How Does the Spring Constant Depend on the Length?

Suppose we have a spring of 6 cm with a spring constant k. What happens if we split the spring into two bits of equal size? There will be a new spring constant for one of these shorter springs, which will be 2k. More generally, a spring’s spring constant is inversely proportional to the spring’s length, assuming we are talking about a specific material spring and thickness.

This means that more the length of the spring, the lesser the force it will require to reach its equilibrium state and similarly vice versa.

So suppose we cut the spring exactly in two in the above example, making two shorter springs each 3 cm in length. A spring constant, which is twice the original, will be applicable for the smaller springs. That is because it is inversely proportional to the spring constant and the length of the spring. That means that on a shorter spring, the original mass of 30 gm would only yield a 1 mm stretch. The larger the constant of the spring, the smaller the extension that a given force generates. This is why smaller springs are more difficult to stretch!

Hooke’s Law Graph

The graph for Hooke’s law has been provided below. Here the material exhibits elastic behaviour up to the yield strength point, after which the material loses elasticity and exhibits plasticity.

This means that once we successfully apply a force larger than the threshold, the spring loses its elasticity and therefore further application of force will make the spring change its shape and retain it. When a material changes its shape and retains that shape when any force is applied to it, then this property is called plasticity.

Think of the items you have seen that are plastic. Once you apply force, it either bends or breaks. It makes no attempt to stretch back or go back into its original shape like a well functioning spring.

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The straight line implies that the material follows Hooke’s law from the origin to the proportional limit approaching yield power. The material loses its elastic existence beyond the elastic limit between the proportional limit and yield strength and begins to exhibit plasticity. The area from the origin to the proportional limit under the curve falls below the elastic range. Under the plastic range, the area under the curve is from a proportional limit to the rupture/fracture point.

To help the students with some of the quick and easy tips to study Physics, we have listed a few points that shall be considered to succeed in the preparation.

• Focus more on the basics of the topic, as you strengthen the basic concepts, the later journey becomes easier.
• Take a note of the small details, missing out on any of the concepts can cost you a lot.
• Always try to use some visual learning techniques such as flowcharts, drawings, diagrams etc to make learning fun and easy.
• Try to simplify the situations and focus on understanding what the questions are asking. Without that, you won’t be able to answer them accurately.
• Make use of different study resources, such as online study material, quizzes, your study notes, classroom videos etc. 
• Physics has a lot of practical learning and it involves the use of equations. Students shall make sure to learn and understand the equations and the related formulas.
• Another important skill to ace in this subject is strengthening your Maths skills. Since it comes with a lot of numerical based questions, you shall be quick and accurate with the calculations.

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