Question
What is the potential energy of a 12-meter-tall antenna on top of a 40-meter-tall tower?
Answers
Answered by
GPT-4o mini
To calculate the potential energy (PE) of an antenna on top of a tower, we can use the formula for gravitational potential energy, which is given by:
\[
PE = m \cdot g \cdot h
\]
where:
- \(m\) is the mass of the object (in kilograms),
- \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)),
- \(h\) is the height above the reference point (in meters).
In this case, the height \(h\) of the antenna on the tower is the sum of its height and the height of the tower:
\[
h = 12 \, \text{meters} + 40 \, \text{meters} = 52 \, \text{meters}
\]
However, to complete the calculation, we need the mass \(m\) of the antenna. Since you did not provide the mass, we will denote it as \(m\).
Thus, the potential energy of the antenna can be expressed as:
\[
PE = m \cdot 9.81 \, \text{m/s}^2 \cdot 52 \, \text{m}
\]
\[
PE = m \cdot 510.12 \, \text{J}
\]
This result shows that the potential energy is dependent on the mass of the antenna. If you provide the mass, you can multiply it by \(510.12 \, \text{J}\) to find the exact potential energy.
\[
PE = m \cdot g \cdot h
\]
where:
- \(m\) is the mass of the object (in kilograms),
- \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)),
- \(h\) is the height above the reference point (in meters).
In this case, the height \(h\) of the antenna on the tower is the sum of its height and the height of the tower:
\[
h = 12 \, \text{meters} + 40 \, \text{meters} = 52 \, \text{meters}
\]
However, to complete the calculation, we need the mass \(m\) of the antenna. Since you did not provide the mass, we will denote it as \(m\).
Thus, the potential energy of the antenna can be expressed as:
\[
PE = m \cdot 9.81 \, \text{m/s}^2 \cdot 52 \, \text{m}
\]
\[
PE = m \cdot 510.12 \, \text{J}
\]
This result shows that the potential energy is dependent on the mass of the antenna. If you provide the mass, you can multiply it by \(510.12 \, \text{J}\) to find the exact potential energy.