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
You're on a roll — Step 1: State the formula for the work done on a spring. The work W done to compress or stretch a spring by a displacement x from its unstretched length is given by: W = (1)/(2)kx^2 where k is the spring constant. Step 2: Convert the given displacements to meters. Initial compression x_1 = 4 cm = 0.04 m. New stretch x_2 = 3 cm = 0.03 m. Step 3: Use the first set of data to calculate the spring constant k. Given W_1 = 12 J for x_1 = 0.04 m. 12 J = (1)/(2)k(0.04 m)^2 12 = (1)/(2)k(0.0016) 24 = k(0.0016) k = (24)/(0.0016) k = 15000 N/m Step 4: Calculate the work done to stretch the spring by 3 cm using the calculated spring constant. We need to find W_2 for x_2 = 0.03 m. W_2 = (1)/(2)kx_2^2 W_2 = (1)/(2)(15000 N/m)(0.03 m)^2 W_2 = (1)/(2)(15000)(0.0009) W_2 = 7500 × 0.0009 W_2 = 6.75 J The correct option is B) 6.75 J. What's next?