The Newton Spring Balance and Hooke’s Law

Professor Mac with a Newton spring balance

Welcome to my post on Hooke’s law and the Newton spring balance. I have released a video to bring this information to life and you may watch this at the bottom of the post. So what is Hooke’s law and what is a Newton spring balance?

The Newton spring balance is used to measure force. This is achieved using a law known as Hooke’s law. The importance of this law may not be obvious to you, but it is used in the design of most items you use every day. By studying the Newton spring balance we may appreciate the way in which the law works and how to use it to measure force.

When you touch an object, you apply a force on the object, whether that object is the key of a computer keyboard, a door handle, a bed or any of the hundreds of items you interact with each day. When you remove that force, by removing your touch, do you see a permanent change in the shape of the object?  Probably the answer is “No”. You would only see a permanent change in shape if you exerted a force large enough to cause damage. The most obvious example of this is when you use a door handle to release a latch and open a door. The handle rotates and then, when you let it go, it returns automatically to its original position. Have you ever wondered why it does that? Well this is because you have just witnessed Hooke’s law in action!

So let’s understand more about Hooke’s law by examining how the Newton spring balance works.

The Newton Spring Balance

In the figure below you can see the Newton spring balance in my laboratory. At the top of the spring balance there is a fixed end and at the bottom a  free end which moves when a force is applied to it. The important feature of the Newton spring balance is, unsurprisingly, the spring.

The Newton spring balance supported from a metal frame

When a force is applied to the spring it extends; the larger the force, the greater the extension.

The spring extends when a force is applied to the Newton spring balance

The relationship between the force applied and the extension of the spring is governed by Hooke’s law. To establish this relationship we need to measure the relationship between force applied and extension. We do this by adding a series of masses, which increases the force on the spring, and we plot this force against the increase in spring extension.

Plotting the applied force against the spring extension

Hooke’s Law

As we add more masses and increase the force applied to the Newton spring balance we have more points to plot on the graph. As seen in the figure below, the points all lie on a straight line, and this is what Hooke’s law defines as the relationship between force and spring extension. Mathematically Hooke’s law is expressed as the force on the spring (F) equals the extension of the spring (x) multiplied by a constant (k) known as the spring constant.

Hooke’s law uses the spring constant to relate spring force to spring extension

The spring constant k is the slope of the line in the force vs spring extension graph. It is calculated by dividing the change of force by the change in spring extension. For the example in the figure below, this is calculated by dividing 5 newtons by 50 mm, which gives a spring constant for this Newton spring balance of 0.1 newtons per mm extension.

The spring constant is calculated by calculating the slope of the line in the force vs spring extension graph

This gives Hooke’s law for this Newton spring balance as “applied spring force” equals 0.1 times the “spring extension”. It is a unique property of this Newton spring balance since all springs have a unique spring constant. The process which has been used above has calibrated the spring. This means that we have established the relationship between applied force and spring extension by conducting a calibration experiment. The reason it is called a “Newton” spring balance is because the spring balance has been calibrated to measure force in newtons.

What do you do with Hooke’s Law?

Once you have calculated Hooke’s law for a Newton spring balance you may then predict the force on the spring by measuring the extension of the spring.

A scale is used to measure the spring extension

It is also possible to use Hooke’s law to convert this scale from measuring spring extension, to a scale which directly measures spring force.

My video

To bring all of this to life I have released a video which you may watch below. In the video you will see how to develop Hooke’s law for a Newton spring balance. You will then see how to use the law and the spring balance to predict the weight of an object of unknown mass. I hope you enjoy it.

All the best. Mac