An ideal spring has the spring constant k = 464 N/m. Calculate the distance this spring must be stretched from its equilibrium position for 26 J of work to be done.
1
To calculate the distance the spring must be stretched, we can use the formula for the potential energy stored in a spring, which is given by:
U = (1/2)kx^2
Where U is the potential energy stored in the spring, k is the spring constant, and x is the displacement from the equilibrium position.
We are given the work done, which is equal to the change in potential energy. So we have:
Work = ΔU
Substituting the formula for potential energy, we get:
Work = (1/2)kx^2
We can rearrange this equation to solve for x:
2Work/k = x^2
Taking the square root of both sides gives:
x = √(2Work/k)
Now we can plug in the given values to compute the distance:
k = 464 N/m
Work = 26 J
x = √(2 * 26 J / 464 N/m)
x = √(52 J / 464 N/m)
x ≈ √0.1121 m^2
Therefore, the distance the spring must be stretched from its equilibrium position for 26 J of work to be done is approximately 0.3354 m.