A spring has a spring constant "k" of 130 N/m. How much must this spring be compressed (in meters) to store 30 J of energy?
To solve this problem, we can use the equation for potential energy stored in a spring:
Potential energy (PE) = (1/2)kx^2
Where:
k = spring constant
x = displacement or compression of the spring
We are given:
k = 130 N/m
PE = 30 J
We need to find x, the compression of the spring.
Rearranging the equation, we get:
(1/2)kx^2 = PE
Substituting the given values, we have:
(1/2)(130 N/m)x^2 = 30 J
Now, let's solve for x:
Multiply both sides by 2 to get rid of the fraction:
130 N/m * x^2 = 60 J
Divide both sides by 130 N/m to isolate x^2:
x^2 = (60 J) / (130 N/m)
x^2 ≈ 0.4615 J/N
To solve for x, take the square root of both sides:
x ≈ √0.4615 J/N
Using a calculator, we find:
x ≈ 0.6801 m
Therefore, the spring must be compressed by approximately 0.6801 meters to store 30 J of energy.