Diving into the Conservation of Momentum: When Does It Fail?

Understanding the principles of physics is crucial for a wide range of scientific and engineering applications. One fundamental principle is the conservation of momentum. However, certain conditions can cause the conservation of momentum to fail. This article will explore specific scenarios where momentum is not conserved, providing a comprehensive guide for those interested in advanced physics and engineering.

When Is Momentum Not Conserved?

Momentum is a vector quantity defined as the product of an object's mass and its velocity. In isolation, the total linear momentum of a closed system remains constant unless acted upon by an external force. Nevertheless, there are specific situations where the conservation of momentum does not hold. In this article, we delve into the various conditions under which momentum conservation may not apply.

External Forces

The most common scenario where momentum is not conserved occurs when an external force affects the system. External forces include elements such as friction, air resistance, and applied forces, which can change the total momentum of a system. For instance, when a car brakes, an external force is applied to slow it down, altering its momentum.

Explosions

In the case of an explosion, while the total mass of the system remains constant, individual pieces of the system can gain or lose momentum due to internal forces. However, if you consider the explosion and the explosive force as part of the system, momentum is conserved. For example, during an explosion, the total momentum before and after the event remains the same, while the components gain or lose momentum individually.

Collisions with External Bodies

When objects collide with external bodies not part of the system, the momentum of the colliding object is affected. A simple example is a ball hitting a wall. The ball's momentum is altered by the wall, leading to a non-conservation of momentum in the ball's isolated system. This phenomenon occurs because the wall exerts a force on the ball, changing its velocity and momentum.

Non-Isolated Systems

A system that is not isolated, meaning it interacts with the environment or other systems, may not conserve momentum within the system. For example, if a 10 kg mass moving at 5 m/s on a frictionless plane is tied to a 10 kg flywheel, the total momentum seems conserved if you consider the 25 units of momentum in the flywheel. However, if you assume the flywheel's 25 units of momentum are zero, as suggested by some physicists like Hehl, you create a significant imbalance in momentum.

Relativistic Effects

At very high speeds, close to the speed of light, classical momentum conservation laws need to be adjusted to account for relativistic effects. While the overall momentum of the universe remains conserved, the conservation of momentum within an isolated system must be considered with relativistic corrections. This is particularly important in high-energy physics and astrophysics.

Conclusion

In summary, momentum is conserved in isolated systems in the absence of external forces. When external forces are present, or when considering systems that are not isolated, momentum may not be conserved. This principle is fundamental in classical physics and has wide-ranging applications in engineering and technology. Whether you are designing a system for a car braking mechanism or analyzing the dynamics of an explosion, understanding these scenarios will help you apply the conservation of momentum correctly.