The Classic Pole in Barn Relativity Question

In summary, the pole-vaulter says that the front end of the pole leaves the barn first, and the back end enters the barn later.
  • #1

Homework Statement


A pole-vaulter holds a 5.0 m pole. A barn has doors at both ends, 3.0 m apart. The pole-vaulter on the outside of the barn begins running toward one of the open doors, holding the pole level in the direction he is running. When passing through the barn, the pole just fits entirely within the barn all at once.

According to the pole-vaulter, which occurs first, the front end of the pole leaving the barn or the back end entering? Explain. What is the time interval between these two events according to the pole-vaulter?

Homework Equations


t' = γ(t - ux/c2)

The Attempt at a Solution


Let S be reference frame of stationary observer
Let S' be reference frame of pole-vaulter
Subscript 1: Front end of pole leaving barn
Subscript 2: Back end of pole entering barn

From stationary observer's POV, back end of pole enters barn at the same time as front end of pole leaves barn. (Is this inference correct??)
t1 - t2 = 0

t2' - t1' = ... = γ[(t1 - t2) + 3u/c2]
Since t2' - t1' > 0, t1' occurs first. Therefore, front end of pole leaves barn first.

Is the calculation correct? Is there a more intuitive way of understanding which comes first?

Thanks!
 
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  • #2
little neutrino said:

Homework Statement


A pole-vaulter holds a 5.0 m pole. A barn has doors at both ends, 3.0 m apart. The pole-vaulter on the outside of the barn begins running toward one of the open doors, holding the pole level in the direction he is running. When passing through the barn, the pole just fits entirely within the barn all at once.

According to the pole-vaulter, which occurs first, the front end of the pole leaving the barn or the back end entering? Explain. What is the time interval between these two events according to the pole-vaulter?

Homework Equations


t' = γ(t - ux/c2)

The Attempt at a Solution


Let S be reference frame of stationary observer
Let S' be reference frame of pole-vaulter
Subscript 1: Front end of pole leaving barn
Subscript 2: Back end of pole entering barn

From stationary observer's POV, back end of pole enters barn at the same time as front end of pole leaves barn. (Is this inference correct??)
t1 - t2 = 0

t2' - t1' = ... = γ[(t1 - t2) + 3u/c2]
Since t2' - t1' > 0, t1' occurs first. Therefore, front end of pole leaves barn first.

Is the calculation correct? Is there a more intuitive way of understanding which comes first?

Thanks!

Yes, your calculations are correct. The intuitive way of understanding it might be to look from the point of view of the pole-vaulter. From his point of view, it's the barn that is moving, and is length-contracted to just [itex]9/5[/itex] meters between the doors. (You've described a length contraction factor, [itex]\frac{1}{\gamma}[/itex], of [itex]3/5[/itex]). So if you stick a 5-meter pole into a barn that is only 9/5 meters long, then of course the front end of the pole will come out the back door before the back end comes through the front door.
 
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  • #3
stevendaryl said:
Yes, your calculations are correct. The intuitive way of understanding it might be to look from the point of view of the pole-vaulter. From his point of view, it's the barn that is moving, and is length-contracted to just [itex]9/5[/itex] meters between the doors. (You've described a length contraction factor, [itex]\frac{1}{\gamma}[/itex], of [itex]3/5[/itex]). So if you stick a 5-meter pole into a barn that is only 9/5 meters long, then of course the front end of the pole will come out the back door before the back end comes through the front door.

Ohhh right! Thanks! :)
 

1. What is the Classic Pole in Barn Relativity Question?

The Classic Pole in Barn Relativity Question is a thought experiment that involves a pole and a barn. It was first proposed by physicist Albert Einstein to illustrate the concept of relativity in physics.

2. How does the Classic Pole in Barn Relativity Question relate to relativity?

In the thought experiment, the pole is moving at a high speed relative to the barn. According to the theory of relativity, the length of an object appears shorter when it is moving at a high speed. This phenomenon is known as length contraction. The Classic Pole in Barn Relativity Question helps to illustrate this concept.

3. Can you explain the paradox that arises in the Classic Pole in Barn Relativity Question?

The paradox arises when considering the perspective of an observer inside the barn and an observer outside the barn. The observer inside the barn sees the pole as being shorter due to length contraction. However, the observer outside the barn sees the pole as being longer because they are not moving at the same speed as the pole. This leads to a contradiction in the lengths of the pole, hence the paradox.

4. What is the significance of the Classic Pole in Barn Relativity Question?

The Classic Pole in Barn Relativity Question helps to demonstrate the principles of relativity and the concept of relative motion. It also highlights the idea that the perception of an event or object can vary depending on the observer's frame of reference.

5. Are there any real-world applications of the Classic Pole in Barn Relativity Question?

The concept of relativity and relative motion plays a crucial role in many areas of modern physics, such as space travel and particle accelerators. The Classic Pole in Barn Relativity Question is a simple example that helps to understand these complex ideas and their practical applications.

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