Hooke's Law is a fundamental principle in physics that describes the relationship between the force applied to a spring and the resulting extension or compression. It states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position, within the elastic limit of the material.

Hooke's Law is expressed by the following equation:

\[ F = -kx \]

Where:

- \( F \) is the force exerted by the spring (measured in Newtons, N)
- \( k \) is the spring constant, a measure of the spring's stiffness (measured in Newtons per meter, N/m)
- \( x \) is the displacement from the spring's equilibrium position (measured in meters, m)
- The negative sign indicates that the force is always opposite to the displacement

Let's calculate the force exerted by a spring with a spring constant of 50 N/m when it is stretched 0.1 meters:

- Identify the known values:
- Spring constant (\( k \)) = 50 N/m
- Displacement (\( x \)) = 0.1 m

- Apply Hooke's Law formula: \[ F = -kx \]
- Substitute the known values: \[ F = -(50 \text{ N/m})(0.1 \text{ m}) \]
- Perform the calculation: \[ F = -5 \text{ N} \]
- Interpret the result:
The negative sign indicates that the force is acting in the opposite direction of the displacement, trying to return the spring to its equilibrium position. The magnitude of the force is 5 N.

Let's visualize Hooke's Law with our example:

This visual representation shows:

- The equilibrium position of the spring (blue line)
- The stretched position of the spring (green line)
- The displacement (\( x \)) of 0.1 m (red dashed line)
- The restoring force (\( F \)) of 5 N acting to return the spring to its equilibrium position (yellow arrow)

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