Define the spring constant as force per unit extension; recall and use the equation k = F / x

1.5.1 Effects of Forces – Spring Constant

What is the Spring Constant?

The spring constant, denoted by k, tells us how stiff a spring is. It is defined as the force required to stretch or compress the spring by one unit of length. Mathematically: $$k = \frac{F}{x}$$ where F is the applied force (in newtons, N) and x is the extension or compression (in metres, m).

Analogy: The Rubber Band

Think of a rubber band.

  • If you pull it gently, it stretches a little – low k.
  • If you pull it hard and it resists strongly, it’s a high k spring.
The more “stiff” the rubber band, the more force you need for the same stretch. This is exactly what the spring constant measures.

Units & Quick Check

Quantity Symbol Units
Force F N (newtons)
Extension/Compression x m (metres)
Spring Constant k N m⁻¹ (newtons per metre)

Step‑by‑Step Example

  1. Pull a spring until it stretches 0.05 m and feel the force you apply: 2.0 N.
  2. Insert the values into the formula: $$k = \frac{F}{x} = \frac{2.0\,\text{N}}{0.05\,\text{m}} = 40\,\text{N m}^{-1}$$
  3. Interpret: The spring has a stiffness of 40 N m⁻¹ – it’s fairly stiff.

Exam Tip 🚀

  • Always check units – if you get N m instead of N m⁻¹, you’ve mixed up the formula.
  • Remember: k is a constant for a given spring; it doesn’t change with the amount of stretch.
  • When a question asks for the force needed to stretch a spring a certain distance, rearrange the formula: $$F = kx$$
  • Use the “rubber band” analogy to explain why a higher k means a stiffer spring.

Revision

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