Ktratc

Methodology

The following materials are used in conducting the experiment – ring, thread, pulleys, force table, set of weights, block of wood, platform balance, graphing paper, ruler and bubble level.

1. Leveling the force table

The students adjusted the legs of the force table and achieved a leveled table using the bubble level.

1. Preparation of the equilibrant

The tip of a thread was tied on the ring and the other end was attached to a 200 g mass. In this experiment, 200g used was a pan containing coins of different values. The mass was weighed using the platform balance. The pulley was set at the 210o. The thread passed through the pulley. This mass served as the equilibrant of the vectors that were attached next.

1. Different cases to KTRATC

There were five cases that were performed with the aim to keep the ring at the center (KTRATC) on the force table.

1. For the first case, another pulley and mass were added to the force table. The added hanging mass and angle were adjusted to KTRATC.
2. Another pulley and mass were added to the force table so there was a total of three hanging masses on different positions now. Again, the position was adjusted to KTRATC.
3. One of the pulleys from case two was adjusted by at least 10o.. The mass was adjusted also adjusted and the ring was centered.
4. The two added hanging masses were made to be perpendicular from each other, regardless of the equilibrant. Their masses were adjusted to KTRATC. The ring was seen to be at the center when the masses were changed.
5. The two added hanging masses were removed first. In this case, the total hanging masses used are four. Their magnitudes and positions were adjusted to KTRATC. Two trials were done.

1. Trial 1

In this trial, two hanging masses with equal magnitudes were added. The aim KTRATC was achieved by adjusting the position of both hanging masses.

1. Trial 2

The magnitudes of the hanging masses were increased, but were still equal.

1. Solving for the vectors

The masses and angles of all the pulleys were hanged on the force table were recorded on every case. After gathering the data, these were all drawn on a graphing paper. The resultant vectors and equilibrants are identified and labeled on the graphs. The percentage error for each case was then calculated. The following equations were used in computing for the resultant vector:

Results and Discussion

Case 1

A mass of 200.03g was attached to the ring and was hanged in the pulley at an angle of 210°. Another hanging mass of 200.09g was attached to the ring at an angle of 30.5°. The magnitude of the mass and the angle of attachment of the second hanging mass allowed the ring to be on the center. The obtained analytical value for the mass and angle of the equilibrant was 183.65g and 210.68°, respectively. This implies that the ring will be more centered if the equilibrant is 183.65g and positioned at an angle of 210.68°.

Through calculation, the obtained percentage error of the mass and the angle of the equilibrant were 8.9% and 12.7% respectively.

Case 2

Two masses of different magnitude at different angle of attachment were hanged. At this point, there were three total number of masses attached to the ring. One of the masses has a magnitude of 147.80g attached at an angle of 275° while the other mass has a magnitude of 295g attached at 62.5°.Using the two added hanged masses, the ring was kept at the center. The obtained analytical value for the mass and the angle of the equilibrant was 159.00g and 199.95°, respectively. This implies that the ring will be more centered if the equilibrant is 159.00g and positioned at an angle of 210.68°.

Through calculation, the obtained percentage error of the mass and the angle of the equilibrant were 25.81% and 8.7% respectively.

 Case 3

From the set-up in Case 2, the ring was not kept at the center by changing only the position of one of the pulleys by at least 10°. However, it was possible to KTRATC by just changing the magnitude of the hanging mass and adjusting its position by at least 10° as well. The mass with a magnitude of 173.47g and positioned at 285° kept the ring at the center. The obtained analytical value of the equilibrant was 193.07g at an angle of 199.95°. This implies that the ring will be more centered if the equilibrant is 193.07g and positioned at an angle of 199.95°.

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