# Vertical energy of a pendulum - is there one?

• jojotank
In summary, the conversation is about a simple pendulum with a string and mass at the end. The question is whether there is a vertical kinetic energy or if it is just a part of the overall kinetic energy. The answer is that kinetic energy uses the full velocity and does not differentiate between vertical and horizontal components.

## Homework Statement

Hello. I was just wondering. You have a simple pendulum . string and a ball with mass at the end. We usually solve examples and we think about conversation of kinetic energy and potentional energy. I was just wandering if there is also something like vertical kinetic energy. Or it is just a part of kinetic energy itself (just the sine part of velocity vector). If it exist, i know it is very small. I was just wondering... Thank you.

no need for them

## The Attempt at a Solution

thinking

Not quite sure what you mean. You can certainly express the velocity of the pendulum in terms of vertical and horizontal components, but the kinetic energy uses the full velocity. Velocity has a direction, but kinetic energy does not.

It is totaly clear now. Thank you.

## 1. What is the vertical energy of a pendulum?

The vertical energy of a pendulum is the sum of its potential and kinetic energy at any given point during its swing.

## 2. How is the vertical energy of a pendulum calculated?

The vertical energy of a pendulum can be calculated using the formula:
E = mgh + 1/2mv^2, where m is the mass of the pendulum, g is the acceleration due to gravity, h is the height of the pendulum, and v is its velocity.

## 3. Does the vertical energy of a pendulum change throughout its swing?

Yes, the vertical energy of a pendulum changes constantly as it swings back and forth. It is highest at the top of its swing (when the pendulum is at its maximum height) and lowest at the bottom of its swing (when the pendulum is at its lowest point).

## 4. How does the vertical energy affect the motion of a pendulum?

The vertical energy of a pendulum is constantly changing, and this affects the motion of the pendulum. As the pendulum swings, the energy is constantly being converted between potential and kinetic energy, causing the pendulum to accelerate towards the center of its swing.

## 5. Is the vertical energy of a pendulum the same as its total energy?

No, the vertical energy of a pendulum is only one component of its total energy. The total energy of a pendulum also includes its horizontal energy and any other forms of energy, such as friction or air resistance, that may be present.