Determine the counterweight of A needed to balance the weight of the bridge deck when θ =...

Determine the counterweight of A needed to balance the weight of the bridge deck when θ = 0°. Show that this weight will maintain equilibrium of the deck by considering the potential energy of the system when the deck is in the arbitrary position θ. Both the deck and AB are horizontal when θ = 0°. Neglect the weights of the other members. Use appropriate numerical values to explain this result.