Experiences

The lever. Equilibrium conditions of a rigid Body.

Gomboli Sandro

Italy

Vocational School

Physics

Laboratory

Direct

In the study of the conditions of equilibrium of a rigid body, the concept of a force and its vector nature, related to rotations of the bodies, is undoubtedly a fix.
This experience wants to show, with simple measures of forces with dyna-mometers, that nothing of the vector sum of the forces acting on a rigid Rod bound (lever) is one of its equilibrium conditions.
Draw for the first time a graph representing an inverse function (Hyperbole) by checking the reverse proportionality between arm and force.
This experience starts the study of the equilibrium conditions of a rigid body, applying and verifying the two cardinal equations of statics and introducing a new physical quantity called “torque”.
The complexity of the subject is made easier by simplifying its treatment as much as possible but leaving intact, thanks to the method adopted, its scientific rigour.
It involves the use of a metal rod, fixed to an end, subject to its force of gravity, to the force of constraint and to the elastic force of a dynamometer placed at distances increasing progressively from its fulcrum.
The constraint is considered ideal and the rod as a rigid body.
A dynamometer is used to measure the force needed to keep the rod balanced at various distances (arms) from the fulcrum of the lever.
On the basis of the results obtained, the two cardinal equations of statics are experimentally tested, within our uncertainties, highlighting their generality.
In particular, the second equation is demonstrated by verifying that the torque is constant, equal and opposed to the moment of the force of gravity of the rod at the various configurations.
The application of the first cardinal equation enables to analytically obtain the force of constraint at the various configurations.
The uncertainties of indirect measurements of the torque and the force of constraint are calculated applying the rules regarding the propagation of uncertainties in indirect measurements.
It is requested to draw a graphic showing the values of the force measured with the dynamometer as a dependent variable of the distance from the fulcrum, considered as the centre of reduction of the moments.
The curve, indicating the inverse function is approximately a branch of a hyperbole.
In order to enable a better traceability, the number of tests (at least six) will have to be superior to the number of the other experiences.
Broadly speaking, by studying the balance of the rod in the various configurations, it is possible to understand the characteristics and the properties of levers such as their mechanical advantage.
In this case some levers of the second and third kind are realized, but the experience could also be extended to the lever of the first kind.
The experience is meant to provide the students with the competence enabling them to apply the laws of Physics in concrete contexts.
This experience turns out to be particularly suitable to the achievement of the above mentioned purpose.