Deanna,+Nikki,+Cheng,+Maddy

= = Lab: Elastic Potential Energy Deanna, Sam, Maddy, Nikki Period 4 Lab date: 3/2 and 3/3 Due: 3/7/11

Part 1:Finding the spring force constant (k)

Purpose: The purpose of this part of the lab was to determine the spring force constant of our spring. This was important because we need k to solve the conservation of energy equation in part 2.


 * Hypothesis**: If we graph the distance by the force, than the slope of the line will be the spring force constant, based on Hooke's Law which says F=-kx, where force is on the y axis, and x is the distance.


 * Materials**: For this experiment we used a stand with a ruler attached, a spring on a hanger, and 10 g masses.


 * Procedure**:
 * 1) Attach the spring to the stand so that it is hanging. Adjust the attached ruler along the stand so that the bottom of the spring is zero.
 * 2) Add mass to the spring and record the weight. Measure where the bottom of the spring is now that the mass has pulled it down.
 * 3) Repeat each weight several times and use excel to find the average distance for each weight.
 * 4) Create a graph using the weight and average distance
 * 5) The slope of the graph is the spring force constant


 * Data**:
 * [[image:magda_data_5.png]] ||


 * Graph**:
 * [[image:magdade_graph_5.png]] ||


 * Sample Calculations**:


 * Percent Difference Between Our Result and the Class Resul**t:


 * Results:** k=3.4595

Part 2: Determining the relationship between the distance the string stretched (x) and the final velocity


 * Purpose**: The purpose of this part of the lab was to determine the relationship between the horizontal distance the spring stretched and the final velocity of the cart after the spring was released.


 * Hypothesis**: We hypothesized that increasing the horizontal distance (x) of stretch, would cause the final velocity of the cart the increase. We expected a direct relationship between the two.


 * Materials**: For this experiment we used a cart with wheels, a paper flag, a track with a meterstick, a photogate timer with Data Studio, and the same spring from the first experiment.


 * Procedure**:
 * 1) Set up a track (making sure it is level and wiped down to minimize friction since we are assuming it is frictionless), a cart (with measured mass), a paper flag attached to the cart (and the width of the flag is measured), attach the same spring from the spring force constant lab to the cart and the end of the track, place a photo gate timer aligned with the paper flag when the spring is not being pulled.
 * 2) Open data studio using photo gate timer
 * 3) Measure where the cart is when not pulled back and this is the zero
 * 4) Pull the cart back to a measured distance and let go of the cart
 * 5) Find the time in the photo gate using data studio
 * 6) Use the time in the photo gate and the width of the paper flag to find the velocity for each trial.
 * 7) Repeats steps four five and six for several different distances
 * 8) Create a graph using the average velocities and the distance to find the relationship between the two
 * Data**
 * [[image:huddspring1.png]]

this is a sample of the collected data from data studio The above table displays the results from our 5 trials. The mass of the cart and the spring force constant remained the same. For each set of trial we stretched the spring a different length and measured the final velocity through the photogate. To solve for the final velocity, we divided the distance through the photogate (the length of the paper flag) by the time given to us on Data Studio. The final velocities for each trial were averaged together. The x distance and the averaged final velocities were used to create the graph below.

From the graph, we aimed to determine the relationship between the stretched x distance of the spring and the final velocity of the cart. The linear line displays the direct relationship between the two. Our r2 value is .9997, which means that our graph is effective at displaying the relationship.
 * Graph**:

m=0.496kg k=3.4595 spring at equilibrium at 113.8cm = 1.138m
 * Sample Calculations**:



==== The lab was pretty simple, however there were still some sources of error. In part one, we only could only obtain results to the second decimal place, so that limited the accuracy of our results. This could be improved by more precise measuring tools. In part two, the cart was on wheels but there was still a small amount of friction that we did not account for. Although, if the photogate timer was not located exactly where the spring was at equilibrium than the final velocity would be slightly off. In addition, our k value was lower than other groups, and since we used k for our calculations in the second part, this influences our results. ==== ====Overall, this lab increased our knowledge of elastic potential energy. Springs apply in a lot of practical application and this experiment demonstrates the effects of the spring’s compression or stretching in conserving energy. The greater the x-distance of the spring, the more kinetic energy, and consequently, velocity, will result.====
 * Percent Error**:
 * Conclusion**: