Group6_4_ch6

= __ **Spring Force Constant Lab** __ = toc __Part A:__ Jake Aronson (Period 2) __Part B:__ Gabby Leibowitz (Period 4) __Part C:__ Gabby Leibowitz __Part D:__ Nicole Tomasofsky (Period 4)

1. Directly determine the spring constant k of several springs by measuring the elongation of the spring for specific applied forces. 2. Measure the elastic potential energy fo the spring. 3. Use a graph to find the work done in stretching the spring. 4. Measure the gravitational potential and kinetic energy at 3 positions during the spring oscillation.
 * __Objective:__**

Part A: The spring force constant will be determined by the slope of the graph of applied force vs. displacement. The two values will be equivalent. Part B: When the spring is at rest, it will be at equilibrium. The minimum displacement is located at the point where the spring is pulled while the maximum displacement is located at the point when the spring reaches its maximum height after being released. The total energy at these points will be equivalent. Knowing the location of these points and the velocities at each enables us to calculate the GPE and KE at each point, as well. While the total energy does not change, the GPE and KE will.
 * __Hypothesis:__**

The lab was split into two parts, Part A and Part B. For Part A, three different springs (red, blue, and white) are set on a rod by the use of clamps as means of attachment. One group member kept an Excel spreadsheet open on their computer in order to record the data for each spring. A 200g mass was attached to each spring. At this point, the current height that each mass hung at was recorded and used as the "zero point" in order to measure the displacement after adding more masses. Using a mass set of differing masses, the mass on each spring was increased 5 times. By use of a meter stick, the displacement that each individual mass caused was abel to be recorded on the spreadsheet. From there, the experimental value for the spring constants were calculated by creating a graph of Force vs. Displacement on Excel and analyzing the slopes. For Part B, only one spring and one mass were used. The mass was taped to a piece of cardboard, making it easily detectable by the motion sensor located underneath. This motion sensor, which was plugged into a group member's laptop by use of a USB cord, opened up Data Studio which allowed the velocity to be calculated at the object's maximum displacement, minimum displacement, and point of equilibrium. After recording this data into the Excel spreadsheet, the results could be further analyzed.
 * __Methods and Materials:__**


 * __Part A Procedure:__**

__Picture__ __Video__ media type="file" key="video a.mov" width="300" height="300"

__**Part A Data:**__ Our initial mass was .2kg, which was "zeroed." The values in the graph were changed according to this zero point.



__Graph:__ This graph of Net Force vs. Displacement displays a linear relationship between the force and displacement of the red, white, and blue springs. The slope of each line represents the spring constant value.

__Class Data:__
 * Group || **Red=25N/m** || **White=40N/m** || ** Blue=30N/m ** ||
 * 1 || 25.200 ||  ||   ||
 * 2 || 26.653 || 37.579 || 30.837 ||
 * 3 || 25.769 || 43.459 ||  ||
 * 4 ||  ||   ||   ||
 * 5 ||  ||   ||   ||
 * 6 || 25.994 ||  || 31.075 ||
 * 7 || 25.115 || 41.91 || 31.63 ||
 * 8 || 27.519 || 40.116 ||  ||
 * 9 || 26.335 ||  || 30.339 ||
 * 10 || 25.068 || 41.087 || 30.446 ||
 * 11 ||  ||   ||   ||
 * 12 || 31.807 ||  ||   ||
 * 13 || 24.500 ||  ||   ||
 * 14 || 24.533 || 39.513 || 31.204 ||
 * 15 || 24.628 ||  || 29.822 ||
 * 16 || 24.371 || 39.748 || 30.468 ||
 * Avg. || 25.96 || 40.49 || 30.73 ||


 * __Part A Analysis:__**

__Sample Calculation of Force:__



__Sample Calculation for Percent Error of Spring Force Constants:__

__Sample Calculations for Percent Difference of Spring Force Constants:__



__**Part B Procedure:**__

__Picture:__ __Video:__ media type="file" key="video b.mov" width="300" height="300"

__Diagram:__


 * __Part B Data:__**



__Graph:__


 * __Part B Analysis:__**

__Sample Energy Calculations:__

__Percent Difference at Equilibrium:__



__Percent Difference at Minimum Displacement:__

__Percent Difference at Maximum Displacement:__




 * __Discussion Questions:__**

Yes, the displacement of the spring vs. force graph indicates that the spring constant is a constant. With analysis of the graph, it can be seen that it is a linear relationship. The relationship shows that each line increases at a constant slope, making (k) the slope of line, and making it constant for each spring.
 * 1) ** Do the data for the displacement of the spring versus the applied force indicate that the data for the spring constant is indeed constant for this range of forces? **

Since the slope indicates the spring force constant, the smallest slope (least steep) would have the softest spring because it would have the smallest spring force constant. In contrast, the line that is the most steep would have the largest slope would therefore have the largest spring force constant.
 * 1) ** How can you tell which spring is softer by merely looking at the graph? **

There amount of energy in the hanging mass never changes, as stated by the Law of Conservation of Energy. The initial amount of energy is equal to the final amount of energy. However the type of energy does change.
 * 1) **Describe the changes in energy of the hanging mass, beginning with it starting at rest, you pulling the mass down and then releasing it, and then the mass cycling through one complete perio**d.

