Stress and strain

When a force is applied to a solid object, it can cause the object to change shape or size. This process is called deformation. Deformation can be caused by:

• Tensile forces: Pulling forces that stretch the object.
• Compressive forces: Pushing forces that squash the object.

For AS Level, we consider only one-dimensional deformations (along the length of a wire or rod).

Load, Extension, and Compression

• Load: The force applied to an object.
• Extension: The increase in length when a tensile force is applied.
• Compression: The decrease in length when a compressive force is applied.

The relationship between load and extension is often linear for small deformations.

Hooke’s Law

For many materials, within the limit of proportionality, the extension is directly proportional to the applied force.

Stress and Strain

To compare deformation in different materials, we use stress and strain, which are independent of the object's size.

• Stress ($\sigma$): The force applied per unit cross-sectional area.
• Strain ($\epsilon$): The extension per unit original length.

Young Modulus

The Young modulus ($E$) is a property of a material that measures its stiffness.

Experiment: Determining the Young Modulus of a Metal Wire

1. Set up: Suspend a long, thin wire vertically with a fixed support. Attach a scale to measure extension.

1. Measure:
   • The original length ($L$) of the wire.
   • The diameter ($d$) of the wire (use a micrometer to find the cross-sectional area $A = \pi d^2/4$).
2. Apply weights: Hang known masses to apply a force ($F = mg$).
3. Record extension: Measure the increase in length ($x$) for each load.
4. Plot graph: Plot force ($F$) against extension ($x$). The gradient gives the spring constant $k$.
5. Calculate Young modulus: Use the formula $E = \frac{F L}{A x}$.