Dropping marble in space station riddle

[PaulMuaddid]

You're in a space station. It's shaped like inner tube of a tire.

It's rotating, you're standing on the floor inside "inner tube" station.
(the floor is the inside part of outer rim of tube)

You are holding a marble, you are standing sideways with respect to rotation.
(the space station is rotating clockwise)

You drop the marble.

Where does the marble fall?

1) to the left of you?
2) right at your feet in the center?
3) to the right of you?
4) it stays floating in air?
5) it floats up?

 

[phinds]

Is this a homework problem?

What do YOU think happens, and why?

 

[berkeman]

You're in a space station. It's shaped like inner tube of a tire.

It's rotating, you're standing on the floor inside "inner tube" station.
(the floor is the inside part of outer rim of tube)

You are holding a marble, you are standing sideways with respect to rotation.
(the space station is rotating clockwise)

You drop the marble.

Where does the marble fall?

1) to the left of you?
2) right at your feet in the center?
3) to the right of you?
4) it stays floating in air?
5) it floats up?

Is this a homework problem?

What do YOU think happens, and why?

You beat me to it phinds! Thread moved to HH.

@PaulMuaddid -- what do you think the answer is and why? Once we hear that, we can offer up opinions.

 

[PaulMuaddid]

No it's not homework. It's just a riddle.

 

[berkeman]

No it's not homework. It's just a riddle.

As I explained in my PM to you, we do not allow riddles that could be somebody's schoolwork.

So show us your sketch of the situation, the trajectory of the marble in a stationary rest frame watching the situation, and the motion of the astronaut's hand. What does the marble look like to the astronaut as it falls?

 

[PaulMuaddid]

You are facing "forward", so your left hand points in direction of motion.
(qualified this, because "where" ball falls depends on how which way you are facing)

 

[phinds]

No it's not homework. It's just a riddle.

So, what do YOU think happens, and why?

 

[PaulMuaddid]

As I explained in my PM to you, we do not allow riddles that could be somebody's schoolwork.

So show us your sketch of the situation, the trajectory of the marble in a stationary rest frame watching the situation, and the motion of the astronaut's hand. What does the marble look like to the astronaut as it falls?

I'm not even sure the ball drops.

Let's say the astronaut is standing in a vacuum

He let's go of ball.

Does the ball drift off in a counter clockwise motion? (since the station is rotating in a clockwise motion).

So the balls path draws out an inner circle in a counter clockwise motion.

Not sure if this is case if there is an atmosphere.

 

[PaulMuaddid]

(the space station is no where near a planet, so a planet does not affect situation)

 

[berkeman]

I'm not even sure the ball drops.

Let's say the astronaut is standing in a vacuum

He let's go of ball.

Does the ball drift off in a counter clockwise motion? (since the station is rotating in a clockwise motion).

So the balls path draws out an inner circle in a counter clockwise motion.

Not sure if this is case if there is an atmosphere.

Hint -- it depends on how big the station is in radius, compared to how far off the "floor" the marble is dropped.

Draw a sketch of the situation, and show circles for the outside of the cylinder that the person is standing on, and the circle inside of that which represents the path of the marble around the axis of the station as the astronaut continues to hold it. If you are outside the space station looking in, and you are not rotating with the station, what does the marble do (from your point of view, not the astronaut's point of view) after it's released? Think Newton's Laws...

 

[PaulMuaddid]

In that case, from my viewpoint, the ball stays where it is, but from viewpoint of astronaut, the ball is moving in a counter clockwise path in air.

 

[berkeman]

In that case, from my viewpoint, the ball stays where it is, but from viewpoint of astronaut, the ball is moving in a counter clockwise path in air.

Nope. From your view outside of the station, the marble is moving right before it was released. Why would stop? What does the act of releasing the marble do? It changes the uniform circular motion of the marble into what?

 

[PaulMuaddid]

Ok, how about this...

Astronaut was holding ball, so ball was traveling with him.

He release marble. The marble "continues" on it's path, thus it hangs in mid space? (from astronauts viewpoint)
(we are in a vacuum, inside station, astronaut is wearing a suit).

 

[berkeman]

Ok, how about this...

Astronaut was holding ball, so ball was traveling with him.

He release marble. The marble "continues" on it's path, thus it hangs in mid space? (from astronauts viewpoint)
(we are in a vacuum, inside station, astronaut is wearing a suit).

Closer, but still more to go. And it doesn't matter if it is a vacuum or air inside the station.

The ball does "continue on". From the outside observer's point of view, what is the shape of that trajectory?

A sketch is important for figuring this out, especially the part that I alluded to about how the motion as seen by the astronaut depends on the ratio of the starting radius to the ball (from the axis of rotation) to the overall station radius.

Draw those two concentric circles starting with a ratio of 1:2 for simplicity. That is, the initial height of the ball is half of the overall radius to the floor of the station. Draw the trajectory of the ball as you see it from outside. Then do some math to figure out how long it takes the ball to hit the floor of the station, versus how long it takes for the astronaut's feet to rotate to the point where the ball hits the floor...

Then change the figure to move the initial circle farther out (like the station is bigger and the astronaut is the same size). Re-do the math and see if that affects the answer...