Final answer:
Hooke's Law states that the restoring force in a spring is directly proportional to the displacement, expressed mathematically as F = -kx, where F is the restoring force, x is the displacement, and k is the spring constant. a) ( F = k times d ) is correct answer.
Step-by-step explanation:
Hooke's Law is a principle of physics that relates the force applied to a spring to the amount of stretch or compression it experiences.
The law is mathematically stated as F = -kx, where F is the restoring force exerted by the spring, x is the displacement of the spring from its equilibrium position (either stretched or compressed), and k is the spring constant, which represents the stiffness of the spring. The negative sign indicates that the restoring force acts in opposition to the displacement.
When you apply Hooke's Law, it implies that the restoring force is directly proportional to the displacement. This relationship remains valid as long as the material does not exceed its elastic limit, meaning the spring will return to its original shape once the force is removed.
The spring constant k is unique to each spring and is measured in newtons per meter (N/m). This constant varies depending on the material's properties and the spring's dimensions.
Using Hooke's Law, you can solve problems involving the deformation of springs, calculate the force constants of springs, and understand the behavior of materials under applied forces within the elastic limit. The law has significant applications in engineering, physics, and various technologies that use elastic components.