Gravity is a natural phenomenon possessed by all the things that have a certain mass and are attracted to one another.
A body kept above the ground has the maximum potential energy to accelerate downwards because gravity is trying to pull the body in a downward direction. Then how does gravity affect potential energy is explained in this article.
How does gravity affect potential energy?
Consider a body of certain mass is placed at a certain height away from gravity since gravity is the force attraction that tries to pull the body towards the ground. The potential energy stored in the body is responsible for the body to move downwards due to gravity. Potential energy is the sufficient energy that the body has gained to begin accelerating.
When a body is falling, how dies gravity affect the potential energy stored in it?
As the body falls on the ground, the potential energy changes its form to kinetic energy due to the “law of conservation of energy.” The body dropping from the greater height acquires maximum velocity; hence the potential energy is lost. The maximum velocity conveys the maximum kinetic energy.
So it is clear that gravity affects the potential energy inversely. If the body has maximum potential energy, then gravity is minimum and vice versa.
General theory of relativity explains that gravity is the curvature of space and time and the energy lies within the curvature. Thus potential energy is also a form of energy, which is affected by the space-time curvature.
Derivation of how does gravity affect potential energy
Assume that a body of mass ‘m’ is placed at a height ‘h’ against the gravity. The body has acquired a certain amount of potential energy ‘PE’ at the height ‘h.’ The force required to accelerate the body which is at height is given by the equation,
Since, when the body begins to accelerate downwards, the potential energy is changed into kinetic energy. Hence the rate of change of potential energy with height gives the force that needs to apply to the body.
From Newton’s second law of motion, the force exerted on anybody is always equal to the mass times the acceleration, i.e., F=m*a.
But here, the acceleration is due to gravity, which is written as,
F = m*g
So putting the above equation in the equation of potential energy, we get
Rearranging the terms,
dPE = (mg) dh
By integrating the above equation, we will get the potential energy equation due to gravity.
PE = mgh
Assume that at the initial position the body possesses zero potential energy. It has the maximum potential energy at the final position and considers the initial position of the body as ground level and the final position of the body as height h.
As the body losses its potential energy and gained kinetic energy, does gravity affect potential energy, as now, it has kinetic energy?
The kinetic energy of the body is given by the equation
Then the total energy of the system is
E = KE + PE
Initially, we considered the body is at height ‘h,’ which has maximum potential energy, and it dies out as it falls and acquires kinetic energy. Hence the equation is given by
KEi + PEi = KEf + PEf
Initially, the body possesses zero potential energy.
Rearranging the terms we get
This implies that the potential energy is the only energy affected by gravity.
Some interesting facts about potential energy
- In 19th century the Scottish physicist termed a stored energy possessed by the object as “Potential energy.”
- Potential energy is called storing energy because the stationary object possesses it, and it can be used later.
- The potential energy has the ability to convert itself into other forms of energy by the exertion of external force.
- Similarly, an object can possess potential energy from other forms of energy when triggered by an external force.
- Gravity can only affect the potential energy when the object is placed vertically.
- The earth’s orbit possesses an attractive force called gravity which is reason for the moon to be in the orbit of earth. This gravitational pull is the reason for the tides on the earth.
- The evaporation of water and forming clouds and condensing into liquid, and then falling back to the earth as rain is the natural process due to gravitational potential energy.
- The moon has gravitational potential energy, which is responsible for pulling the ocean water to the natural basin.
- Tidal energy is the reference to the sun having gravitational potential energy.
Frequently asked questions
Does gravity affect potential energy when the spring is clamped vertically?
The potential energy is acquired by the spring is due to its geometry and orientation.
The spring compresses more when you apply the force in the direction of acceleration due to gravity. If you measure the forces acting on the spring at a different position, the spring exhibits a different value. This means that the spring potential energy will be more when you clamped vertically and compress in the downward direction.
Does gravity associate with potential energy changes?
Yes, the gravity associated with potential energy changes with distance.
As gravity depends on the distance between the ground and the object’s height, the potential energy associated with it also depends on them. Thus as the distance increases, the potential energy is also increased by decreasing the force of gravity.
Why does mass affect the force of gravity?
Newton’s law of gravitation defines that mass is directly corresponds to the gravitational force.
There was no theory to explain why mass affects gravity, but by studying certain scientific theories, it is said that every mass on earth emits a tiny particle called the graviton, which is responsible for a body to attract the other body towards it. Thus body with greater mass possesses more gravitational attraction.
Can an object possess infinite gravitational potential energy?
Ideally, the object with infinite height and mass can have infinite gravitational potential energy.
In the real-world application, infinite gravitational potential energy is difficult to achieve as an object with infinite mass is impossible. If we place an object at infinite height, there must be no gravitational attraction to pull the object downward. Hence an object cannot possess infinite gravitational potential energy.
Does the gravitational potential energy depend on the direction?
Physical quantity depends on the direction is called as vector quantity but the potential energy is not associated with direction but it is associate with magnitude.
The subcategory of the potential energy is the gravitational potential energy. The gravitational potential energy corresponds to the initial and final point of the object, not the path traced by the object while traveling toward its final destination. Hence gravity is independent of the direction of the object.