Acylinder is rising with an acceleration of 1.5m/s^2. determine the size of each force that was labled

We don't know which forces are labelled, because you decided
not to include the picture.

Using the information you've included, all we can say is:

--  The sum of all horizontal forces is zero, because the object
is not accelerating horizontally.

--  The sum of all vertical forces is (mass of the cylinder) times (1.5 m/s²).