Is Energy Conserved in Pendulum Motion?

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Homework Help Overview

The discussion revolves around the conservation of energy in pendulum motion, specifically examining the relationship between kinetic and potential energy throughout the swing of a pendulum.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to prove that the sum of kinetic and potential energy is constant during the pendulum's swing, expressing confusion over their calculations at different points in the swing.
  • Some participants inquire about the assumptions that can be made, such as whether gravitational force can be considered conservative.
  • Others suggest examining the role of tension in the system and its impact on energy conservation.

Discussion Status

Participants are exploring various aspects of the problem, including the definitions of energy types and the implications of different forces acting on the pendulum. Guidance has been offered regarding assumptions and the nature of forces involved, but no consensus has been reached on the solution.

Contextual Notes

The original poster indicates that this question was encountered during an exam, suggesting a need for clarity on the principles of energy conservation in a pendulum system. There is also a mention of potential language barriers affecting communication.

maracxos
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Hello!
I need to solve this problem
proof that sum of kinetic and potentional energy in every part of pendulums(every dot of pendulums swing) swing is equal...
Sorry for bad eanglish
 
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Is this for homework? What have you tried so far?
 
no it is not for homework i had that question on exam and i didnt know the answer and i have thinked and thinked after that abaut that and i don't know the solution I have tried to solve that problem with trigonometry but nothing after that i try to solve energy for some dot A on the swing and for some dot B on the swing but my results for dot A and B are not the same...
 
maracxos said:
proof that sum of kinetic and potentional energy in every part of pendulums(every dot of pendulums swing) swing is equal...
Sorry for bad eanglish

If you describe the motion of the pendulum by the angle, say theta, and the write down the kinetic energy T and the potential energy V you will see that T is quadratic in the time derivative of theta and V is only a function of position theta.
In such a system the Hamiltonian H will be the total energy H = T + V = E and since H does not depend explicitly on time the partial derivative of H with respect to time is zero and hence H is conserved during the motion of the system.
 
Welcome to PF!

maracxos said:
Hello!
I need to solve this problem
proof that sum of kinetic and potentional energy in every part of pendulums(every dot of pendulums swing) swing is equal...
Sorry for bad eanglish

Hi maracxos! Welcome to PF! :smile:

What are you allowed to assume?

Can you assume that gravitational force is conservative?

If so, then just prove that there is no work done by the only other external force … the tension. :smile:
 
Ok thank you!
 

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