluid.
Understanding the Relationship
Let's delve deeper into why the density of the liquid equates to the slope in this specific graphical representation:
- Archimedes' Principle: This principle states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.
- Graph of Weight vs. Displaced Volume: When we graph the weight of the displaced fluid against the volume of that displaced fluid, we're essentially visualizing the relationship described by Archimedes' principle.
- Slope as Density: The slope of this graph represents the rate of change of weight with respect to volume. Since density is defined as mass per unit volume (and weight is proportional to mass), this slope directly corresponds to the fluid's density. The reference states: "The slope of the graph of weight versus the volume of the displaced fluid will be equal to the density of the fluid."
Why This is Important
- Determining Fluid Density: This principle provides a practical method for determining the density of an unknown fluid. By measuring the weight of displaced fluid for different volumes, we can plot a graph and easily determine the density by calculating the slope.
- Consistent Measurement: This method works under the assumption that the object's density remains constant during submersion. This is usually a valid assumption for solid objects that do not deform significantly when submerged.
- Practical Application: In laboratory settings and engineering applications, this approach can be used for quality control in fluid manufacturing, scientific experiments, or to verify calculations in hydrostatic applications.
Summary
The key takeaway is that the slope of the graph derived from plotting the weight against the volume of displaced fluid directly represents the density of that fluid. This concept is rooted in Archimedes' Principle and provides a practical method to determine fluid density.
