Suppose that 5 J of work is needed to stretch a spring from its natural length of 28 cm to a length of 48 cm. (a) How much work is needed to stretch the spring from 36 cm to 40 cm?

Question

Suppose that 5 J of work is needed to stretch a spring from its natural length of 28 cm to a length of 48 cm.

(a) How much work is needed to stretch the spring from 36 cm to 40 cm? (Round your answer to two decimal places.)

(b) How far beyond its natural length will a force of 15 N keep the spring stretched? (Round your answer one decimal place.) in cm

Answer 1

W₁ = k(l₁² - l₀²)/2; k = 2W₁/(l₁² - l₀²) = 10J/(0.48²m²- 0.28²m²) = 65.79 N/m

(a) W₂ = 65.79[(0.40 - 0.28)² - (0.36 - 0.28)²]/2 = 0.26 J

(b) F = k(l - l₀); l - l₀ = F/k = 15N/65.79N/m = 0.228 m = 22.8 cm