If the work required to stretch a spring 3 ft beyond its natural length is 15 ft-lb, how much work is needed to stretch it 27 in. beyond its natural length?

8.4 ft-lb

Explanation:

Work = change in energy

W = ½ kx²

When x = 3 ft, W = 15 ft-lb:

15 ft-lb = ½ k (3 ft)²

k = 30/9 lb/ft

When x = 27 in = 2.25 ft:

W = ½ kx²

W = ½ (30/9 lb/ft) (2.25 ft)²

W = 8.4375 ft-lb

Rounding to 2 sig-figs, it takes 8.4 ft-lb of work.

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