Work done and elasticity

Physics · Forces. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Work is done when a force moves an object through a distance. Doing work transfers energy. Work done against friction raises the temperature of the object and its surroundings.

To stretch, bend or compress an object, more than one force must act. A single force would only make it accelerate. If the object returns to its original shape when the forces are removed, the deformation is elastic. If it stays changed, the deformation is inelastic.

For a spring, the extension is directly proportional to the force, up to the limit of proportionality. Beyond that point the force–extension graph is no longer a straight line.

Rules to remember

work done = force × distance moved along the line of action of the force (W = Fs).
1 joule = 1 newton-metre: 1 N moving an object 1 m.
force = spring constant × extension (F = ke); k in N/m, e in m.
extension = stretched length − original length.
elastic potential energy = ½ × spring constant × extension² (E_e = ½ke²).
On a force–extension graph, the straight line through the origin shows F is proportional to e; it ends at the limit of proportionality.

Common mistake

Students use the total length of the spring instead of the extension, or leave the extension in centimetres. Subtract the original length first and convert to metres.

Worked example

A spring has a spring constant of 40 N/m. It is stretched by 15 cm, within its limit of proportionality. Find the force needed and the energy stored.

Convert: 15 cm = 0.15 m.
F = k × e = 40 × 0.15 = 6.0 N.
E_e = ½ × k × e² = 0.5 × 40 × 0.15² = 0.5 × 40 × 0.0225 = 0.45 J.

Answer: Force 6.0 N; energy stored 0.45 J

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