91Ó°ÊÓ

When discussing the stretching of a wire or spring due to an applied force, Hooke's Law is a fundamental principle. This law describes how elastic materials respond to forces. It states that the force required to either stretch or compress a spring is directly proportional to its elongation or compression.

This can be mathematically expressed as:

• \[ F = kx \]

where:

• \( F \) is the force applied,
• \( x \) is the elongation (or compression), and
• \( k \) is the spring constant.

In simple terms, Hooke's Law implies that the force needed to change the length of a spring is linearly related to how much you stretch or compress it.

In the exercise, a weight of 200 N was attached, resulting in the wire stretching. With this constant force and considering the constant proportionality defined by Hooke's Law, we can calculate other variables, such as elongation or energy.

The spring constant (\( k \)) is a measure of a spring's stiffness. A higher spring constant means the spring is stiffer, requiring more force to stretch or compress it the same amount compared to a spring with a lower \( k \).

In the exercise, we used the given values of force (200 N) and elongation (0.001 m) to calculate \( k \) using the Hooke’s Law formula:

• \[ k = \frac{F}{x} \]

Substituting the known values:

• \[ k = \frac{200 \, N}{0.001 \, m} = 200,000 \, N/m \]

This large spring constant indicates the wire is quite stiff, as it requires significant force to produce even a small deformation. Determining \( k \) is pivotal for calculating other quantities such as the elastic potential energy stored in the material.

Understanding how to measure and interpret elongation is key when working with elastic materials. Elongation represents the change in length from the material's original state. In calculations or practical scenarios, it is important to use consistent units, typically meters in the International System of Units (SI).

In the given exercise, elongation was initially provided in millimeters (1 mm), which was converted to meters as:

• \[ 1 \, mm = 0.001 \, m \]

This conversion ensures accuracy in further calculations, such as determining the spring constant or elastic potential energy. Recognizing the original and altered lengths gives vital insight into the stress and strain relationship.

Accurate elongation measurements allow for precise computations of other properties in material science and engineering contexts. It serves as the foundation for discussing how materials behave under different forces.