GCSE Physics Tutorial - Finding Work Done and Elastic Potential Energy
When stretching or compressing a spring, work is done to change its shape, storing elastic potential energy in the process. In some cases, the relationship between force and extension may be directly proportional, making it easier to calculate the work done and elastic potential energy using different methods.
Finding Work Done using the Area Under the Graph: If the force-extension relationship is linear (directly proportional), the graph of force (F) against extension (ΔL) is a straight line passing through the origin. The work done (W) to stretch or compress the spring can be calculated by finding the area under the graph.
To calculate the work done using the area under the graph:
Measure the extension (ΔL) of the spring from its original position.
Measure the corresponding force (F) applied to the spring.
Plot the force-extension data on a graph.
Calculate the area under the graph up to the point of extension (ΔL) from the x-axis to the graph. This area represents the work done (W) in joules (J).
Finding Elastic Potential Energy using the Elastic Potential Energy Equation: Elastic potential energy (EPE) is the energy stored in a stretched or compressed spring. It can also be calculated using the elastic potential energy equation:
EPE = 0.5 * k * (ΔL)^2
Where: EPE = Elastic Potential Energy (in joules, J) k = Spring constant (in newtons per meter, N/m) ΔL = Extension or compression of the spring (in meters, m)
If the force-extension relationship is directly proportional (linear), the spring constant (k) can be determined from the graph. The spring constant is the gradient of the linear graph and is given by:
k = ΔL / F
Once the spring constant is known, the elastic potential energy can be calculated using the elastic potential energy equation.
Comparing the Two Methods: When the extension is directly proportional to the force, both methods should give the same result for the work done and elastic potential energy. If there is any discrepancy between the two, it may be due to experimental errors or inaccuracies in measurements.
Finding work done and elastic potential energy in a linear force-extension relationship can be done using the area under the graph and the elastic potential energy equation. Both methods should yield the same results, provided the extension is directly proportional to the force. These calculations are essential in understanding the energy changes that occur when stretching or compressing a spring.
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