__Energy Conversation Calculations:__



__Sample Percent Difference Calculation:__




 * __Conclusion:__**

The goal of Part A was to determine the spring force constant of each of the three springs. Our group hypothesized that the actual spring force constant, as written on the box, would be equivalent to the slope of the trend-line in a Force. vs. Displacement graph. This was proven accurate by hanging differing masses on the springs (each spring was given the same amount of mass, but the values of the masses for each trial changed) and measuring the displacement caused by each mass. As a result, we were able to create the graph of Force vs. Displacement of each spring. By analyzing the equation of each trend-line, we discovered that the slope did, in fact, serve as the spring constant. The graph showed that the red spring had a slope and spring constant of 22.019 N/m. The graph also showed that the white spring had a slope and spring constant of 29.5 N/m. Finally, the graph showed that the blue spring had a slope and spring constant of 25.924 N/m. Considering the theoretical values for the spring constants were 25 N/m (red), 40 N/m (white), and 30 N/M (blue), our results proved relatively accurate. In our analysis, we used both percent error and percent difference to assess the accuracy of our results. We started with the percent error calculation to determine the amount of error between our experimental results and the theoretical results on the box. For the red spring, we had a 11.92% error, for the white spring, we had a 13.53% error, and for the blue spring, we had a 26.25% error. These values prove that we achieved fairly accurate results. Next, we calculated the percent difference of our results compared to the average results of the class. For the red spring, we had a 15.18% percent difference, for the white spring, we had a 15.58% percent difference, and for the blue spring, we had a 27.14% difference. Once again, these values show that our results were pretty accurate. There are many sources of error that could have occurred during this experiment that contributed to our percent error and percent difference values. One source of error could have been the human error that resulted in slightly inaccurate results. It was left up to a group member to keep the spring still as to measure it at an accurate height. This original height that was found was the basis for all the displacement that was recorded by adding the different masses. If the spring was moving during this measurement, the "zero point" could have been measured inaccurately, tampering the rest of the results. In addition, the displacement measurements could have also been slightly off, negatively affecting our overall results, the slope of the line, and ultimately, the spring force constant. Finally, the rounding that took place when measuring these distances also could have also attributed to this error. In order to fix this source of error and get completely accurate results, there would have had to have been a device that measured the height of the spring at each point. However, since this is a lab designed for a physics class, this is unrealistic, and a better approach might be just using all three group members to measure the displacement- one would hold down the meter stick, one would hold the spring still, and one would determine the distance.

The goal of Part B was to prove the fact that the total energy at the maximum, minimum, and equilibrium points were equivalent. Our group hypothesized that these results would be equal, and, after calculating the velocities and heights at each of the three points, our hypothesis was proven relatively true. By using our knowledge of the Law of Conservation of Energy, we were ultimately able to demonstrate that the energy was, in fact, fairly close to equal. However, these results were not exactly equal, as they should be. To analyze the accuracy of our results, we averaged the three values and found the percent difference from each individual point to its average. We did this for the maximum, minimum, and equilibrium positions. Our group achieved a .613% different at equilibrium, a .563% difference at the minimum point, and a .408% percent difference at the maximum point. These results were extremely accurate. However, these slight percent error values can be attributed to the sources of error that existed within this experiment. First, we relied on the motion detector to determine our results. If we released the spring closer to the motion detector, our results would have been more accurate, and vice versa. It is unlikely that we stretched the spring equal distances away from the motion detector for each trial, therefore, altering our results. Also, in order to achieve accurate results, it was critical for the motion detector to be placed exactly in the center of the mass it was measuring. It is probable that the motion detector was placed slightly off-center, also having an overall negative impact on our data. In order to fix this source of error, our group would have had to somehow clamp the motion detector to the table, to ensure that it was centered and un-moving, and stretch the mass as close to the motion detector as possible.

Both Part A and B can be related to the real-life application of bungee jumping. An engineer designing a bungee jump has to account for weight because the spring can only hold a certain amount of weight. By knowing the spring constant, this can be calculated in order to make the activity safe for the jumper.