Hooke's Law: Calculating Spring Constants

Hooke’s law describes that an elastic object like a spring stretches in a proportion to the force that acts on them. This law holds true up to this day and has become a very important law in the concepts of force and motion.

The Hooke’s law give the following equation: \( \small F = -kx \). Here the minus (-) sign describes the flow is in the opposite direction of the force compressing the spring. The \( F \) is the force exerted on the spring, while \( k \) is the spring constant and \( x \) is the displacement of the spring.

Hooke's Law

The force that cause object to move in a way is relates to the Newton’s law of motion. In his third law of motion, which says: for every action there is an equal and opposite reaction. This law holds true for spring that stores energy and use it as mechanical energy.

Springs deforms when compressed or stressed to return in their original shape. You can see spring in many things that you use in your daily activity such as a pen, trampolines, mattress and shock absorbers in cars and bikes. The harder you pull the spring, it pulls back with the same force. Here is the Hooke’s law experiment on calculating spring constants.

Materials Required

  1. Spring with different coil
  2. Ruler
  3. Wooden plank
  4. Weighing scale
  5. Weight blocks

Procedure

  1. Fix one end of each springs on the wooden plank. Makes sure there is enough distance between each spring.
  2. Place the wooden plank on a height. For this you can use some books stacking up on the table or a countertop.
  3. Place the wooden plank on the stack so that the springs should hang down. While doing this you need to make sure that there is enough space for the spring and the bottom.
  4. It’s time to measure the equilibrium position. With the help of a ruler, measure the position of each spring.
  5. Weigh blocks on the weighing scale and record it in kilograms.
  6. Attach the weight to each spring and measure the displacement using the ruler.
  7. Now it’s time to calculate the gravitational force that is applied by the mass of blocks attached on the spring.

\( \small F_{g} = mg \)

Where,

\( \small F_{g} \) = gravitational force.

\( \small m \) = mass

\( \small g \) = gravitational constant of Earth

Using this formula you can calculate the gravitational force that equal to the force applied by the spring. While, use Hooke’s law formula to calculate the spring constant.

Observation

Hooke’s law represents deformation of linear elastic. The elastic is the spring that returns to its original form after the force is removed. While, the linear is the relationship between the displacement and the force.

However, the law remain true only when the material has the ability of elasticity. If the spring is permanently deformed or not being in its normal shape, then the Hooke’s law will not be holds true to the nature of the spring.


Practise This Question

A uniform pressure P is exerted on all sides of a solid cube at temperature tC. By what amount should the temperature of the cube be raised in order to bring its volume back to the value it had before the pressure was applied? The coefficient of volume expansion of the cube is α and the bulk modulus is β.