Conservation of energy - pendulum

[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

 

[Hootenanny]

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

 

[kyle8921]

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.