Control Variable:
Number of bobs
Results:
The first bob weighs 14.42 ± 0.05 grams attached to a 55 ± 0.05 cm, string releasing the bob at 70° ± 0.5 having an average time of 2.76 ± 0.01 seconds. Adding another bob which give a total weight of 30.17 ± 0.05 grams attached to a 55 ± 0.05 cm string, releasing the bob at 70° ± 0.5 having an average time of 1.22 ± 0.01 seconds. Adding the last bob which give a total weight of 46.34 ± 0.05 grams attached to a 55 ± 0.05 cm, string releasing the bob at 70° ± 0.5 having an average time of 1.21 ± 0.01 seconds (Table 1).
Table 1: The measurements of the pendulum’s period with the varied weights of the bobs attached.
Conclusion:
As the mass of the bob increases, the period of the pendulum decrease. As indicated in table 1, the first bob with a mass of 14.42 ± 0.05 grams had an average time of 2.76 ± 0.01 seconds. The second bob that weighs 15.75 ± 0.05 grams was added to the 55 ± 0.05 cm string with the first bob, the total weight was 30.17 ± 0.05 grams. It took both bob to swing one complete cycle in an average time of 1.22 ± 0.01 seconds, having a difference of 1.54 ± 0.01 seconds. Demonstrating that adding a greater mass can quicken the period of the pendulum. Finally attaching the last bob with a mass of 16.17 ± 0.05 grams, the total mass was 46.34 ± 0.05 grams. It had an average time of 1.21 ± 0.01 seconds having slight differences of 0.01 ± 0.01 seconds. This supports statement of the conclusion that as the mass of the bob increases, the period of the pendulum decreases. The source of error is human error in timing of the swing using a stopwatch. By relying on human reflexes will result in inaccurate and inconsistent start and finishes. The timing method was not sufficient for this experiment. Having a timing method more suitable of this experiment would produce an accurate timing result.
Lab 1 Part 2 – To determine how the displacement affect the period of a pendulum.
Hypothesis:
As the displacement increases, the period of the pendulum to swing one whole cycle will increase. The reason which could make this hypothesis true is that increasing the displacement is similar to creating a longer distance for the pendulum to swing back and forth. Such as, walking 10 m and back will be longer than walking 5 m and back. Thus having the pendulum swing a higher distance will most likely increase the period of the pendulum.
Methods:
- Obtain one rubber stopper (bob).
- Determine the mass of bob using the scale that measures to the nearest 0.05 grams
- Attach a string to the ring clamp.
- Attach a meter stick to the ring stand such that the zero on the scale is aligned with the point where the string is attached.
- Locate the 55 cm ± 0.05 on the scale of the ruler and attach the bob. Such that the top of the bob aligned with the point where it measures 55 cm ± 0.05.
- Remove the ruler.
- Attach a protractor in front of the ring clamp such that the vertex is aligned with the point where the string is attached.
- Angle the string to 70° cm ± 0.5 by pulling by the bob.
- Get the stop watch ready.
- Quickly remove the protractor and begin timing as you release the pendulum.
- Measure the total time required for the pendulum to swing three cycles.
- Divide your result by three.
- Repeat the process above twice and continue to step 11.
- Calculate the average of the three results.
- Repeat the procedure but adjusting the displacement angle to 60° cm ± 0.5.
- Repeat the procedure but changing the displacement angle to 50° cm ± 0.5.
Control Variable:
Angle of displacement
Results:
The bob that remained consisted throughout the trail weighs 15.73 ± 0.05 grams, attached to a string that also stayed consisted throughout the trial measures 55 ± 0.05 cm, setting the displacement at 70° ± 0.5 having an average time of 1.59 ± 0.01 seconds. Adjusting the pendulum to a 60° ± 0.5 had an average time of 1.54 ± 0.01 seconds. Changing the angle of the pendulum being released to 50° ± 0.5, having and average time of 1.47
± 0.01 seconds.
Table 2: The measurements of the pendulum’s period having different measurements of displacements.
Conclusion:
As the displacement increases, the period of the pendulum increases. Referring to table 2, the first displacement was released at 70 ± 0.5° resulting an average time of 1.59 ± 0.01 seconds. The second displacement was set at 60 ± 0.5°, having a degree difference of 10 ± 0.5°. The second displacement had an average time of 1.54 ± 0.01 seconds having a difference of 0.05 ± 0.01 seconds. The last displacement was set at 50 ± 0.5° had an average time of 1.47 ± 0.01 seconds, having a time difference of 0.07 ± 0.01 seconds compared to the second displacement. This also confirms the conclusion statement, as the displacement increases the period of the pendulum increases. The source of error is human error in timing of the swing using a stopwatch. By relying on human reflexes will result in inaccurate and inconsistent start and finishes. The timing method was not sufficient for this experiment. Having a timing method more suitable of this experiment would produce an accurate timing result.
