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.