HELP! Block up incline...

[justagirl]

There's a block of mass M that's pulled up an incline by a force T. The block starts from rest and is pulled a distance L by the force T. The incline, which is frictionless, makes an angle (a) with respect to the horizontal.

1) Write down the work done by force T.

That would just be W = T*L right?
...Even though net work would be W = TL - mg sin (a)

2) Calculate the potential energy of the block as a function of the position L.

U = mgh = mgLsin(a), right?

3) From the work and the potential energy calculate the kinetic energy of the block as a function of position L.

Okay... so since the force is conserved, KE + PE + W = 0, right??
So KE = -W - PE
= - (TL - mg sin (a)) - mgLsin(a))

Is that correct or no??

4) Calculate the acceleration of the block, a, as a function of position L. Calculate the velocity from the acceleration and kinetic energy as a function of position. Show that the kinetic energies calculated in these two ways are equivalent.

I can't get this part to work. I put acceleration = F/M = (T-mg sin (a)) / m but how do I get it in terms of L? And how do I integrate the acceleration function with respect to L??

Thank you! All help is greatly appreciated!!