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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.
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How do you calculate a spring constant using Hooke's law?
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Jun 20, 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.
Dec 23, 2022 · Learn about Hooke's law and how to calculate the spring constant, including the formula and insight on a spring's impact on force.
- Overview
- What is the formula for the spring constant?
- What is Hooke's Law?
- How does spring length affect the spring constant?
- Practice Problems
- Solutions to Practice Problems
- How do I display Hooke's Law on a graph?
1 What is the formula for the spring constant?
2 What is Hooke's Law?
3 How does spring length affect the spring constant?
If you push or pull on a spring and then let it go, it snaps right back to its original position. The
tells you how much force the spring exerts when it does that, but how do you figure out what the spring constant is? You're in luck because there's a simple formula you can use. Read on to learn how to apply the formula to find the spring constant, then try your hand with a few practice problems.
to find the spring constant for an ideal spring.
The formula to find the spring constant is
When you push or pull a spring, it bounces back to its original rest position or equilibrium. The spring constant, measured in
(Newton/meters or Newtons per meter), tells you the proportional force exerted by the spring that causes it to bounce back. These variables have a linear relationship:
Force (the force applied to the spring)
Hooke's law states that when a force compresses or stretches a spring, it will bounce back to its rest position with an equal and opposite force.
is known as the spring constant because it's always the same for a given spring. You can express this law mathematically with the equation
The negative symbol indicates that the force of the spring constant is in the opposite direction of the force applied to the spring. It does
indicate that the value is negative.
Hooke's law is actually pretty limited. It only applies to perfectly elastic materials within their elastic limit—stretch something too far and it'll break or stay stretched out.
Hooke's law is based on Newton's third law of motion, which states that for every action there is an equal and opposite reaction.
The spring constant is inversely related to the spring's equilibrium length.
This means that the longer your spring is, the less force it will need to bounce back to its rest position or equilibrium. A shorter spring, on the other hand, requires more force to bounce back. This makes sense if you think of springs you've encountered—the spring constant measures the stiffness of a spring, and short springs tend to be stiffer than long springs.
For example, if you cut a spring in half, its spring constant will double. If you doubled the length of the spring, on the other hand, its spring constant would be half what it was.
This also means that when you apply the same force to a longer spring as a shorter spring, the longer spring will stretch further than the shorter spring.
Since the spring constant is measured in
Use the equation for Hooke's Law without the negative symbol, which doesn't have a mathematical function:
If a person who weighs steps on a scale, the scale's spring compresses by . What is the spring constant of the scale's spring?
The person's weight is equivalent to the force applied to the spring.
Remember to convert the
since the spring constant is measured in
The spring constant is .
You aren't given the distance the spring is stretched when the first is added to it, but that doesn't matter because the spring constant is always the same. Plug the values for the second weight into the formula to find the spring constant:
The formula to find the spring constant is
Here, the force is
and the distance the spring stretches when that force is added is
, so your equation is
Hooke's Law describes a directly proportional linear relationship between the force exerted on a spring and the distance it moves.
Within this relationship, the spring constant is the slope of the line on a graph. The distance values are the coordinates and the applied force values are the coordinates.
If you're given a line that represents a spring that obeys Hooke's Law (also called an
), you can find the spring constant by finding the slope of the line using the basic slope formula
A line with a spring constant as a slope will always cross through the origin of the graph.
This article was reviewed by
This is known as Hooke's law and commonly written: F = − k x Where F is the force, x is the length of extension/compression and k is a constant of proportionality known as the spring constant which is usually given in N/m .
- 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...
The force exerted back by the spring is known as Hooke's law F → s = − k x → Where F s 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.
Apr 15, 2008 · We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need ...
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