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The spring constant, often symbolized as \( k \), is a measure of a spring's stiffness. It tells us how much force is needed to compress or stretch a spring by a certain length. In Hooke's Law, the spring constant is central to determining the relationship between force and displacement. The larger the spring constant, the stiffer the spring, meaning it requires more force to produce a certain displacement.
This value is generally expressed in Newtons per meter (N/m). You can think of it as how strongly a spring resists deformation. For instance, a spring with a constant of 84810.13 N/m, as calculated from the exercise, is quite stiff and would need a substantial force to compress or extend it by one meter.

Force and displacement are closely linked through Hooke's Law, which is expressed as \( F = kx \). Here, \( F \) represents the force applied to the spring, \( k \) is the spring constant, and \( x \) is the displacement from the spring's natural length.
When force is applied to an object, such as stepping onto a spring scale, it causes the spring to compress or stretch, which is termed displacement. The amount of displacement depends on how much force is applied and how stiff the spring is. For example, in the exercise, stepping onto the spring applies a force of 670 N and results in a displacement of 0.0079 m.
This principle helps us measure forces such as weight by observing how much a spring compresses under a known force. Understanding this relationship allows for practical applications in a range of devices, including weight scales.

Converting units is essential when working with physics equations to ensure that calculations remain accurate. In the context of weight measurement using a spring scale, it's important to convert displacement measurements from centimeters to meters.
Since the standard unit of length in these calculations is meters, even small differences in units can greatly affect the results. For instance, the displacement of 0.79 cm must be converted to meters by dividing by 100, resulting in 0.0079 meters.
Unit conversion ensures consistency and helps in maintaining the integrity of calculations when using Hooke's Law and similar equations. Always remember to align your units to match the standard as required by the equation you're working with.

Weight measurement using a spring scale involves applying Hooke's Law. In the exercise, a spring scale measures weight by determining how much a spring compresses under the weight of a person.
The force exerted by a person's weight is counterbalanced by the spring's resistance. The compressed distance (or displacement) allows us to calculate the weight, provided we know the spring constant. For instance, with a given spring constant of 84810.13 N/m, the exercise computed a second person's weight as around 288 N when the spring compressed by 0.0034 m.
This method effectively turns the physical action of stepping on a scale into measurable data, capturing precise weight measurements through the spring's mechanical properties. Understanding and applying these principles allows us to accurately gauge weight in everyday situations.