# Balance of forces

How a dynamometer works

Dynamometer is a measurement mechanism that gives us the intensity of a force from another body. This force produces a visible deformation in some objects, which can then be measured. In this way, we say that the measurement of this deformation provides, in an indirect way, the intensity of the force that produced it.

In our daily life we ​​find different types of materials, among them the so-called plastic materials , which are, for example, modeling clay, clay, etc. These plastic materials when deformed do not return to their original shape. Another type of material inserted in our daily life is the elastic material, which, when deformed, tends to return to its original shape when the force applied to it ceases. Basic examples of elastic material: rubber, spring, etc.

To measure forces using the deformation of bodies, it is necessary to use objects or materials that do not undergo permanent deformation when such forces are applied. The deformation must be elastic and measurable.

The most common dynamometer we will find makes use of an elastic spring. When supporting an object, which is intended to determine the weight, the spring undergoes a deformation until it is able to balance its weight, that is, until its force is equal (in intensity) to the weight of the body.

If another body, whose mass is twice the weight, is placed on the same spring, the spring force of the spring will be greater and its deformation will also be doubled. A third body, weighing three times as much as the first, will require an even greater elastic force than the previous ones, and the spring deformation will be three times greater than in the first case. Within the spring’s elastic range, its distension is regular: spring deformation and elastic force are directly proportional.

As the elastic force has the same modulus as the weight of the body, in this situation, by measuring the deformation of the spring, we will be indirectly determining the weight of the object. For the numerical reading of this force we have to calibrate the dynamometer using previously known masses and marking on a scale the positions corresponding to the weights of the respective masses.

But then how can we determine the weight of the masses? It’s quite simple, just multiply the masses by the acceleration due to gravity ( P = m .g ).

Therefore, we can conclude that the dynamometer, used to measure forces, can give us values ​​of forces of any direction and of any nature. Depending on what we are going to measure, we use dynamometers with different springs. The springs that are used can be more or less elastic and are then characterized by a quantity called the spring constant ( k ). The SI unit of the spring constant is N/ m.

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