Final answer:
Force and spring stretch have a directly proportional relationship described by Hooke's Law, where a spring extends by a certain amount that is linearly related to the magnitude of the applied force.
Step-by-step explanation:
The relationship between force and spring stretch in a mechanical engineer's experiment can be understood through Hooke's Law, which states that the force exerted by a stretched (or compressed) spring is proportional to the displacement (the change in length) from its rest position.
In the context of the given mechanical engineer's experiment, this relationship is specifically described as a spring stretching 2.5 millimeters for each 1-N force applied. This implies a direct proportionality where the spring's displacement, measured in millimeters, increases linearly with the amount of force, measured in Newtons (N), applied to it. The slope of the graph of the restoring force versus spring stretch (displacement) is the force constant k, measured in Newtons per meter (N/m), which indicates the spring's stiffness.
Experimentation with mechanical systems such as springs can involve measuring the force they exert and determining the spring constant to tell us about the system's characteristics.