Calculating the Force Required for a Given Spring Extension

Hooke's law is a fundamental principle in the field of physics, particularly in the behavior of elastic materials under stress. This law states that the force required to extend or compress a spring is directly proportional to the displacement of the spring from its equilibrium position. Mathematically, this relationship is expressed as:

F kx

Where:

F is the force applied k is the spring constant (stiffness of the spring) x is the extension (or compression) of the spring

In this article, we will explore an example where a spring with a force of 10 N is extended by 20 mm, and we will determine the force required to extend the spring by an additional 5 mm.

Example Problem: Calculating the Force for a 5 mm Extension

Given: A force of 10 N causes an extension of 20 mm.

We need to find the force required to extend the spring by an additional 5 mm.

Step 1: Calculate the Spring Constant (k)

The spring constant can be calculated using the given force and extension:

k F / x

Substitute the given values:

k (10 N) / (20 mm) (10 N) / (0.02 m) 500 N/m

Step 2: Calculate the New Force for a 5 mm Extension

Now that we have the spring constant, we can find the force required for a 5 mm extension. Using the formula F kx:

F (500 N/m) * (0.005 m) 2.5 N

Thus, the force applied that causes an extension of 5 mm is 2.5 N.

Additional Notes on Hooke's Law and SI Units

Hooke's law is a simple yet powerful principle, but it's crucial to apply it accurately. Here are a few important points to consider:

Ratios and Proportions

The ratio of 5 mm to 20 mm can be used to solve similar problems. To apply this ratio, convert the units to meters (m) for consistency. In this case, the 5 mm corresponds to 0.005 m, and the 20 mm corresponds to 0.02 m. The ratio is:

(5 mm / 20 mm) (0.005 m / 0.02 m)

This simplifies to:

0.25 0.25

SI Units and Proper Writing Format

When writing expressions using SI units (International System of Units), it's important to include a space between the coefficient and the unit symbol. For instance, you should write "10 N" and "20 mm" instead of "10N" and "20mm". This accuracy is crucial, especially in scientific contexts, as it enhances clarity and reduces the potential for errors in calculations.

For example, when writing "twelve meters," it’s correct to write "12 meters" instead of "twelvemeters".

Conclusion

Understanding and applying Hooke's law is key to solving problems related to the behavior of springs. By knowing the spring constant and applying the correct SI units, you can accurately determine the force required for any given extension or find the extension achieved by applying a particular force.

Whether you're a student, an engineer, or just curious about physics, mastering this concept is essential for solving real-world problems involving springs.