What is the work done in compressing a spring from an initial compression of 0.10 m to a final compression of 0.30 m if the spring stiffness is 500 N/m?

Answer and explanation

Correct answer: C. 20.0 J

  1. Step 1: Work done on a spring equals the change in elastic potential energy: W = 0.5 k (x_f^2 - x_i^2).
  2. Step 2: Substitute values: W = 0.5 500 ((0.30)^2 - (0.10)^2).
  3. Step 3: Compute squares: (0.30)^2 = 0.09, (0.10)^2 = 0.01.
  4. Step 4: Difference: 0.09 - 0.01 = 0.08.
  5. Step 5: Calculate: 250 * 0.08 = 20.0 J.
Answer
20.0 J.
Why not the others: '40.0 J' calculates 0.5 500 (0.3 - 0.1)^2 = 10 J or forgets factor 0.5; '10.0 J' evaluates based on Delta x squared (0.2)^2; '25.0 J' uses average force incorrectly.

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