# Free Tutorial in Basic Physics - Mass and Weight

Mass and weight are some of the fundamental concepts in Physics. They are related to each other and this tutorial article in basic Physics tries to provide a clear understanding of these closely related entities in an informative and easy-to-understand way.

### Introduction

Mass is the fundamental property of an item or body. It is actually the amount of the matter in it. Every matter or item is comprised of some material that has its own characteristic properties. The same volume of different materials has remarkably different masses depending upon the material with which it is composed of. The mass in a piece of iron is much larger than the same-sized wooden piece. We get the indication of the mass of a body by the weight which is actually the force with which the Earth is pulling it. In this lesson, we will learn about mass and weight in detail and learn other concepts that are associated with them.

### Mass and weight

The mass of a body is measured in units like gram or kilogram (1 kilogram = 1000 gram) or pounds or ounce (1 pound = 16 ounces) etc. It denotes the material contained in a body. If the material is having 100 grams of mass in it then the same material having double the mass will have 200-gram of mass. Another point worth noting here is that every material has a volume also that is its dimensions - how long it is or how thick it is or how big or small it is and when we see it we feel it but we cannot ascertain its mass just like that because mass is an inherent characteristic and some big appearing volumes could have smaller masses while some small looking objects might have higher masses. For example, a piece of plastic is having very little mass while a piece of same-sized iron has more mass.
Generally, students get confused while understanding mass and weight and use these two terms interchangeably. But there is a big difference as the mass is the quantity of material in a body while weight is the force with which it is being pulled or attracted to the Earth. Remember that mass is the quantity of material in units like gram or kilogram and any other such unit but weight is a force and it has a different unit like gram-force or kilogram-force or dyne or Newton etc. As we said that weight is the force with which it is attracted or pulled by the Earth so let us now understand this force in more detail.

### Understanding weight in more detail

We had learnt about gravity in one of our earlier tutorials. Let us again understand that the force of gravity of Earth pulls things towards it. That is the reason that we are glued to the Earth and are not free to move up until we do efforts to jump with our body against that gravitational force. Earth is a huge body and it attracts us with a good amount of this force that we feel like our weight. Due to the continuous gravitational force of Earth on a body, a free-falling body gets an acceleration and then falls on the surface of the Earth with some velocity that it had acquired during that time. It is obvious that if a body falls from greater heights its velocity will be more when it strikes the Earth's surface. In Physics we define the force (F) applied on a body as equal to its mass (m) multiplied by acceleration (a) produced in the body by that force and is represented by the popular equation -
F = ma
The acceleration produced in a free-falling body on the Earth is called 'acceleration due to gravity' and is denoted by 'g' and its value is about 9.81 metre per second square at the surface of the Earth.
So, our weight (w) is nothing but the force equal to our mass (m) multiplied by the value of g. Based on the formula F = ma, we can write weight in form of a formula as -
w = mg
We have to remember this equation and then there will be a clear-cut distinction between mass and weight in our minds.

The acceleration due to gravity (g) is created by the force of attraction on a body by Earth. The gravitational force applied by Earth on a body is proportional to its mass but inversely proportional to the square of its distance from the Earth. So if a body is far from the Earth in the sky then it is obvious that the force of attraction will be less than what it would have been on the surface of Earth and from it, this can be inferred that the value of g starts decreasing when we go up. Similarly, if a body is inside the Earth then the force of attraction on the body is such that it also gives a slight reduction in the value of g when we go deeper inside the Earth say as in a deep well. Further, Earth is slightly elliptical on the poles and due to that its force of attraction at the poles as compared to the equator is also slightly different and that also creates a difference in the value of g between these places. As these differences are of minor nature for our practical application on the surface of the Earth we take its average value as 9.81 metres per second square.

### Units of mass and weight

There are many different units of mass and weight but in MKS system the unit of mass is in kilogram (kg) and the unit of weight is in Newton. In common communication, we use the unit kg-force for the weight but many people skip using the word 'force' with mass and use simply kg for it which is scientifically incorrect but is in great practice. So, we have to remember that whenever in common communication we say that the weight of a body or object is say 50 kg then what we mean is 50 kg-force which is actually 490.5 Newton (1 kg-force = 9.81 Newtons).
In CGS system the unit of mass is gram and the unit of weight is gram-force known as dyne (1 gram-force = 1 dyne). In FPS system the unit of mass is a pound and the unit of weight is the pound-force.
Some other common conversions for weight between some of these units are —-> 1 Newton = 100000 dynes and also 1 Newton = 0.225 pound-force.

### Does weight change from place to place

This is the question that students often ask and the answer is that weight is the force and if that force changes then the weight would also change. For example on Moon, the force of gravitational attraction is less as Moon is not as massive a body as Earth. So the weight of a body is significantly reduced on Moon. Astronauts felt it and they did not feel inconvenient because they were trained about this aspect before landing there.

On the Moon where the acceleration due to its gravity is about one-sixth of that of Earth, the weight of a body on the Moon also becomes one-sixth of the weight that it had on Earth. So a man weighing 84 kg on Earth will have only 14 kg weight on Moon. He would feel so light there and could even jump more. Let us now consider one of the planets Jupiter of our solar system. Jupiter is a very massive body far bigger than Earth and its gravitational attraction is 25 times more than that of Earth and it is obvious that a person of weight 84 kg will have an enormous weight of 2100 kg on Jupiter! He would simply be glued there and not able to move.

### Conclusion

Mass is the amount of matter in a body or object and weight is the force with which it is being pulled down by the Earth. If we know the mass of a body then we can find out about its weight depending upon the acceleration due to gravity at that place.

 How does a rocket that has gone out of the Earth's gravitational field return to Earth?The rocket will have extra rocket firing systems in it which would fire when they are to be sent back to Earth. Why does a weight kept on a slope sometimes not slide down?If the frictional resistance of the slope surface is more than the component of weight force in the direction of the slope surface, then such a thing is possible. If a body is just kept on the surface of the Earth, then what are the forces acting on it?There will be two forces on it. One is the weight force of the body downwards. Second is the reaction force of Earth on it. The value of reaction force is same as that of the weight of the body. If Earth is having so much mass why does it not fall down?We are living on Earth and we have a feeling of falling down. For Earth, there is no such frame of reference as it is spinning around itself and moving around the Sun and there is no up or down for it. Earth has only a sense of 'towards the Sun' or 'away from the Sun'.