Final answer:
To find the force experienced by the aluminum barrier, combine the nonlinear equation of the magnetic force with that of the nonlinear force of the air spring, accounting for the non-conservative forces that may be present. Integrate these forces over the respective distances or compressions to obtain the net force on the barrier.
Step-by-step explanation:
To determine the force experienced by the aluminum barrier suspended with a permanent magnet above and an iron disc with an air spring below, you need to consider both the magnetic force and the force exerted by the air spring. The magnetic force is nonlinear and decreases with the square of the distance, according to an inverse square law, whereas the force exerted by the air spring can be described by a nonlinear equation that likely adheres to Hooke's Law where force is proportional to displacement.
Combining these two equations involves setting up an equation of forces that accounts for the balance of forces on the barrier. The net force on the barrier is the magnetic force minus the force absorbed by the air spring. This equation can be expressed as:
Fnet = Fmagnetic - Fair spring
To solve this, you'd need the specific non-linear equations for both forces. Using principles of conservation of energy and mechanical equilibrium, you can find the net force by integrating the force over the distance or compressions they act upon. As the compression in the spring increases, its ability to absorb force also increases, lessening the force felt by the barrier.
Forces such as gravitational force and non-conservative forces, such as those due to air resistance or thermal energy, can also play a part in such a system but be excluded as per the given scenario. If the magnetic force does indeed follow an inverse square law, the equation would be similar to F = C/d², where C is a constant, and d is the distance between the magnet and the iron disc.