Spring Energy Lab
Purpose
We are going to use the Law of Conservation of Energy to estimate k for a spring in a marble launcher. Also we are going to establish a relationship betwwen the compression of the spring and its potential energy. Then, we are deriving an equation in order to make a comparison between spring force and compression.
Equipment
We used a marble launcher, a marble, about 6 meters of paper, and a marker. The paper was turned into a measuring device by useing a marker and marking each .1 meter mark.
Procedure
First, we decided the best way to calculate the potential energy of a spring, which we determined to be: find where KE of the marble is = 0, so that the mable has all PE. The PE of the marble is equal to the PE of the spring because we assume complete energy conversion without loss due to drag and friction. Then, we came up with a way to measure PE. In order to measure PE, we knew that it was mgh, we shot the marble straight up using the launcher and with the giant measuring paper determined the height at which the marble was at KE=0, or the peak of its travel. After that, we set it up in a stairwell, and did 3 trials for each of the 5 different levels of compression for the spring in the launcher. Finally, we used our data to find a line of best fit, or regression line, which would give us the approximate k value, and the amount of error.
Data
energy_of_a_spring.xlsx | |
File Size: | 13 kb |
File Type: | xlsx |
Data Analysis
The data seen in the spreadsheet was collected during the 3 trial per level of compresion. The graph shows the relation between potential energy and compression of a spring, and it was fitted with a polynomial function of degree 2, because we were determining the k value of the spring, and the potential energy of a spring is (1/2) k x^2, which is also a polynomial function of degree 2. Therefore, our approximate k value was determined by setting 7.5284(x^2)=(1/2)(k)(x^2), and solving for k, which equals 15.0588. The other part of the polynomial, .495x+.0133, is considered error for this lab, which could have come about through drag, friction, and operating errors. Also the force of the spring in terms of compression is 15.0588x + 0.495. This equation for force is determined by taking the derivative of the PE equation, with respect to compression.
Conclusion
In conclusion, we successfully determined a k value for the spring, and we created a comparision between PE of the spring and compression of the spring, as well as Spring force and compression of the spring by using equations that were based on x, the compression of the spring, and real life data.