Purpose: The purpose of the lab is to prove the theory and validate the statement that, "In the absence of all other external forces except gravity, a falling body will accelerate at 9.8m/s^2.
Materials/ Procedure: The apparatus consisted of many parts including a long metal tripod stand which is used as a track for the falling electromagnet. Before beginning the process the wooden cylinder with a ring attached to it must be attached to the electromagnet, acting as a conductor for the electric spark to hit the paper strip. This electromagnet is powered by a spark generator which allows it to mark its distance as it free falls from the top of the tripod to the bottom. There is a long strip of spark paper which is zapped with around 60Hz of electricity leaving dark enough dots to see where it was zapped by the electromagnet. After the apparatus is done recording the dots zapped on the paper the first part is done now the mathematical solving and analyzing comes into play.
part 2 procedure: Since we were limited to only one apparatus we were given strips that were made from previous classes in order to give us more time to work on the mathematical part of the lab by using excel. Every 1/60th of a second was the time frame used for the electromagnet to shock the paper strip. We determined a starting point of the paper and then measured the distances apart from each of the dots generated by the spark. The direction is shown but can also be found by analyzing the distances from left to right as they get larger. We were then asked to make at least 20 or more data points that would be plugged into an excel sheet and used to solve mathematically.
The table to the right is a list of the data we took. The 1st column is representational of time which in our case we took every sixtieth of a second which explains why we got such small decimals for time in column 1. The 2nd column is the distances we recorded between each point of the falling electromagnet the first point we recorded being the origin. The change in distance is represented by the 3rd column which means how much more it traveled from the previous distance. The 4th column is when when we doubled our time frame for the shock to hit the strip which is every hundred and twentieth of a second. Which would be the midpoint between two of the sixtieth of a second intervals. The 5th column was the average velocity of the falling object on a hundred and twentieth of a second time interval. Using this data we set up a time vs distance graph.
 |
| Distance vs. Time |
We found out by using curve fit that the line is representational of a parabola. This equation is almost identical to the position equation used in physics 2A (x(t)= Xo+Vot+1/2at^2 ). By using this graph we can now have an equation where we can derive the v(t)(velocity vs. time) equation and also derive the a(t)(acceleration vs. time) equation which will give us an acceleration of 9.56m/s^2. This differs from the already given value of g= 9.8m/s^2. This tells us that somewhere along the way we had error or the computer may have miscalculated.
 |
| Velocity vs. Time |
We derived the acceleration from here by taking the derivative of the equation given.
V(t)= 954x+42.529
Giving us a g value of 9.54m/s^2 which isn't the g value of 9.8m/s^2.
Class data: We did an entire graph together as a class and found that the average class values were also off from the actual value of g (9.8m/s^2). The picture on the bottom shows the first column as the solved g values for each group. The second is the difference between the class average at the bottom of column one and the actual deviations of groups. The third column shows the average of the second column squared and square rooted to find the mean of the deviation from the class average to their solved g value. The class average was about 20.12.
We were able to find the range of the g value as a class which was between 916 to 996 giving a possible error of about +/- 2.
Given by the lab packet, we found the percentage of it being between our data was around 95 percent. An error could have been made with measuring accurately causing our numbers to be off by a few tenths.
Final Thoughts: Although we did not solve an exact value for g we did get fairly close in our data and identified a relationship using excel spreadsheet to solve for the g of our strip paper. Our class average of about 950 and our groups value of 956 differs in the excepted value of 980. Which gives us reason to believe there was a small error in recording the data causing our numbers to easily differ from group to group. We learned that by doing this lab we will run into some trial and error after analyzing our data. We also retouched on our skills with excel spreadsheet and how to input equations to get the results, although we didn't solve for g exactly we did learn about excel and how solving mathematically may not always get you the exact value, but doesn't mean your wrong.
No comments:
Post a Comment