Newton's Law of Gravitation
Earth and Space

Measuring mass and gravity force

Physics Narrative for 11-14 Supporting Physics Teaching

Two different measurements

Remember that mass does not vary. If you measured the mass of an object here on Earth and on the Moon, you would find it was exactly the same. This is in line with common sense. If you take an object to the Moon, it is the same object, it looks exactly the same, and will have exactly the same reluctance to change its motion.

The simplest way to measure mass is not to compare the response of different objects to a force (so to gauge the mass in terms of their inertia or reluctance to accelerate). It is easier to compare two things with a beam balance than to measure their accelerations. If the masses are the same, the gravitational force on each will be the same and the beam will balance.

This beam will balance anywhere – even on the Moon where the gravitational field is much less, but is the same for both sides of the balance. At one time, this kind of balance was used by greengrocers, so when they gave you 1 kilogram of potatoes, they were comparing the mass of the potatoes with a standard 1 kilogram mass. The unit of mass, 1 kilogram is defined in terms of a standard 1 kg mass that is held in Sevres, just outside Paris. The mass of other objects is measured by comparing them to this mass.

Nowadays, many balances are based on the idea of measuring the force of the object on the balance. The object is placed on the balance and gravity pulls it down, compressing something in the balance and giving a reading. Such balances should be calibrated in newtons as this is the unit of force.

Of course, any set of bathroom scales that you are likely to use at home will be calibrated in kilograms (and stones and pounds). In day-to-day life we take our weight in kilograms. In scientific contexts we measure force in newtons – here the supporting force provided by a balance. This is a good example of a situation where everyday and scientific ways of talking and thinking differ from one another.

Newton's Law of Gravitation
is expressed by the relation F=G(m_1)(m_2)/r^2
can be used to derive Kepler's First Law

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