Motion Under Gravity – Equation of Motion with Examples

In the universe, when an object is lifted or away from the ground, then a force is applied to the object in the downward direction. This force is known as the gravity force. When an object moves due to the application of the gravity force, its motion is known as a motion under gravity. The gravity of the earth pulls the object towards itself with an acceleration which is known as acceleration due to gravity. This force occurs due to the gravitational pull of the earth which follows the concept of Gravitational forces.

In this article, a brief information regarding the concept of motion under gravity is provided. It discusses important topics such as vertical motion under gravity, equation of motion under gravity, motion under gravity formula, and gravity examples.

A Mathematical Formulation of Motion Under Gravity

When a body is resting on the horizontal surface, then a downward force is acting on the object due to the action of the gravity force. These gravity forces always try to attract the object which confirms the nature of the force as an attractive force.

Consider an object of mass “M” resting on the horizontal surface, then the force which is applied on the object due to the action of gravity force will be the weight of the object “W”. The acceleration by which an object is attracted towards the earth is the acceleration due to gravity which is denoted by “g”.

Hence, according to Newton’s second law,

$F=ma$

On substituting the values in the above relation, the weight of the object will be given as;

$W=Mg$

The value of acceleration due to gravity is $9.8~\dfrac{m}{s^2}$. The S.I unit of mass is the kilogram (kg). The SI unit for weight is Newton (N).

In case of the absence of air resistance, the object will directly fall on the ground at the same rate without considering its mass, shape, or size.

Equation of Motion Under Gravity

When an object undergoes a motion due to the action of gravity, then are some standard equations of motion that are followed for the analysis of the motion of the object. Just like the equation of motion for normal horizontal forces, there is the following equation of motion under gravity which is given below,

• $v=u+g t$

• $h=u t+\dfrac{1}{2} g t^{2} $

• $v^{2}=u^{2}+2 g h$

Among all of the given equations related to the concept of equations of motion under gravity, there is a sign convention followed for the acceleration due to gravity. It is taken as positive for downward direction and negative for upward direction.

Vertical Motion Under Gravity

Various relationships have been generated based upon the equation of motion under gravity and the condition of applied forces on the body under vertical motion due to gravity.

The Velocity of a Body Dropped From a Height

When an object is dropped from a certain height of the object it is taken as “h”. Initially, the object is at rest and then dropped from that height; it means that its initial velocity is zero. When the object hits the ground, there must be some final velocity of the body.

Therefore, the equation of motion which is referred to is given as,

$v^{2}=u^{2}+2 g h$

The value of “g” will be taken as positive, which depicts the motion of an object in a downward direction.

$\begin{align} v^{2} &=(0)^{2}+2 g h \\ v^{2} &=2 g h \\ v &=\sqrt{2 g h} \end{align}$

Hence, the final velocity of the object is given as $\sqrt{2gh}$.

Examples of Gravity Forces

There are various examples related to the motion under gravity is given below:

• Whenever the ball throws in an upward direction, the ball will come back to the ground due to the action of gravity.

• The movement of the person on the ground will happen only because of the gravity force which holds the person to the ground.

• Due to the presence of gravity forces, tides are controlled in terms of their short-term periodic movement which occurs due to the rise and fall of water in water bodies.

• Various daily-life activities are controlled by the gravity forces such as jumping, sliding, walking, running, dancing, etc.

• The movement of the celestial bodies around the sun is controlled by the action of gravitational forces for the proper alignment and rotation about their axis.

Conclusion

Conceptual knowledge about the concept of gravitational force, which attracts the bodies towards it with the acceleration due to gravity, is provided. The article starts with the clarification of the first query, i.e. what is gravity force. It explains the motion under gravity with the proper derivation. It also discusses the motion under gravity, gravity examples, motion under gravity formula, equation of motion under gravity, and vertical motion under gravity. It covers the major section of the gravitational forces for a better understanding of the concept.