Hooke's Law Lab and theoretical y-value Really need some help

[exparrot]

I did a Hooke's Law lab in class last week and one of the post-experiment questions asks to explain why the graph made should be a straight line and what should the slope and y-intercept be in terms of quantities in this lab? I know that Hooke's Law demonstrates that the amount a spring is stretched (displaced) is directly proportional to the restoring force, thus the line of the graph would be linear. For my graph, I have the length of the spring in meters (x-axis) vs. the F (m*g) in Newtons. The slope would be the k constant and the y-intercept, I assume, would be 0 as if you have 0 displacement, the resultant restoring force would be 0. Okay so I answer that just fine and move on to question 2. Question 2 asks me find the percent difference between the experimentally obtained y-intercept and the theoretical value obtained in question 1. My experimentally obtained y-intercept is 0.0014, and if I assumed correctly in the previous question, my theoretical y-intercept is 0. How would I go about finding the percent difference? I would have 0 in the denominator and I wouldn't get a percent difference, although there is clearly a small difference. Is my theoretical value for the y-intercept correct? I would really appreciate the help! Thanks!

 

[Delphi51]

I have the length of the spring in meters

This suggests that you used not the spring stretch x, but its original length L plus the stretch x. If so, your y-intercept will not be zero.

But most likely, you used the extension x on the horizontal axis and everything you wrote makes sense. If you predict 0 and get 0.0014 the % difference between them does not make much sense, but I would use 100% if I had to have such an answer.

 

[kerimek]

I would first like to commend you on your understanding of Hooke's Law and how it relates to the graph made in your lab. Your explanation of the linear relationship between displacement and restoring force is correct, as well as your identification of the slope as the k constant and the y-intercept as 0.

Moving on to question 2, it is important to note that the theoretical y-intercept is not always 0. It depends on the specific experiment and the values of the variables involved. In this case, the theoretical y-intercept can be determined by calculating the restoring force at 0 displacement using the k constant and the length of the spring. This value may not be exactly 0, but it should be close.

To find the percent difference between the experimentally obtained y-intercept and the theoretical value, you can use the following formula:

Percent difference = |(experimental value - theoretical value)| / theoretical value * 100%

In this case, the theoretical value would be the value you calculated in question 1, using the k constant and the length of the spring. The experimental value would be the value you obtained from your graph, which is 0.0014. This will give you a percent difference, which will indicate how close your experimental value is to the theoretical value.

In conclusion, it is important to understand that the theoretical y-intercept is not always 0 and can be calculated using the k constant and the length of the spring. To find the percent difference, you can use the formula provided, with the theoretical value being the value calculated in question 1. I hope this helps and good luck with your lab!