In this video, we deal with the derivation of the so-called belt friction equation, which goes back to the scientists Euler and Eytelwein and is therefore also referred to as the Euler-Eytelwein formula.
The belt friction equation represents the relationship between the forces at the two ends of a belt or a rope for the limiting static case when it is wrapped around an object. The difference between the two rope forces is the frictional force between the rope and the object.
An example of the application of the belt friction equation is the lowering of an object on a rope that is wrapped several times around a balcony railing. The frictional force between the rope and the railing ensures that even relatively heavy objects, such as a cabinet, can be held with relatively little effort.
The belt friction equation also plays a central role in belt drives where the belt wraps around a pulley. In this case, the difference between the forces in both sections of the belt is the frictional force between the belt and the pulley. Friction is used to drive the pulley through the belt.
00:00 Application of the belt friction equation
01:07 Experimental setup and procedure
02:11 Factors influencing the frictional force
04:12 Derivation of the belt friction equation
05:15 Force diagram
05:49 Coulomb's law of friction
07:02 Separation of variables
07:50 belt friction equation according to Eytelwein and Euler
08:43 Example
11:23 Limitations of the belt friction equation
12:07 Frictional force = peripheral force
12:46 Belt drive
13:14 Example: Holding a Cabinet
14:57 Example: Lowering a Cabinet
16:17 Example: Lifting a Cabinet