In this two part lab we sought out to demonstrate simple harmonic motion by observing the behavior of a spring. For the first part we needed to observe the motion or oscillation of a spring in order to find k, the spring constant; which is commonly described as how stiff the spring is. Using the equation Fs=-kx or, Fs=mg=kx; where Fs is the force of the spring, mg represents mass times gravity, and kx is the spring constant times the distance, we can mathematically isolate for the spring constant k.
We can also graph the data collected and the slope of the line will reflect the spring constant. In the second part of the lab we used the equation T=2? mk, where T is the period of the spring. After calculating and graphing the data the x-intercept represented k, the spring constant. The spring constant is technically the measure of elasticity of the spring.
Data: mass of weight | displacement| m (kg)| x (m)| 0. 1| 0. 12| 0. 2| 0. 24| 0. 3 | 0. 36| 0. 4| 0. 48| 0. 5| 0. 60|
We began the experiment by placing a helical spring on a clamp, creating a “spring system”. We then measured the distance from the bottom of the suspended spring to the floor. Next we placed a 100g weight on the bottom of the spring and then measured the displacement of the spring due to the weight . We repeated the procedure with 200g, 300g, 400g, and 500g weights. We then placed the recorded data for each trial into the equation Fs=mg=kx. For example: 300g weight mg=kx 0. 30kg9. 8ms2=k0. 36m 0. 30kg 9. 8ms20. 36m=k 8. 17kgs=k
Here we graphed our collected data. The slope of the line verified that the spring constant is approximately 8. 17kgs. In the second part of the experiment we suspended a 100g weight from the bottom of the spring and pulled it very slightly in order to set the spring in motion. We then used a timer to time how long it took for the spring to make one complete oscillation. We repeated this for the 200g, 300g, 400g, and 500g weights. Next we divided the times by 30 in order to find the average period of oscillation. We then used the equation T2=4? mk to mathematically isolate and find k. Lastly we graphed our data in order to find the x-intercept which should represent the value of k.
Derived Data: mass of weight | time of 30 osscillation | avg osscilation T| T2| | m (kg)| t (s)| t30 (s)| T2 s2| | 0. 10| 26. 35| 0. 88| 0. 77| | 0. 20| 33. 53| 1. 12| 1. 25| | 0. 30| 39. 34| 1. 31| 1. 72| | 0. 40| 44. 81| 1. 49| 2. 22| | 0. 50| 49. 78| 1. 66| 2. 76| | Going back to our equation T2=4? 2mk .
We found the average period squared and the average mass and set the equation up as T2m=4? 2k. Since T2 is our change in y and m is our change in x, this also helped us to find the slope of our line. We got T2m equals approximately 4. 98s2kg. We now have 4. 98s2kg= 4? 2k. Rearranging we have k=4? 24. 98s2k= 7. 92N/m. Plotting the points and observing that the slope of our line is indeed approximately 4. 98 we see that the line does cross the x-axis at approximately 7. 92. Conclusion Prior to placing any additional weight onto our spring we measured the length of spring to be 0. 8m. So if we hooked an identical spring and an additional 200g the elongation of our total spring would be approximately 0. 8m; accounting for twice our spring and the . 24m the additional weight added. However, I believe the additional weight of the second spring would slightly elongate the initial spring; bringing it roughly over a meter. Since our spring elongation has almost tripled I believe that an effective spring constant would be triple that of what we found it to be initially, making a new spring constant of 24. 51kgs
At Solution Essays, we are determined to deliver high-quality papers to our clients at a fair price. To ensure this happens effectively, we have developed 5 beneficial guarantees. This guarantees will ensure you enjoy using our website which is secure and easy to use.
Most companies do not offer a money-back guarantee but with Solution Essays, it’s either a quality paper or your money back. Our customers are assured of high-quality papers and thus there are very rare cases of refund requests due to quality concern.Read more
All our papers are written from scratch and according to your specific paper instructions. This minimizes any chance of plagiarism. The papers are also passed through a plagiarism-detecting software thus ruling out any chance of plagiarism.Read more
We offer free revisions in all orders delivered as long as there is no alteration in the initial order instruction. We will revise your paper until you are fully satisfied with the order delivered to you.Read more
All data on our website is stored as per international data protection rules. This ensures that any personal data you share with us is stored safely. We never share your personal data with third parties without your consent.Read more