Why is a1 = 2*a2 in a pulley system?

[asi123]

Homework Statement

Hey guys.
I have the following pulley system (in the pic).
I wrote down all the equations.
The thing I don't get is the accelerations equation (a1 = 2*a2). I understand that I can get to this equation somehow by the length of the rope, but how?
Thanks.

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

The thing I don't get is the accelerations equation (a1 = 2*a2). I understand that I can get to this equation somehow by the length of the rope, but how?

Hi asi123!

You get it by double-differentiating x₁ = 2x₂ …

and that is simple geometry … when m₂ moves a distance x₂, m₁ moves a distance x₁ = 2x₂.