An ideal spring has the spring constant k = 395 N/m. Calculate the distance this spring must be stretched from its equilibrium position for 28.9 J of work to be done.
To calculate the distance the spring must be stretched to do a certain amount of work, you can use the formula for the work done by a spring:
W = (1/2) k x^2,
where W is the work done (28.9 J in this case), k is the spring constant (395 N/m), and x is the distance stretched from the equilibrium position (what we're trying to find).
Rearranging the formula, we have:
x^2 = (2W) / k,
x^2 = (2 * 28.9 J) / 395 N/m,
x^2 = 0.366582 N*m / N/m,
x^2 = 0.927 m.
Taking the square root of both sides, we find:
x = √0.927 m.
Therefore, the spring must be stretched approximately 0.963 meters from its equilibrium position for 28.9 J of work to be done.