A pair of wedges are located on a horizontal surface. The coefficient of friction (both sliding and static) between the wedges is μ, the coefficient of friction between the bottom wedge B and the horizontal surface is μ, and the angle of the wedge is θ. The mass of the top wedge A is m, and the mass of the bottom wedge B is M = 2m. A horizontal force F directed to the left is applied to the bottom wedge as shown in the figure.
[Figure: Two wedges - wedge A on top of wedge B, with wedge B on a horizontal surface. Force F points left on wedge B. Angle θ shown on the wedge interface.]
Determine the range of values for F so that the top wedge does not slip on the bottom wedge. Express your answer(s) in terms of any or all of m, g, θ, and μ.