What does it mean to say mass and weight are proportional to each other?

Mass and weight are often discussed together in the context of physics, but they are not the same thing. When we say that mass and weight are proportional to each other, we mean that as one increases, the other increases at a consistent rate.

For example, let’s consider an object on Earth. If we have a rock that has a mass of 10 kilograms, we can calculate its weight using the formula:

Weight (N) = Mass (kg) × Gravitational Acceleration (m/s²)

On Earth, gravitational acceleration is approximately 9.81 m/s². So, the weight of the rock would be:

Weight = 10 kg × 9.81 m/s² = 98.1 N

Now, if we were to take another rock with a mass of 20 kilograms, its weight would be:

Weight = 20 kg × 9.81 m/s² = 196.2 N

From this, we can see that as the mass of the object increases from 10 kg to 20 kg, its weight also increases from 98.1 N to 196.2 N. The ratio of weight to mass remains constant, showing that they are proportional to each other, as long as we are within the same gravitational field (like on Earth).

This proportional relationship is important in physics, as it helps us understand how forces act on objects and how they behave under different conditions.