Bouncing a ball on an elevator that is ascending

My question may be simple but I'm curious, let's say I start bouncing a ball like a footballer with my foot on an elevator, and it starts moving upwards (with acceleration) and then it stabilises itself moving upwards with no acceleration at a constant velocity. My question is if the ball will or not start bouncing less due to the upward motion of the elevator.

My thoughts are that it depends, if the elevator is accelerating upwards then the ball will get a force pointing downwards so that it will start reaching less height than if we would be bouncing it on a stationary case.

And if the elevator is not accelerating but moving upwards with constant velocity, it doesn't feel any difference with the stationary case since there is no acceleration, but I don't know

This means that if the acceleration is $$a$$, the effective gravitational acceleration experienced inside the elevator is going to be $$g' = g+a$$
• Wouldn't it be $g'=g-a$ the gravitational acceleration that the balls experiences? Like by applying newtons 2nd law, $ma-mg=mg'$ Commented Jul 25, 2023 at 14:15
• If the acceleration is upwards as stated, then equivalent gravity is higher, and hence $g' = g + a$. Commented Jul 25, 2023 at 14:37