Weight

Local gravitational force acting on a mass and gravitational acceleration.

General idea of the topic

Weight is the force with which a celestial body attracts a body. Near the Earth's surface it is modelled with a very simple expression, proportional to mass, and its direction is always toward the centre of the planet. It is the starting point of many dynamics problems.

The topic separates two ideas that everyday language mixes: mass, a property of the body that does not change from place to place, and weight, a force that does depend on the local gravitational field. With that distinction you understand what a scale reads and what happens to weight on the Moon, in an accelerating elevator or in orbit.

What the student is expected to understand

By the end, the student should be able to calculate weight from mass and the strength of the gravitational field, draw it correctly on a free-body diagram and explain why the reading of a scale can differ from weight.

The student should also be able to identify when the uniform-field approximation is reasonable and when it is necessary to take into account that the gravitational strength changes with height.

Recommended learning route

1. Definition and Mathematical Expression: defines weight as a force, writes its expression and fixes the units, keeping mass and weight clearly apart.
2. Weight in Different Contexts: compares weight on Earth, on the Moon and in other contexts, and analyses apparent weight in situations with acceleration.

Physical criterion to acquire

The physical criterion is not to confuse mass with weight and to remember that weight is a force with direction and sense: vertical, downward, applied at the centre of gravity. The simple expression holds only while the gravitational field can be considered uniform in the region of the problem.

Connection with real problems

• scales, balances and load weighing.
• elevators, amusement rides and rockets during lift-off.
• comparison of weight on the Moon and on other planets.
• design of structures that must support their own weight.

Final goal of the topic

The final goal is to use weight as a force within a mechanical model, to tell it apart from mass and from the reading of a scale, and to judge when the uniform-field approximation is enough.