Philip,+Sean,+Bick,+Rick


 * Law of Conservation of Energy With Spring Lab**


 * Objective:** To find the "k" value (spring force constant) of a certain spring. To find the relationship between EPE, GPE, and KE

Part 1: The larger the mass placed on a hanging spring, the more it will stretch out. We hypothesize this because the GPE, as shown by the formula GPE = mgh, will increase as the mass increases. Therefore, the EPE will increase as well. And since "k" is constant, and there is no KE, the x value has to increase (EPE = 1/2 k x^2), therefore increasing the length that it stretches out.
 * Hypothesis:**

Part 2: The farther the horizontally stretched spring is stretched, the faster the velocity will be once it snaps back. We hypothesize this because the KE formula is 1/2 mv^2 = KE. Therefore, if the x value in the EPE equation increases, the KE will have to increase as well. And since the mass will remain constant, and there is no GPE, the velocity will have to increase.


 * Materials:**
 * Frictionless Track
 * Cart which won't produce friction
 * Spring (same spring for both experiments 1 & 2)
 * Data Studio Photogate Timer
 * Laptop w/USB port
 * Ring Stand
 * Masses (2, 5, and 10 g)
 * Picket (1 cm and made of paper)

Part 1:
 * Procedure:**
 * Attach the spring to a ring stand with a hanging mass on the lower part of the spring
 * Measure the distance that it is displacing the spring downwards. This will be the "zero point"
 * Gradually add masses (in very small increments)
 * Measure the displacement distance with every added mass
 * Record this data on an excel spreadsheet
 * Calculate the data into a graph (the slope should be the "k" value)
 * Do each trial with the masses multiple times

Part 2:
 * Lay down the frictionless track
 * Place the cart on the track
 * Attach the same spring from Part 1 onto one side of the cart and one end of the track
 * Attach the picket onto the spring-holding edge of the cart
 * Set up the Photogate Timer just before the end of the track where the spring is attached
 * Attach the Photogate Timer to the laptop and set up DataStudio to Photogate Timer mode
 * Pull the cart back in small increments as shown by the measurements on the track
 * Release the cart and record the time it took to cross the Photogate Timer on DataStudio
 * Take this data and calculate the velocity by using the time it took the picket to cross the Photogate Timer
 * Do each trial with the masses multiple times
 * Record this data on an excel spreadsheet
 * Calculate the data into a graph (the relationship shown between distance pulled back and velocity should be linear)


 * Graph (Part 1)**:

Percent Difference:




 * Graph (Part 2)**




 * Data:**

Part 2




 * Sample Calculations:**

Theoretical Velocity for .1 m stretched.

Experimental Velocity for .1 m stretched. Width of "flag" is .01 m.




 * Percent Error:**

For .1 m stretched




 * Conclusion and Error Analysis:**

Our hypotheses in these respective experiments were shown to be correct. Upon analyzing our data, it can be found that the spring's stretch distance did indeed increase with a greater hanging mass. Also, we found that the velocity increased the further away we pulled the cart. These demonstrate the fundamental principles of Hooke's Law as well as the Law of Conservation of Energy. We found both of these relationships to be direct and linear between GPE vs. EPE and KE vs. EPE.

Although our execution of this experiment was pristine, there were some experimental qualities which could not be fixed. First of all, despite the fact that the track had no friction in an ideal scenario, this situation was far from perfect. The wheels from the cart would rub up against the borders of the track, and the spring would move around. This caused for the force to come from different angles and therefore effect the cart's movement in an unintended manner. Another intangible which we couldn't account for was the fact that it was impossible for the Photogate Timer to be placed at the direct end of the track because of the problems that the paper picket presented.