A chain of mass `m=0.80kg` and length `l=1.5m` rests on a rough-surfaced table so that one of its ends hangs over the edge. The chain starts sliding off the table all by itself provided the overhanging part equals `eta=1//3` of the chain length. What will be the total work performed by the friction forces acting on the chain by the moment it slides completely off the table?

Explanation

To solve the problem, we need to analyze the situation step by step. The chain is resting on a rough table, with part of it hanging off the edge. When a certain portion of the chain (1/3 of its total length) hangs off the edge, it begins to slide off due to gravity. We need to calculate the total work done by the friction forces acting on the chain until it slides completely off the table.

### Step-by-Step Solution:

1. **Identify the parameters:**
- Mass of the chain, \( m = 0.80 \, \text{kg} \)
- Length of the chain, \( l = 1.5 \, \text{m} \)
- Overhanging length, \( \eta = \frac{1}{3} l = \frac{1}{3} \times 1.5 \, \text{m} = 0.5 \, \text{m} \)
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