Connection between Pressure, Surface Density and Height?

In summary, the conversation is about the need for background equations to support the reasoning for a lab experiment involving dropping a basketball and measuring its bounce height. The first part of the experiment determined the ideal pressure for the ball to be 9PSI through a data-logger test. The second part involved dropping the ball on different surfaces with varying densities and a logarithmic equation was derived. The speaker is looking for additional equations that can support the results, particularly for the second part. They mention the possibility of using displacement=Height/(Pressure, Density) and ask for any helpful equations from physicists.
  • #1
Whtbrd
1
0
[Mentors' note: moved from technical forums so no template]

Hi All,

Working on a lab write-up, and I need background equations to support the reasoning for my experiment.

To outline briefly, two-part experiment, first part was finding the ideal pressure for a basketball, where I inflated it, dropped it, and used a data-logger to see the height it returned to. This provided me with results that showed 9PSI was ideal, from a test of 8PSI-10PSI (+0.5)

Second part, was using my ideal pressure, dropping the ball on different surfaces, based on their density (g/m^3), this has given me a logarithmic equation, which makes sense, as the higher density, the ball will bounce higher, but won't bounce higher than it started at.

Basically, looking for any supporting equations found by physicists that can prove this should work, particularly for part 2. Guessing it'll look something like displacement=Height/(Pressure, Density), with pressure and density in the denominator.

If anyone has any equations that they think will be helpful, please link to an article on them.

Thanks,
 
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  • #3
Whtbrd said:
dropping the ball on different surfaces, based on their density
How can you be sure they don’t differ in other ways that might be more important? Water is denser than wood, but my guess is it would bounce higher off the wood (depending on temperature).
 

FAQ: Connection between Pressure, Surface Density and Height?

What is the relationship between pressure and surface density?

The relationship between pressure and surface density is known as the hydrostatic equilibrium. This means that the pressure exerted by a fluid at any given point is directly proportional to its surface density at that point. In other words, an increase in surface density will result in an increase in pressure, and vice versa.

How does the height of a fluid column affect pressure and surface density?

The height of a fluid column has a direct impact on its pressure and surface density. As the height of the column increases, the pressure at the bottom also increases due to the weight of the fluid above it. This increase in pressure also leads to an increase in surface density, as the weight of the fluid is distributed over a larger area.

What is the formula for calculating pressure in a fluid column?

The formula for calculating pressure in a fluid column is P = ρgh, where P is the pressure, ρ is the surface density, g is the acceleration due to gravity, and h is the height of the fluid column. This formula is known as the hydrostatic pressure equation.

How does the pressure change with increasing height in a fluid column?

In a fluid column, the pressure increases with increasing height. This is due to the weight of the fluid above pushing down on the lower layers of the column. As the height increases, so does the weight of the fluid, resulting in a higher pressure at the bottom of the column.

What is the significance of understanding the connection between pressure, surface density, and height?

Understanding the connection between pressure, surface density, and height is crucial in many scientific fields, such as meteorology, oceanography, and atmospheric sciences. It allows us to predict and understand the behavior of fluids in different environments, such as in the atmosphere or in the ocean. This knowledge also has practical applications, such as in the design of structures that can withstand high pressures, like deep-sea vessels or high-altitude aircraft.

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