Why Does a System Behave as if It Has a Larger Mass in Water Compared to Air?

[ACE_99]

Homework Statement

This problem was presented as part of a lab write up. In the lab we were studying damped oscillations. We were asked to determine the mass indirectly based on values that we measured then compare it to the actual masses. We found that the calculated masses were much greater than the actual masses. The question is:

Explain why the system, that was moving in water, behave as if it has a much larger mass than the same system moving in air?

The Attempt at a Solution

I realize that this is probably a really simple question but for some reason I just cannot figure out an answer, any help would be great.

Sorry if this is in the wrong place.

 

[Redbelly98]

I can only take an educated guess, not seeing your actual setup or details of the procedure.

From Newton's 2nd Law: m = F/a

How is "a" different in the water vs. in air?

 

[thomate1]

I would first clarify the concept of damped oscillations for the person asking the question. Damped oscillations occur when a system experiences a resistance force that decreases its amplitude over time. In the case of a system moving in water, the resistance force is caused by the viscosity of the water, which acts against the motion of the system and causes it to slow down more quickly than if it were moving in air.

Therefore, the system in water experiences a greater resistance force and loses more energy over time, leading to a smaller amplitude and shorter period of oscillation. This can give the appearance of a larger mass, as the system is not able to complete as many oscillations as it would in air before coming to a stop.

Additionally, the density of water is much greater than that of air, which can also contribute to the perceived increase in mass. This is because the inertia of the water surrounding the system adds to the overall resistance force, making it more difficult for the system to move and giving the appearance of a larger mass.

In summary, the system behaves as if it has a larger mass in water due to the combined effects of increased resistance force and higher density compared to air. This highlights the importance of considering the medium in which a system is moving when analyzing its behavior and making comparisons to theoretical values.