Determine the fractional change in the mass of a spring upon being compressed by 1 cm . At its natural length, the spring has a mass of 200 g and a spring constant of 500 N m ⁻¹ .

Step-by-step solution

Energy stored in the spring is given by U = 1 2 kx^2 . Substituting the given values: U = 1 2 500 (0.01)^2 = 0.025 J By mass-energy equivalence, the change in mass is m = U c^2 . The fractional change in mass is m m = U mc^2 . Substituting the values: m m = 0.025 0.2 (3 10^8)^2 m m = 0.025 0.2 9 10¹⁶ = 0.025 1.8 10¹⁶ m m = 2.5 1.8 10⁻¹⁸ 1.388 10⁻¹⁸ 1.4 10⁻¹⁸