Coefficient of kinetic friction and Energy

[Leid_X09]

Homework Statement

Starting from rest, a 10.6 kg block slides 3.20 m down to the bottom of a frictionless ramp inclined 30.0° from the floor. The block then slides an additional 4.50 m along the floor before coming to a stop.
(a) Determine the speed of the block at the bottom of the ramp.
(b) Determine the coefficient of kinetic friction between block and floor.
(c) Determine the mechanical energy lost due to friction.


I already solved a) for 5.60 m/s, which is the correct answer. I'm having issues with b, because I know that the equation should be -Fk(4.5m) + 1/2mv^2 = W but I don't know how to apply this equation to find the frictional force. How am i supposed to calculate the work done without finding the frictional force, and vice versa? is there another equation I am not aware of?

 

[Redbelly98]

-Fk * 4.5m is the work done on the block. It will equal the change in energy of the block as it slides 4.5 m along the floor.