The length of a light elastic string is 1.40 m when the tension is 5 N. When the tension is increased to 7 N, its length becomes 1.56 m. Assuming Hooke's law, find the natural length of the string in metres.

Question

G1 Physics · Accepted Answer

Let the natural length be l₀ and the effective spring constant be K. Under tension 5 N, extension is 1.40 - l₀. So 5 = K(1.40 - l₀). ...(1) Under tension 7 N, extension is 1.56 - l₀. So 7 = K(1.56 - l₀). ...(2) Divide or eliminate K: 5/(1.40-l₀) = 7/(1.56-l₀). Cross-multiplying: 5(1.56-l₀) = 7(1.40-l₀). 7.8 - 5l₀ = 9.8 - 7l₀ ⇒ 2l₀ = 2 ⇒ l₀ = 1.0 m. Answer: 1.