8.1 - Density and Buoyant Forces

An eccentric salesman arrives at your lab peddling what he claims is an extraordinarily rare and dense "Elixir Oil," sold by weight at an exorbitant price. He places a beaker filled with this shimmering oil onto a sensitive digital scale, proudly announcing its initial weight.

Before finalizing the price, he insists on checking the oil's "consistency" with his own special silver spoon. He carefully lowers the spoon into the oil, holding it steady so it is submerged but not touching the bottom or sides of the beaker. You, a keen physics student, observe that the reading on the digital scale increases the moment the spoon enters the oil and remains higher while he holds it there.

Your Task:

Analyze this situation using your understanding of fluid principles and forces.

1. Explain the Observation: 

   • Explain what happens to the value of the scale reading. 

   • Suppose the spoon was supported by light spring, would the spring lengthen, shorten or remain the same length?  Use physics principles to justify your explanation.

2. Free-Body Diagrams: Draw clear free-body diagrams for:

   • The beaker of oil (while the spoon is submerged).

   • The spoon (while submerged in the oil and held by the salesman/spring). Label all relevant forces (e.g., gravitational force, buoyant force, normal force, applied force from the hand, etc.). Ensure your diagrams illustrate Newton's Third Law pairs where appropriate between the spoon and the fluid.

3. Quantify the Change: Let the density of the "Elixir Oil" be ρ and the volume of the spoon submerged in the oil be V. Derive an expression for the increase in the force measured by the scale in terms of ρ, V, and g (the acceleration due to gravity).

4. The Sales Pitch: 

   • Does this demonstration provide any valid scientific evidence for the oil being particularly dense or having special properties? 

   • Does the type of spoon (e.g., silver) matter in this context? Explain why or why not from a physics perspective.

An eccentric salesman arrives at your lab peddling what he claims is an extraordinarily rare and dense "Elixir Oil," sold by weight at an exorbitant price. He places a beaker filled with this shimmering oil onto a sensitive digital scale, proudly announcing its initial weight.

Before finalizing the price, he insists on checking the oil's "consistency" with his own special silver spoon. He carefully lowers the spoon into the oil, holding it steady so it is submerged but not touching the bottom or sides of the beaker. You, a keen physics student, observe that the reading on the digital scale increases the moment the spoon enters the oil and remains higher while he holds it there.

Your Task:

Analyze this situation using your understanding of fluid principles and forces.

1. Explain the Observation: Why does the scale reading increase even though the spoon is not touching the beaker? Use physics principles to justify your explanation.

2. Free-Body Diagrams: Draw clear free-body diagrams for:

   • The beaker of oil (while the spoon is submerged).

   • The spoon (while submerged in the oil and held by the salesman). Label all relevant forces (e.g., gravitational force, buoyant force, normal force, applied force from the hand, etc.). Ensure your diagrams illustrate Newton's Third Law pairs where appropriate between the spoon and the fluid.

3. Quantify the Change: Let the density of the "Elixir Oil" be ρ and the volume of the spoon submerged in the oil be V. Derive an expression for the increase in the force measured by the scale in terms of ρ, V, and g (the acceleration due to gravity).

4. The Sales Pitch: Does this demonstration provide any valid scientific evidence for the oil being particularly dense or having special properties? Does the type of spoon (e.g., silver) matter in this context? Explain why or why not from a physics perspective.