# Conservation of energy - pendulum

• Treefrog123
In summary, the conversation discusses finding tension in a rope when a person is swinging on it. The height, length, mass, and weight of the person are known, and the question is whether tension is constant throughout the swing or if it varies. The suggestion is to examine the forces at an angle from the rest position to determine the maximum tension.
Treefrog123
If I have a person swinging on a rope (like a pendulum) and I know the height above the reference level that the person starts swining from, as well as the length of the rope and the person's mass and weight... how can I find tension in the rope? Is tension constant throughout the entire swing? My first thought was that the tension is not constant, and is at a maximum when the rope is hanging straight down, but how do I know if this is true?

Thanks

Try looking at the forces at some angle displaced from its rest position.

for your question. I can confirm that the conservation of energy principle applies to a pendulum system. This means that the total energy of the system (kinetic energy + potential energy) remains constant throughout the swing, as long as there is no external force acting on the system.

To find the tension in the rope, you can use the conservation of energy equation: initial energy = final energy. In this case, the initial energy would be the potential energy of the person at the starting height, and the final energy would be the sum of the kinetic energy and potential energy at any point during the swing.

As for whether tension is constant throughout the entire swing, you are correct in thinking that it is not. The tension in the rope will vary depending on the position of the person on the swing. When the person is at the bottom of the swing, the tension will be at its maximum as the person's weight is pulling directly down on the rope. As the person swings upward, the tension will decrease as the weight is pulling at an angle.

To confirm this, you can use the equation for tension: T = mg + ma, where m is the mass of the person, g is the acceleration due to gravity, and a is the centripetal acceleration. As the person swings, the value of a will change, resulting in a varying tension in the rope.

I hope this helps answer your question. Remember, the conservation of energy principle is a powerful tool in understanding and analyzing physical systems.

## What is conservation of energy?

Conservation of energy is a fundamental principle in physics which states that energy cannot be created or destroyed, it can only be transferred from one form to another. This means that the total amount of energy in a closed system remains constant over time.

## How does conservation of energy apply to a pendulum?

A pendulum is a simple mechanical system that demonstrates the conservation of energy. As the pendulum swings back and forth, it constantly converts between potential energy (when it is at the highest point) and kinetic energy (when it is at the lowest point). The total amount of energy (potential + kinetic) remains the same throughout the motion.

## What factors affect the conservation of energy in a pendulum?

The conservation of energy in a pendulum is affected by several factors, including the mass of the pendulum bob, the length of the pendulum, and the amplitude of the swing. A longer pendulum or a heavier bob will have more potential energy, while a larger amplitude will result in a greater amount of kinetic energy.

## Can the conservation of energy be violated in a pendulum?

No, the conservation of energy is a fundamental principle of physics and cannot be violated in any physical system, including a pendulum. This means that the energy of a pendulum will always remain constant, although it may be transferred between different forms.

## How is the conservation of energy useful in understanding pendulum motion?

Understanding the conservation of energy is essential in understanding pendulum motion. It allows us to predict the behavior of the pendulum and its energy at any point in time. By knowing the initial conditions of the pendulum, we can determine its potential and kinetic energy at any point in its swing. This knowledge is crucial in many real-world applications, such as designing pendulum clocks or calculating the energy efficiency of a swing ride.

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