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Ee = ½ × k × e2
- The work done, or the elastic potential energy stored, while stretching or compressing a spring can be calculated using the equation: Ee = ½ × k × e2 Where: Ee = elastic potential energy in joules (J) k = spring constant in newtons per metre (N/m) e = extension in metres (m)
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What is a spring force calculator?
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How much force does a spring exert?
May 18, 2024 · We created the Hooke's law calculator (spring force calculator) to help you determine the force in any spring that is stretched or compressed. You can also use it as a spring constant calculator if you already know the force.
- Overview
- Key terms
- Hooke’s law
- How to analyze a spring force vs. displacement graph
- Common mistakes and misconceptions
- Learn more
Review the key concepts, equations, and skills for spring potential energy and Hooke's law. Understand how to analyze a spring force vs. displacement graph.
[What happens when a spring is stretched too far?]
The force required to stretch an elastic object such as a metal spring is directly proportional to the extension of the spring for small distances. The force exerted back by the spring is known as Hooke's law
F→s=−kx→
Where Fs is the force exerted by the spring, x is the displacement relative to the unstretched length of the spring, and k is the spring constant.
The spring force is called a restoring force because the force exerted by the spring is always in the opposite direction to the displacement. This is why there is a negative sign in the Hooke’s law equation. Pulling down on a spring stretches the spring downward, which results in the spring exerting an upward force.
The area under the force in the spring vs. displacement curve is the work done on the spring. Figure 1 shows a plot of force on the spring vs. displacement, where displacement is 0 when the spring is unstretched. The work done on a spring stores elastic potential energy Us in the spring until the spring goes back to its original length. Therefore, Us is equal to the work done and also to the area under the curve.
The area is a triangle with the following equation:
Us=12base⋅height=12x⋅kx=12kx2
Note that the spring constant k is the slope of the line since k=|F→||x→| .
Although the spring force is a restoring force and has a negative sign, the elastic potential energy Us cannot be negative. As soon as the spring is stretched or compressed, there is positive potential energy stored in the spring.
For deeper explanations of elastic potential energy, see our video introducing springs and Hooke's law and the video on potential energy stored in a spring.
To check your understanding and work toward mastering these concepts, check out the exercise on calculating spring force and the exercise on calculating elastic potential energy.
Within certain limits, the force required to stretch an elastic object such as a metal spring is directly proportional to the extension of the spring. This is known as Hooke's law and commonly written:
- nominal length = original/initial length
- It just tells us that the exerted by the spring will be in the opposite direction to the force applied.
- It varies between spring to spring, depending on what it is made of, the shape of the spring, and the width of the wire.
- gravity won't change the rigidity of the spring, so I think it is the same on other planets
- The nominal length is 50m. But the spring is being extended not compressed and therefore, the formula is L = Li + x= 50 mm +50 mm = 100 mm
- The spring has some length when it is relaxed, right? That's the initial length.
- I think we are only interested in the absolute value. You need not include the negative sign.
- Hooke's law doesn't say that the constant k is negative. The negative sign is only saying that the force is in the opposite direction of the displa...
- I think you're confused as to the difference between gravitational force and potential energy. Close enough to the Earth's surface, we always feel...
Dec 22, 2020 · The spring constant, k, appears in Hooke's law and describes the "stiffness" of the spring, or in other words, how much force is needed to extend it by a given distance. Learning how to calculate the spring constant is easy and helps you understand both Hooke's law and elastic potential energy.
When a spring is stretched or compressed, so that its length changes by an amount x from its equilibrium length, then it exerts a force F = -kx in a direction towards its equilibrium position. The force a spring exerts is a restoring force, it acts to restore the spring to its equilibrium length.
Discover the phenomena of springs and Hooke's Law. Explore how force applied to a spring results in compression or elongation, and how this relationship is linear. Uncover the concept of restorative force and how it counteracts applied force, keeping our spring in equilibrium. Created by Sal Khan.
- 10 min
- Sal Khan
Oct 10, 2023 · The Hooke's Law Calculator uses the formula Fs = -kx where F is the restoring force exerted by the spring, k is the spring constant and x is the displacement, or distance the spring is being stretched.
