How is the work done to hoist the counterweight related to the potential energy of the counterweight at its specified height?

The work done to lift the counterweight equals the potential energy acquired

Explanation:

since this is vertically applied force on the counterweight, and the distance the force is displacing the counterweight is in the same direction as the applied force, it equals the gained potential energy

u=13

v=30

s/t=u+1\2at

=13+431/2

=13+265.5

=278.5

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