In the 19th-century, while studying springs and elasticity, English scientist Robert Hooke noticed that many materials exhibited a similar property when the stress-strain relationship was studied. There was a linear region where the force required to stretch the material was proportional to the extension of the material. This is known as Hooke’s Law. In this article, let us learn about Hooke’s law in detail.
Table of Contents
What is Hooke’s Law?
Hooke’s Law Experiment
Hooke’s Law Solved Example
Hooke’s Law Graph
Hooke’s Law Applications
Hooke’s Law Disadvantages
Frequently Asked Questions – FAQs
What is Hooke’s Law?
Stress and strain take different forms in different situations. Generally, for small deformations, the stress and strain are proportional to each other, and this is known as Hooke’s Law.
Hooke’s law states that the strain of the material is proportional to the applied stress within the elastic limit of that material.
When the elastic materials are stretched, the atoms and molecules deform until stress is applied, and when the stress is removed, they return to their initial state.
Mathematically, Hooke’s law is expressed as:
F = –kx
In the equation, F is the force, x is the extension in length, k is the constant of proportionality known as the spring constant in N/m.
Interested to learn more about spring? Below are the links:
Potential Energy Of A Spring
Elastic Potential Energy And Spring Potential Energy
Hooke’s Law Experiment
Consider a spring with load application, as shown in the figure.
Depending on the material, different springs will have different spring constants, which can be calculated. The figure shows us three instances, the stable condition of the spring, the spring elongated to an amount x under a load of 1 N, and the spring elongated to 2x under a load of 2 N. If we substitute these values in the Hooke’s law equation, we get the spring constant for the material in consideration.
Hooke’s Law Solved Example
A spring is displaced by 5 cm and held in place with a force of 500 N. What is the spring constant of the spring?
Solution:
We know that the spring is displaced by 5 cm, but the unit of the spring constant is Newtons per meter. This means that we have to convert the distance to meters.
Converting the distance to meters, we get
5 cm = 0.05 m
Now substituting the values in the equation, we get
F = –k.x
500 N = – k x 0.05 m
Now, we need to rework the equation so that we can calculate the missing metric, which is the spring constant, or k. Looking only at the magnitudes and therefore omitting the negative sign, we get
500 N/0.05 m = k
k = 10000 N/m
Therefore, the spring constant of the spring is 10000 N/m.
Hooke’s Law Graph
The figure below shows the stress-strain curve for low carbon steel.
From the origin till the proportional limit nearing yield strength, the straight line implies that the material follows Hooke’s law. Beyond the elastic limit between proportional limit and yield strength, the material loses its elasticity and exhibits plasticity. The area under the curve from origin to the proportional limit falls under the elastic range. The area under the curve from a proportional limit to the rupture/fracture point falls under the plastic range.
The material’s ultimate strength is defined based on the maximum ordinate value given by the stress-strain curve (from origin to rupture). The value provides the rupture with strength at a point of rupture.
The video explains to you the general stress-strain graph of an elastic material experiencing tensile load and what are various stages in it. Within the elastic limit it follows Hooke’s law. As we keep on increasing the load, other stages and points like proportionality limit, yield point, fracture point, ultimate tensile strength are achieved, and they have been well explained in this video.
Hooke’s Law Applications
Following are some of the applications of Hooke’s Law:
It is used as a fundamental principle behind the manometer, spring scale, and the balance wheel of the clock.
Hooke’s law sets the foundation for seismology, acoustics and molecular mechanics.
Hooke’s Law Disadvantages
Following are some of the disadvantages of Hooke’s Law:
Hooke’s law ceases to apply past the elastic limit of a material.
Hooke’s law is accurate only for solid bodies if the forces and deformations are small.
Hooke’s law isn’t a universal principle and only applies to the materials as long as they aren’t stretched way past their capacity.
Frequently Asked Questions – FAQs
Q1
Does Hooke’s Law apply to all materials?
Hooke’s spring law applies to any elastic object of arbitrary complexity, as long as a single number can express the deformation and the stress.
Q2
Is Hooke’s Law linear?
Hooke’s Law is linear. Hooke’s law states that the restoring force is proportional to the displacement.
Q3
When does Hooke’s Law fail?
Hooke’s law applies to a perfectly elastic material and does not apply beyond the elastic limit of any material.
Q4
Why is Hooke’s Law negative?
In Hooke’s law, the negative sign on the spring’s force means that the force exerted by the spring opposes the spring’s displacement.
Q5
Why do we need Hooke’s Law?
Hooke’s Law is essential because it helps us understand how a stretchy object will behave when stretched or compacted.
Q6
Why are the bridges declared unsafe after a long use?
Due to repeated stress and strain, the materials used in the bridge loses elastic strength and ultimately may collapse. Hence, bridges are declared unsafe after long use.
Q7
How are we able to break the wire due to repeated bending?
When the substance is subjected to repeated strain, the elastic properties of the material get greatly impaired. This property is called elastic fatigue. Thus, we are able to break the wire by repeated bending.
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Mathematically, Hooke's law states that the applied force F equals a constant k times the displacement or change in length x, or F = kx. The value of k depends not only on the kind of elastic material under consideration but also on its dimensions and shape.
Hooke's Law experiment involves stretching a spring and measuring the amount of force needed to produce a given amount of stretch. By comparing the force applied with the resulting change in length, scientists can understand how materials behave under different conditions.
Hooke's law states that the strain of the material is proportional to the applied stress within the elastic limit of that material. When the elastic materials are stretched, the atoms and molecules deform until stress is applied, and when the stress is removed, they return to their initial state.
EXPLANATION: Hooke's law states that within the elastic limit stress is directly proportional to strain. Hence, option 1 is the answer. The ratio of stress to strain is known as an elastic modulus.
To calculate price elasticity, divide the change in demand (or supply) for a product, service, resource, or commodity by its change in price. That figure will tell you which bucket your product falls into.
This illustrates that as applied stress on material increases the strain also increases linearly and after a certain point that is elastic or yield limit the curve becomes non-linear.
Hooke's Law Formula: The formula for Hooke's Law is that force is equal to the negative of the spring constant multiplied by the displacement. The negative sign indicates it is a restoring force that is always opposite the direction of displacement.
Normally you plot extension along the x axis and load on the y axis. If the material behaves according to Hookes Law it should be a roughly straight line through the origin. At higher loads it will probably curve over something like this but the exact shape will depend on the material.
elasticity, ability of a deformed material body to return to its original shape and size when the forces causing the deformation are removed. A body with this ability is said to behave (or respond) elastically.
Ans : Hooke's law can be used to compute elasticity: F = KL. The elongation is denoted by L, and a highly elastic material, such as rubber, has a very low value of k because it can be stretched readily with a tiny force.
The elastic force can be calculated using the following equation F = ke, where k is the spring constant and e is the extension caused by an external force.
It's used to determine stability or instability in a spring, and therefore the system it's intended for. As a formula, it reworks Hooke's Law and is expressed through the equation: k = – F/x. Where k is the spring constant, F is the force applied over x, and x is the displacement by the spring expressed in N/m.
According to the theory of elasticity, stresses and strains are generalized as ε ij = f(σ ij ), γ ij = f(τ ij ), σ ij = f(ε ij ), and τ ij = f(γ ij). These quantities are treated as second-rank tensors, and the matching mathematical framework of tensor analysis can be found elsewhere [3, 4].
By convention, the minus or negative sign is present in F= -kx. The restoring force F is proportional to the displacement x, according to Hooke's law. When the spring is compressed, the coordinate of displacement x is negative. Zero when the spring is at its normal length.
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