Hooke's Law Calculator

Understanding Hooke's Law Calculator

Hooke's Law states that the force needed to extend or compress a spring is proportional to the displacement from equilibrium. Valid within the elastic limit.

How to use this calculator

1. Enter the spring constant, which tells how stiff the spring is.
2. Enter the displacement from the spring's natural length, using a positive or negative value if your calculator asks for direction.
3. Read the force result, which comes from Hooke's Law.
4. Check the sign of the answer, because it shows the force acts opposite the direction of the stretch or compression.

The formula explained

Hooke's Law uses the formula \(F = -kx\) to compute the restoring force of a spring. The minus sign means the force points opposite the displacement.

• F = spring force, measured in newtons \(\text{N}\)
• k = spring constant, measured in newtons per meter \(\text{N/m}\)
• x = displacement from the spring's natural length, measured in meters \(\text{m}\)

Step by step method

1. Find the spring constant \(k\) and the displacement \(x\).
2. Multiply \(k\) by \(x\) to get the force size.
3. Apply the minus sign to show the force opposes the displacement.

Worked example

Problem. A spring has spring constant \(k = 150\,\text{N/m}\) and is stretched \(0.08\,\text{m}\) from its natural length. Find the spring force.

1. Use \(F = -kx\).
2. Substitute the values, \(F = -(150)(0.08)\).
3. Compute the result, \(F = -12\,\text{N}\).

Tips and common mistakes

• Make sure \(x\) is measured from the spring's natural length, not from some other reference point.
• The negative sign is important, because it shows the force acts in the opposite direction to the stretch or compression.

Frequently asked questions