Answer: The work done by a horizontal spring with spring constant k expanding from a compression distance of x to an extension distance of x due to an attached mass is kx².
Step-by-step explanation:
When a spring expands or compresses, it does work on the object attached to it. The work done by a spring on an object is given by the formula:
W = (1/2) k (x₂² - x₁²)
where W is the work done by the spring, k is the spring constant, x₁ is the initial compression distance, and x₂ is the final extension distance.
In the given scenario, the spring is expanding from a compression distance x to an extension distance of x due to an attached mass. The initial compression distance is x₁ = -x, and the final extension distance is x₂ = x. Therefore, the work done by the spring is:
W = (1/2) k (x₂² - x₁²) = (1/2) k [(x)² - (-x)²] = (1/2) k (2x²) = kx²
Hence, the work done by a horizontal spring with spring constant k expanding from a compression distance of x to an extension distance of x due to an attached mass is kx².