A student investigates springs made of metal wire, as shown in Fig. 1.1. cross-sectional area A metal wire Fig. 1.1 The student constructs several springs from wire of thickness t. Each spring has a different cross-sectional area A. The student investigates how the spring constant k varies with A. It is suggested that the relationship between k and A is k = (βpt⁴)/(A^(3/2)N) where ρ is the density of the metal, N is the number of turns of wire on the spring and β is a constant. Design a laboratory experiment to test the relationship between k and A. Explain how your results could be used to determine a value for β. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to: • the procedure to be followed • the measurements to be taken • the control of variables • the analysis of the data • any safety precautions to be taken.