A horizontal spring with a spring constant k = 322 N/m is uncompressed from a length of 1.4 cm back to its unstretched length. Calculate the change in potential energy in Joules to 2 s.f.
Lack of better data, assume the 1.4 cm is the difference between stretched and unstretched length.
Work done = Δpotential energy
= (1/2)k(Δx)²
First change everything to SI units then the result will be in joules.
To calculate the change in potential energy of a spring, we need to know the spring constant (k) and the displacement of the spring from its original position.
In this case, the spring constant (k) is given as 322 N/m. The displacement, or change in length of the spring, is from 1.4 cm to its unstretched length (0 cm).
The formula for the potential energy stored in a spring is:
Potential energy = (1/2) * k * x^2
where k is the spring constant and x is the displacement of the spring.
Let's calculate the change in potential energy step by step:
1. Convert the given displacement from centimeters to meters:
x = 0.014 m
2. Substitute the values into the formula:
Potential energy = (1/2) * 322 N/m * (0.014 m)^2
3. Simplify the equation:
Potential energy = (1/2) * 322 N/m * 0.000196 m^2
4. Calculate the result:
Potential energy = 0.0316 J (to 2 significant figures)
Therefore, the change in potential energy of the spring is approximately 0.0316 Joules.