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.