Lab 3 Part 3 – To determine how the length of string affect the period of a pendulum.
Hypothesis:
As the length of the string increases, the period of the pendulum to swing one whole cycle will increase. Reasoning which could make this hypothesis true is it is easier to travel quickly in small distance than a larger distance. Sampling the child’s swing and the adult’s swing, the child’s swing has a smaller distance to swing from compared to the adult’s swing which allows them to swing at a larger distance. Thus the pendulum will swing faster on a shorter string than a longer string.
Methods:
- Obtain one rubber stopper (bob).
- Determine the mass of bob using the scale that measures to the nearest 0.05 grams
- Attach a string to the ring clamp.
- Attach a meter stick to the ring stand such that the zero on the scale is aligned with the point where the string is attached.
- Locate the 55 cm ± 0.05 on the scale of the ruler and attach the bob. Such that the top of the bob aligned with the point where it measures 55 cm ± 0.05.
- Remove the ruler.
- Attach a protractor in front of the ring clamp such that the vertex is aligned with the point where the string is attached.
- Angle the string to 70° cm ± 0.5 by pulling by the bob.
- Get the stop watch ready.
- Quickly remove the protractor and begin timing as you release the string.
- Measure the total time required for the pendulums to swing three cycles.
- Divide the result by three.
- Repeat the process above twice and continue to step 11.
- Calculate the average of the three results
- Repeat the procedure replacing the string with another string with a length of 65 cm ± 0.05.
- Repeat the procedure replacing the string with another string with a length of 75 cm ± 0.05.
Control Variable:
Length of string
Results:
The mass of the bob stayed consisted throughout the trial. A string measured 55 cm ± 0.05 cm having a bob attached at the end releasing it at 70° ± 0.5 having an average time of 1.08 ± 0.01 seconds. Replacing the string with a length of 65 cm ± 0.05 cm and setting the pendulum at 70° ± 0.5 having an average time of 1.18 ± 0.01 seconds. Changing the string that measures 75 cm ± 0.05 cm having a bob attached at the end of the string, releasing it at 70° ± 0.5 having an average time of 1.32 ± 0.01 seconds (Table 3)
Table 3: The measurements of the pendulum’s period with different length of strings.
Conclusion:
As the length of the string increases, the period of the pendulum increase. As indicated in table 3, the first string measured 55 ± 0.05 cm had an average time of 1.08 ± 0.01 seconds. The second string measured 65 ± 0.05 cm having a length difference of 10 ± 0.05 cm. The second string had an average time of 1.18 ± 0.01 seconds, having a difference of 0.10 ± 0.01 seconds. Indicating that, the pendulum travels faster with a smaller string than a larger string. The last string measured 75 ± 0.05 cm, which adds 10 ± 0.05 cm to the second string, had an average time of 1.32 ± 0.01 seconds having a difference of 0.14 ± 0.01 seconds. This also supports the conclusion statement, as the length of the string increases, the period of the pendulum increases. The source of error is human error in timing of the swing using a stopwatch. By relying on human reflexes will result in inaccurate and inconsistent start and finishes. The timing method was not sufficient for this experiment. Having a timing method more suitable of this experiment would produce an accurate timing result.
Discussion:
After completing three experiments with all three factors, weight of the bob, the change of displacement and the length of the string affected the period of a pendulum. The time increased as both the displacement and length of string increased. Considering both factors caused the pendulum to travel a longer distance increasing the period. The only increasing factor that causes the pendulum’s period to decrease is the weight of the bob. As the mass of the bob increases the period of the pendulum decreases, by increasing gravitational force from the mass of bob. The following table on Lab 3 – part 1, 2 and 3 had one factor of either the weight of the bob, the displacement and the length of the string (the independent variables). The tables show that each factor had an effect of the pendulum’s period (the dependant variable).The results was, when increasing the two factors, displacement or length of string increase the period of a pendulum. However, when increasing the mass of the bob, the period of the pendulum decreases. Either way, all three factors, weight of the bob, the displacement, and the length of the string affect the period of a pendulum.
