Name: gravitational and elastic energy stored
Uploaded: 2023-09-22T11:49:37.000Z
Duration: 1 min 9 s
Channel: JoVE

Potential energy is the ability of a body to do work due to its position.
The gravitational potential energy change is the negative of the work done on a body by force, equal and opposite to its weight, in bringing the body to a specific position from a reference position or datum where the gravitational potential energy is considered zero.
On lifting a body, the work done by the gravitational force is negative, and so its potential energy increases. On moving the body downward, the reverse is observed.
Elastic potential energy is the negative of the work done due to the restoring force generated in a deformed elastic body that tries to restore its undeformed position.
For a compressed spring, the change in the elastic potential energy is positive, while the work done by the spring force on the mass is negative. The same is observed when the spring is stretched from an undeformed position.
If both gravitational and elastic forces act on a body, the potential energy is the sum of both energies.

potential energy

Potential Energy

A conservative force, such as a gravitational or elastic force, gives the body the capacity to do work. This capacity, measured as the potential energy, depends on the body's location or “position” relative to a fixed reference position or datum. The gravitational potential energy is considered zero at the reference point. Suppose a body is located at some vertical distance above a fixed horizontal reference or datum. In that case, the weight of the body has positive gravitational potential energy since it has the capacity to do positive work when the body is moved back down to the datum. Likewise, if the body is located at a vertical distance below the datum, the gravitational potential energy is negative since the weight does negative work when the body is moved back up to the datum.
If the height is taken as zero at the datum and the vertical upward distance is considered positive, then at some height above the datum plane, the gravitational potential energy is expressed as the product of the weight of the body and its height from the datum plane. Mathematically, this is expressed as follows:
<img alt="Gravitational potential energy equation Vg=mgh; physics formula; educational diagram." src="/files/ftp_upload/14358/PT_14358_Equation_1.svg" style="text-align: center; height: 15px;" data-altupdatedat="1761830439000" data-alt="Equation 1">
If the body is at some distance below the datum plane, its gravitational potential energy becomes negative. Note that the datum plane for zero potential energy is arbitrary because it does not affect the change in the potential energy.
The work done on an elastic body is stored in the body in the form of elastic potential energy. This energy is available to do work on some other body while relieving its compression or extension. When a force compresses a spring, it causes a displacement x, which is directly proportional to the applied force. The elastic potential energy of the spring for a compression of x is the total work done on the spring and is expressed as follows:
<img alt="Elastic potential energy equation \(V_e=\frac{1}{2}kx^2\); physics formula." src="/files/ftp_upload/14358/PT_14358_Equation_2.svg" style="text-align: center; height: 30px;" data-altupdatedat="1761830439000" data-alt="Equation 1">
When a spring is stretched, the force acts in the direction of the displacement, thus doing positive work on the spring and increasing its potential energy. The same is observed when a spring is compressed from an undeformed position.

A conservative force, such as a gravitational or elastic force, gives the body the capacity to do work. This capacity, measured as the potential energy, ...

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gravitational and elastic energy stored

Gravitational and elastic potential energy are forms of stored energy from conservative forces. A conservative force, such as gravity or an elastic force, gives a body the capacity to do work. This capacity is measured as potential energy and depends on the body’s position relative to a fixed reference point, or datum.

For gravitational potential energy, the datum is the level where the energy is taken as zero. If a body is above this reference plane, its weight has positive gravitational potential energy because it can do positive work as the body moves back down to the datum. If the body is below the datum, the gravitational potential energy is negative because the weight does negative work as the body is moved up to the reference level.

If height is measured upward from the datum as positive and zero is set at the reference plane, gravitational potential energy equals the body’s weight multiplied by its height. If the body is below the datum plane, the value becomes negative. The choice of zero potential energy is arbitrary, because only the change in potential energy matters.

Elastic potential energy is stored when work is done on an elastic body, such as a spring. This stored energy can later do work on another body as the spring returns toward its original shape. When a force compresses a spring, it produces a displacement x that is directly proportional to the applied force, and the elastic potential energy is the total work done on the spring.

A stretched spring also gains elastic potential energy because the force acts in the same direction as the displacement and does positive work on the spring. The same increase in potential energy is seen when a spring is compressed from its undeformed position.

Gravitational and Elastic Energy Stored

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Explore how gravity and springs store energy as potential energy, including positive and negative gravitational values and elastic energy in stretched or compressed springs.

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Gravitational and Elastic Energy Stored

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