Circular Motion

Hypothesis

In this experiment, the factor that will be changed is the radius of the string. As the radius of the string decreases, the speed of the revolving rubber stopper increases. This would happen because as the radius decreases, the rubber stopper takes less time to circle around with the constant centripetal force on it. In other words as the radius decreases, the size of the circle decreases, hence it takes less time to cover a smaller circle, with the same force acting on the rubber stopper. In other words, the radius of the string is inversely proportional to the velocity of the stopper.

                        Radius(r)   ~        1

          Velocity(v)

Design

Materials required

• Rubber stopper
• String
• Washers
• Plastic tube
• Meter Stick
• Marker

Procedure

1. When all the materials are acquired, the apparatus should be set up like this:

2. With the use of a marker and a meter stick, I’d make a mark on the lower end of the string so that the first data point (0.800m) is the radius.
3. I’d measure the mass of the stopper and the washers with the help of the weighing scale.(the weight of the washers is the centripetal force, in our case 1.19 N)
4. Then I would start revolving the stopper without touching any part of the apparatus except the plastic tube.
5. The timer will time 10 rotations with the stop watch.
6. I’d note down the time and repeat steps 4, 5 and 6 two more times to get three trials.
7. Now, decrease the radius with the help of the marker and the meter stick to get the next data point.(in our case it was 0.700m)

Data collection

        The table below shows the time for 10 rotations. The time is then divided by 10 to get the time for 1 rotation.

        Average time of one rotation at decreasing radius

Data

• Time of one Rotation= 0.68s
• Uncertainty of Rotations= ±0.001s

• Average Time= 0.68s
• Uncertainty of Average Time= 0.68s ± 0.05s
• Velocity= 7.39 ms-1

Velocity Uncertainty= 0.04785

Conclusion

        Overall, the experiment was carried out with minimum errors and followed as the procedure. There were eight data points with three trials each. The experiment was related to one factor that affected the motion of the rubber stopper in circular motion. In this experiment, that factor was the length of the string (radius). As stated in the hypothesis, the radius was decreased which would increase the velocity of the stopper. But as it can be seen from the data table and graph that as the radius decreased the velocity also decreased. Hence, the radius of the string is directly proportional to the velocity of the stopper. This proves my hypothesis wrong which stated that as the radius decreases, the velocity increases.

        In my experiment, the radius was decreased which decreased the time elapsed but decreased the velocity as well. This would have happened because as the radius decreased, the stopper actually has to move faster in order to cover the larger circle in the same amount of time. The stopper actually covers much more area of the circle when the radius is larger without taking more time. This theory is exactly opposite as stated in my hypothesis.

Evalutation

        As it can be seen from my graph and the data table that there were some errors in my experiment. The percent error that was calculated to be 13.5 % assures the fact that there were flaws in my experiment. One big error was that when the stopper was revolving, the hand often touched the string of the stopper. This often altered the centripetal force acting on the string, hence changing the values of my data. Another error was that not all the time the radius mark (the mark on the string with the marker) used to be exactly under the plastic pipe. Because of this, the values of the radius were altered hence changing the velocity factor in my experiment.

Self-improvements

        The errors/flaws stated above can be prevented by a number of steps. Always during the experiment, the only part the hand should touch is the plastic tube only. Even if the hand touches any other part of the apparatus, the experiment should be stopped carefully and the trial should be re-done. Also, instead of using a marker on the string, he string should be tapped or tagged at the point needed. The tag should be greater than the radius of the hole of the plastic tube so that the tag does not pass through the hole, hence it will not alter the value of the desired radius.