Understanding Weight and Mass: A Simple Example with Falling Rocks

Introduction
In this article, we will explore the fundamental concepts of mass and weight through a simple example involving two rocks of different masses falling near Earth's surface. The question posed is: Assume that g10N/kg and there is no air resistance. Two rocks of mass 5kg and 10kg are falling near Earth's surface. What is the weight of each rock? This article will explain the difference between mass and weight, and why the answer to the question involves recognizing these differences.

Mass and Weight
At the atomic level, matter is composed of particles with physical property measures such as mass and weight. Mass is an intensive property, which means it is a measure of the amount of matter in an object. Regardless of where the object is located, its mass remains constant. This is why the mass of a 5 kg rock on Earth is the same as the mass of that same rock on the Moon. On the other hand, weight is a extensive property, which is a measure of the force of gravity between two objects. In simpler terms, weight is the effect of gravity on the mass of an object.

In the context of these two rocks, the mass of the rocks is the same as it would be anywhere else in the universe. However, the weight of the rocks, as a result of Earth's gravitational force, is different due to the difference in their masses.

Free Fall and Weight
When an object is in free fall, it experiences gravity. The acceleration due to gravity on Earth's surface is approximately 9.81 m/s2, but for the sake of simplicity, we will assume it to be 10 m/s2. In the vacuum of free fall, there is no air resistance. Therefore, both the 5 kg rock and the 10 kg rock will fall at the same rate, despite their different masses. Despite this, they still have weight because gravity is still acting on them.

According to Newton's law of universal gravitation, the force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. In our scenario, the distance from the rocks to the center of the Earth is considered constant, so the weight of the rocks is determined based on their masses and the gravitational force.

The formula to calculate weight is:

Weight (N) mass (kg) x acceleration due to gravity (m/s2)
Weight (N) 5 kg x 10 m/s2 50 N
Weight (N) 10 kg x 10 m/s2 100 N

This means the 5 kg rock has a weight of 50 Newtons, and the 10 kg rock has a weight of 100 Newtons. These values reflect the force that gravity exerts on each rock. Even in the absence of air resistance, the weight of the rocks must be taken into account due to the gravitational force acting upon them.

Conclusion
The key takeaway from this example is the distinction between mass and weight. While mass is a constant value and does not change regardless of the gravitational field, weight is a measure of the force acting on an object due to gravity. Therefore, even in a free-fall scenario with no air resistance, the rocks still have a weight determined by their respective masses and the gravitational pull of the Earth. This example serves as a practical demonstration of how these concepts apply to everyday phenomena.

Related Keywords
- Weight
- Mass
- Free fall
- Gravitational force
- Newton's law of universal gravitation