Murtagh,+Andrew,+Steven,+Justin

= **__ Lab 1: Elastic Potential Energy __** = toc

**Class:** Period 2 **Date Completed:** March 7, 2011 **Date Due:** March 8, 2011
 * Group Members:** Andrew Miller, Chloe Murtagh, Steve Thorwarth, Justin Tosi

First, find the spring force constant of the second spring. After we accomplish this, we want to find the final velocity that results from the elastic potential energy. We can find this because of the Law of Conservation of Energy, that energy is only transfered and never created or destroyed. The addition of mass to the spring should change the distance the spring stretches. As we add more mass, the spring should stretch more. The slope of our graph between the force of the added weights and the distance the spring stretched will be the spring force constant. This number should be between 3.5N/m and 4.5 N/m. The father we stretched the spring on the track, the less time it takes the paper to go through the photogate timer. Also, the further we pulled back the cart, the faster final velocity.
 * Purposes:**
 * Hypotheses:**
 * Materials:**
 * Metal cart
 * Spring
 * Various Weights
 * Photogate
 * Computer (Data Studio and Excel)
 * Ruler and meterstick


 * Procedure 1: Finding the Spring Force Constant**

1. Set up spring on stand. 2. Place weights in increments of 2 g onto spring. 3. Allow spring to reach equilibrium, then measure where point is on ruler (located on the stand). 4. Record data.

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 * Procedure 2: Finding the Final Velocity of the Cart**

1. Attach spring and photogate timer to end of track. 2. Attach cart to spring. 3. Measure length of sheet of paper attached to cart (this will be distance cart travels through photogate timer). 4. Pull cart back certain distance, and release, allowing it to run through photogate timer. 5. Record time in photogate using data studio. 6. Find final velocity experimentally (d/t) and compare to theoretical. 7. Graph results.

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 * Data: **

Data 1: Finding Spring Force Constant:







Data 2: Finding Final Velocity of Cart

DataStudio Data:

First 10 Trials:



Last 3 Trials:










 * Sample Calculations: **

__**Force of the Spring (with free body diagram):**__ Picture from: 

__**Experimental Final Velocity:**__

__**EPEi:**__ EPEi = KEf 0.074 = 1/2 M V^2  0.074 = 1/2 (.5012) V^2  V^2 = 0.295  V = 0.54 m/s

__**Theoretical Final Velocity:**__


 * Error Calculations: **

Percent Difference between Our Spring Force Constant and Class Average:





Percent Error Sample Calculation:



Our data and conclusions seem to suggest that our hypotheses were correct. First, we hypothesized that by adding different weights to the spring, and measuring the change in distance the spring stretched, and graphing these 2 factors against each other, we would find the spring constant of this spring in the **slope**. This was supported by our data, as the spring constant we found using this method was only 3.2088% different from the spring constant the rest of the class came up with. For the second part of our experiment, we hypothesized that the farther we pulled the spring, the faster the final velocity would be, mirroring the expression: EPE = KE (1/2)kx^2 = (1/2)mv2 with "x" representing the distance we pulled the spring back. Our results also proved this conclusion, as the velocity readings we got from the experiment were, on average, 3.29239837% different than our hypothesized values for velocity.
 * Conclusion: **

As stated, the error for our first section was 3.2088%. Our results probably differed from those of the rest of the class because we were all using slightly different springs and different weights. Also, the measuring was difficult because of the hanging weight and therefore, may not have been as precise. For the second part of the experiment, our average error percentage came out to be 3.29239837%. The possible error most likely stemmed from a few factors. First - the measuring of the distance we pulled the cart back was not that precise, because the ruler itself did not extend many decimal place readings, and the way we decided the measurement was a very "rough eyeballing". Also, if we measured the strip of paper even the slightest bit inaccurately, it would have made a significant difference. We assumed that the track was absolutely frictionless, so that was also a source of error.

To improve the first part of this experiment, everyone in the class could have done their trials with the same spring, therefore we would know that, theoretically, we should all get the same spring constant. To improve the second part, we could have used a more precise measuring tool for the distance we pulled the cart back, and for the tiny strip of paper. We could have also figured out the "work" of the equation - the friction on the track.