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Elastic Potential Energy Equation:
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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 recoverable when the spring returns to its original shape.
The calculator uses the elastic potential energy equation:
Where:
Explanation: The equation 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, mechanical systems, and analyzing oscillatory motion in various applications.
Tips: Enter spring constant in N/m and displacement in meters. Both values must be positive (spring constant > 0, displacement ≥ 0). 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 equation?
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: Can this equation be used for compression as well as extension?
A: Yes, the equation works for both compression and extension, as long as x represents the magnitude of displacement from the equilibrium position.
Q4: What are typical values for spring constants?
A: Spring constants vary widely depending on the spring. Soft springs might have k values around 10-100 N/m, while stiff springs can have k values of 1000-10000 N/m or more.
Q5: Is elastic potential energy always positive?
A: Yes, since both k and x² are always positive (or zero), elastic potential energy is always non-negative. Zero energy occurs at the equilibrium position (x = 0).