To stretch the spring by 4 mm, it is necessary to do a work of 0.02 J. What work must be done

To stretch the spring by 4 mm, it is necessary to do a work of 0.02 J. What work must be done to stretch this spring by 40 cm?

Data: Δl1 (deformation at the first tension of the spring) = 4 mm; A1 (work done during the first tension of the spring) = 0.02 J; Δl ^ 2 (deformation at the second tension of the spring) = 40 cm.

SI: Δl1 = 4 mm = 0.004 m; Δl ^ 2 = 40 cm = 0.4 m.

1) Determine the coefficient of spring stiffness: A1 = k * Δl1 ^ 2/2, whence k = 2A1 / Δl1 ^ 2 = 2 * 0.02 / 0.004 ^ 2 = 2500 N / m.

2) We calculate the work when the spring is stretched by 40 cm: A2 = k * Δl2 ^ 2/2 = 2500 * 0.4 ^ 2/2 = 200 J.

Answer: It will take 200 J.