What is the formula for calculating potential energy stored in a spring?

Get ready for the SIFT Mechanical Comprehension Test with engaging flashcards and multiple choice questions. Each question offers hints and explanations to optimize learning. Excel in your exam preparation!

The formula for calculating the potential energy stored in a spring is derived from Hooke's Law, which states that the force exerted by a spring is proportional to its displacement from the equilibrium position. The potential energy (U) stored in a compressed or stretched spring can be described with the formula ( U = \frac{1}{2} k x^2 ), where ( k ) is the spring constant that indicates the stiffness of the spring, and ( x ) is the displacement from the equilibrium position.

The factor of ( \frac{1}{2} ) accounts for the work done in stretching or compressing the spring. When a spring is stretched or compressed, the force applied gradually increases as a function of ( x ), starting from zero when the spring is at its natural length up to ( kx ) at maximum displacement. The work done on the spring (which is equal to the potential energy stored) is the area under the linear force-displacement graph, resulting in the ( \frac{1}{2} k x^2 ) formula.

This understanding of potential energy in springs is critical in many applications, ranging from mechanical systems to engineering designs. The other formulas do not appropriately reflect the relationship

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