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Elastic Strings and Springs

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  Edexcel IAL Mechanics 3 (WME03)

Elastic Strings and Springs

The big idea: Tension is proportional to extension, and the energy stored is the area under the tension–extension graph.

Summary — What This Chapter Covers
  • Hooke's law: T = λx/l (λ modulus of elasticity, l natural length).
  • Elastic potential energy = λx2/(2l).
  • A string can only be in tension; a spring can also be compressed.
1. Hooke's Law
Hooke

T = λx/l

In equilibrium, balance the tension against the other forces.

Worked Example

A 0.5 kg mass hangs at rest on an elastic string of natural length 0.8 m and modulus 24 N. Find the extension.

2. Elastic Potential Energy
EPE

Energy stored

Include EPE in work–energy equations alongside KE and gravitational PE.

Practice Question

Find the energy stored when that string is stretched by 0.2 m.

Memorise
Tension

λx/l

EPE

λx²/(2l)

Strings

Slack when x < 0

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