# Belt Friction

### Model Description

Investigate belt friction.  This demonstration should take 3-5 minutes.

### Engineering Principle

These training aids provide a vehicle to discover the forces acting on a belt or rope when pulled over a fixed drum.

The basic equation for belt friction:

$\frac{T_2}{T_1} = e^{\mu\beta}$

where $\mu =$ coefficient of friction (either static or kinetic and $\beta =$ angle of surface contact between the belt and the drum (measured in radians).

### What You Need

Item Quantity Description/Clarification
Oject to suspend 1 The example uses a hatchet for dramatic effect, but any object that you can tie a rope to easily will work. $10; 3 minutes Rope 1 Thin rope long enough to wrap around a pole enough times to hold the object stationary.$5-10
Fixed drum 1 Some type of drum to wrap the rope around. \$10; 20 minutes

### How It’s Done

Before Class: Prepare some type of fixed horizontal drum.  The example uses a horizontal pole clamped to two vertical poles. Tie the rope to the object and wrap the rope around the drum tightly enough times to hold it stationary without tying it off.  This shows that static coefficient of friction for that amount of angle of surface contact can hold the object pulling on the rope with just the resistance provided by the self-weight of the loose end of the rope.

In Class: Discuss why and how the supported object is suspended and not moving when the rope is not tied off at either end.

Additional Application: Start taking off wraps so that the object slowly starts to lower.  Now the demo is using the kinetic coefficient of friction.

### Cite this work as:

John Richards (2018), "Belt Friction," https://www.handsonmechanics.org/statics/419.