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# An observer on the ground and an observer on the train in the figure for Question 7 each measure the distance between two posts located along the tracks. The observer on the ground measures the distance to be 100 meters. Does the observer on the train obtain a measurement that is less than, equal to, or greater than 100 meters? Why?

## less than $100 \mathrm{m}$

Gravitation

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##### Andy C.

University of Michigan - Ann Arbor

LB
##### Marshall S.

University of Washington

##### Aspen F.

University of Sheffield

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### Video Transcript

In this exercise, we have an observer on the ground that measures a length l equal to 100 meters between two posts located on a train track. And we want to know what would be the length al prime measured by an observer inside a train that's moving relative to the train trip. So notice that the the length L equal to 100 meters it is the proper length between the two posts. Okay, And that's because this is the length as measured by the by the reference rain that's at breast with relation to the *** dream tracks. And we know that the proper length is the maximum length measure. All other observers that are moving relative to the the length that met. I've heard that the reference ring, the measure, the proper length we'll measure a smaller, um, small early. Okay, so what we have is that l prime that's the length measured by the movie Observer is equal to l divided by Goma, where Goma is defined as 1/1 minus V squared. Overseas square is always greater than what so noticed that l prime is always smaller than L, which is 100 meters. So what we have is the l prime the distance that will be measured by D. This is the way we measured by the observer on the train is smaller than 100 meters.

#### Topics

Gravitation

##### Andy C.

University of Michigan - Ann Arbor

LB
##### Marshall S.

University of Washington

##### Aspen F.

University of Sheffield

Lectures

Join Bootcamp