This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 2: Calculate the force exerted by the mass. Given: Mass m = 1 kg Acceleration due to gravity g = 9.8 m/s^2 The force (F_2) acting on the spring is the weight of the mass: F_2 = mg F_2 = 1 kg × 9.8 m/s^2 F_2 = 9.8 N Step 3: Calculate the extension of the spring (x_2) when supporting the mass. Using Hooke's Law (F_2 = kx_2) and the spring constant k = 8 N/m from Step 1: x_2 = (F_2)/(k) x_2 = 9.8 N8 N/m x_2 = 1.225 m Step 4: Calculate the natural length (L_0) of the spring. The total length of the spring when supporting the mass is given as 2.49 m. This total length is the sum of the natural length and the extension. Total length L = L_0 + x_2 L_0 = L - x_2 L_0 = 2.49 m - 1.225 m L_0 = 1.265 m The natural length of the spring is 1.265 m and the spring constant is 8 N/m.