# Relative Acceleration

## Homework Statement

An elevator is going up from the ground with acceleration aelevator/ground.
When the elevator's height measured from the ground is h, its velocity us velevator/ground (assume that t = 0 in this condition), a ball is thrown up with velocity vball/elevator relative to the elevator. The gravitational acceleration is g.
What is the acceleration of the ball with respect to the ground ?
In what time does the ball height get maximum measured from the ground ?

2. Relevant equation
v(t) = v(0) + a t

## The Attempt at a Solution

I thought that the ball acceleration relative to the ground is aelevator/ground/ - g
And, the ball velocity relative to the ground is Vb/e+Ve/g
So, the time it takes to get maximum height is :
0 = Vb/e+Ve/g + (aelevator/ground - g) t
t = - (Vb/e+Ve/g) / (aelevator/ground - g)
t = (Vb/e+Ve/g) / (g - aelevator/ground)

Am I right ?
I'm in doubt because someone in yahoo answer says that the acceleration is just -g (see https://id.answers.yahoo.com/question/index?qid=20101112142831AAzmKKU ). It is in Bahasa Indonesia, not English)

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BvU
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Hello Terry, and a (belated) welcome to PF :)

You want to ask yourself what force(s) is (are) working on the ball once it's in the air.

For an acceleration aeg - g a force Fnet = m ( aeg - g ) is needed. I can see how gravity exercises a force Fg = - mg but I have trouble imaginiing where a force Fa = m aeg would have to come from.

Hello Terry, and a (belated) welcome to PF :)

You want to ask yourself what force(s) is (are) working on the ball once it's in the air.

For an acceleration aeg - g a force Fnet = m ( aeg - g ) is needed. I can see how gravity exercises a force Fg = - mg but I have trouble imaginiing where a force Fa = m aeg would have to come from.
Thanks for your nice welcome :)
Hmm i'm not quite sure.. But, I think it is the force from the elevator. Since the elevator is accelerating, it has force, right ?
So, what do you think about the ball acceleration relative to the ground ?

BvU
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How can the accelerator exercise a force on the ball once it's in the air ?

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• terryds
How can the accelerator exercise a force on the ball once it's in the air ?
Hmm... I think it's because the ball is in the elevator.
What i thought is that the ball is thrown in the elevator.
But, I know that the question (problem statement) doesn't mention that the ball is in the elevator.
It seems that I have misunderstood the question. :L

Thanks for your answers for guiding me to the understanding of the problem :)

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BvU
Homework Helper
2019 Award
No. Not so. Someone riding in the elevator throws up the ball. You did not misunderstand the exercise. So bear with me, since this is a very important concept (Newton and Einstein preceded us wondering about such things!)

A similar example is a marble on the floor of a departing train: it will roll backwards until it hits something that moves and accelerates with the train. When we stand in the train, we have to lean forward (or hold on to something). And backward when the train brakes. In such circumstances we find ourselves in "an accelerating frame of reference". Our accelerating elevator is such a frame too. If it's not accelerating (and also if it IS ) objects with mass inside feel gravity. Objects that are attached to the accelerator (standing on the floor, fixed to the wall or the ceiling) "feel" an additional force F = ma : To go with the accelerator, you need to undergo an additional force F = ma, e.g. from the floor pushing you up. So you feel heavier when it takes off upwards, and lighter when it brakes and decelerates.

The elevator can't exercise such an extra force on the ball, once it's in the air. (Like -- in the horizontal acceleration situation -- the train floor can't accelerate the marble. For a passenger the marble seems to accelerate under an apparent force. Spooky. For someone on the platform, the marble lies still and the train pulls away under it !)

• terryds
No. Not so. Someone riding in the elevator throws up the ball. You did not misunderstand the exercise. So bear with me, since this is a very important concept (Newton and Einstein preceded us wondering about such things!)

A similar example is a marble on the floor of a departing train: it will roll backwards until it hits something that moves and accelerates with the train. When we stand in the train, we have to lean forward (or hold on to something). And backward when the train brakes. In such circumstances we find ourselves in "an accelerating frame of reference". Our accelerating elevator is such a frame too. If it's not accelerating (and also if it IS ) objects with mass inside feel gravity. Objects that are attached to the accelerator (standing on the floor, fixed to the wall or the ceiling) "feel" an additional force F = ma : To go with the accelerator, you need to undergo an additional force F = ma, e.g. from the floor pushing you up. So you feel heavier when it takes off upwards, and lighter when it brakes and decelerates.

The elevator can't exercise such an extra force on the ball, once it's in the air. (Like -- in the horizontal acceleration situation -- the train floor can't accelerate the marble. For a passenger the marble seems to accelerate under an apparent force. Spooky. For someone on the platform, the marble lies still and the train pulls away under it !)
Thanks. You helped me a lot.
So, when the ball is in the air (not in the floor nor the roof of the elevator), its acceleration with respect to the ground is the gravitational acceleration.
And, when the ball is on the floor or on the roof of the elevator, its acceleration will be the same as the elevator acceleration with respect to the ground.
Am I right ? (I just want to ensure that I really understand this concept.. Hehe)

BvU
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