How Do You Calculate the Coefficient of Kinetic Friction in a Pulley System?

[psycovic23]

"Two blocks are attached to a string that passes over a frictionless pulley. One of the blocks is 4kg and rests on a rough horizontal surface. The other block is a 2kg block that hangs over the edge of the surface. When the system is released, the 2 kg mass falls from rest and attains the speed of 2m/s after traveling a distance of 3 meters"

The first question is "what is the loss in mechanical energy" and I get 56J, which is right according to my teacher. However, the second question is "what is the coefficient of kinetic friction between the 4 kg block and the rough surface?"

What I do is:

Loss in mechanical energy = energy of friction

Thus:

56 = Fd =
56 = umgd =
56 = u * 4 * 9.8 * 3m

and I get .47. However, the answer is .40. What am I doing wrong?

 

[Astronuc]

How did you obtain 56 J?

Also think, what is the tensile force in the string?

There is friction, and there is the force required to accelerate the 4 kg mass laterally. What is the lateral acceleration of the 4 kg block?