Savchenko Problem 2.1.50

The key insight is that the wedge itself must accelerate horizontally to produce an acceleration direction steeper than the wedge's slope. Since the plane is frictionless, the body and wedge push on each other, and you need to apply Newton's second law to both objects simultaneously. The body's acceleration angle $\beta$ being greater than $\alpha$ tells you the wedge is recoiling backward, so treat their accelerations as coupled through the normal force between them—use components and the constraint that the body stays on the wedge surface to find the wedge's mass.

The key insight is that the wedge itself must accelerate horizontally to produce an acceleration direction steeper than the wedge's slope. Since the plane is frictionless, the body and wedge push on each other, and you need to apply Newton's second law to both objects simultaneously. The body's acceleration angle $\beta$ being greater than $\alpha$ tells you the wedge is recoiling backward, so treat their accelerations as coupled through the normal force between them—use components and the constraint that the body stays on the wedge surface to find the wedge's mass.