- Spring scales have two basic designs. The first, and most recognizable, is a tension spring scale. With this design, you place an object on a hook or pan beneath the scale and the spring inside the scale stretches. The second design is a compression spring scale. Many grocery store produce departments have these types of scales. For this design, you place an object on a pan that then compresses the spring. Regardless of whether your scale is a tension or compression scale, it obeys Hooke's Law.
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Hooke's Law for springs states that the restorative force (F) in a spring is proportional to the distance (x) it is stretched or compressed. This proportionality constant, or stiffness coefficient (k), is different for different springs. In equation form, Hooke's Law looks like this:
F = -kx
Using Hooke's law, you can measure the distance a string is stretched, and if you know the stiffness coefficient, calculate the force being applied. - When you hang a weight on a tension scale or place a weight on a compression scale, the spring moves. The indicator on the scale moves with the spring and stops at the correct weight measurement when the spring no longer changes length. Most compression scales use a set of gears and rods to translate the motion of the spring to the indicator, but the indicator on a simple tension scale is attached directly to the spring and slides when the spring stretches.
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The initial calibration of the scale requires the use of Hooke's Law. If the spring has a stiffness coefficient of 10 lb/in, then the mark for 5 lbs. would be 0.5 inches from the zero mark because of Hooke's Law:
5 lb = (-10 lb/in)(-0.5 in)
Since tension scales stretch downward, the distance is expressed as a negative number by convention.
