Balanced arm balance and a dynamometer graduated in kilograms
These measuring instruments are present in different moments of our daily lives. For example, a few years ago we saw at fairs using a dynamometer calibrated in grams or kilograms (which are units of mass and not of force) to measure the mass of products. We can determine the mass of an object by making the quotient of its weight by the local gravity where the dynamometer was calibrated.
What happens to this instrument, calibrated in grams here on Earth, if it is taken to the Moon? If we could sell something on the Moon using a dynamometer calibrated on Earth to determine its mass, we would be at a big loss. Any object weighs six times less on the Moon than it does here on Earth, so the deformation that its weight would cause on the spring would be six times less.
As the dynamometer was calibrated here on Earth, it would erroneously mark a mass also six times smaller. To indicate the correct value, it would have to be recalibrated on the Moon.
At fairs, the two-pan scale, also known as the equal-arm scale, is still used to measure mass. In it, the measurement is obtained by comparison: the object of unknown mass is placed on one of the dishes, and standard objects of known masses are placed on the other dish until static equilibrium is reached.
What would happen if we measured the mass of that same object on the Moon with the balance of equal arms? This instrument can be used on the Moon without any problems. The decrease in gravitational force is the same for all objects, and the dishes, as on Earth, would remain in equilibrium on the Moon.
The dynamometer that was calibrated on Earth and taken to the Moon would bankrupt a marketer because he does not compare two gravitational forces (as the two-armed balance does), but a gravitational force with an elastic force. With this change of location, the gravitational force decreases. The spring does not change, but begins to balance itself in a new position with less strain than the balanced strain on Earth.
Thus, we conclude that a dynamometer will always indicate the value of the traction or the normal force to which it is subjected. So we have:
– if the normal (or the traction) has a module equal to the weight of the body used in the experiment, the dynamometer will be indicating the value of the weight of the object;
– if the normal (or traction) has a module different from the weight of the body, the indication of the dynamometer will represent what is usually called the apparent weight of the object, that is, its unreal sensation of weight at that moment;
– on pharmacy scales, the measuring scale is graduated to measure masses. The reasoning of the two previous items is valid, but one must think that a transformation was carried out through the equation P = mg or its corresponding m = P/g.