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A spring has force constant K. What is the work required to increase its extension from l1 to l2?

1. K(l2 − l1)
2. (K/2)(l2² − l1²)
3. (K/2)(l2 + l1)
4. (K/2)(l2² − l1²)

Correct answer: (K/2)(l2² − l1²)

Solution

Spring potential energy is U = (1/2)K l^2, so the work needed to change the extension from l1 to l2 is U2 - U1 = (K/2)(l2^2 - l1^2).

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