# Whether to conserve energy for just the small block or the wedge+block system?

Let the mass of small block be $m$ and that of wedge be $M$ Now when the block slides down to the lowest point the change in its Gravitational potential energy is $mgh$.

Suppose it has velocity $u$ along the incline(w.r.t. wedge). Let $v$ be velocity of wedge.

So, its final $KE = \frac{1}{2}m(v^2+u^2+2uv\sin\beta)$ where $\beta$ is the angle of wedge.

Now in this situation how do we apply energy conservation i.e. do we conserve energy only of the block

$$mgh + 0 = 0+ \frac{1}{2}\left(m(v^2+u^2+2uv\sin\beta\right)$$

OR

that of the wedge+block system

$$mgh + 0 + PE_{wedge} +0 = 0 + \frac{1}{2}m\left(v^2+u^2+2uv\sin\beta\right) + PE_{wedge} + \frac{1}{2}Mv^2$$