I have an inclined plane with angle $\alpha$ with a block on it and a friction coefficient of $\mu$. I want to find $\alpha$ for which its acceleration, $a$, is maximum. Intuitively, 90$^o$ makes sense (regardless of the value of $\mu$) and anything above it would have the same acceleration as 90$^o$ since the block would fall off.

Mathematically, $$mg\sin\alpha - \mu mg\cos\alpha = ma,$$ and trying to find the maximum is giving me different answers for different values of $\mu$. What am I missing here?

I have an inclined plane with angle $\alpha$ with a block on it and a friction coefficient of $\mu$. I want to find $\alpha$ for which its acceleration, $a$, is maximum. Intuitively, 90$^o$ makes sense (regardless of the value of $\mu$) and anything above it would have the same acceleration as 90$^o$ since the block would fall off.

Mathematically, $$mg\sin\alpha - \mu mg\cos\alpha = ma,$$ and trying to find the maxima(using Wolfram alpha) is giving me different answers for different values of $\mu$. What am I missing here?

Say I have an inclined plane, with angle $\alpha$ with a block on it, with a friction coefficient of $u$ and I want to find the alpha for which its acceleration is maximum. Intuitively, 90 makes sense(regardless of the value of $u$) and anything above it would have the same acceleration as 90 since the block would fall off.

Mathematically, $mgsin\alpha - umgcos\alpha = ma$ here, trying to find the Maxima is giving me different answers for different values of $u$. What am I missing here?

I have an inclined plane with angle $\alpha$ with a block on it and a friction coefficient of $\mu$. I want to find $\alpha$ for which its acceleration, $a$, is maximum. Intuitively, 90$^o$ makes sense  (regardless of the value of $\mu$) and anything above it would have the same acceleration as 90$^o$ since the block would fall off.

Mathematically, $$mg\sin\alpha - \mu mg\cos\alpha = ma,$$ and trying to find the maximum is giving me different answers for different values of $\mu$. What am I missing here?