A vertical spring carries a mass m = 2 kg. With g = 9.8 m/s^2 and k = 10 N/m, what is the equilibrium extension d?

A vertical spring carries a mass m = 2 kg. With g = 9.8 m/s^2 and k = 10 N/m, what is the equilibrium extension d?

• A. 1.96 m
• B. 0.98 m
• C. 19.6 m
• D. 0.2 m

Answer: (A)

At equilibrium, the spring’s upward force balances the mass’s downward weight. The spring force is k d, and the weight is m g. So set k d = m g and solve for d: d = (m g) / k. With m = 2 kg, g = 9.8 m/s^2, and k = 10 N/m, d = (2 × 9.8) / 10 = 1.96 m. The weight is 19.6 N, and the spring must extend 1.96 m to provide that force. Other options correspond to spring forces that are too small or too large to balance the weight.

At equilibrium, the spring’s upward force balances the mass’s downward weight. The spring force is k d, and the weight is m g. So set k d = m g and solve for d: d = (m g) / k. With m = 2 kg, g = 9.8 m/s^2, and k = 10 N/m, d = (2 × 9.8) / 10 = 1.96 m. The weight is 19.6 N, and the spring must extend 1.96 m to provide that force. Other options correspond to spring forces that are too small or too large to balance the weight.