Tom,+Richie,+Tyler,+Rory

=__Elastic Potential Energy__= Tom, Tyler, Rory, Richie Period 4 Due: 3/7/11


 * __Part 1:__** Find the spring force constant (k).


 * __Purpose:__** To find the spring force constant of a specific spring so that we are able to solve the energy conservation problem in part 2 of the lab.


 * __Hypothesis:__** We believe that if the weight hanging on the end of a spring and the distance that it stretches out is graphed, the slope of the line will be equal to the spring force constant of the spring. We assume this because of Hook's Law, which states that force is equal to the negative spring constant multiplied by the distance it stretches out. If this equation is re-written in terms of slope it would be k=F/x.


 * __Materials:__**
 * 1) Spring
 * 2) Ruler
 * 3) Varied masses
 * 4) Stand
 * 5) Mass hanger


 * __Procedure:__**
 * 1) Attach the spring to the hanger and attach the mass hanger to the spring.
 * 2) Make sure that the ruler is at the lowest position on the stand so that it can read the distances for all the runs.
 * 3) Measure the distance that the spring extends when there is no mass on the hanger.
 * 4) Place a 10g mass to the mass hanger and measure the distance.
 * 5) Repeat step four while adding 10 extra grams with each repetition.
 * 6) Record the data and enter it into an excel spreadsheet.
 * 7) The slope of the line will be the spring force constant.

__**Data:**__



**__Conclusion:__** The data from the results proved our hypothesis correct. Our group hypothesized that there would be a linear trendline for the data gathered. We also hypothesized that the slope of the line would be equal to the spring force constant, in which it was. Due to the simplicity of the experiment, there were not as many areas for discrepancy. One area, however, is the accuracy of the measurements. The end of the spring was not able to be held against the ruler so precise measurements could not be made. Close estimations could be made, however. Another area of error would be the springiness of the spring. It may sound silly, but due to the constant movement of the spring, an exact measurement could not be made, regardless of the tools given. If the experiment were to be repeated, we would use another ruler to hold closer to the spring. As for the movement of the spring, nothing can really be done for it.


 * __Part 2:__** Finding the relationship between the distance the spring is stretched (x) and the final velocity (v)


 * __Purpose:__** To find the relationship between the distance the spring is stretched (horizontally) and the final velocity of the object the spring is attached to.


 * __Hypothesis:__** We believe that the further the spring is stretched the greater its elastic potential energy will be. With a higher amount elastic potential energy the spring will be able pull an object with a greater amount of force thus giving the object a higher final velocity.


 * __Materials:__**
 * 1) Spring
 * 2) Metal track (frictionless) with centimeter markings along side
 * 3) Stopper with place to attach spring
 * 4) Cart
 * 5) Folded piece of paper (1 to 2 cm in length)
 * 6) Photogate timer
 * 7) Computer to run Data Studios on


 * __Procedure:__**
 * 1) Set up metal track on flat surface (make sure track is free of debree to ensure minimal
 * 2) Tightly secure the stopper and photogate timer to the track
 * 3) Attach the spring to the front of the cart and the piece of paper to the top so that it is sticking up
 * 4) Place the cart on the track and attach the spring to the stopper
 * 5) Adjust the photogate timer so that it is only reading the piece of paper sticking off of the cart
 * 6) Using cm markings on track, measure where the back of the cart rests when the spring has not been stretched
 * 7) Stretch the cart back 10 cm from the previous position and release it so that the spring pulls it through the photogate timer
 * 8) Repeat step 7 until a sufficient amount of data has been collected

__**Data:**__


 * __Sample Calculations:__**

Theoretical Velocity:



Experimental Velocity:

Percent Error:

**__Conclusion:__** As with the previous experiment, the hypothesis was proven correct by the data gathered in the experiment. The further back the spring was brought, the faster it went. Increasing kinetic energy shows that the elastic potential energy increases, due to the fact that they are directly proportional (as shown in the calculations above). However, the experiment had multiple flaws. Each of these flaws could slightly differ the data. For example, the "frictionless" track is not really frictionless. Our group assumed it was frictionless for the sake of the experiment. But basing our experiment on the assumption that the track is frictionless when there is really friction (despite how minimal it may be) would alter the data. Also, when the cart is released, a force may be added to the motion of the cart (ex. an accidental push). This may add unwanted acceleration to the cart. One last place where error could have been made was the stoppers for the cart. Inside the stoppers are magnets used to attract the cart to the stopper in order to minimize bounce-back. But depending on how close the photogate timer is to the stopper, these magnets could influence the motion of the cart by accelerating it towards the stopper. If our group were to redo the experiment, we would employ different methods and/or tools in order to make the data collected more accurate. In order to fix the problem with the "frictionless" track, oil may be added to the track to reduce friction. As for the force added to the cart, a mechanical release system would ensure that no extra force would be added. And lastly, for the magnets in the stopper, we would use some sort of stopper without a magnet in order to make sure no extra forces are at work in the experiment.