For the two questions that follow, please write out your detailed solution on paper. Please include a sketch of forces, equation(s) you used, algebraic manipulations, substituted values, and the final answer with units.

Q1. A fisherman's scale consists of a spring that hangs from a support. The equilibrium length of the spring is 7 cm. When a 1.4 kg fish is weighed, the spring stretches to a new length of 11.5 cm.

a) What is the spring constant (k) of this spring?

Please draw figures showing the forces and the change in length of the spring.

Give your answer to four significant figures with the units.

(10 points, out of which 4 points are for the figure with correct forces and labels, and 1 point is for the answer to 4 significant figures with units).

b) What is the elastic potential energy stored in the spring when it is stretched by this fish? Give your answer to three significant figures with the units.

(5 points, out of which 2 points are for the correct equation with its name, and 1 point is for the answer to 3 significant figures with units).