If a wire 30 cm long is extended to 30.5 cm by a force of 300 N. find the strain energy of wire

Analyze the question A wire is stretched by a force, and we need the energy stored in it (strain energy, also called elastic potential energy).

Concept For a wire obeying Hooke's law, the strain energy equals the work done in stretching it:

Strain energy = ½ × F × e

where F is the force and e is the extension.

Solution

• Original length = 30 cm
• New length = 30.5 cm
• Extension, e = 30.5 − 30 = 0.5 cm = 0.005 m
• Force, F = 300 N

Energy = ½ × 300 × 0.005 = ½ × 1.5 = 0.75 J

Answer 75 J)**.

Common mistake Many students forget to convert cm to m. Using 0.5 cm directly gives 75 J (option C), which is wrong. Always convert to metres when the answer is in joules.

Tip Remember that strain energy is the area under the force-extension graph, which is a triangle: ½ × base × height = ½Fe. Do not use F × e, because the force increases gradually from 0 to 300 N rather than staying constant.