Variable friction Work Done

A block of mass \(2 \text{ kg}\) and length \(1 \text{ m}\) is placed on a rough surface (having variable kinetic friction coefficient). A horizontal force \(F\) is applied such that block moves slowly. If total heat lost in this process is \(\frac{4N}{3}\) Joule. Find the value of '\(N\)'.

Assume \(g = 10 \text{ m/s}^2\), (\(\mu_k = x\) for \(0 \leq x \leq 1\) & \(\mu_k = 0\) for \(x \geq 1\))

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