Rubik cube torque experiment - Correct equations and experiment set up?

Question

Background

I am attempting to experimentally find out the average torque required to rotate a single face of a Rubik cube. Little to no data is available as it varies from cube to cube. Some people have used a torque wrench but this is not an option currently.

Experiment Set Up

A picture of the setup can be seen below:

The cube is clamped to the table, string is wrapped around one face of the cube and weight is incrementally added to the bag. The mass is then recorded for the cube to rotate >=90 degrees. I constructed the following moment diagram:

Equations

Then I used the following equations to convert the mass of the cube to rotational torque.

F1=m * a = Acting Force

m= Recorded Mass ,a=Gravitational Acceleration

Torque=M1= F1 * X * sin⁡(90)

Question

I did this a set of times to then find the average torque required to rotate the cube face. Are my calculations correct? and is this a viable way to measure the torque of the cube?

Answer 1

From what I see, in order to measure the torque you should have put the side view. See below and imagine that the blue line around the face is the rope. From that view its possible to see if your calculation about the correct axis of rotation is obtained.

More specifically, you are interested in the rotation about the x-axis (as it is drawn in the image below). Currently, the only torque we can (somewhat) measure is around the Z-Axis.

So the torque around the Z-axis is (assuming its in the middle):

$$M_z = F\cdot 19[mm]$$

That torque will create (a slight) pressure on the bottom adjacent sections and it will increase the friction (however, that is not something you can easily avoid - to be honest I don't have something ready to suggest apart from trying different weights at different locations).

Now regarding the other size (for $M_x$) which you are more interested, you are on the right track, but I suspect you will see a LOT of scatter in the data.