Force Constant of Spring and Its Elastic Potential Energy

Force Constant of Spring and Its Elastic Potential Energy

Introduction to Spring Force Constant

In this section, we will discuss the force constant of a spring and its corresponding elastic potential energy. Consider a spring with one end fixed, and a force \( F \) is applied at the other end, which stretches the spring by a length \( x \). This relationship can be expressed by Hooke's Law as:

\[ F \propto x \] or equivalently: \[ F = Kx \] where \( K \) is the spring constant.

The spring constant \( K \) is a measure of the stiffness of the spring. It represents how much force is required to stretch or compress the spring by a unit length.

Units of Spring Constant:

  • SI Unit: \( \text{N/m} \) (Newton per meter)
  • CGS Unit: \( \text{dyne/cm} \) (dyne per centimeter)

Note that the spring constant is a scalar quantity, just like surface tension and surface energy.

Elastic Potential Energy Stored in a Spring

Now, let's consider a spring with one end fixed and a force \( F \) applied at the other end, which stretches the spring by a length \( x \). According to Hooke's law, we have:

\[ F = Kx \]

When the length of the spring increases by \( x \), the average force applied is \( F = Kx \). When the displacement is zero (\( x = 0 \)), the force is also zero.

The energy stored in the spring due to this displacement is called the elastic potential energy, and it is given by:

\[ U = \frac{1}{2} K x^2 \]

This is the energy stored in the spring due to the deformation caused by the applied force. It is called elastic potential energy because the energy is stored elastically in the spring.

Short Questions and Answers:

  1. What physical quantity does the spring constant represent?

    Answer: The spring constant represents the rigidity (stiffness) of the spring.

  2. Give an example of a physical quantity that is dimensionally similar to the spring constant.

    Answer: Surface tension is an example of a physical quantity that is dimensionally similar to the spring constant.

  3. If a spring with spring constant \( K \) is cut into two equal pieces, what will be the spring constant of the pieces?

    Answer: If a spring with spring constant \( K \) is cut into two equal pieces, the spring constant of each piece will be \( 2K \).

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