Gravitational potential = Mass x Gravity x height
Energy
So as you can see from this equation if you keep gravity and mass constant and increase the height you will increase the gravitational potential energy.
From another equation we can see how G.P.E will effect the oscillation.
Kinetic energy = Half x mass x velocity2
G.P.E = Kinetic energy
Mass x gravity x height = half x mass x velocity2
So from these equations you can see that as you increase G.P.E you will in turn increase the kinetic energy. This means that the pendulum will swing faster as the angle increases. So and increase in angle might not mean an increase in time for one oscillation.
Air resistance
If there were no other forces acting on it, the pendulum it would keep swinging until it hit something. However, it slows down quite quickly so we know that there must be another force acting on it. This force is friction caused by air resistance. If we could vary the amount of air resistance acting on the pendulum then we could vary its speed.
However, without a vacuum, it is impossible to vary the air resistance and so we can’t use this variable.
But the air resistance will be the same for all experiments so it will be a fair test.
Weight of the pendulum
The bob on the end of the pendulum has a certain mass that is used to create the kinetic energy of the pendulum. If I use the G.P.E equation it shows that if I increase the mass of the bob I should increase the G.P.E and this in turn will increase the kinetic energy of the bob.
But if I use another equation it shows that if you increase the mass of the bob it will increase the force that is needed to stop it.
FORCE = MASS x ACCELERATION
If I use this equation I can prove that if I increase the mass of the bob the longer it will take for the pendulum to return to its start position.
So if I increase the mass of the bob I will increase the G.P.E but I will also increase the force needed to stop it and there should be no increase in the time for one oscillation.
Preliminary Work:
In my preliminary work I will be investigating the factors that I have just stated above, to see if there is any relation between the time for one oscillation and the factors that I have just stated.
Factors to investigate
- Length of pendulum
- Mass of bob
- Angle of release
Angle of release:
Method:
1.Apperatus needed for this experiment:
- Clamp Stand
- Clamp
- 400mm of fish wire
- 30g Mass
- stopwatch
- protractor
- two wooden blocks
2. We set-up the apparatus as shown in the diagram. I pulled the pendulum taught and raised it to my first point of release.
3. I let the pendulum go and at the same time started the stopwatch, I let the pendulum swing ten times before stopping the stopwatch. This technique will reduce the error in starting and stopping the stopwatch.
4. I recorded the time and repeated the experiment three times for each of the six different angles to get a reliable average.
Diagram:
Results:
Conclusion:
From my results I can conclude that the angle of release does not effect the time period of one oscillation. The bigger the angle the bigger the proportion of the circle is taken up by the arc. More of the 360o of the circle is taken up meaning there is a bigger displacement in the oscillation. This in turn increases the time taken for an oscillation.
But if you increase the angle of release you are releasing it from a greater height and therefore increasing the gravitational potential energy.
Gravitational potential = Mass x Gravity x height
Energy
So as you can see from this equation if you keep gravity and mass constant and increase the height you will increase the gravitational potential energy.
From another equation we can see how G.P.E will effect the oscillation.
Kinetic energy = Half x mass x velocity2
G.P.E = Kinetic energy
Mass x gravity x height = half x mass x velocity2
So from these equations you can see that as you increase G.P.E you will in turn increase the kinetic energy.
My graph did show slight differences in some of the readings I think this is because of my measuring inaccuracies with the stopwatch. This would have created slight fluctuations in my results.
Mass of bob:
Method:
1.Apperatus needed for this experiment:
- Clamp Stand
- Clamp
- 400mm of fish wire
- 30g, 40g, 50g, 60g, 70g, 80g Mass
- stopwatch
- protractor
- two wooden blocks
2.We set-up the apparatus as shown in the diagram. I pulled the pendulum taught and raised it to the point of release.
3. I let the pendulum go and at the same time started the stopwatch, I let the pendulum swing ten times before stopping the stopwatch. This technique will reduce the error in starting and stopping the stopwatch.
4. I recorded the time and repeated the experiment three times for each of the six different masses to get a reliable average.
Diagram:
Results:
Conclusion:
From my results I can conclude that increasing the mass of the pendulum does not effect the time period of an oscillation. The bob on the end of the pendulum has a certain mass that is used to create the kinetic energy of the pendulum. If I use the G.P.E equation it shows that if I increase the mass of the bob I should increase the G.P.E and this in turn will increase the kinetic energy of the bob.
But if I use another equation it shows that if you increase the mass of the bob it will increase the force that is needed to stop it.
FORCE = MASS x ACCELERATION
My theory on increasing the mass of the pendulum was proved by the results that I have obtained.
My graph did show slight differences in some of the readings I think this is because of my measuring inaccuracies with the stopwatch. This would have created slight fluctuation.
Length of the pendulum:
Method:
1.Apperatus needed for this experiment:
- Clamp Stand
- Clamp
- 100mm, 200mm, 300mm, 400mm, 500mm and 600mm of fish wire
- 12g Mass
- stopwatch
- protractor
- two wooden blocks
2.We set-up the apparatus as shown in the diagram. I pulled the pendulum taught and raised it to the point of release.
3. I let the pendulum go and at the same time started the stopwatch, I let the pendulum swing ten times before stopping the stopwatch. This technique will reduce the error in starting and stopping the stopwatch.
4. I recorded the time and repeated the experiment three times for each of the six different lengths to get a reliable average.
Diagram:
Results:
Conclusion:
From my results I can conclude that the length of the pendulum does effect the time period of an oscillation. The path at the bottom of the pendulum is like an arc of a circle, with the piece of string a radius. Then according to the circle theorem: C=2πr the circumference will increase as the radius increases. As the circumference increases the bigger the displacement will be from the starting point and the longer the pendulum will take to return to its starting point.
My results have proved this theory so the length of the pendulum will be the factor that I will investigate in my real experiment.