Spring has Sprung
Purpose: To determine the mathematical relationship between the force applied to a spring and the change in its length for two different springs.
Hypothesis:
The applied force will be (circle one - directly proportional, inversely proportional, proportional to the square, proportional to the square root) to the change in length (Dx) of a spring. I think this because:
How will the mathematical model and/orgraph of the stiff spring differ from that of the looser spring?
Procedure notes:
You can apply force to the spring by hanging slotted weights from it or by clamping one end to a table and pulling on the spring with a spring scale or Vernier force probe connected to the computer. The Vernier probe will need to be calibrated with a known force or standard weight. The length of the spring can be measured with a ruler. Remember, however, you are graphing the change in length so don’t forget to record the initial length of the spring. Also, do not stretch the spring out close to its limit – it ruins the spring and complicates the mathematical model.
Data:
Spring #1 – initial length (m) =
|
Length of spring (m) |
Change in length, Dx (m) |
Applied force, F (N) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Spring #2 – initial length (m) =
|
Length of spring (m) |
Change in length, Dx (m) |
Applied force, F (N) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Data Analysis/Conclusion:
Graph force, F (in N) vs change in length of spring, Dx (in m) for both springs on the same graph. Regardless of which was the dependent or independent variable, graph F on the y-axis and Dx on the x-axis. Print out your graphs and attach them to this sheet.
Mathematical models:
Spring #1:
Spring #2:
Was your hypothesis correct? Why or why not?
How do the mathematical models differ for the two springs?
The area under the curve of a force vs displacement graph from gives the elastic potential energy stored in a spring. From your mathematical models above, derive an equation for the elastic potential energy (Eel) stored in each spring in terms of force (F) and displacement (Dx) Energy is measured in joules (1 j = 1 Nm = 1 kgm2/s2).
The accepted equations for force and
elastic potential energy for a spring include a term called the spring
constant, k (in N/m). What do you think
the spring constants are for spring #1 and spring #2? Explain.