| Links | | | |
| Journal Entries |
| Thursday May 5 |
|
| Friday May 6 |
|
| Tuesday May 10 |
|
| Thursday May 12 |
|
| Friday May 13 |
|
|
| Analysis |
Discussion of Analysis
In the pictures we analyzed, the pendulum is clearly visible in two positions and the full length of the string is visible, meaning the angle seen is the true angle that the pendulum swung to in the amount of time between the two flashes. Using Adobe Photoshop, we measured the angle swung out by the string between the two flashes.
To find the amount of time between flashes, we used the rotating clock method. We first took a picture of a
rotating disk. The disk had one hand on it that was illuminated by the two flash units, giving the position of the hand at the times of the two flashes.
Again, we used Adobe Photoshop to Measure the angle swept out by the hand in the time between the two flashes. Knowing the period of 1 rotation of the disk (by measuring the frequency using a stroboscope and the formula p = 1/f), we were able to find the amount of time between flashes, since the ratio of the angle swept to the number of degrees in a circle is equal to the ratio of amount of time between flashes to the period of the disk.
This told us the amount of time it took the pendulum to swing through the angle that it swung through in our other picture.
We also needed to find the distance traveled by the pendulum, in addition to the time, to calculate the velocity of the pendulum. To help us in this, we took a scale photo to help us in converting Photoshop measurement units to real life units.
We used a known distance on a photo of a ruler and measured it to find its length in Photoshop units to make a conversion factor to convert the radius of the arc swung out by the pendulum from Photoshop units to real-life centimeters. Using the radius, we calculated the circumference of the circle which the pendulum traveled along. Since the ratio of the angle swept out to the number of degrees in a circle is equivalent to the ratio of the arc length traveled to the circumference of the circle, we were able to calculate the length of the arc the pendulum traveled, and therefore the distance traveled. Knowing the distance traveled by the pendulum and the amount of time it took to travel that distance, we were able to divide the distance by the time and calculate the average velocity of the pendulum between the two positions at the times of the two flashes.
Measurments Value Absolute Uncertainty % Uncertainty
Angle Clock 132.7 degrees +- .5 degrees .4
Frequency 57 hz +- .5 hz .9
Angle String 34.9 degrees +- .5 degrees 1.0
String Length 7.535 psu +- .2 psu 3.0
Distance Act. 12.7 cm +- .2 cm 2.0
Distance Photo 3.1317 psu +- .2 psu 6.0
TOTAL 27.1 m/s +- 2.7 m/s 10.
|
|
|
