Question: What is the acceleration of each body, if they slip along the incline? What is the normal between them? Assume the incline to be frictionless and neglect air resistance.
My teacher solved this by assuming the acceleration of both masses to be same, and so the normal force then came out to be zero. How do we know that this assumption about the accelerations is correct?
My teacher also said that even if we don’t consider both bodies’ acceleration to be the same, Newton’s second law can be applied to each to get equations for each: (the sign convention I’m going to be following is positive in the direction of motion and negative opposite to the direction of motion)
For $m_2$ the acceleration is $a_2$ and the normal force between $m_2$ and $m_1$ be $N$:
For $m_1$ the acceleration is $a_1$:
He then justified the assumption that the acceleration of both bodies is same by saying that if accelerations of the bodies were different then the normal force between them would be zero and by plugging the value of N in the equation for each body, we’ll get $a=g\sin\theta$ for each mass
I get that if $a_2 < a_1$, the bodies would lose contact and no normal would exist between them. But if $a_2 > a_1$, wouldn’t the normal be between them be non-zero? How does my teacher’s justification hold if $m_2$ doesn’t accelerate slower than $m_1$ does?