Momentum is conserved whenever total mechanical energy is conserved.

I believe this is false. Am I correct?

Momentum is always conserved. The statement is true but mechanical energy conservation is not a necessary condition.

The statement is true but the reverse statement is not.

No, you are incorrect. The statement, "Momentum is conserved whenever total mechanical energy is conserved," is actually true.

To understand why, let's first clarify the concepts of momentum and mechanical energy:

- Momentum is a property of moving objects and is defined as the product of an object's mass and its velocity. So, an object with a larger mass or a higher velocity has more momentum.

- Mechanical energy, on the other hand, refers to the sum of an object's kinetic energy (energy of motion) and potential energy (energy due to its position or state).

Now, when considering a system of objects, if there is no external force acting on the system, the total momentum of the system remains constant. This principle is known as the law of conservation of momentum.

Similarly, if there is no external work done on the system, meaning there is no energy added or taken away from the system, the total mechanical energy of the system remains constant. This principle is known as the law of conservation of mechanical energy.

It's important to note that momentum and mechanical energy are different quantities. However, in cases where there are no external forces acting on a system, the conservation of mechanical energy implies the conservation of momentum. This is because both concepts are closely related and intertwined in such scenarios.

In situations where external forces or work are present, momentum and mechanical energy may not be conserved independently. For example, in an inelastic collision where energy is lost to other forms (such as heat or sound), the total mechanical energy may not be conserved, but momentum still is.

Therefore, momentum is conserved whenever total mechanical energy is conserved, making the statement true.