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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

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The second part of the question is easy. With no acceleration, the problem is equivalent to when the elevator is stationary.

The first part requires Eistein's equivalency principle says that from the perspective of a lab (or an elevator) that is accelerating with a constant value, the situation is identical to a stationary lab under equivalent gravity.

This means that if the acceleration is $a$, the effective gravitational acceleration experienced inside the elevator is going to be $g' = g+a$

So solve the equations of projectile motion for the ball bounce, but use this higher gravity value to see what the effect is on the height and/or time to bounce.

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  • $\begingroup$ Wouldn't it be $g'=g-a$ the gravitational acceleration that the balls experiences? Like by applying newtons 2nd law, $ma-mg=mg'$ $\endgroup$
    – Alysid
    Commented Jul 25, 2023 at 14:15
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    $\begingroup$ If the acceleration is upwards as stated, then equivalent gravity is higher, and hence $g' = g + a$. $\endgroup$ Commented Jul 25, 2023 at 14:37

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