Variable friction Work Done

A block of mass 2 kg2 \text{ kg} and length 1 m1 \text{ m} is placed on a rough surface (having variable kinetic friction coefficient). A horizontal force FF is applied such that block moves slowly. If total heat lost in this process is 4N3\frac{4N}{3} Joule. Find the value of 'NN'.

Assume g=10 m/s2g = 10 \text{ m/s}^2, (μk=x\mu_k = x for 0x10 \leq x \leq 1 & μk=0\mu_k = 0 for x1x \geq 1)

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