What Is a Force Meter?

You've no doubt heard the word "force" used in all sorts of ways, most of them either ill-defined ("force field," "force of a magnetic field") or unrelated to physical science ("force play," "fighting force.")

A force in physics is anything that acts to accelerate something with mass. There are a number of equations relating force to other quantities, such as work, pressure and energy, but the most basic is ​F = ma​, which states that a mass ​m​ experiences an acceleration ​a​ when subjected to a net force ​F​, acting in a specified direction with a specified magnitude.

Because knowing the specific values of forces is essential in engineering and other industries the world over, instruments for precisely determining force are easy to obtain.

Units of Force

The SI (metric) unit of force is the newton (N), while the SI units of mass and acceleration are kilograms (kg) and meters per second squared (m/s2). Thus the N is a derived unit, and it translates to kg m/s2.

Since any gravitational field tends to accelerate all masses in its reach, the result is what humans call weight in everyday terms. Thus a household or health-club scale is a force meter of sorts, because while it ​displays​ your mass in kilograms (or your equivalent weight in pounds) it actually ​measures​ your weight as a result of gravity, on Earth equal to 9.81 m/s2.

Hooke's Law

Most force meters you are likely to encounter take advantage of a principle called Hooke's law, named after Robert Hooke, whose work in the 1600s spanned physics, chemistry, biology and virtually all other fields of inquiry during this time of rapid scientific progress.

The law states that the force required to stretch an elastic material (such as a spring) a given distance is proportional to the distance the spring is stretched from its equilibrium point:

The negative sign implies that the force ​opposes​ the stretch, being equal in magnitude but precisely opposite in distance.

Applications of Hooke's Law Besides the Force Meter

Hooke's law has been applied in every field of engineering and construction you can name or even imagine. In the early days of clock-making, springs were essential for ensuring precise function, as timekeeping in the 17th and 18th centuries was not quite yet a matter of GPS synchronization.

Hooke's law has been invoked in the making of manometers (pressure gauges), equipment in the world of acoustics and seismicity, and, as the 21st century progresses, in nanotechnology applications as well. But its utility in a simple force meter is perhaps the easiest way to explain it even today.

Force Meter: The Spring Meter

Hooke's law can be applied to a spring on a horizontal surface, such that the force exerted on the object by gravity is balanced by the upward force of the surface (the normal force). If the force required to stretch the spring 1.5 m is 300 N, you can calculate ​k​ in Hooke's law, the ​spring constant​:

F=-kx\implies 300\text{ N}=k(1.5\text{ m})\implies k = 200\text{N/m}

A ​force meter​ is instead a vertical construct, and it has a spring that is calibrated such that a mass subjected to Earth's gravity will move the spring downward from its resting (equilibrium) position by a known, fixed amount. Thus a mass of 10 kg is known to have a weight of (1 kg)(9.81 m/s2) = 98.1 N, and the force meter can be labeled in accordance with this principle.

Note that in order to stretch a spring or any elastic object twice the distance it has already been stretched, twice the force must be applied and so on, as dictated by Hooke's law. In reality, no material is perfectly elastic, and all springs break down, either by "wearing out" or breaking traumatically under sufficient stress or strain.

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