Weight, Freefall And Weightlessness

Weight

We know that every planets attract every objects towards their centres. The force with which an object is attracted towards the centre of the planet is called its weight. Its SI unit is Newton $(N)$ and its CGS unit is Dyne. It is a vector quantity. It is measured by using a spring balance.

If a body has mass $m$ then the weight of the body is given by,
$$W=mg$$ [where $g$ is acceleration due to gravity]

Weight is dependent upon acceleration due to gravity of the planet. As the acceleration due to gravity varies from place to place, the weight of the body also varies from place to place. Acceleration due to gravity $g$ depends upon many factors such as radius, depth and height from the surface, so weight of the body also depends upon such factors. The place where there is more acceleration due to gravity, there is more weight of a body.

[Variation of Acceleration due to Gravity]

Weight is more at the poles of earth as there is maximum value of $g$. Weight is less at the equator as there is minimum value of $g$. As the value of $g$ decreases with the increase in height from the earth’s surface, weight of a body also decreases with the increase in height from the earth’s surface. As the value of $g$ decreases with the increase in depth from the earth’s surface, weight of a body also decreases with the increase in depth from the earth’s surface.At the centre of the earth, the value of $g$ is zero. So, weight of a body is also zero at the centre of the earth.

Freefall

When a body is falling under the influence of gravity only, then the motion is called free fall. There is no any influence of air resistance during free fall. Free fall happens when the acceleration due to gravity is equal to the acceleration of the falling body i.e, $g=a$. When a body falls in vacuum or in space, then the body is falling with free fall. Since there is no atmosphere on the moon, a body falls freely on the surface of the moon. Due to air resistance, there is no free fall of any falling body on earth. When a falling body is in free fall, the body feels weightlessness as it does not feel any reaction force.

Weightlessness

We feel our weight whenever we stand , walk, run or do such activities as we feel the reaction of the floor. But in some condition, we will not feel our weight. Thus, weightlessness can be defines as that condition in which a body does not feel its own weight.

A body having mass feels weightlessness under the following conditions:

• When a body falls with free fall or when a body is falling with the acceleration equal to the acceleration due to gravity i.e, $a=g$.
• When a body is at the centre of the earth or in the space as there is zero acceleration due to gravity and, $$W=mg=m\cdot 0=0$$
• When a body is in the artificial satellite and the artificial satellite is revolving around a heavenly body.

As shown in the figure, an artificial satellite is revolving around the earth in an elliptical orbit due to the centripetal and centrifugal forces. Centripetal force is the force of gravity which keeps the satellite in its orbit. Centrifugal force is opposite to gravity. The satellite at the position $A$ should go to the position $B$ due to the centrifugal force and inertia but centrifugal force brings the satellite at the position $C$ which causes the weightlessness of every objects which are inside the artificial satellite.

We feel weightlessness when we stand in a lift moving down

There is not any upward force exerted by the floor of the lift when the lift is in free fall.
In this condition,
The apparent weight is,
$$R=m(g-a)$$
Where,
$R=$ Apparent weight
$m=$ Mass of the falling body
$g=$ Acceleration due to gravity
$a=$ acceleration of the falling body
But, since the body is in free fall, $a=g$.
Therefore, $$R=m(g-g)=0$$
Thus, apparent weight is zero and the body feels weightlessness.