Mechanical energy in a pendulum

In summary: To do this, you need to find the velocity of the pendulum at the bottom of its swing. This can be done using the conservation of energy equation: Etotal=Ek+Eg. You have the value for Eg from your previous calculation, and you can use the velocity you just calculated to find Ek. Once you have both Ek and Eg, you can add them together to find Etotal.(a) In summary, a pendulum was set up and measurements were made to calculate the mechanical energy at the start position and the lowest point of the pendulum's swing. The mass and diameter of the pendulum bob were determined, as well as the initial height and the time interval of the photogate light interruption. Using this data
  • #1
Shaley
12
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A pendulum was set up and measurements were made to enable the mechanical energy to be calculated at the start position S and the lowest point of the pendulums swing L.

The mass of the pendulum bob was determined on an electronic scale and its diamter was measured using calipers. The initial height was measured with a meter stick. At the lowest point of its swing, the pendulum bob broke a photogate light beam. The time interval that the light was interrupted was recorded on an electronic timer attached to the photogate.
Use the following data to complete a report.
MAss of pendulum bob = 240.3 g
Diameter of pendulum bob = 3.50 cm
Initial height of pendulum bob = 48.0 cm
Length of pendulum string = 2.14 m
Time interval of photogate light interruption = 11.8 ms

Your report should include the following:
(a) conclusion as to whether or not the pendulum demonstrated the law of conservation of energy
(b) calculations of the efficiency of the pendulum as a mechanical machine

I am really confused how to even start this question. I think that I should figure out the Emechanical = Ek + eg

=1/2(240.3)(0) + 240.3(9.8)(.48)
=1130.37J

to calculate the speed of when it hit, I did the following:

The clue is the diameter of the bob
it broke the beam for 11.8 *10^-3 seconds
it is .035 meters in diameter
so it went
.035 meters in 11.8^10^-3 seconds
which is about 2.97 meters/s

From here, I don't really know where to go. Please help me.
 
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  • #2
Shaley said:
I am really confused how to even start this question. I think that I should figure out the Emechanical = Ek + eg

=1/2(240.3)(0) + 240.3(9.8)(.48)
=1130.37J
You have made a good start. There is an issue with the units here; to get energy in Joules, you must use m, kg, and s for the other units. One of quantities in your Eg calculation is in the wrong units.

to calculate the speed of when it hit, I did the following:

The clue is the diameter of the bob
it broke the beam for 11.8 *10^-3 seconds
it is .035 meters in diameter
so it went
.035 meters in 11.8^10^-3 seconds
which is about 2.97 meters/s

From here, I don't really know where to go. Please help me.
You can now do the calculation of Etotal=Ek+Eg for when the pendulum is at the bottom of its swing.
 

Related to Mechanical energy in a pendulum

1. What is mechanical energy in a pendulum?

Mechanical energy in a pendulum refers to the sum of kinetic energy and potential energy that is present due to the motion of the pendulum. Kinetic energy is the energy possessed by the pendulum due to its motion, while potential energy is the energy stored in the pendulum due to its position.

2. How does the length of a pendulum affect its mechanical energy?

The length of a pendulum does not directly affect its mechanical energy. However, the length of a pendulum does affect its period, which is the time it takes for one full swing. A longer pendulum will have a longer period and therefore, a lower frequency and less mechanical energy. A shorter pendulum will have a shorter period and therefore, a higher frequency and more mechanical energy.

3. Is the mechanical energy of a pendulum constant?

Yes, the mechanical energy of a pendulum is constant as long as there is no external force acting on it. This is due to the conservation of energy principle, which states that energy cannot be created or destroyed, only transferred from one form to another.

4. What happens to the mechanical energy of a pendulum when it swings back and forth?

As a pendulum swings back and forth, its mechanical energy remains constant. However, the energy is constantly being transferred between kinetic and potential energy. At the highest point of the swing, the pendulum has the most potential energy and the least kinetic energy. At the lowest point of the swing, the pendulum has the most kinetic energy and the least potential energy.

5. Can the mechanical energy of a pendulum be increased?

Yes, the mechanical energy of a pendulum can be increased by increasing its amplitude, which is the distance from the center point to the maximum point of the swing. This will result in a higher potential energy and therefore, a higher total mechanical energy. However, this increase in energy will cause the pendulum to have a longer period and a lower frequency.

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