Final answer:
To calculate the distance a bow spring is compressed from equilibrium with a spring constant of 900 N/m and 205 J of potential energy stored, we use the elastic potential energy formula. The calculated compression distance is approximately 0.68 meters.
Step-by-step explanation:
To calculate the distance from equilibrium when a bow with a spring constant of 900 N/m has stored 205 J of potential energy, we use the formula for the elastic potential energy stored in a compressed or stretched spring: PE = 1/2 k x^2.
To find the displacement (x), we rearrange the formula to solve for x:
x = √(2 * PE / k)
Here, PE is the potential energy stored in the spring, and k is the spring constant.
Substituting the given values:
x = √(2 * 205 J / 900 N/m)
x ≈ √(410 J / 900 N/m)
x ≈ √(0.4555 m^2)
x ≈ 0.68 m
Thus, the spring is compressed by approximately 0.68 meters from its equilibrium position.