# Hooke’s law

## Hookes law

Hook’s law states that the extension of a material is directly proportional to the applied force provided the elastic limit is not exceeded.
i.e. the material returns to its original length when the stretching force is removed, provide the elastic limit is not exceed

In short:𝐅𝐨𝐫𝐜𝐞∝𝐞𝐱𝐭𝐞𝐧𝐬𝐢𝐨𝐧

𝐅𝐨𝐫𝐜𝐞=𝐤(𝐞𝐱𝐭𝐞𝐧𝐬𝐢𝐨𝐧) 𝐅=𝐤𝐞

Where k is the proportionality constant or material constant in Nm-1, Where, F is the stretching force in newtons and e is the extension in metres. Extension,e=New length−Original length 𝒆=𝒍𝒏−𝒍𝒐.

It is also important to note that;

Where F1 is stretching force producing extension e1 and
F2 is stretching force producing extension e2 on the same material.

Example1:
A spring is stretched by 0.05m by a weight of 5N hung from one end.
(i) What weight will stretch it by 0.03m?
(ii) Determine the spring constant.

Solution:

Example 2:
A spring increases its length from 20 cm to 25cm when a force is applied. If the spring is constant is 100N/m. Calculate the force.

Solution:

Experiment to verify Hook’s law.

Original length of the spring lo is noted.

Then various loads are suspended on the spring and the corresponding new length, ln of spring for each is noted.
The extension, e produced is calculated from; Extension,𝒆=𝒍𝒏−𝒍𝒐
The readings are noted in a table below.

Thus, the load is directly proportional to the extension “e”. This verifies Hooke’s law.

A graph of load against extension

Explanation
Along OB, the load is proportional to extension in that the extension increases as the load increases.Point “B” is called elastic limit.

Beyond B (elastic limit), the graph is not a straight line meaning that extension is no longer proportional to the load. The material becomes plastic. This is indicated by a kink at C, which is called yield point.

Beyond C, the material behaves plastically. i.e. it does not regain its shape and size. Therefore, it undergoes plastic deformation. This goes on to the breaking point E.

Point D represents the maximum stress (Breaking stress) the material can withstand fracturing.

Explanation of sketch of load against extension according to kinetic theory

OB the molecules are pulled slightly farther apart but can move back to original position when stretching force is removed. The deformation is called elastic.

Beyond C, layers of atoms slip over each other. The molecule move farther apart but cannot move back to original position when stretching force is removed.

Tensile stress, Tensile strain and Young’s modulus.

Tensile stress:

Is the force acting per cross section area of a material. Its S.I unit is Nm-2 or Pa.

Tensile strain:
Is the ratio of extension to original length of a material. It has no units.