what happens in a freely falling elevator?

[Physicsfan]

Imagine a foot ball player enters an elevator holding the ball.The elevator chain breaks and at that same instant he drops the ball to the elevator floor.will the ball ever fall to the floor?

[Sisyphus]

It won't hit the floor as long as the elevator is free falling - the elevator and football will just accelerate at the same rate, and everything inside the elevator will appear to be weightless.

 

However, realistically the elevator will have a relatively low terminal velocity, pushing the air in the shaft out of the way, while the football will experience very little air resistance, since its surrounding air is carried with it. It will fall faster and reach the floor.

 

And of course, it will definitely hit the floor once the elevator reaches the bottom of the shaft.

[Physicsfan]

how about this situation: the football player drops the ball a few seconds after the chain breaks

[Sisyphus]

The situation would be the same.

[Physicsfan]

According to me it should fly up to the ceiling

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because the the elevator would already have gained more velocity by then

[Sisyphus]

No, because the football and the player have been accelerating along with it. If they're all falling together, they appear weightless, and nothing happens when the player lets go.

[Leader Bee]

Isn't this thought experiment similar to the one where you fire a bullet inside a perfectly stable train with no windows or knowledge of the outside world it will move just as fast as you would expect when firing it in a normal situation on the ground rather than expecting it to travel at the bullets muzzle velocity plus the speed of the train?

[Physicsfan]

No, because the football and the player have been accelerating along with it. If they're all falling together, they appear weightless, and nothing happens when the player lets go.

 

Oh! i didn't consider that.

So when two bodies fall freely, they do not exert a force on each other.

is that because the accelaration of the first body with respect to the second is zero?

Edited May 14, 2010 by Physicsfan
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[Leader Bee]

My understanding is that because they share the same (Or very similar) reference frame they act just as they would in any other situation.

[Physicsfan]

Isn't this thought experiment similar to the one where you fire a bullet inside a perfectly stable train with no windows or knowledge of the outside world it will move just as fast as you would expect when firing it in a normal situation on the ground rather than expecting it to travel at the bullets muzzle velocity plus the speed of the train?

 

what would the speed of the bullet with respect to the surrounding outside the train be like if it is fired in a direction opposite to the direction of the moving train?

but if the bullet was fired at a target in the train, then the bullet would hit the target with the same velocity as if it were fired from outside.

[Sisyphus]

A bullet fired on the train will have normal muzzle velocity relative to the train. Relative to the ground outside, it will have normal muzzle velocity plus the train's (and gun's) velocity.*

 

*Not 100% true because it disregards special relativity, but for velocities as small as those possessed by trains and bullets, it's an extremely close approximation.

[Physicsfan]

I think the velocity with respect to the surrounding would be the same,but with respect to the person in the train it would be faster. if fired in a direction opposite to the train

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A bullet fired on the train will have normal muzzle velocity relative to the train. Relative to the ground outside, it will have normal muzzle velocity plus the train's (and gun's) velocity.

wont the velocity of the gun be the same as that of the train?

[Sisyphus]

I think the velocity with respect to the surrounding would be the same,but with respect to the person in the train it would be faster. if fired in a direction opposite to the train

 

Well, that's incorrect. The gun gives the bullet an acceleration relative to the gun. It doesn't care what the ground outside is doing. It doesn't care that the Earth is spinning or going around the sun, which is itself moving through the galaxy.

 

It doesn't matter whether you consider the ground outside motionless and the train moving, or the train motionless and the ground moving underneath it. The physics works exactly the same.

 

wont the velocity of the gun be the same as that of the train?

 

Yes, that's what I meant.

[Physicsfan]

The gun gives the bullet an acceleration relative to the gun. It doesn't care what the ground outside is doing. It doesn't care that the Earth is spinning or going around the sun, which is itself moving through the galaxy.

 

Ok.But as Leader Bee said, the train is enclosed.So the velocity of the bullet as seen by the person inside the train is th muzzle velocity,because the bullet accelarates relative to the gun and the gun is stationary with respect to the person.is this right?

 

But as the bullet moves in one direction, then the person is moving in the opposite direction.So to the velocity of the bullet as seen by the person is the velocity of the bullet+the velocity of the train, right?

Edited May 14, 2010 by Physicsfan

[Leader Bee]

Yes, with no knowledge of what is going on outside it would appear as though the gun has a standard muzzle velocity WRT the trains occupants; If there was another reference frame where people outside the train could see inside the muzzle velocity would be Muzzle velocity + Train speed.

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But as the bullet moves in one direction, then the person is moving in the opposite direction.So to the velocity of the bullet as seen by the person is the velocity of the bullet+the velocity of the train, right?

 

No, this is incorrect because the bullet is still moving, as with our elevator and football scenario, relative to the stationary gun up until the point it is fired ( not being a physics bod it probably still is moving relative to the gun once fired but I cant explain the reason ) therefore the inertia of the bullet(correct?) is moving towards the shooter and this would appear to have a negative effect in velocity on the projectile with respect to the person firing the bullet -- I think.

Edited May 14, 2010 by Leader Bee
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[Physicsfan]

I was talking about firing the bullet in the direction opposite to that of the train.is that what you are talking about too?

[Sisyphus]

Ok.But as Leader Bee said, the train is enclosed.So the velocity of the bullet as seen by the person inside the train is th muzzle velocity,because the bullet accelarates relative to the gun and the gun is stationary with respect to the person.is this right?

 

Yes.

 

But as the bullet moves in one direction, then the person is moving in the opposite direction.So to the velocity of the bullet as seen by the person is the velocity of the bullet+the velocity of the train, right?

 

 

You should get used to thinking about velocity only relative to something specific. There is no such thing as just "moving."

 

"The person is moving in the opposite direction." Relative to what? Not himself. Not the gun. Not the train.

 

Let's give numbers. The train is moving at 100m/s relative to the ground. The gun fires bullets at 500m/s. A bullet fired from a gun that is not moving relative to the train will always be going 500m/s relative to the train and anyone on the train. To someone not moving relative to the ground outside, the bullet will be moving at 600m/s if it is fired forwards, or 400m/s if fired backwards.

 

Or think of this: the train is moving at 500m/s relative to the ground. Someone on board fires a bullet towards the rear of the train. To that person, the bullet flies normally. To someone standing outside, the bullet doesn't move at all. It just falls straight to the ground, while the train rushes by under it.

[Physicsfan]

"The person is moving in the opposite direction." Relative to what? Not himself. Not the gun. Not the train.

with respect to the bullet.and the bullet is moving in a direction opposite to that of the train, that is, opposite to the direction of the person moving with the train.

To someone not moving relative to the ground outside, the bullet will be moving at 600m/s if it is fired forwards, or 400m/s if fired backwards.

if by forward you mean in the direction of the train, then i thought the velocity of the bullet as seen by the passenger was 400m/s, because the passenger is already moving at a speed of 100m/s.

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when two bodies are moving with different velocities relative to the same thing in the same direction,the their velocities with repect to each other would be obtained by subtracting the two velocities right?

Edited May 14, 2010 by Physicsfan
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[Sisyphus]

if by forward you mean in the direction of the train, then i thought the velocity of the bullet as seen by the passenger was 400m/s, because the passenger is already moving at a speed of 100m/s.

 

The passenger already has a speed of 100m/s relative to what? The ground outside? That doesn't matter. It doesn't matter any more than his velocity relative to Mars. The bullet always has the same velocity relative to the gun.