Is it true or false that momentum is conserved when total mechanical energy is conserved?
To determine if it is true or false that momentum is conserved when total mechanical energy is conserved, we need to understand the definitions of momentum and mechanical energy and their conservation principles.
Momentum refers to the quantity of motion of an object and is defined as the product of its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction. The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it.
Mechanical energy, on the other hand, is the sum of kinetic energy (energy of motion) and potential energy (energy due to position or configuration) of an object or a system. The conservation of mechanical energy occurs when no external work is done on the system, and the sum of kinetic and potential energy remains constant.
Now, let's address the statement. When total mechanical energy is conserved, it means no external work is done on the system. This implies that there are no external forces acting on the system, as work is the transfer of energy by a force acting on an object through a displacement. Without external forces, the total momentum of the system would be conserved due to the principle of conservation of momentum.
Therefore, it is true that momentum is conserved when total mechanical energy is conserved, as both conditions require the absence of external forces acting on the system.