Purpose- To analyze spring displacement and develop a
mathematical model describing the relationship between spring force and the distance stretched. - Calculate the force constant of the spring - Apply the mathematical model to determine an expression for the potential energy of the spring. Equipment- Spring
- Masses - Triple beam balance - Meter Stick - Ring Clamp for mounting spring - Ruler |
Procedure1. Set up the equipment. Placed the triple beam balance on the table and hung the spring off of it. Taped a meter stick to the triple beam balance to be able to measure displacement. Gathered masses that would be able to hook on the end of the spring. Got a clear ruler to help accurately read the meter stick.
2. First measured equilibrium of the spring. Added masses to the spring and each time, measured where the bottom of the spring was on the meter stick. Wrote down the masses (g) and the corresponding place on the meter stick (cm). 3. Converted the masses from g to kg by dividing by 1000. Found the displacement by subtracting the location of the spring with a mass from the location of the spring at equilibrium. Converted cm to m by dividing by 100. DataThe data collected in the experiment is in a chart on the excel document on the button below.
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Data Analysis
The equation f(x) = 27.007x + 0.2536 was the best fit line for the force v displacement data on Excel.
The best fit line and the data points are on the Excel document on the button below.
The best fit line and the data points are on the Excel document on the button below.
Force Constant (k) of the Springk = 27.007
The work to find k is on the document on the button below. |
Potential Energy (U) of the SpringU(x) = -13.504x^2
The work to find U(x) is on the document on the button below. |
Conclusion
The purpose of the experiment was to analyze spring displacement and develop a mathematical model describing the relationship between spring force and the distance stretched. f(x) = 27.007x + 0.2536 is the equation for force v displacement. The purpose was also to calculate the force constant of the spring; the force constant (k) is 27.007. The final purpose was to determine an equation for the potential energy (U) of the spring; the equation is U(x) = -13.504x^2.
The y-intercept (0.2536) in the force v displacement equation was error because when the displacement is zero, the force should be zero, but this error could be the result of the weight of the spring. Because U(x) = (1/2)kx^2 and k was positive, the potential energy equation for the spring should have been positive. This was caused by using the formula F = -dU/dx.
The y-intercept (0.2536) in the force v displacement equation was error because when the displacement is zero, the force should be zero, but this error could be the result of the weight of the spring. Because U(x) = (1/2)kx^2 and k was positive, the potential energy equation for the spring should have been positive. This was caused by using the formula F = -dU/dx.