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A uniform plank (Young's modulus Y, cross-sectional area A) is pushed across a smooth horizontal surface by a constant horizontal force F applied at one end. What is the compressive strain in the plank at the end where the force is applied (the maximum strain, in the direction of F)?

1. F / (A*Y)
2. 2F / (A*Y)
3. (1/2) * (F / (A*Y))
4. 3F / (A*Y)

Correct answer: F / (A*Y)

Solution

At the driven end the section must transmit the full force F to the rest of the plank, so stress = F/A and strain = F/(A*Y).

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