Height and potential energy are the proportional quantities influencing one over the other.
Potential energy is not the transferable quantity; the object’s height largely influences it. How does height affect potential energy? To know the answer, let us discuss it in this article.
How does height affect potential energy
As the height largely influences the potential energy, it shows some average deviation from the height of the object. When the object is at a greater height, the potential energy possessed on the object is more. As the object begins to move down, the potential energy will transform into kinetic energy and the object overcome from the potential energy at the ground level.
When you try to push the object in the upward direction, you will feel difficult to push as the height increases. At that instance, the stored potential energy is more. Because potential energy is the maximum available energy that required to convert into other forms. At a higher altitude, you require more energy to make the object move. So as the height increases, the potential energy is also increase.
A car at the top of the hill possesses huge amount of potential energy than the car on the ground. The potential energy is more vertical because the car is elevated to a greater height. If the car descends, it loses the maximum amount of potential energy due to a decrease in height. Loss of potential energy corresponds to gain of kinetic energy which causes the motion of the car by increasing its velocity.
How does height affect gravitational potential energy
Have you ever thrown a ball upward?
If yes, have you observed that the ball is moving a little slowly while moving upward compared to when it returns to the ground?
In order to answer the above phenomena, let us consider the equation of gravitational potential energy,
PE = m* g* h
Where m is the mass, g is the acceleration due to gravity, and h is the height of the object.
The above says that, the potential energy and the height are correlated to one another.
It is clear that increase in height, the gravitational potential increases proportionally.
When an object is raised and separated by a certain distance from the earth’s center, the object is at that place opposite to the gravitational pull. So it requires more energy to attract the object towards it. The stored potential energy came into the action at this instance. The kinetic energy is the converted form of potential energy and makes the object return back to the ground. So as the height increases, the object possesses more potential energy to return to the ground.
Another example of height affecting the gravitational potential energy is the ride on a roller coaster. The relation between the work-energy is illustrated by the roller coaster, which converts the total mechanical energy into the work by the influence of external force. Initially, the roller coaster is at the top of the track loop at a greater height.
As the train car of the coaster begins to descend through turns, loops, ups, and downs, only the force of gravity acts on the roller coaster car as an internal force. The force of gravity thus causes to do the work. At the top, it possesses more incredible potential energy, and hence the coaster car descends quickly on the application of force. It means that the gravitational potential energy is greater at the greater heights.
How does doubling height affect potential energy
As the height doubles, the potential energy of the system also doubles.
Consider the equation of gravitational potential energy, the height of the object is doubled, so that the equation can be written as;
PE = m* g* (2h)
Since the height is doubled, the new potential energy is given as
(PE)’ = 2 m* g* h
(PE)’ = 2 PE
Consider the example of the hammer and the nail. A hammer is required to fix the nail in the wooden block. Let the hammer be at a certain height h; the force is needed to fix the nail. To fix it on the wooden board, the work has to be done on the nail. The hammer has the potential energy because it has only changed its position. The work needed to fix the nail is done by the hammer due to its height. If the height is doubled, more force is required to do the work on the nail. Now the hammer has doubled potential energy to do the work and make the nail to fix on the block.
Frequently asked Questions
Is elastic potential energy also affected by the height?
Yes, the elastic potential energy is also affected by the height. The influence of height can be illustrated by the example given below.
The deformation of the elastic body either by expansion or by compression results in the elastic potential energy. If a spring is hung vertically with a clamp and expanded at a distance, the amount of deformation can be equal to the height. Thus more deformation means more potential energy.
Does the production of electricity is based on the theory of potential energy?
At the top of the waterfall, the gravitational potential energy is more which is responsible for water to flow sdown the hill.
A waterfall is a beneficial form of potential energy. As the potential energy at the top of the waterfall is very high, it falls with a greater velocity and converts into kinetic energy. If a turbine is placed at the bottom of the waterfall, the force of the waterfall on the turbine makes the turbine rotate and produce electricity.
Is height is the only factor that affects the potential energy?
The potential energy is affected by various factors like mass, velocity, acceleration depending on the type of potential energy acting on the system.
As gravitational potential energy is largely influenced by the mass of the object and elastic potential energy is influenced by the amount of deformation, and electric potential energy depends on the nature of the charge discharged. Thus height is one of the factors that potential energy depends on.
Does tripling the height affect the potential energy?
Tripling the height is similar to doubling the height. It also has the same influence on potential energy.
By increasing the height triple times, the potential energy also increases its value by triple time. The height can be increased to n times to get more potential energy, but we cannot achieve the infinite height as infinite height means the object must be away from the gravitational pull.
Can a body possess infinite potential energy?
Classical mechanics states the potential energy as the capacity to cause the work on the body. It is impossible for a body to possess infinite energy to do the work.
If a body possesses infinite potential energy means, either the body has infinite mass, or the body is kept at a height greater than the radius of the earth. This is contrary to the mass-energy equivalence. Thus a body cannot possess an infinite amount of potential energy.
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I am Keerthi K Murthy, I have completed post graduation in Physics, with the specialization in the field of solid state physics. I have always consider physics as a fundamental subject which is connected to our daily life. Being a science student I enjoy exploring new things in physics. As a writer my goal is to reach the readers with the simplified manner through my articles.