Group5_4_ch11

toc =Mass on a Spring 2= A: Gabby Leibowitz B: Matt Ordover C: Maxx Grunfeld D: Mike Poleway


 * Objectives:**
 * To directly determine the spring constant K of a spring by measuring the elongation of the spring for specific applied forces
 * To indirectly determine the spring constant K from measurements of the variation of the period T of oscillation for different values of mass on the end of the spring
 * To compare the two values of spring constant k

We hypothesize that if we use the same spring for both areas of the lab, the spring force constant will not change. There should be a direct relationship between the period and the mass. Therefore, we hypothesize that as the mass increases, the period should as well, and vice versa.
 * Hypothesis:**


 * Procedure:**

There are two methods to this lab.

Method 1: The spring is set to equilibrium after a mass is added. That position becomes the "zero" value. After this, more mass is added and the displacement of the spring is recorded as well as the amount of mass added. This process repeats five times. The data recorded is then used to determine the spring force constant.

Method 2: Masses are placed on the same spring as used in method one. One group member pulls the spring down while another group member uses a stop watch to measure how many seconds it takes for 10 oscillations. That time is divided by 10 to get the period. This data is recorded and used to determine the spring force constant. The process is continued five times, each time adding a different amount of mass and seeing how the period is affected.


 * Data:**

Part 1

Part 2


 * Sample Calculations:**










 * Discussion Questions:**

Yes. As the force (or weight) increases, the displacement increases. It is a linear relationship. The slope of the line indicates the spring constant, and it indicates that the spring constant in constant for the range of forces.
 * 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**

By using the time for 10 oscillations, we can minimize error. Taking the period for only one oscillation is largely dependent on reflexes and usually not accurate; a small error would have a large impact on the results if we had only used the period for one oscillation.
 * 2. Why is the time for more than one period measured?**

Both k values should be similar. For part one, our k value was 40.478 N/m, while our k value for part two was 48.212 N/m. These results were not perfect, but they were decent. The more accurate one is probably the first k value of 40.478. This is for two reasons; 1) it is much easier to measure a set distance than the period of a moving object and 2) the r^2 value for the first one was better than for the second method, at 99.3% compared to 99%.
 * 3. Discuss the agreement between the k values derived from the two graphs. Which is more accurate?**


 * 4. Generate the position with respect to time equation and the corresponding graph for**
 * position / time Acos(wt) or Acos(2πft)
 * velocity / time = 2πf(Acos(2πft)
 * acceleration / time = 2πf^2(Acos(2πft)



F=-kx F=-8.75*(-.15) F=1.3125 N
 * 5. A spring constant k = 8.75 N/m. If the spring is displaced -0.150 m from its equilibrium position, what is the force that the spring exerts?**


 * 6. A massless spring has a spring constant of k = 7.85 N/m. A mass m = 0.425 kg is placed on the spring, and it is allowed to oscillate. What is the period T of oscillation? **




 * 7. We neglected to take into account the mass of the spring itself. Are your results any better when using the more accurate relationship m + 1/3 ms (where m is the hanging mass and ms is the mass of the spring)? Redo graph #2 using the square root of m + 1/3 ms, and explain these results. **



After making the new graph, our results slightly improved. Our exponent became closer to 0.5, now at 0.46 rather than 0.44. Our R^2 value also increased but only extremely slightly. Although there was a small change, it didn't improve our results drastically and we maintained pretty consistent values.

The objective of this lab was to use two different methods to find the k value of a spring. Our hypothesis was mostly correct; there was a direct relationship between mass and the period. As mass increased, so did the period. However, the comparison between the k value of the first part of our lab to the second part of our lab was not so good. Our lab results were not perfect, however. Using the first method, we got a k value of 40.478 N/m, and using the second method we got a k value of 48.212 N/m. This resulted in a percent difference of 19.1%. To check our accuracy, we found the percent error for the second part of the lab. The exponent should ideally have been ½, but in our case it was .4413. This was a percent error of 11.74%. This also signified that our results were not entirely accurate. There were many reasons for our percent error and difference. The most prominent one was the fact that we used a hand timer instead of an automated timer. We managed to lower the error due to that by timing 10 oscillations and dividing by 10 to get the period for one oscillation. We could have used the motion sensor to accurately measure the period as well. That was the main reason why our comparison of the two values was different. The reason we did not have a good percent error was also probably due to that. It also may have been because the spring was overused or damaged a bit. A real life application would be shock absorbers for a bike. Some bikes, usually mountain bikes, have them; when you hit a bump it helps absorb some of the shock so that the rider does not feel the full force of it. The longer the period of the shock absorber, the smoother the ride.
 * Conclusion:**