According to Hooke's law, how is the force related to the extension of a spring?

According to Hooke's law, how is the force related to the extension of a spring?

• A. The force is inversely proportional to the distance of extension.
• B. The force required is constant, regardless of the distance.
• C. The force needed to extend or compress a spring is proportional to that distance.
• D. The force varies with temperature only.

Answer: (C)

Hooke's Law states that the force exerted by a spring is directly proportional to the amount it is extended or compressed from its equilibrium position. Mathematically, this is expressed as \( F = kx \), where \( F \) is the force applied, \( k \) is the spring constant (a measure of the stiffness of the spring), and \( x \) is the extension or compression from the spring's rest position. This relationship indicates that as the distance of extension (or compression) increases, the force increases proportionally. This means if you double the extension, the force required to achieve that extension also doubles, reflecting a linear relationship. In contrast, the other options present misunderstandings of Hooke's Law. The inverse relationship, a constant force regardless of extension, and temperature dependence do not align with the fundamental principles outlined by Hooke’s findings. According to Hooke’s Law, it is the proportionality between force and extension that accurately describes the behavior of ideal elastic springs.

Hooke's Law states that the force exerted by a spring is directly proportional to the amount it is extended or compressed from its equilibrium position. Mathematically, this is expressed as ( F = kx ), where ( F ) is the force applied, ( k ) is the spring constant (a measure of the stiffness of the spring), and ( x ) is the extension or compression from the spring's rest position.

This relationship indicates that as the distance of extension (or compression) increases, the force increases proportionally. This means if you double the extension, the force required to achieve that extension also doubles, reflecting a linear relationship.

In contrast, the other options present misunderstandings of Hooke's Law. The inverse relationship, a constant force regardless of extension, and temperature dependence do not align with the fundamental principles outlined by Hooke’s findings. According to Hooke’s Law, it is the proportionality between force and extension that accurately describes the behavior of ideal elastic springs.