How is Normal Force on Table affected by two Blocks sliding on Triangle?

Question

Suppose we have a triangle with mass M as shown:

Clearly, the normal force of from the system to the table is $Mg$.

But what if we added two blocks of equal mass m on sides BC and AC of triangle ABC? What would the normal force from the system (=triangle plus two blocks) to the table be then? (assuming all contact surfaces are frictionless, so the two blocks immediately start sliding off). Assume the triangle does not move on the surface it is on.

I believe the answer is $(2m+M)g$ but I am not sure if the two masses of mass $m$ that are sliding down the triangle affect the normal force in any way.

Answer 1

The normal force would be $g(M + m(\cos^2 \theta_1 + \cos^2\theta_2))$

where the $\theta$'s represent the angles at the bottom of the triangles.

This is because the force on the object must be equal to the acceleration of its center of mass. The center of mass of the triangle-plus-blocks system is accelerating down, so the net force on it is down. The normal force is therefore weaker than gravity.

I got the precise numbers because I memorized that a block sliding frictionlessly down a slope has acceleration $g\sin\theta$. The vertical component of their accelerations is $g\sin^2\theta$. This is the amount that the normal force is reduced, so each block contributes an amount $mg - mg\sin^2\theta = mg \cos^2\theta$ to the normal force.