If a woman is standing in an elevator, she feels a force of gravity pushing her against the floor. As the elevator accelerates upwards, this force increases. She still feels as if a ‘gravitational’ force has increased. In other words, if the value of g suddenly increased, she would feel the same as if she were in an upward accelerating elevator.
Hence, the force of acceleration is no different from the force of gravity.
If the elevator’s cord were cut, she would experience free fall. She experiences ‘acceleration’ that completely cancels the effect of gravity ! That is, she no longer feels any gravity (she is in the same situation as an astronaut in an earth orbit).