# Calculate ME of a Pendulum: Length 130 cm, Amplitudes 2.1 & 3.9 cm

• mikefitz
In summary, a pendulum of length 130 cm has a mechanical energy of 7 mJ when it swings with an amplitude of 2.1 cm. The total energy is proportional to the square of the amplitude and can be calculated using the gravitational potential energy (GPE) of the bob. The total energy increases when the amplitude of the swing increases.
mikefitz
A pendulum of length 130 cm swings with an amplitude of 2.1 cm. Its mechanical energy is 7 mJ. What is the mechanical energy of the same pendulum when it swings with an amplitude of 3.9 cm?

Well I know that energy is conserved in such a system; what I don't know is how to calculate KE and PE of this pendulum (also, I know that mass is independent of frequency). I've read that total ME is proportional to the square of the amplitude, though I'm not sure how to work that into my solution.

My book does have a chapter on simple pendulums, with equations for calculating the period, frequency, and angular frequency - what it does not have are equations for calculating a pendulums energy. Any help? thanks

mikefitz said:
A pendulum of length 130 cm swings with an amplitude of 2.1 cm. Its mechanical energy is 7 mJ. What is the mechanical energy of the same pendulum when it swings with an amplitude of 3.9 cm?

Well I know that energy is conserved in such a system; what I don't know is how to calculate KE and PE of this pendulum (also, I know that mass is independent of frequency). I've read that total ME is proportional to the square of the amplitude, though I'm not sure how to work that into my solution.

My book does have a chapter on simple pendulums, with equations for calculating the period, frequency, and angular frequency - what it does not have are equations for calculating a pendulums energy. Any help? thanks
The stored energy in a swinging pendulum is the gravitational potential energy (GPE) of the bob. When the bob is not moving, all the energy is GPE. For any harmonic oscillator it is true that the total energy is proportional to the square of the amplitude. A pendulum is very nearly a hamonic oscillator, as long as the angles are small and the small angle approximation is valid. You shouild expect a calculation of the energy based on GPE to be consistent with the general behavior of harmonic oscillators.

OlderDan, I really don't know how to translate that thought into an equation to solve this problem; can you explain it in a way that would me it easier for me to visualize what is going on? Thanks

mikefitz said:
OlderDan, I really don't know how to translate that thought into an equation to solve this problem; can you explain it in a way that would me it easier for me to visualize what is going on? Thanks
Let the zero of GPE be at the lowest point of the pendulum's swing. As it swings to either side, the height of the bob increases relative to this lowest position. When the bob is displaced 2.1cm and released it will rise to its maximum height (for that initial displacement) above the lowest point and its total energy will be the GPE associated with that rise. Knowing the energy for this displacement will enable you to determine the mass of the bob. When it is displaced 3.9cm it will have a higher maximum height and a higher total energy. You only need to compare the heights associated with these two displacements and the associated GPEs to answer the question.

## 1. How do you calculate the ME of a pendulum?

To calculate the ME (maximum energy) of a pendulum, you will need to know the length of the pendulum, the amplitude (maximum displacement) of the pendulum, and the gravitational constant. You can then use the formula ME = (mgh)/2, where m is the mass of the pendulum, g is the gravitational constant, and h is the height of the pendulum at its maximum displacement.

## 2. What is the length of the pendulum in this example?

The length of the pendulum in this example is 130 cm.

## 3. How do you measure the amplitude of a pendulum?

The amplitude of a pendulum is measured by finding the maximum displacement from the equilibrium position. In this case, the amplitudes are 2.1 cm and 3.9 cm for the two different amplitudes given.

## 4. How does the length of a pendulum affect its ME?

The length of a pendulum has a direct effect on its ME. The longer the length of the pendulum, the greater the potential energy and therefore the greater the ME. This is because a longer pendulum has a higher maximum displacement and therefore a higher height at its maximum displacement.

## 5. Is it important to consider the gravitational constant when calculating the ME of a pendulum?

Yes, it is important to consider the gravitational constant when calculating the ME of a pendulum. The gravitational constant, denoted by g, is a measure of the strength of gravity on Earth. It is necessary to include this value in the formula for ME to accurately calculate the energy of the pendulum at its maximum displacement.

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