The difference between mass and weight

Commonly grouped under the generic term ‘weight’, the properties of mass and weight are actually completely different

(Image source: Pixabay)

Outside of the world of physics ‘weight’ is a generic term used to refer to an object’s mass – the amount of matter an object has, directly dictated by its amount of and type of atoms – and its weight, the force created when a mass is acted upon by a gravitational field. This is because most masses on Earth have weight and the relationship between the two factors is directly proportional – ie, the more massive an object is, the greater its weight. 

However, in the world of physics – which deals with objects of infinite mass under wildly varying forces, not just the relatively stable force of Earth’s gravity – mass and weight are distinct. To understand the distinction fully between mass and weight it is important to understand their fundamental principles.

Newton’s law of universal gravitation states that every massive particle in the universe attracts every other massive particle to some extent, and considering the size of Earth it has a pretty big pull. On Earth this resultant force is gravity (g) and its average numerical value is 9.81m/s2 – meaning that, ignoring air resistance, the speed of an object falling freely near the Earth’s surface increases by about 9.81 metres per second every second. However, gravity pulls down on both airborne and ground-based objects and this force acting upon a mass is an object’s weight.

For example, an apple has a mass of roughly 100 grams and on Earth that apple is pulled down by gravity at 9.81m/s2 , or roughly by the force of one newton (a newton is a unit of measurement equal to the amount of net force required to accelerate a mass of 100 grams at a rate of one metre per second per second). This means that the apple has a weight of one newton, but a mass of 100 grams. Equally, the average human weight in newtons is 700, while their average mass is 70kg. The human’s / apple’s weight is therefore the force of gravity acting upon their mass, while their mass is purely the amount of matter they are made up from.

In physics, however, there are objects that are not affected by Earth’s gravity, of varying atomic density and with a mass to weight ratio that is not directly proportional, hence the distinction.

Newton spring scale

(Image credit: Svjo)

As weight is technically a force – the force of gravity acting upon a mass – a different device is used to measure it accurately. The newton spring scale works by the principle of Hooke’s Law (the extension of a spring is in direct proportion to its load) and unlike a traditional set of scales, allows for the Earth’s gravitational pull on an object’s mass to be accurately determined.

Interestingly, however, because Earth’s gravitational field can vary depending on where you are (see the nearby map of the Earth’s southern ocean) and that weight is used generically on Earth to ascertain mass, industrial spring scales – which measure local weight – must be individually calibrated to be legally accepted in commerce. 

For example, at the Earth’s equator, acceleration due to gravity is measured at 9.7803, while in Aberdeen, Scotland, it is measured at 9.8322. This means that a produce’s mass would technically weigh more in Aberdeen than at the equator, making fine measurements difficult to attain.

This article was originally published in How It Works issue 12

For more science and technology articles, pick up the latest copy of How It Works from all good retailers or from our website now. If you have a tablet or smartphone, you can also download the digital version onto your iOS or Android device. To make sure you never miss an issue of How It Works magazine, subscribe today!