The Relation Between Force Constant and Potential Energy

What is the relationship between the force constant and potential energy of a spring?

How can we calculate the distance a spring must be stretched for a specific potential energy?

Answer:

When dealing with a spring, the potential energy stored in it is directly proportional to the force constant and the distance it is stretched. The formula that relates them is:

W = 1/2 * k * x^2

To calculate the distance a spring must be stretched for a given potential energy, we can use the formula above. Let's take the example given in the data where the potential energy is 27 J and the force constant is 10000 N/m.

We can rearrange the formula to solve for x:

27 = 1/2 * 10000 * x^2

Solving for x, we get:

x^2 = 0.0054

x = 0.03√6 m ≈ 0.07 m

Therefore, the spring must be stretched approximately 0.07 meters for its potential energy to be 27 Joules.