A spring of force constant 1500NM^-1 is acted upon by a constant force of 75N . Calculate the potential energy stored at the spring .
We can use Hooke's law to calculate the potential energy stored in the spring. Hooke's law states that the force required to compress or extend a spring is proportional to the displacement of the spring from its equilibrium position. Mathematically, this can be written as:
F = kx
where F is the force exerted on the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
We are given the force constant k = 1500 Nm^-1 and the constant force F = 75 N. We can solve for the displacement x:
75 N = (1500 Nm^-1) x
x = 75 N / 1500 Nm^-1
x = 0.05 m
Now that we know the displacement from the equilibrium position, we can calculate the potential energy stored in the spring, which is given by the formula:
PE = 1/2 kx^2
PE = 1/2 (1500 Nm^-1)(0.05 m)^2
PE = 0.5 * 1500 * 0.0025
PE = 1.875 J
The potential energy stored in the spring is 1.875 Joules.