Weight | Mass

 

The weight and mass of a body are important quantities which affect the force that could act on it. While the weight and mass of a body are sometimes used interchangeably, they are however different technically.

The weight of a body is the force of gravity exerted on a body, causing it to fall freely to the Earth’s centre with acceleration due to gravity, g.

Stating it mathematically,

W (weight) = m (mass) g (acceleration due to gravity)

Therefore,                W = mg

Since weight is a force, its unit is also the Newton. g, the acceleration due to gravity is same for all bodies, irrespective of the size of their masses, when they fall freely under the force of gravity.

 The value of g is approximately 9.8 m/s2.

However, the values of g on an object differ slightly at different positions or places on the Earth. This gives rise to the difference between weight and mass.

Difference Between Weight And Mass

As was said earlier, the weight of a body is the force of gravity on it, causing it to fall with an acceleration due to gravity. The value of the weight of a body is the product of its mass and acceleration due to gravity.

i.e., W = mg

For the fact that acceleration due to gravity, g differs slightly from place to place on the Earth, the weight of a body also differs, depending on where on Earth the body is.

For instance, a body at the Poles will have a greater weight than when it is at the Equator. As a matter of fact, the weight of a body decreases as you go from the Polar Regions of the Earth to the Equator, because acceleration due to gravity, g, of the body decreases from the Poles towards the Equator.

Here are the reasons why acceleration due to gravity, g, decreases from the Poles to the Equator: 

  1. Since the Earth is spinning, part of the weight of a body at the Equator is used up in providing the centripetal force to keep it moving in a large circle. Though the effect of this is small, it however reduces the value of g slightly.

  1. The radius at the Equator is greater than at the Poles, making objects at the Equator to be farther from the Earth’s centre than at the Poles. The implication of this is that acceleration due to gravity, g, is less at the Equator than at the Poles.

In the case of mass, the mass of a body is the quantity of matter in it. The mass of a body remains the same irrespective of the place on the Earth or universe it is – whether at the Poles or the Equator, the mass of a body doesn’t change.

In fact, while the weight of a body will differ on the moon or other planets where the value of acceleration due to gravity, g, is different, its mass will remain the same.

 Apparent Weight And Weightlessness

We can demonstrate the concept of apparent weight and weightlessness of a body by using the lift or elevator system.

A boy on a lift or elevator will experience two forces on him.

1)  The force of gravity pulling him down, i.e. his weight W, and 2) the reaction of the floor of the lift on him, R, acting upward. 

  • If the lift is still, or moving at constant velocity,                                 then  W = mg = R

  • If the lift moves upward with acceleration, a, then the force on the boy will be        F = R-mg = ma

Therefore,              R = ma + mg

 Or                         R = m(a+g)

The Apparent Weight of the boy when the lift accelerates upward is therefore,

W = R = m(a+g), indicating that the boy appears to weigh more under this condition. 

  • if the lift goes downward with acceleration, a, the force on the boy is given as

 F = mg – R = ma

 R = mg – ma

R = m(g – a)

 The Apparent Weight of the boy is

 W = R = m(g-a), indicating that the boy weighs less under this condition.

From the above equation, if the acceleration, a, the lift descends with equals g, then Apparent Weight, W will become zero.

The condition where Apparent Weight equals zero is known as weightlessness. This condition is normally experienced by astronauts in outer space.

See calculation of force based on Apparent Weight here.