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 1: Convert the given displacements from millimeters to meters. The initial stretch x_1 caused by the force F is 85 mm. The target stretch x_2 for which work done is to be calculated is 1 mm. We know that 1 mm = 10^-3 m. x_1 = 85 mm = 85 × 10^-3 m = 0.085 m x_2 = 1 mm = 1 × 10^-3 m = 0.001 m The applied force is F = 20 N. Step 2: Calculate the spring constant (k) using Hooke's Law. Hooke's Law states that the force F required to stretch or compress a spring by a distance x is given by F = kx, where k is the spring constant. Using the given force F = 20 N and the corresponding stretch x_1 = 0.085 m: k = (F)/(x_1) k = 20 N0.085 m k ≈ 235.294 N/m Step 3: Calculate the work done (W) to stretch the spring by 1 mm. The work done to stretch a spring by a distance x from its equilibrium position is given by the formula W = (1)/(2)kx^2. We need to find the work done for a stretch of x_2 = 0.001 m. W = (1)/(2) k x_2^2 W = (1)/(2) (235.294 N/m) (0.001 m)^2 W = (1)/(2) (235.294) (0.000001) W = 117.647 × 0.000001 W = 0.000117647 J Rounding to three significant figures: W ≈ 1.18 × 10^-4 J The work done to stretch the spring by 1 mm is 1.18 × 10^-4 J. Send me the next one 📸