Question

Can a single object of mass 4 explode into two objects each of mass greater than 2 ? Explain your reasoning.

Short answer

No, a single object of mass 4 cannot explode into two objects each of mass greater than 2. This would violate the law of conservation of mass, which states that the total mass of a system must remain constant.

Step-by-step solution

Understand Law of Conservation of Mass

The law of conservation of mass states that in any closed system isolated from external forces, the amount of mass remains constant over time, regardless of the processes operating inside the system.

Apply the Law to the Given Problem

In this scenario, an object of mass 4 is breaking down into two smaller objects. According to the law of conservation of mass, the total mass before and after the break down should remain the same. This means that the total mass of the two smaller objects should add up to the mass of the original object, which is 4.

Reasoning based on the Law

The given scenario asks if each of the two smaller objects can have a mass greater than 2. However, if each object were to have a mass greater than 2, the total mass would exceed the original mass of 4, which contradicts the law of conservation of mass. Hence, a single object of mass 4 cannot explode into two objects each of mass greater than 2.

Key concepts

Mass Conservation in Closed Systems

At the heart of many scientific investigations is the Law of Conservation of Mass, a principle stating that the total mass in an isolated system remains constant, no matter what internal changes the system undergoes. Consider a balloon being inflated; the mass of air entering the balloon is equal to the increase in the balloon's mass. This law is crucial when studying chemical reactions, nuclear reactions, and even large-scale physical processes.

In a closed system—one sealed off from its surroundings—mass cannot enter or leave. So, when an object of mass 4, for instance, breaks apart or 'explodes' within the system, the resulting fragments must have a combined mass equal to 4. This concept is pivotal in analyzing physical problems, as it establishes a baseline for predicting the outcomes of various processes within such an isolated system. It ensures the fundamental understanding that in the absence of external influences, mass is conserved and can neither be created nor destroyed.

Conservation Laws in Physics

Conservation laws serve as the building blocks for our understanding of physics. They imply that certain quantities remain unchanged in an isolated system as it evolves over time. These conserved quantities provide powerful tools for physicists, as they simplify complex problems by offering invariants. For example, conservation of energy allows us to equate the initial energy of a system to its final energy—useful in studying roller coasters or pendulums.

Mass conservation is one such law applied to systems where matter is not transformed into energy, such as in non-nuclear reactions. It is important to note that these laws apply under specific conditions, typically in systems isolated from external influences. The conservation laws also underpin the law of conservation of mass, stating that for any system closed to all transfers of both matter and energy, the mass must remain constant over time, just like in our textbook example.

Mass Distribution in Explosions

Explosions represent a dramatic example of mass redistribution, where a single entity rapidly breaks into smaller pieces. In an explosion within a closed system, the law of conservation of mass dictates that the sum of the masses of the smaller pieces must equal the mass of the original object before the explosion.

Even in the absence of complex calculations, the conservation of mass can provide a critical insight. For instance, if an object of mass 4 explodes, we know immediately that the system cannot contain fragments each exceeding the mass of 2 without violating the conservation law. This scenario illustrates that while the energy of the object may be distributed unevenly among the fragments, causing differences in their speeds and trajectories, the total mass strictly adheres to the conservation principle.

Principles of Modern Physics

The principles of modern physics extend beyond the traditional laws of motion and incorporate quantum mechanics, relativity, and the concept of energy-mass equivalence as introduced by Einstein's famous equation, E=mc^2. This equation bridges the gap between mass and energy, showing that they are interchangeable under certain conditions, particularly in high-energy physics.

Nonetheless, in classical contexts such as the explosion problem we're examining, mass remains conserved separately from energy. Modern physics recognizes the conservation of mass as a limiting case of the more general conservation of mass-energy. So in low-energy environments typical of everyday life and most chemical reactions, mass conservation as a concept is essentially accurate. It is only when dealing with nuclear reactions or conditions with extreme energy that the lines blur, and we must consider the interplay between mass and energy in a more complex dance governed by the broader laws of physics.