Is it true or false that momentum is conserved when total mechanical energy is conserved?
momentum is always conserved
To determine if it's true or false that momentum is conserved when total mechanical energy is conserved, we need to understand the concepts of momentum and mechanical energy conservation.
Momentum is the product of an object's mass and its velocity. It's a vector quantity that represents an object's motion. Momentum is conserved in an isolated system when there are no external forces acting on it. This means that the total momentum before an event or interaction will be the same as the total momentum after.
Mechanical energy, on the other hand, refers to the sum of an object's potential energy and kinetic energy. It's a scalar quantity that relates to an object's motion and position. Mechanical energy is conserved when there are no non-conservative forces, such as friction or air resistance, acting on an object.
Now, to answer the question, it is generally false that momentum is conserved when total mechanical energy is conserved. This is because momentum conservation only requires that the net external force acting on the system is zero, while mechanical energy conservation requires the absence of non-conservative forces.
However, there are situations where momentum and mechanical energy can both be conserved simultaneously. One example is when all the forces acting on a system are conservative forces (such as gravitational or elastic forces). In such cases, the absence of non-conservative forces ensures that both momentum and mechanical energy are conserved.
In summary, momentum and mechanical energy conservation are related but distinct concepts. While momentum can be conserved independently of mechanical energy, mechanical energy conservation requires the absence of non-conservative forces.