# 1.3 Mass and weight

Mass

The mass of a body is the quantity of matter it contains.  It is constant for a body irrespective of its position and surroundings. By the ‘mass’ of an object, we mean how much material is present in it. It is constant everywhere in the universe.

The mass of a body is measured by a beam/Physical balance by comparing it with a known standard mass.

S.I unit : kilogram (Kg)

Weight

Weight is the gravitational force acting on a body mass. Transforming Newton’s Second Law related to the weight as a force due to gravity can be expressed as

Weight = mass x gravitational force

W = m g

where

W = weight(newton)

m= mass (Kg)

g  = gravitational force ($m/s^{2}$)

Scientists often use the word ‘field’. We say that there is a ‘gravitational field’ around the Earth and that any object that enters this field will be attracted to the Earth.

The value of the gravitational field strength on Earth is 9.8 N/kg, though we usually round it up to 10 N/kg to make the calculations easier. A gravitational force of 10 N acts on an object of mass 1 kg on the Earth’s surface.

How do you weigh something?

The balance is level when the forces pulling down both sides are the same. In the balance shown, if the forces are of 10 N and 20 N on the one side balance the force of 30 N on the other side. The balance compares the weight of the objects on each side. If the balance is on the surface of the Earth, then the masses of these objects are 1 kg and 2 kg on one side, and 3 kg on the other. So the balance also allows you to compare masses.

A spring balance can also be used for weighing things but works in a different way.

The top of the spring is hung from a hook, and the spring is stretched by the weight of the pan attached to its lower end. The scale can then be adjusted so that the pointer is aligned with the ‘zero’ mark.

For example, a 3 Kg mass is placed in the pan, the spring stretches further due to the extra weight, and the new pointer position can be marked. In the spring balance shown, the pointer should be at the 30 N mark if the scale is set correctly. If this balance were moved to the Moon, the weight would be less, and the spring would not stretch so far. In fact, the pointer would indicate a weight of 4.8 N.

So the spring balance measures the weight of the object in newtons. For non- scientific use, these balances are often given a scale that indicates the mass of the object in kg, without the need for any calculations. This scale gives the correct mass on the surface of the Earth, but would definitely not give the correct mass if the spring balance were moved to the Moon.