Understanding Parallel Springs & the Equal Extension Assumption"

[andyrk]

When springs in parallel are replaced by a new spring of a new effective spring constant, for the proof of this, i.e

k_eff=k₁+k₂​

Why do we assume the extension in the springs to be equal?

 

[Pythagorean]

If you imagine two adjacent blocks being held together by two springs, if you stretch the blocks apart, the springs stretch equally.

 

[andyrk]

In the attachment, why is the extension of the springs same?

 

[Pythagorean]

For the sake of the derivation, you assume that the little block is pulled evenly so that both springs are extended the same amount.

 

[Nickie]

I understand the concept of parallel springs and the equal extension assumption. When multiple springs are connected in parallel, the effective spring constant is equal to the sum of the individual spring constants. This is because the springs share the same load and therefore, the total extension is divided equally among them.

The assumption of equal extension in parallel springs is based on the principle of Hooke's law, which states that the force exerted by a spring is directly proportional to its extension. In this case, when multiple springs are connected in parallel, they all experience the same applied force. Therefore, the extensions of the individual springs must be equal for the total force to be distributed equally among them.

This assumption is also supported by the fact that parallel springs are typically designed and manufactured to have similar properties, such as length, material, and stiffness, which contribute to the equal extension assumption.

However, it is important to note that this assumption may not hold true in all cases. Factors such as manufacturing tolerances, variations in material properties, and uneven distribution of load can lead to unequal extensions in parallel springs. In such cases, more advanced mathematical models and experimental data may be needed to accurately determine the effective spring constant.

In conclusion, the equal extension assumption in parallel springs is a simplifying assumption that is based on the principles of Hooke's law and the design of the springs. While it may not always be perfectly accurate, it provides a good approximation for most practical applications.