If the total mechanical energy of a particle is zero, is its linear momentum necessarily zero? Is it necessarily nonzero?
Answers
Answer:Mathematically, momentum is the body's mass multiplied by its velocity. If the body has 0 mechanical energy, then that means it's kinetic energy is also 0, which means it's velocity is 0, which finally means it's momentum is 0.
Explanation:
Yes, necessarily the momentum can be non-zero.
But the question is that how it can be non-zero, as mathematically when we calculate and the kinetic energy is 0 then the momentum also becomes 0.
The don't forget that, momentum is the tendency of changing state by virtue of rest and motion, it is not that tendency of changing the state from motion to rest.
Moreover, it should also have to be kept in mind that while a body gradually loses its potential energy then at the same time it gains kinetic energy at the same rate that of the losing potential energy and when a body loses its kinetic energy then at the same time it gains potential energy by the same rate of losing the kinetic energy. So, either the body gains the tendency to stay in rest or in motion and in this case only the momentum can be non-zero.