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?

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.

To find the mass of the original block, we can use the principle of conservation of momentum. In this case, the total momentum before the explosion is equal to the total momentum after the explosion.

Let's denote the mass of the original block as M.
The total momentum before the explosion is zero since the block is stationary initially.

After the explosion, the momentum of the left piece (L) is given by:
MomentumL = massL * velocityL

The momentum of the right piece (R) is given by:
MomentumR = massR * velocityR

Since both pieces come to a stop, their final velocities are zero.

Now, we know that momentum is conserved, which means the total momentum after the explosion is zero as well.

Therefore, we can write the equation:
MomentumL + MomentumR = 0

Substituting the expressions for momentumL and momentumR, we get:
massL * velocityL + massR * velocityR = 0

Since velocityL and velocityR are both zero, this equation becomes:
massL * 0 + massR * 0 = 0

This simplifies to:
0 = 0

As a result, the masses of the individual pieces (massL and massR) do not matter for calculating the mass of the original block.

Therefore, we cannot determine the mass of the original block from the given information about the pieces and their distances.