x = F/x
Pe = (1/2) k x^2
Pe = (1/2) k x^2
Potential energy (U) = (1/2)kx^2
Where:
- U is the potential energy stored in the spring
- k is the force constant of the spring
- x is the displacement of the spring from its equilibrium position
In this case, we are given the force constant (k) as 1500 N/m. However, we need to determine the displacement (x) of the spring caused by the constant force of 75 N.
To find the displacement (x), we can use Hooke's Law, which states:
Force (F) = -kx
Rearranging the formula, we have:
x = -F/k
Substituting the given values, we get:
x = -75 N / 1500 N/m
x = -0.05 m
Since the displacement (x) is squared in the potential energy formula, we take the absolute value:
x^2 = (0.05 m)^2
x^2 = 0.0025 m^2
Now we can calculate the potential energy (U) using the formula:
U = (1/2)kx^2
Substituting the given values:
U = (1/2)(1500 N/m)(0.0025 m^2)
U = 1.875 J
Therefore, the potential energy stored in the spring is 1.875 joules.