Elastic potential energy in a stretched spring

Steps:

• Calculate extension: x = new length - unstretched length = 0.5 m - 0.3 m = 0.2 m.
• Use formula for elastic potential energy: E = (1/2) k x², where k = 400 N/m.
• Substitute values: E = (1/2) × 400 × (0.2)² = 200 × 0.04 = 8 J.

Why A is correct:

• Matches the formula E = (1/2) k x², which stores energy as (1/2) force × distance for linear springs.

Why the others are wrong:

• B: Uses full k x² = 16 J, ignoring the 1/2 factor.
• C: Equals k x = 80 N × 0.1 m (misapplied work), not energy.
• D: Equals k × length = 400 × 0.5 = 200 J / 4 (arbitrary error).

Final answer: A