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Dec 22, 2020 · The formula for Hooke’s law specifically relates the change in extension of the spring, x , to the restoring force, F , generated in it: F = −kx F = −kx. The extra term, k , is the spring constant. The value of this constant depends on the qualities of the specific spring, and this can be directly derived from the properties of the spring ...
- 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
Jun 21, 2023 · Calculation Step by Step. Measure the force applied on the spring in Newton (N). If the spring’s load is in kg, convert it into N by multiplying it with gravitational acceleration 9.81 m/s 2. Determine the displacement in the spring, the distance by which it is compressed or stretched.
Dec 23, 2022 · Hooke’s law gives the force a spring exerts on an object attached to it with the following equation: F = – kx. The minus sign shows that this force is in the opposite direction of the force that’s stretching or compressing the spring. The variables of the equation are F, which represents force, k, which is called the spring constant and ...
Hooke's Law is a principle that describes how elastic materials behave when they are stretched or compressed. In this article, you will learn how to use Hooke's Law to calculate the force, displacement, and spring constant of a spring system. You will also see some examples and applications of Hooke's Law in physics. Khan Academy is a free online platform that offers courses in various ...
- What is nominal length?nominal length = original/initial length
- I didn't understood what that minus in formula was for?It just tells us that the exerted by the spring will be in the opposite direction to the force applied.
- The spring constant is the same for all springs or different? explain.It varies between spring to spring, depending on what it is made of, the shape of the spring, and the width of the wire.
- is spring constant is same on another planet?gravity won't change the rigidity of the spring, so I think it is the same on other planets
- I have a question on example 2a. If the nominal length is 50mm, and the compression is of 50mm then ...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
- I don't understand what the length notations of springs refers to. For example, strain is defined as...The spring has some length when it is relaxed, right? That's the initial length.
- Why is k=E.A/L? if we put K = -F.x and E=stress/strain = (F/A)/(x/L) = F.L/(A.x) then we get -F.x = ...I think we are only interested in the absolute value. You need not include the negative sign.
- in exercise 1, when we divided F over K, why the K isn't negative as hooke's law said?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...
- In exercise 1, how come the F (force) is equal to mg, not mgh? When the person steps on, there is st...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...
2 days ago · You can now calculate the acceleration that the spring has when coming back to its original shape using our Newton's second law calculator. You can use Hooke's law calculator to find the spring constant, too. Try this simple exercise - if the force is equal to 60 N 60\ \mathrm{N} 60 N, and the length of the spring decreased from 15 c m 15 ...
The spring is not stretched beyond the limit of proportionality and it stretches by 15 cm. Calculate the spring constant. Show answer Hide answer. F = 3 N. e = 15 cm = 0.15 m. F = ke.
