Additional elastic potential energy as difference in (1/2)kx²

Steps:

• Spring constant k = initial force / extension = 2 N / 0.05 m = 40 N/m.
• Initial PE = (1/2) × 40 × (0.05)² = 0.05 J.
• Total force after adding 4 N = 6 N; total extension = 6 / 40 = 0.15 m.
• Final PE = (1/2) × 40 × (0.15)² = 0.45 J.
• Additional PE due to 4 N = 0.45 J - 0.05 J = 0.40 J.

Why D is correct:

• Elastic potential energy formula (1/2)kx² gives total stored energy; difference calculates increase from added weight.

Why the others are wrong:

• A: 0.07 J misapplies extension or force in energy calculation.
• B: 0.13 J incorrectly uses average force or partial extension.
• C: 0.20 J assumes linear energy without squaring extension properly.

Final answer: D