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 mass to kilograms. The given mass is m = 400 g. m = 400 g × 1 kg1000 g = 0.400 kg Step 2: Use the formula for the period of a mass-spring system to find the spring constant. The period T of a mass-spring system is given by the formula: T = 2((m)/(k)) where m is the mass and k is the spring constant. Step 3: Rearrange the formula to solve for k. Square both sides of the equation: T^2 = (2)^2 (m)/(k) T^2 = 4^2 (m)/(k) Now, solve for k: k = (4^2 m)/(T^2) Step 4: Substitute the given values and calculate k. Given m = 0.400 kg and T = 2.0 s. k = 4^2 (0.400 kg)(2.0 s)^2 k = (4^2 (0.400))/(4.0) k = ^2 (0.400) Using ≈ 3.14159: k ≈ (3.14159)^2 × 0.400 k ≈ 9.8696 × 0.400 k ≈ 3.94784 N/m Rounding to two significant figures (based on the period): k ≈ 3.9 N/m The spring constant is: 3.9 N/m Drop the next question.