Conservation of energy in a CM system moving at constant velocity

• Leo Liu
In summary, the conversation discusses the use of the equation ##1/2m_1v_{1c}^2+1/2m_2v_{2c}^2=1/2m_1v_{1c}'^2+1/2m_2v_{2c}'^2## to demonstrate that the angles of deflection in a collision between two particles are the same in the centre of mass frame. However, there is doubt about the validity of applying the conservation of energy to a moving system, as the kinetic energies of the same object measured by different observers may vary. It is noted that while kinetic energy is frame variant, energy is conserved in all frames.
Leo Liu
My book uses ##1/2m_1v_{1c}^2+1/2m_2v_{2c}^2=1/2m_1v_{1c}'^2+1/2m_2v_{2c}'^2## to show that the angles of deflection of the collision between two particles are the same in the centre of mass frame. However, I am doubtful that one can apply the conservation of energy to a "moving" system because the kinetic energies of the same object measured at different observers are different. Is this method valid?

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In what situation? I don't see anything wrong with that except for the lack of parentheses where they belong.

Leo Liu said:
I am doubtful that one can apply the conservation of energy to a "moving" system because the kinetic energies of the same object measured at different observers are different. Is this method valid?
Frame invariant and conserved are two completely independent concepts. KE is frame variant, it has different values in different frames. But in all frames energy is conserved, its value stays the same over time.

vanhees71 and Leo Liu

1. What is conservation of energy in a CM system moving at constant velocity?

Conservation of energy in a CM (center of mass) system moving at constant velocity means that the total energy of the system remains constant, even as the individual components may exchange energy with each other. This is because the total kinetic energy of the system is equal to the total potential energy, and as the system moves at a constant velocity, there is no change in kinetic or potential energy.

2. Why is conservation of energy important in a CM system?

Conservation of energy is important in a CM system because it helps us understand and predict the behavior of the system. It allows us to determine the total energy of the system at any given point and how that energy is distributed among its components. This is crucial in many scientific fields, such as mechanics and thermodynamics, and helps us make accurate calculations and predictions.

3. How does conservation of energy apply to real-world situations?

Conservation of energy applies to real-world situations in many ways. For example, in a simple pendulum, the potential energy at the highest point is equal to the kinetic energy at the lowest point, demonstrating conservation of energy. In more complex systems, such as a car moving at a constant speed, the energy of the car (kinetic energy) is equal to the energy of the fuel (chemical potential energy) being used to power it.

4. What factors can affect conservation of energy in a CM system moving at constant velocity?

The main factor that can affect conservation of energy in a CM system moving at constant velocity is external forces acting on the system. These forces, such as friction or air resistance, can cause energy to be lost or gained by the system, leading to a change in its total energy. However, if the system is isolated with no external forces, conservation of energy will still hold true.

5. How is conservation of energy related to the laws of thermodynamics?

Conservation of energy is closely related to the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or transformed. In a CM system moving at constant velocity, the total energy remains constant, demonstrating the first law of thermodynamics. Additionally, the second law of thermodynamics states that the total entropy (disorder) of a closed system will always increase over time, which can also affect the total energy of a system.

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