What is the Formula for Work Done in Stretching a Spring?
Discover the formula W = (1/2) k x² for calculating work done in stretching a spring, derived from Hooke's Law.
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The expression for the work done in stretching a spring is given by W = (1/2) k x^2, where W is the work done, k is the spring constant, and x is the displacement from the spring's equilibrium position. This formula results from the integration of Hooke's Law, indicating that the work done is proportional to the square of the displacement.
FAQs & Answers
- What is Hooke's Law? Hooke's Law states that the force exerted by a spring is directly proportional to its displacement from the equilibrium position, expressed as F = kx, where F is the force, k is the spring constant, and x is the displacement.
- How is the work done in stretching a spring derived? The work done in stretching a spring is derived by integrating Hooke's Law. The formula W = (1/2) k x^2 comes from calculating the area under the force versus displacement graph, which represents the total work done.
- What do the variables in the work done formula represent? In the formula W = (1/2) k x^2, W represents the work done, k is the spring constant that measures the stiffness of the spring, and x is the displacement of the spring from its equilibrium position.
- How does the spring constant affect the work done? The spring constant (k) affects the work done because a higher spring constant indicates a stiffer spring, requiring more force and, consequently, more work to stretch it a given distance.