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You must have wondered at least once how spring can regain its normal shape even though you put huge force while stretching and compressing it. Why does one need to put additional stress to modify the position of the spring? This is the spring’s potential energy; its formula is illustrated as PE = force x displacement. Let us understand the physics behind the elastic substances such as springs in this article and look into spring potential energy and the spring formula.
Spring’s potential energy; its formula, and detailed definition
The potential energy of spring is a type of stored energy similar to electrical and gravitational potential energy. But, this energy is mainly associated with elastic objects like spring.
Suppose there is a vertically hanging spring from the ceiling. Someone, on the other hand, tries to pull it down.
You can quantify the exact stored energy due to this system. However, you’ll need to know how far the string gets pulled. Also, what reaction does that specific spring have when applied with an external force?
Note that spring potential energy depends on x, the distance spring has covered from its equilibrium position. The spring constant is k. The spring constant defines how much force a spring needs to take to extend by 1 m. It is expressed in the units of Newtons/meter.
The spring constant is based on Hooke’s law. It works as a force needed for the spring to stretch up to x meters from its respected equilibrium position.
The equation for the potential energy of spring
The equation for the potential energy stored in a spring when it is stretched or compressed is expressed as:
PEspring = F * x
Spring potential is a type of energy; hence, the result of the potential spring formula equation is measured in joules (J).
What is an ideal spring?
An ideal spring does not have any appreciable mass and friction. The idea in this spring formula defines the amount of work done to extend this spring.
The equation is similar to equations of rotational energy and kinetic energy.
But it replaces:
- v in the kinetic energy equation with x
- Mass m with spring constant k
How to find spring potential energy and its formula?
We can use a few simple steps to find spring potential energy; its formula with the help of Hooke’s law.
We know that:
The potential energy PE of spring is equal to work done by it.
And work done is the product of distance and force. Here we get before from Hooke’s law.
In this spring formula, displacement in the spring’s position is considered as the distance value.
Let’s take x as the distance/displacement from the position of equilibrium.
When spring is pulled at the distance x, the work done through the spring is calculated as:
W (work done) = 0∫x Fdx = -∫kx dx = -k(x)²/2
Next, we’ll find the amount of work done by the pulling force.
The work done due to the Fp (pulling force) is :
Fp = k (xm)²/ 2
The work done due to Fp (pulling force) is considered as positive. It is because it overcomes the spring force.
Thus,
W (Work done) = k x² / 2
In the case where distance/displacement is lesser than zero, then to find out work done by the force of spring:
Ws (Work done due to spring force) = – kx² / 2
To find out the work done amount due to the F (external force) is = + kxc²/2.
In the scenario where the object displacement from xi ( Initial displacement) to xf ( Final displacement) is provided, the work done is calculated as:
Ws = – xi∫xf kx dx = k xi²/2 – k xf ²/2
The above equation indicates that work done by the spring force is based on the displacement’s endpoints. Hence, we can deem the spring force the conservative force as it solely depends on original and final positions. This is why work done remains in the form of the spring’s potential energy.
Additionally, if we consider a cyclic process, the amount of work done by the force of spring becomes zero.
Conclusion
The potential energy of the spring formula is an essential topic in physics. Thus, we have tried to explain all the essential details about the potential energy of the spring formula. This article discussed the potential energy of a spring, its formula, and what makes a spring ideal. Take a look at the equation for the potential energy stored in a spring when stretched or compressed mentioned above. Also, we have compiled a set of commonly asked questions regarding the topic that you can check out below.
