Gravitation

05 Mass and Weight

Mass is one of the fundamental quantities in physics, and the most basic property of matter.
The mass of a body is the quantity of matter or material contained in it.
The SI unit of mass is kilogram.
It is a scalar quantity.
Themass of a body does not normally change at any time.
For certain extreme cases when a huge amount of energy is given or taken from a body, as in a nuclear reaction in which tiny amount of matter is converted into the huge amount of energy, it reduces the mass of the substance.

W = m \times g

The weight of a body is the force with which it is attracted towards the centre of the earth.
It is the measure of the force of gravity acting on a body.

Force = mass \times acceleration

W = m g

W = m \times g

= 1 kg \times 9.8 m / s^{2}

= 9.8 \times 1 kg \times 1 m / s^{2}

W = 9.8 Newton ‘ s (or 9.8 N)

Weight is a vector quantity.
Since the value of g (the acceleration due to gravity) changes from place to place, the weight of a body also changes from place to place.
Where , g=0 the weight of a body becomes zero and we feel true weightlessness.
Shape of the earth is not completely spherical, but an oblate spheroid.
So, a person standing at the equator is further away from the center of the earth than a person standing at the North Pole.
We know that acceleration due to gravity is proportional to the inverse of square of the distance between two objects.
So, a person standing at the North Pole would experience more weight as he is closer to the center of the earth than a person standing at the equator as g would be more in the first case.

Differences between Mass and Weight:

Mass	Weight
Mass can never be zero.	Weight can be zero. As in space if no gravity acts upon an object, its weight becomes zero.
Mass is a scalar quantity. It has magnitude.	Weight is a vector quantity. It has magnitude and is directed toward the center of the Earth or other gravity well.
Mass is commonly measured in kilograms and grams.	Weight is commonly measured in Newtons.
Mass doesn’t change according to location.	Weight varies according to location.
Mass may be measured using an ordinary balance.	Weight is measured using a spring balance.

Weightlessness:

Case 1:

In an elevator, we feels as if our weight is been reduced while the elevator goes down.
That is because the weight we feel is the perceived weight or “effective weight” which is the equal and opposite force that the floor exerts on you due to your weight.
If we remove the floor and let ourselves fall freely there is nothing to exert a force on and hence we will feel weightless even though there is acceleration due to gravity and mass.
This is because the effective weight is equal to zero.
When the elevator is going down it is actual moving in the direction of the gravity, hence reducing net acceleration due to gravity, thereby reducing our weight.

Case 2:

Astronauts in the international space station face a similar situation.
As the space stations are orbiting the earth it is actually falling towards the earth indefinitely and everything in it is falling including the astronauts.
So the astronauts experience weightlessness and can float freely around.
Thus, weight can increase or decrease depending on the acceleration due to gravity but the mass remains unchanged.