There is a cube of ice the top of inclined plane (for 20 degress) with height 4 meters. The inclined plane can move without friction along the surface. The mass of the ice is 1/4 of the mass of inclined plane. Calculate the acceleration of the inclined plane, when the ice will be at the middle of the inclined plane.
The Attempt at a Solution
I tried to draw the forces acting on the cube. That are
x-axis along the inclined plane: M/4 g sin(20) - a_1 M/4 cos(20) = M/4 a_2... (where a_1 is the acceleration of the inclined plane)
y-axis perpendicular to the inclined plane: F_n + M/4 a_1 sin(20) = M/4 g cos(20)=0 ... (where F_n is the perpendicular force of the plane)
Forces acting on the inclined plane:
x-axis: F_n sin(20)= M*a_1
y_axis: F_n * cos(20) + M*g= F_s...(where F_s is the force of the surface to the incline)
The first three eqatuions give a_1 and a_2, since M is canceled out after substituting for F_n. I think, this would give correct answer. However, since this is probably a well known problem, I am interested in other possible approaches.