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4. (1 pt) A hydroelectric power facility converts the gravitational potential energy of water behind a dam to electric energy. What is the gravitational potential energy relative to the generators of a lake of volume 50.0 km³ (mass=5.00 x 10¹3 kg), given that the lake has an average height of 40.0 m above the generators? 5. (2 pts.) An archer pulls her bowstring back 0.444 m by exerting a force that increase uniformly from zero to 333 N. (a) What is the equivalent spring constant of the bow? (b) How much work does the archer do in pulling the bow? 6. (3 pts.) A toy gun uses a spring to project a soft rubber sphere horizontally. The mass of the sphere is 150 grams, the spring constant is 8.0 N/m, the barrel of the gun is 15 cm long, and a constant frictional force of 0.032 N exists between the barrel and the projectile. (a) How much work does friction do over the 15 cm for which it acts? (b) How much potential energy is built up into the spring if it is compressed 5.0 cm for this launch? (c) With what speed does the projectile leave the barrel?