From the sliding distance and coefficients of friction, you can calculate the initial kinetic energy and momentum of piece L.
From the fact that the total momentum must remain zero, you can conclude that the momenta of the two pieces are equal and opposite.
Having solved for the momentum of piece R, you can solve for its mass also.
Add the two masses to obtain the original mass.
In the figure, a stationary block explodes into two pieces L and R that slide across a frictionless floor and then into regions with friction, where they stop. Piece L, with a mass of 2.0 kg, encounters a coefficient of kinetic friction μL = 0.40 and slides to a stop in distance dL = 0.15 m. Piece R encounters a coefficient of kinetic friction μR = 0.50 and slides to a stop in distance dR = 0.39 m. What was the mass of the original block?
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