How is lifting a counterweight of a trebuchet considered doing work? Use the definition of work (W = Fd) in your description.

As the counterweight falls through the height h, its gravitational potential energy is converted to the kinetic energy of the missile; its energy due to its motion, and the gravitational potential energy of the missile; the work done to raise it up from the ground against the force of gravity.

Explanation:

If we assumed that all of the gravitational potential energy was transferred to kinetic energy of the missile:

Eg = Ek

m₁g∆h = ½m₂v

Be that as it may, this equation doesn't remain constant since work must be done to lift the shot facing the power of gravity before it is shot into the air. We can accordingly say that the gravitational potential energy of the counterweight when it is suspended, h meters over the ground is equivalent to the expansion of kinetic energy of the missile and the expansion in the gravitational potential energy of the missile:

m₁g∆h = 1/2m₂v

2 + m₂g∆h