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Elastic Potential Energy Formula:
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Elastic potential energy is the energy stored in elastic materials as a result of their stretching or compressing. It represents the work done to deform the spring and is fully recoverable when the spring returns to its original shape.
The calculator uses the elastic potential energy formula:
Where:
Explanation: The formula shows that elastic potential energy depends quadratically on displacement and linearly on the spring constant. The factor of 1/2 comes from the work-energy principle.
Details: Understanding elastic potential energy is crucial in physics and engineering for designing springs, shock absorbers, trampolines, and various mechanical systems. It's fundamental to Hooke's Law and conservation of energy principles.
Tips: Enter spring constant in N/m and displacement in meters. Both values must be positive numbers. The calculator will compute the elastic potential energy in Joules.
Q1: What is the spring constant (k)?
A: The spring constant measures the stiffness of a spring. A higher k value means a stiffer spring that requires more force to stretch or compress.
Q2: Why is the displacement squared in the formula?
A: The displacement is squared because the force required to stretch a spring increases linearly with displacement (Hooke's Law: F = kx), and work (energy) is the integral of force over distance.
Q3: What are typical units for elastic potential energy?
A: The SI unit is Joules (J), but it can also be expressed in foot-pounds, ergs, or other energy units depending on the system of measurement.
Q4: Does this formula work for all springs?
A: This formula applies to ideal springs that obey Hooke's Law within their elastic limit. For non-linear springs or those stretched beyond their elastic limit, different calculations are needed.
Q5: Can elastic potential energy be negative?
A: No, elastic potential energy is always positive or zero since both k and x² are always positive (we consider the magnitude of displacement).