A lot of work

A uniform rod of mass \(m\) and \(l\) is supported horizontally at its ends by my forefingers. Whilst I am slowly bringing my fingers together to meet at the centre of the rod, it slides on either one or other of them. How much work do I have to do if \(\dfrac{\mu_\text{kinetic}}{\mu_\text{static}}=k\)?


Courtesy: Peter Gnadig.
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