What is Free Fall?
A free-falling object is an object that is falling under the sole influence of gravity. Any object being acted upon only by the force of gravity is in a state of free fall.
When you leave a stone, it will free-fall towards the ground. But if you throw it, it’s not free fall. That’s because gravity is not the only force acting on the stone, but your applied force is in play as well.
When the object is free-falling towards the earth, there is a force of gravity acting on it that accelerates its speed.
Gravitational Force of Earth
What is Newton’s Second Law of Motion?
According to Newton’s second law of motion, the force acting on an object is equal to the
product of its mass and acceleration.
it can be represented by using the following formula:
(𝑭 = 𝒎 × 𝒂)
In the case of a freely falling object, the above formula can be modified by replacing ‘a’ with ‘g’. Here, ‘g’ is nothing but the acceleration due to gravity.
(𝑭 = 𝒎 × 𝒈)
What is the value of Acceleration due to Gravity (g)?
Let us try to find the value of acceleration due to gravity. For this, we will consider the case of a freely falling object. Consider a stone of mass ‘m’ falling freely under the influence of gravity only.
According, to Newton’s second law the force acting on the stone will be:
𝑭 = 𝒎 × 𝒈
——————-(1)
Now, if we consider the mass of the Earth to be ‘M’ and the distance between the stone of mass ‘m’ and the Earth to be ‘d’. Then, the force of gravitation between them will be,
As the distance between the center of the stone to the earth’s surface is negligible, we can consider ‘d’ as the radius ‘R’ of the earth. The gravitational force formula is given as,
Now on equating both the equations we get,
Dividing both sides by the mass of the object ‘m,’
𝑴x𝒈 = 𝑮 (𝑹𝟐)
The values of universal gravitational constant, the mass of the earth ‘M,’ and the radius of the earth ‘R’ are,
𝑮 = 𝟔. 𝟔𝟕𝟑 × 𝟏𝟎−𝟏𝟏𝑵 𝒎𝟐 𝒌𝒈−𝟐
𝑴 = 𝟔 × 𝟏𝟎𝟐𝟒 𝒌𝒈
𝑹 = 𝟔. 𝟒 × 𝟏𝟎𝟔 𝒎
On substituting them, we get the value of acceleration due to the gravity as,
𝒎
𝒈 = 𝟗. 𝟖