A spring has a spring constant "k" of 460 N/m. How much must this spring be compressed (in meters) to store 60 J of energy?
60 = 1/2 k x^2
x = √(120 / 460)
To answer this question, we need to use the formula for potential energy stored in a spring:
PE = (1/2) * k * x^2
where PE is the potential energy, k is the spring constant, and x is the displacement.
We are given the spring constant k as 460 N/m and the potential energy PE as 60 J. We need to find the displacement x.
Let's rearrange the formula to solve for x:
x^2 = (2 * PE) / k
Substituting the given values into the equation:
x^2 = (2 * 60 J) / 460 N/m
x^2 ≈ 0.2609 m^2
To find the displacement x, we take the square root of both sides:
x ≈ √(0.2609 m^2)
x ≈ 0.5102 m
Therefore, the spring must be compressed approximately 0.5102 meters to store 60 J of energy.