You observe that after sliding down a distance of 2.61 m along a 5 m long track that is inclined at 20 degrees to the horizontal, a block of wood has a velocity of 0.13 m/s. If the coefficient of kinetic friction between the wood and the surface of the track is 0.40, what was the block's initial velocity at the beginning of the 2.61 m distance. [Please use g=9.81m/s^2 and give your answer with 2 decimal places in the SI system of units.]
See attached document.
The Attempt at a Solution
See attached document for work done so far.
Note: I forgot to include what L (length of ramp) was in my original drawing of the diagram in word so it is towards the bottom of the diagram for when I solve for forces.
I'm having trouble with finding mass. My professor likes students to answer by showing a step-by-step process in solving the problem, hence all the algebra on the attached document. I was unable to find a way to solve for mass from what I have done so far. I'm not sure if I'm missing an equation that should be there or a force in the diagram that I missed. Otherwise, I have to solve for the initial velocity. I also had trouble lining up what each force was for determining kinetic energy for the system. As the block slides down the ramp, I know that energy outputs are due to friction and gravity. I also know the equation for kinetic energy is:
KE = 1/2mv^2
I wondered if this equation could be applied twice for this problem but wasn't for sure. Any input is appreciated.