Two masses m₁ and m₂ are placed touching each other on an inclined plane forming an angle θ with the horizontal the coefficient of friction between the inclined plane and m₁ is µ₁ and that of between plane and m₂ is µ₂ where µ₁ > µ₂.

(a) Find the interaction force between the two masses.

(b) What is the minimum angle q at which masses start sliding.

(a)    Let R be the interaction force and F₁ and F₂ be the frictional force on m₁ and m₂, respectively.

m₁a = m₁g sin θ + R – µ₁N₁           m₂a = m₂g sinθ – R – µ₂N₂

N₁ – m₁gcosθ = 0                        N₂ – N₂ – µ₂ cosθ = 0

(b)    The two masses begin to slide just when the acceleration of m1 is not zero.

The limiting case is given by

m₁g sinθmin + R – µ₁m₁g cosθmin = 0

Using R from part (a)