Mass

Mass is a difficult, strange and sophisticated concept but it is important to build up an understanding of it. Students may have been introduced to the word by teachers slowly introducing the difference between mass and weight and learning how to use the words correctly.

Experiments show that the more trolleys you pile together, the bigger the force which is needed for a given acceleration or the less acceleration we get for a standard pull. There is something about these chunks of matter that makes them difficult to accelerate; not difficult in the sense of a rough backward drag of friction but a sluggishness, a slowness to get moving. The effect of a small resultant force is slow but sure; you can get any amount of motion if you wait for it. Newton himself described mass as a ‘quantity of matter’. You could call it the amount of stuff related to the number of atoms in the object. This is inertial mass.

The weight of an object is the pull of the Earth on that object and so it is a force. Gravitational mass is what makes a body exert and experience a gravitational force.

A useful thought experiment:

Imagine experimenters in a space ship in outer space, free from a gravitational field, trying to pull a trolley along horizontally on a frictionless table. They use a spring to exert a pull so that the trolley accelerates. Then they hang the trolley vertically on the same spring, holding the top of the spring in one hand. They accelerate the trolley again by pulling it upwards with the spring. For the same stretch of spring in each case what differences are noticed between the motions? [none]

By drawing ‘leading diagrams’ on the board one can mislead students temporarily into believing that vertical and horizontal have real meaning and are different. They may realize they have been tricked. The directions may be at right angles to each other, but vertical is defined only where there is a gravitational field. Hopefully, they will be left with a feeling that mass is still there needing a force to accelerate it and gaining the same acceleration with the same force whatever the direction of the pull.

Early in the 20th Century, Einstein showed that the inertial and gravitational masses of any object are equivalent. The standard unit for mass is the kilogram. Until 2019 this was defined as the mass of a lump of metal kept in Sèvres in France. Since 2019 it has been defined in terms of the Planck constant, the speed of light and hyperfine transition frequency of 133cs (which defines the second).