Changing shape
- To stretch, bend or compress an object, more than one force must be applied to it.
- Elastic deformation: the object returns to its original shape when the forces are removed.
- Inelastic deformation: the object does not return to its original shape when the forces are removed.
Hooke's law
- The extension of an elastic object, such as a spring, is directly proportional to the force applied, provided the limit of proportionality is not exceeded.
- F = k e: force (N) = spring constant (N/m) × extension (m).
- A stiffer spring has a bigger spring constant. The same equation applies to compression.
- Beyond the limit of proportionality, the force–extension graph curves and extension is no longer proportional to force.
Energy in springs
- A force that stretches or compresses a spring does work, and elastic potential energy is stored in the spring.
- Provided the spring is not inelastically deformed, the work done equals the elastic potential energy stored: Eₑ = ½ k e².
- The area under a force–extension graph (up to the limit of proportionality) equals the energy stored.
Required practical: force and extension
- Hang a spring from a clamp stand next to a vertical ruler. Record the position of the bottom of the spring with no load.
- Add masses one at a time (for example 100 g = 0.98 N) and record the new position each time.
- Extension = new length − original length. Plot force against extension; the gradient of the straight part is the spring constant.
- Wear eye protection, and don't overload the spring.
Key terms
- Elastic deformation
- A change of shape that is reversed when the forces are removed.
- Inelastic deformation
- A change of shape that remains when the forces are removed.
- Extension
- The increase in length of a spring or elastic object.
- Spring constant
- The force needed per metre of extension, in N/m.
- Hooke's law
- Extension is directly proportional to force, up to the limit of proportionality.
- Limit of proportionality
- The point beyond which extension is no longer proportional to force.
- Elastic potential energy
- Energy stored in a stretched or compressed object: Eₑ = ½ke².