The Difference between Mass and weight

In our day to day use of language we often make no distinction between mass and weight. But in physics the two words mean different entities. In fact when we say that the weight of a bag of rice is 50 kg, we actually refer to their masses. In this respect the use of the word weight of an object is scientifically wrong. But what is the difference between mass and weight?

Definition of Mass in Physics

All objects are made of materials. Mass of an object refer to the amount of material present in an object. This property of the material does not depend on location, shape or state of motion, according to Newtonian physics. The mass of the objects depends on the number and kind of atoms and the bonds by which the object is formed. The international unit of mass is kg. A heavy mass is expressed in units of tones. One tone is 1000 kg. Small masses are expressed in units of gram. Thus the mass of your pencil is 5 gram. Thousand gram make one Kilogram. More appropriate meaning of mass comes from Newton’s law F = m×a.

Thus the mass of an object is the ratio of F and acceleration. If the mass is greater it resists the increase of velocity more for the same applied force. Mass is thus related to inertia of motion.

Definition of Weight

We know that if a body is thrown upward, it comes back to the earth. This is due to the weight of the body, which push the object towards the earth. We can say the force of gravity causes this downwards pull.

The force by which the earth attracts an object to its center is called its weight. If the mass of an object is m and the acceleration due to gravity at a place is g, the weight of an object is W = mg.

The unit of weight is newton. The weight of an object with mass 10 kilogram is,

W = 10 × 9.8 newton = 98 newton.

Generally we can determine the weight of an object by using a spring balance.

The difference between mass and weigh

The relation between mass and weight:

We know that the amount of material in an object is its mass. It is a constant parameter, which does not change due to change of its location to any height above the earth. If an astronaut has a mass 75 kg, it will remain unchanged when he is in the surface of the earth or on the surface of the moon or in an orbit of the moon or earth. The amount of material by which an astronaut is built does not change due to change of position and that is why its mass remain unchanged.

Since the mass of an object is constant, its weight changes due to change in the value of g. As he go more and more above the surface of the earth,the weight of an object becomes less and less. The reason for which the value of the acceleration due to gravity changes are also the causes of change in weight of an object. The weight of an object is not an fundamental parameter. For example, an object may have weight at one place and may not have any weight at another place. At the centre of the earth, the value of acceleration due to gravity is zero and therefore, the weight of an object there must also be zero. At a distant space, where there is no gravitational force, the weight of an object must be zero.

The Moon’s gravitational acceleration is about 1/6 of the Earth’s surface.

You can find out that weight of 1 kilogram of material at the surface of the moon is about 1.63 newton.

The Earth’s surface,

gravitational acceleration g = 9.8 ms⁻²

So, The Moon’s gravitational acceleration is g′ = g/6 = 9.8/6 ms⁻²

W = mg′

= 1×(9.8/6) = 1.63 N
The weight of an object at a location depends on a distance if the point of measurement from the center of the earth. If the distance is increased, the force of gravity due to earth at that point decreases. As a result, the weight of an object there decreases. At the surface of the earth the weight of mass 1 kilogram is 9.8 newton. But at a distant point from the earth, its weight decreases with the increase of distance.

The weight of an object vary slightly also at different positions on the surface of the earth. One reason for this is that, the earth is not a perfect sphere and the acceleration due to gravity is not same at all the points on the earth’s surface. However, this variation is so small that it can be detected only by using a very sensitive weighing machine. We neglect this variation in most of our calculation. An object will weigh maximum at the two poles. At these places one kilogram will weigh 9.83 newton. At the equator, this weight will be least with a value of 9.78 newton. At the equinoctial point, the weight is 9. 79 newton.

The weight of a body increases in proportion to its mass. Therefore, the instruments which are used to determine weight can also be used to measure the mass of the object. Often spring balance is calibrated in units of kilogram. Balances and weighing instruments are calibrated in such a way that we sometimes use the kg unit for measuring both mass and weight. It is of course wrong practice. Weight is a form of force and for scientific calculation it should be expressed in units of newton. When we buy a packet of rice or milk on which one kg is marked, we understand that each of these packets one kilogram mass. But their weights are not 1 kg. On the surface of the earth they will weigh 9.8 newton. These packets will weight different from planets to planets or on the moon, although their masses will remain unchange.

The difference between mass and weight, dimension unit 

Reference : NCTB