
This question is about the double inclined plane.

What we have here is a pretty intimidating setup.

We have what we could view as 2 inclined planes

one inclined at an angle α and one inclined at an angle β.

We have two massesm1 and m2and of course we're pretending there's no friction,

because we just don't want to deal with that right now.

I want to know if I set this system up and then release it, how is it going to accelerate.

Just to be consistent, let's call clockwise direction,

so if this one's moving up then this one's moving down the plane.

We'll call that positive acceleration +a.

For this question I'm going to tell you that the acceleration looks something like this.

Now, what's going on here?

Well, the acceleration is gthe acceleration due to gravity

times this modifier of some sort.

What I want you to do is in each of the red boxes

put either a 1 or a 2 if the relevant mass is mass 1 you put a 1, 2 you put a 2.

In the blue boxes, I want you to put either a plus, a minus, multiplication sign,

or division sign, depending on what you think makes sense.

Now, you could just solve this equation.

You could do F = ma for both of the blocks and get an answer.

Or you could try using your intuition.

See what makes sense. Think of limiting cases.

What happens when m1 gets really big or m2 gets really big.

What happens if β is really small or α is really small?

Thinking this way should be able, in theory, to tell you exactly

what symbols go in the blue and red boxes. Good luck.