Extension Calculator

Hooke's Law Extension Calculator

Use this calculator to determine the extension of a spring or elastic material when a force is applied, based on Hooke's Law.

Understanding Hooke's Law and Extension

Hooke's Law is a fundamental principle of physics that describes the elasticity of materials. It states that the force (F) required to extend or compress a spring by some distance (x) is directly proportional to that distance. This relationship is expressed by the formula: F = kx, where 'k' is the spring constant.

In simpler terms, the more force you apply to an elastic object like a spring, the more it will stretch or compress. The 'spring constant' (k) tells you how stiff the material is; a higher 'k' means a stiffer spring that requires more force to achieve the same extension.

The Formula Used

This calculator uses a rearranged version of Hooke's Law to find the extension:

Extension (x) = Force (F) / Spring Constant (k)

Where:

• Extension (x): The change in length of the spring or elastic material from its equilibrium (unstretched) position, measured in meters (m).
• Force (F): The external force applied to the material, measured in Newtons (N). This could be the weight of an object, a push, or a pull.
• Spring Constant (k): A characteristic property of the spring or material, representing its stiffness. It is measured in Newtons per meter (N/m).

How to Use the Calculator

1. Enter Force Applied: Input the magnitude of the force being applied to the spring or elastic material. Ensure this value is in Newtons (N).
2. Enter Spring Constant: Input the spring constant of the material. This value is unique to each spring and indicates its resistance to deformation. Ensure this value is in Newtons per meter (N/m).
3. Click "Calculate Extension": The calculator will instantly display the resulting extension of the material in meters.

Practical Examples of Extension

Let's explore how Hooke's Law applies in various scenarios:

• Example 1: A Simple Door Spring
  Consider a door closer spring with a spring constant of 200 N/m. If you apply a force of 10 Newtons to open the door slightly, the extension of the spring would be:
  Extension = 10 N / 200 N/m = 0.05 meters (or 5 cm)
• Example 2: Industrial Shock Absorber
  An industrial shock absorber might have a very high spring constant, say 50,000 N/m. If it needs to absorb a sudden impact force of 10,000 Newtons, the extension (compression) would be:
  Extension = 10000 N / 50000 N/m = 0.2 meters (or 20 cm)
• Example 3: A Fishing Rod Tip
  The tip of a fishing rod acts like a spring. If its effective spring constant is 5 N/m and a fish pulls with a force of 0.5 Newtons, the tip's extension would be:
  Extension = 0.5 N / 5 N/m = 0.1 meters (or 10 cm)

This calculator provides a quick way to understand and apply Hooke's Law, helping you predict how much an elastic object will deform under a given load.

Calculated Extension:

' + extension.toFixed(4) + ' meters