Conservation of energy of a pendulum

In summary, a pendulum with a mass of m, length of L, and force constant of k is suspended from the ceiling and attached to a spring fixed to the floor directly below the pendulum support. The unstressed length of the spring is L/2 and the distance between the floor and ceiling is 1.5L. When the pendulum is pulled aside at an angle θ with the vertical and released from rest, the speed of the pendulum bob can be obtained by using conservation of energy, taking into account the potential energy of the stretched spring and the extra height gained.
  • #1
knowNothing23
35
0
A pendulum is suspended from the ceiling and attached to a
spring fixed to the floor directly below the pendulum support. The
mass of the pendulum bob is m, the length of the pendulum is L, and the force
constant is k. The unstressed length of the spring is L/2 and the distance between
the floor and ceiling is 1.5L. The pendulum is pulled aside so that it makes an
angle θ with the vertical and is then released from rest. Obtain an expression for
the speed of the pendulum bob as the bob passes through a point directly below
the pendulum support.

I'll set point 1, when the pendulum is about to move and point 2, when it reaches the lowest point. Then use conservation of energy. I'm not sure, where to include the potential energy of the spring. Please, help.
 
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  • #2
knowNothing23 said:
A pendulum is suspended from the ceiling and attached to a
spring fixed to the floor directly below the pendulum support. The
mass of the pendulum bob is m, the length of the pendulum is L, and the force
constant is k. The unstressed length of the spring is L/2 and the distance between
the floor and ceiling is 1.5L. The pendulum is pulled aside so that it makes an
angle θ with the vertical and is then released from rest. Obtain an expression for
the speed of the pendulum bob as the bob passes through a point directly below
the pendulum support.

I'll set point 1, when the pendulum is about to move and point 2, when it reaches the lowest point. Then use conservation of energy. I'm not sure, where to include the potential energy of the spring. Please, help.

When you pull it aside [to your point 1] the spring will be stretched - some stored energy there, and the bob will be further from the floor than when at point 2 so the extra height will give some PE gain..

When the bob passes through its lowest point [your point 2] there is no energy stored in the spring, and the extra height [so PE] has also gone.
Your conservation of energy should work from there.
 
  • #3
Thank you, Peter. Now, it's clear.
 

FAQ: Conservation of energy of a pendulum

What is the principle of conservation of energy?

The principle of conservation of energy states that energy cannot be created or destroyed, but can only be transferred or transformed from one form to another.

How does a pendulum demonstrate the conservation of energy?

A pendulum demonstrates the conservation of energy through its oscillation. As the pendulum swings back and forth, the potential energy at the top of its arc is converted into kinetic energy as it moves downwards, and then back into potential energy as it swings back up. This cycle continues without any energy being lost.

What factors affect the conservation of energy in a pendulum?

The conservation of energy in a pendulum is affected by the mass and length of the pendulum, as well as the amplitude of its swing. These factors determine the amount of potential and kinetic energy present in the system.

Can the conservation of energy be violated in a pendulum?

No, the conservation of energy cannot be violated in a pendulum. As long as there is no external force acting on the system, the energy will remain constant and be transferred between potential and kinetic forms.

How does friction affect the conservation of energy in a pendulum?

Friction can cause some energy to be lost in a pendulum, as it converts kinetic energy into heat. This means that over time, the amplitude of the pendulum's swings will decrease, but the total energy of the system will still remain constant.

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