Energy conservation in simple pendulum

In summary, the conversation discusses the application of the energy conservation law in a simple pendulum with mass m and length l. The position of the pendulum is determined by the angle \theta and the string does not do any work. The conversation also suggests using the work-energy theorem to prove the application of the energy conservation law.
  • #1
imjudit
1
0
Hello everyone! I've found this problem in my exercises book, and I'm having slight troubles solving it.
"Consider a simple pendulum with mass m, on a string with l length. Considering that the position of pendulum is determined with the angle [itex]\theta[/itex] and noting that the string DOES NOT do any work, considering all the forces acting on the pendulum show that the energy conservation law is applied"

Well, I know how to prove that the ECL is applied without using the forces (considering that the Ep is 0 at the lowest point, and that the Ek is 0 at the highest).
Any ideas?

Thanks in advance

(I wasn't sure if this is supposed to go to "homework" section, since it isn't a homework...)
 
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  • #2
The (so called) law of mechanical energy conservation is the work-energy theorem in disguise in the case when only conservative act on the system to which one may add non-conservative forces that do no work, as is the case here. The work energy theorem says$$\Delta K=W_{net}$$Just find expressions for the work done by gravity ##W_g## and the change in kinetic energy ##\Delta K##. Remember that the change in gravitational potential energy is the negative of the work done by gravity.
 

1. What is a simple pendulum?

A simple pendulum is a weight (or bob) suspended from a fixed point by a string or rod. It is a physical system that exhibits periodic motion.

2. How does energy conservation apply to a simple pendulum?

In a simple pendulum, energy conservation refers to the principle that the total energy of the system (kinetic energy + potential energy) remains constant throughout its motion. This means that as the pendulum swings back and forth, the energy is constantly being converted between potential and kinetic energy, but the total amount remains the same.

3. How does the length of a pendulum affect energy conservation?

The length of a pendulum has a direct impact on its energy conservation. The longer the pendulum, the slower it swings and the less energy it has. This is because the longer pendulum has a greater distance to cover and therefore takes longer to complete each swing, resulting in less kinetic energy.

4. How does friction affect energy conservation in a simple pendulum?

Friction can cause energy to be lost in a simple pendulum. As the bob swings back and forth, it encounters air resistance and friction at the pivot point. This causes the pendulum to gradually lose energy, resulting in smaller and smaller swings until it eventually comes to a stop.

5. Can energy be conserved in a pendulum without any external force acting on it?

Yes, energy can be conserved in a pendulum without any external force acting on it. As long as there is no friction or air resistance, the pendulum will continue to swing back and forth with the same amount of energy. This is known as an ideal or simple pendulum, where all the energy is converted between potential and kinetic energy without any loss.

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