Amanda,+Emily,+Emily,+Elena

= = =__ Lab 1: Elastic Potential Energy __= = = toc
 * Group Members:** Amanda Donaldson, Elena Solis, Emily Burke, Emily Van Malden
 * Class:** Period 2
 * Date Completed:** March 7, 2011
 * Date Due:** March 8, 2011

__** PART 1: FINDING THE SPRING FORCE CONSTANT **__ __**Purpose:**__ Determine the spring force constant of a spring we are given.

__**Hypothesis**__: By adding various masses to a spring we will be able to view the change in position. The slope of our graph will be the spring force constant which should be between the values of about 3.5N/m and 4.5 N/m.


 * __Materials:__** The materials we used included spring stand (with ruler), a spring, varying masses, and excel to record data.


 * __Procedure:__**
 * 1) Gather and set up materials. Hang the spring from the spring stand and find what the value of zero is on the ruler.
 * 2) Attach a mass hanger to the.
 * 3) Add a mass to the mass hanger and record.
 * 4) Measure the change in distance and record.
 * 5) Repeat steps 3-4 for various trials (a total of 5-7 trials).
 * 6) Create a Force-Distance graph with the added mass (in Newton's) and the change in distance (in meters).
 * 7) Add a trendline to the graph and find the slope. The slope is the spring force constant.


 * __Data:__**




 * __Graphs:__**

//Percent Difference://
 * __Calculations:__**

After completing the first part of the lab, we proved our hypothesis correct. As we added greater mass to the mass hanger attached to the spring, the farther down the spring is pulled. As mass increased distance pulled down (position) also increased. The slope of the graph was the spring force constant, k, and was between about 3.5 and 4.5 based on the spring. Our slope was 3.8463 and our r squared value was 0.9999. Our squared value was precise and correct which shows little error. Some error might include the measuring of the distance the spring was pulled down on the ruler of the stand. Additionally if the spring was still "springy" and bouncing up and down ever so slightly the recorded measurement of distance might be off. In conclusion this lab contained very little area for percent error and our results were excellent!
 * __Conclusion:__**

__** PART 2: RELATIONSHIP BETWEEN SPRING FORCE CONSTANT AND VELOCITY **__
 * __Purpose:__** The purpose of this lab is to determine the velocity based on the spring force constant. Also, in this second part, we are proving the Law of Conservation of Energy, that energy is not created or destroyed, it is just transferred.


 * __Hypothesis:__** The greater the starting distance (farther the cart is initially pulled back on the track), the less time it takes the small piece of paper to go through the photogate timer (larger the distance from the end of the track the cart is starting from, the less time it takes to pass through the timer).


 * __Materials:__** The materials we had in this lab included a metal track, a cart, a photogate timer and a spring (connecting the cart to the end of the metal track). We used data studio and excel on the computer to record our data.


 * __Procedure:__**
 * 1) Gather and set up materials. Put the metal track on the table. Attach spring to cart (connect through hoop) and track (hook and tape). Place cart on track. Put the photogate timer on the track.
 * 2) Open DataStudio and select photogate timing. Delete the column of the table that says "Time Between Gates" and only use "Time In Gate".
 * 3) Drag cart back to a starting distance from the photogate timer and record.
 * 4) Start the timing in DataStudio and release cart. Repeat three times at the same starting distance recording the time in seconds for each trial.
 * 5) Repeat steps 2-4 five times (you should have five different starting measurements and three trials for each).

__**Data:**__

Graph - Newton's First Law We made this graph in order to prove Newton's first law of Thermodynamics - that energy can not be created or destroyed but instead transferred to different forms. To calculate EPE, which was the energy we started with, we used the formula EPE = (1/2)*k*x^2. K was our spring force constant for our personal spring which was 3.8643 for all calculations. The x was the distance we had control over - the distance the spring got stretched out by the varying masses. The KE was calculated by (1/2)*m*v^2. The mass for our cart was .499 g for all calculations. The velocity was calculated by the photogate timer for from that we got the time it took the paper flag (with a width of .009 m every time) to cross the sensor (or travel .009 m). We used v = d/t or .009/ the time form the photogate timer to find our actual velocity. Our slope was .8542 which is good. The closer the slope is to one, the better we prove that now energy was lost in transition. However, realistically it makes sense that the KE is a little bit lower then (.8542 *) the original EPE because each time a small amount of energy is given off as heat from friction.
 * __Graph:__**

 To find the data for this graph we had to go to two sources - we got the distance physically by measuring how far the weight dragged the spring down. Then we set up the following equation and solved for v in terms of x to find their relationship. EPE = KE (1/2)*k*(x^2) = (1/2)*m*(v^2) k*(x^2) = m*(v^2) (x^2) = (m*(v^2))/k x = SQRT((m*(v^2))/k) If we plug in the values we know: x = SQRT((.499*(v^2))/3.8643) x = 2.58v


 * __Calculations:__**

__//Actual Velocity://__



//__Theoretical Velocity ﻿ __//





__//Percent Error://__





__//Percent Difference Between EPE and KE://__



After completing this lab we found our hypothesis to be true. The greated the starting distance, the less time it takes the small piece of paper to go through the photogate timer. With the spring being stretched out further there is more tension that pulls the cart back faster. Starting from a short distance made the cart go a lot slower. Our percent error of 6.65 came from using our own K value in stead of the class value. Having a 6.65% error, we should have tried using the class average for K to see if it would make any difference. It might have brought our error down to a smaller number. Also, upon measuring our distance we might have made some mistakes. The position of the cart was estimated in milimeters and we could have been a lot more accurate. We were all looking at it from different views so someone saw a different distance than the person next to them. We did not include friction because we have calculated the friction on these tracks before and it is miniscule. In conclusion our lab had little percent error which was great, but there were things that we could have done to make it even smaller.
 * __Conclusion:__**