Jae,+Tucker,+Danielle

Jae, Jessica, Danielle Period 4 Date Due: 3/7/11
 * Elastic Potential Energy **


 * Part 1: ** Finding the Spring Force Constant (k)


 * Purpose:** The purpose of part 1 is to find the spring force constant for our particular spring. This constant (k) will be used in part 2 of the lab in our conservation of energy equations.


 * Hypothesis:** Being that the spring compressed and extends pretty easily we hypothesize that it is a soft spring and will have a low spring force constant.

**Materials:** 1. Spring with a hanger 2. Stand with attached ruler 3. 10g Masses

1. Attach Spring to a stand so that it is hanging. Adjust the ruler on the stand so that it is as low on the stand as it can go while still measuring the end of the spring. If possible make it so that the end of the spring is at the 0 mark on the ruler 2. Measure the distance the spring extends before mass is added. 3. Add mass to the end of the spring. 4. Measure the distance the spring extended with the mass and record. 5. Repeat steps 3 and 4 four more times, adding the same amount of mass each time. 6. Create a graph using the weight and the average distance the spring moved 7. The slope of the graph is the Spring Force Constant
 * Procedure:**


 * Data:**
 * Graph:**

Percent Difference Between our Spring Constant and the class average
 * Sample Calculations:**

The data shows that we were essentially correct in our hypothesis. The spring was not very long itself but given that it was rather soft it did stretch pretty far with increasing increments of weight, which would in fact suggest as we hypothesized that the spring force constant was not very large. Again, this was shown to be true in the slope of the graph, which represents the spring force constant. This we know because the equation for spring force constant is: Fs = -kx where Fs equals the weight hanging from the spring, x is the displacement, and k is obviously the spring force constant. The negative in the equation is not significant because it merely represents the fact that the spring force must be opposite the weight to counterbalance it. Because our graph is one of weight versus displacement the slope of the graph must be k, which we found to be 3.7133, a pretty small constant as hypothesized.
 * Conclusion:**


 * Part 2: ** Relationship Between Spring Extension (x) and Final Velocity (v)


 * Purpose:** The purpose of this lab is to determine the relationship between the compression or extension of a spring to the final velocity of the object attached to the spring--using the spring force constant found in Part 1.


 * Hypothesis:** We predict a direct relationship--that the further back the spring is pulled, the higher the final velocity the cart will have.

1. Track (with stopper and meter stick) 2. Cart 3. Same spring from Part 1, without hanger 4. DataStudios (Photogate timers)
 * Materials:**

1. Set up the track (make sure that it is flat on the surface of the table). 2. Attach a 1 cm paper flag to the end of your cart. 3. Attach the stopper to the end of the track. 4. Attach the DataStudios Photogate Timer to the end of the track so that only the paper flag will pass through it at the very end of the track. This must be done so that you are recording the very final velocity. Open the Photogate timer on the computer. 5. Attach one end of the SPring to the cart and the other end to the stopped on the track 6. Record where the end of the cart is when the spring is not being compressed or extended 7. Pull cart back and record the displacement of the cart 8. Let cart go and make sure it passes through the photogate timer. Use the information from DataStudios to calculate the final velocity 9. Record displacement and final velocity on a graph and determine the relationship
 * Procedure:**

**Data:**

**Graph:**

**Sample Calculations:** Theoretical velocity for trial 1 Experimental Velocity for trial 1 Percent Error for each trial % Error =

10 cm: = 19.01%

20 cm: =11.4%

30 cm: =8.55%

40 cm: = 6.89%

50 cm: =7.31%

**Conclusion:** The percent error for the different lengths of stretching generally followed a pattern where as the length of stretching increased the amount of error decreased. This is most likely because the further the spring was stretched the greater the final velocity right before it stopped was. Therefore it would have been easier for the photogate to measure these greater velocities because the movement was less subtle compared to the smaller velocities (the smaller velocities were just barely above zero so it was harder to detect). In terms of sources of error there were several. First, the spring often got stuck to the magnet on the stopper on the track on the way back as it compressed back to equilibrium. This most likely affected some of the trials in that this pulling of the string towards the magnet that also pulled the cart could have made some of the experimental velocities appear larger. It would have affected how quickly the paper flag traveled through the photogate and how far it traveled. Also, another issue was making sure the cart stopped at the correct time so the paper flag only traveled through once and the correct velocity was obtained. Since the cart was attached to a spring when it shot back it then would propel forward again and we had to make sure to catch it before that happened. It's possible it was not caught in time, affecting the velocity measured or that by putting our hand on the cart this affected the velocity measured by perhaps shoving it forward a little bit. In order to eliminate this error it would be ideal to develop a different track that had a stopper that was preferably not magnetic so as not to interfere with the metal spring. Also, it would be most useful to have some sort of braking mechanisms that would stop the cart at the correct time so it it does not propel forward after shooting back. Overall, we were correct in our hypothesis because as the data shows the velocity consistently increased the more the distance stretched was increased. Also, our graph does show the direct linear relationship we predicted between the final velocity and the stretching distance of the spring.