Investigation: Mechanical Energy in a Pendulum

[trossi]

Homework Statement

a pendulum was set up and measurements were made to enable the mechanical energy to be calculated at the start position and the lowest point of the pendulum's swing. The mass of the pendulum bob was determined on an electromic scale, and its diameter was measured using calipers. The initial hieght was measured using a metre stick. At the lowest point of its swing, the pendulum bob broke a photogate (spart or light generator) light beam. The time interval that the light was interrupted was recorded on an electronic timer attached to the photogate.

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: 11.8ms

Homework Equations

For my report I need to calculate mechanical energy at the start position and at the lowat point of the pendulum's swing.
I also need to include:
- a conclusion as to whether or not the pendulum demonstrates the law of conservation of energy
-my calculations of the efficiency of the pendulum as a mechanical machine


I'm not sure how to approach this question

 

[dynamicsolo]

What is the definition of mechanical energy?
What types of energy are included in it?
How do you calculate the values of those energies?
What measurements have you made that will help you find the quantities needed for calculating those energies?

One of the things you are asked to do is to compare the mechanical energy at the moment when you released the bob and at the moment when it was at the bottom of the swing, crossing the photogate (why do you make a time measurement then?).

 

[Moetasim]

as I do not have access to the data and measurements taken during the investigation. However, I can provide a general response to the content provided.

Firstly, the investigation seems to have been conducted in a thorough and precise manner. The use of an electronic scale, calipers, and a photogate to measure the mass, diameter, and time interval of the pendulum respectively, shows attention to detail and accuracy.

To calculate the mechanical energy at the start position and lowest point of the pendulum's swing, the following equations can be used:

- For potential energy at the start position: PE = mgh (where m is the mass, g is the acceleration due to gravity, and h is the initial height)
- For potential energy at the lowest point: PE = mgh (where h is the length of the pendulum string)
- For kinetic energy at the lowest point: KE = 1/2mv^2 (where m is the mass and v is the velocity, which can be calculated using the time interval and length of the pendulum string)

To determine if the pendulum demonstrates the law of conservation of energy, the total mechanical energy (potential energy + kinetic energy) at the start position should be equal to the total mechanical energy at the lowest point. If they are not equal, then there may have been some energy lost due to friction or other factors.

To calculate the efficiency of the pendulum as a mechanical machine, the following equation can be used:

- Efficiency = (useful energy output / total energy input) x 100%

The useful energy output in this case would be the kinetic energy at the lowest point, and the total energy input would be the potential energy at the start position.

In conclusion, the investigation appears to have been conducted properly and the provided data and measurements can be used to calculate the mechanical energy, determine if the law of conservation of energy holds true, and calculate the efficiency of the pendulum as a mechanical machine.