Understanding the Work Done by a Spring: Formula Explained
Learn the formula for work done by springs, including its derivation from Hooke's Law and its applications in physics.
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The formula for work done by a spring is W = 1/2 k x^2, where W represents the work done, k is the spring constant, and x is the displacement from the equilibrium position. This formula derives from Hooke's Law, capturing how the energy stored in a compressed or stretched spring is proportional to the square of its displacement.
FAQs & Answers
- What is Hooke's Law? Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position, mathematically represented as F = -kx, where F is the force, k is the spring constant, and x is the displacement.
- How do you calculate the spring constant? The spring constant (k) can be calculated by rearranging Hooke's Law: k = F/x, where F is the force applied to the spring and x is the displacement from the equilibrium position.
- What does the work done by a spring represent? The work done by a spring represents the energy transferred when the spring is either compressed or stretched, which is stored as potential energy in the spring.
- Can the work done by a spring be negative? Yes, the work done by a spring can be negative when the spring is being compressed, as the energy is effectively being taken from the spring rather than added.