# Forces and Motion: Hooke's Law

## Forces and Motion: Hooke’s Law

• Hooke’s Law states that the force needed to extend or compress a spring by some distance is proportional to that distance.
• This relationship holds as long as the elastic limit/elastic deformation of the spring is not exceeded.
• The elastic limit is the maximum extent to which a solid material may be stretched without permanent deformation.
• Extensions beyond the elastic limit lead to plastic deformation where the material does not return to its original shape and size after the force is removed.
• The formula for Hooke’s Law is F = kx where: F is the force applied in Newtons (N), k is the spring constant in Newtons per meter (N/m), and x is the extension or compression distance in meters (m).
• The spring constant (k) tells you how stiff a spring is. It is the ratio of the force applied to the spring to the displacement caused by it.
• If the graph of force against extension for an object is a straight line that passes through the origin, the object is obeying Hooke’s Law.
• In such a graph, the gradient is equal to the spring constant (k).
• When a material or spring does not obey Hooke’s Law, it is said to be non-linear or have non-linear elasticity.
• Examples of situations where Hooke’s Law applies include the extension of a spring under load or the bending of a beam.
• Understanding Hooke’s Law is crucial when designing structures and materials that must withstand certain amounts of force without deforming, including bridges, buildings, and vehicle suspension systems.