Is Momentum Always Conserved with Total Mechanical Energy?

[student000]

Is momentum always conserved when total mechanical energy is conserved?

My understanding is that this is false, but unsure.

 

[kuruman]

Consider a ball falling from rest. Neglecting air resistance, its momentum continuously increases (not conserved), but its mechanical energy remains unchanged.

 

[kerimek]

You are correct, this statement is false. While momentum is always conserved, total mechanical energy may not always be conserved in a system. This is because mechanical energy includes both kinetic energy (associated with the motion of an object) and potential energy (associated with the position of an object). In certain situations, such as when there is friction or external forces acting on the system, some of the mechanical energy may be lost or converted into other forms (such as heat or sound). However, the total momentum of the system will still remain constant. So, while momentum is always conserved, total mechanical energy may not be in all cases.