5 Evaluating a Model
Hooke’s Law is a model that was created to describe the relationship between the force applied to a spring and the distance the spring stretches or compresses. Like many models, Hooke’s law has some limitations. Your objective for this lab will be to evaluate the validity of Hooke’s Law. To do so, you will need to design and carry out an experiment to determine how well Hooke’s Law works in the real world. It will be up to you to come up with suitable criteria to evaluate the validity of this model.
What is Hooke’s Law:
Learning Goals:
- Evaluate the validity of a Model (Hooke’s Law).
- Use graphical representations to analyze data.
Evaluating a Model
Design and carry out an experiment that will allow you to evaluate the validity of Hooke’s Law. You will need to use the IOLab’s Force sensor to measure force but you can choose any method you want to measure position (with or without the IOLab device). Recall that Hooke’s Law describes the distance an elastic material is stretched to be proportional to the force applied to it, which can be expressed mathematically as:
F = – k x
Q1: Describe how you carried out your experiment. You can include a picture or diagram of your setup if that makes it easier to describe.
Include a graph of force applied vs distance the spring was displaced. You will want to do a curve fit to determine the spring constant. If you create this in google sheets you can plot force versus displacement as a scatter plot and under “Customize” you can choose “Series”. Then check the “Trendline” box and in the “Label” dropdown menu choose “Use Equation”. This will display on the top of your graph in the format of y = mx + b. If you want to make the graph directly in the IOLab software, you can click on the cloud icon 
, then click on “Tutorials”, then click on “Graphs and Data”. Under “Pages” on the left, click on “Parametric Plot”. This tutorial will show you how to do this. Q2: Include a screenshot of your force vs displacement graph. Be sure that your graph is professional in appearance and contains appropriate labels and units. It should also show the trend line and equation of the line. Q3: What is the spring constant of your spring as determine from a curve fit (trend line)?
Use the data you collected to evaluate the validity of Hooke’s Law. Decide what criteria you will use to evaluate this model. Essentially you want to determine how well Hooke’s Law really works. Q4: What criteria are you using to evaluate the validity of Hooke’s law? Q5: Using your collected data and graph of force versus displacement, evaluate the validity of Hooke’s Law. (Is it valid, invalid, mostly valid?) This should be a short discussion based on the criteria you came up with to evaluate Hooke’s Law.
Grading Rubric:
Points are assigned for each question according to the following:
| 1 | 5 Points – BOTH of the following are true: (1) there is a written and/or pictorial description of the experimental setup, (2) the way the experiment was setup and performed is clear and understandable.
2.5 Points – Only ONE of the following is true: (1) there is a written and/or pictorial description of the experimental setup, (2) the way the experiment was setup and performed is clear and understandable. 0 Points – NEITHER of the following is true: (1) there is a written and/or pictorial description of the experimental setup, (2) the way the experiment was setup and performed is clear and understandable. |
| 2 | 5 Points – ALL of the following are true: (1) a professional looking screenshot is included (zoomed in appropriately, everything is labeled, appropriate units are included), (2) the equation of the line is present.
2.5 Points – Only ONE of the following is true: (1) a professional looking screenshot is included (zoomed in appropriately, everything is labeled, appropriate units are included), (2) the equation of the line is present. 0 Points – Neither of the following is true: (1) a professional looking screenshot is included (zoomed in appropriately, everything is labeled, appropriate units are included), (2) the equation of the line is present. |
| 3 | 4 Points – The reported spring constant is accurate (within 20% of the actual spring constant) AND appropriate units are included.
3 Points – The reported spring constant is accurate (within 20% of the actual spring constant) BUT appropriate units are not included. 2 Points – The reported spring constant is NOT accurate (it is greater or less than 20% of the actual spring constant) BUT appropriate units are included. 1 Point – The reported spring constant is NOT accurate (it is greater or less than 20% of the actual spring constant) AND appropriate units are not included. 0 Points – The spring constant is not reported. |
| 4 | 5 Points – Legitimate criteria are stated.
2.5 Points – Criteria are stated but they are not clear or do not make sense. 0 Points – No criteria are stated. |
| 5 | 5 Points – ALL of the following are true: (1) There is a sentence describing the validity of Hooke’s Law (that it is valid, invalid, mostly valid, etc.), (2) There is a discussion evaluating Hooke’s Law that is based on the collected data and the graph of force versus displacement.
2.5 Points – Only ONE of the following is true: (1) There is a sentence describing the validity of Hooke’s Law (that it is valid, invalid, mostly valid, etc.), (2) There is a discussion evaluating Hooke’s Law that is based on the collected data and the graph of force versus displacement. 0 Points – NEITHER of the following is true: (1) There is a sentence describing the validity of Hooke’s Law (that it is valid, invalid, mostly valid, etc.), (2) There is a discussion evaluating Hooke’s Law that is based on the collected data and the graph of force versus displacement. |
