Is Energy Conserved in Pendulum Motion?

In summary, if you assume gravitational force is conservative then you can simply prove that there is no work done by the only other external force, the tension.
  • #1
maracxos
3
0
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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  • #2
Is this for homework? What have you tried so far?
 
  • #3
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...
 
  • #4
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.
 
  • #5
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:
 
  • #6
Ok thank you!
 

1. What is a pendulum?

A pendulum is a weight suspended from a pivot point that is free to swing back and forth in a regular motion due to the force of gravity. It is often used in scientific experiments to demonstrate principles of motion and energy.

2. How does a pendulum work?

A pendulum works by converting potential energy (stored in its height) into kinetic energy (in the form of motion). As the pendulum swings back and forth, it is constantly converting between these two forms of energy.

3. What factors affect the period of a pendulum's swing?

The period of a pendulum's swing (the time it takes to complete one back-and-forth motion) is affected by the length of the pendulum, the force of gravity, and the initial angle of release. The longer the pendulum, the longer the period; the stronger the force of gravity, the shorter the period; and the smaller the initial angle, the shorter the period.

4. How do you calculate the period of a pendulum?

The period of a pendulum can be calculated using the equation T = 2π√(l/g), where T is the period in seconds, l is the length of the pendulum in meters, and g is the acceleration due to gravity in meters per second squared. This equation assumes small angles of release and neglects air resistance.

5. How can a pendulum be used to measure the force of gravity?

A pendulum can be used to measure the force of gravity by measuring the period of its swing and plugging it into the equation T = 2π√(l/g). By rearranging the equation to solve for g, the value of gravity can be determined. This method is often used in physics experiments and has been used historically to accurately measure the force of gravity on Earth.

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