Physics Book Problem: Berlin-Paris Train Error

In summary, the conversation discusses the error in the total distance covered by a train traveling from Berlin to Paris and whether it is correct to write the distance as 890,010m. While the answer for a is found, the book states that the answer for b is incorrect, but it is not clear why. It is explained that writing 890,000m can also be considered as it is the same as 890km. However, the accuracy of the distance and measurement points are also taken into consideration.
  • #1
iampaul
93
0

Homework Statement



A train travels 890 km from Berlin to Paris and then overshoots the end of the track by 10m.

Homework Equations



a.What is the %error in the total distance covered
b.Is it correct to write the distance by the train as 890,010m?Explain.

The Attempt at a Solution


I got the answer for a. The book says that the answer for b is no. But I am not sure why. Can someone help me with b.
 
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  • #2
iampaul said:

Homework Statement



A train travels 890 km from Berlin to Paris and then overshoots the end of the track by 10m.

Homework Equations



a.What is the %error in the total distance covered
b.Is it correct to write the distance by the train as 890,010m?Explain.

The Attempt at a Solution


I got the answer for a. The book says that the answer for b is no. But I am not sure why. Can someone help me with b.

have you ever read the headline in the news paper "65,000 attend football final" and thought that if only you had gone there would have been 65 001 people there! I don't think that would be true either, for the same sort of reason.
 
  • #3
for B., Since 1Km=1000m, Writing 890,000m can be considered because it is the same as 890km. There's nothing wrong in using any of the two.
 
  • #4
andorei said:
for B., Since 1Km=1000m, Writing 890,000m can be considered because it is the same as 890km. There's nothing wrong in using any of the two.

At best, 890 km is specified to three significant figures, so to add another 10m really is insignificant. Berlin might actually be 890.2 km away anyway.
There is a chance that the distance is supposed to be only 2 figure accuracy. Berlin might be 892 km away, but it is rounded to 890.

And the football crowd of 65,000 was probably rounded to the nearest 1000 people!
 
  • #5
Not to mention that neither the train nor Berlin are mathematical points. So how would one go about measuring the "distance" between the train and Berlin? Where in Berlin do you put one point of your measuring tape and where on the train do you put the other end?
 
  • #6
thanks a lot!
 

1. What is the Berlin-Paris Train Problem in Physics?

The Berlin-Paris Train Problem in Physics is a thought experiment that involves two trains traveling at different speeds and the concept of relativity. It was first proposed by Albert Einstein in 1905 to demonstrate the principles of special relativity.

2. What is the main question behind the "Berlin-Paris Train Problem"?

The main question behind the "Berlin-Paris Train Problem" is: what happens to the measurements of time and distance for an observer on one of the trains as it passes by the other train at a high speed? This question aims to explore the effects of relative motion on our perception of time and space.

3. How does the "Berlin-Paris Train Problem" relate to the theory of relativity?

The "Berlin-Paris Train Problem" is a thought experiment that illustrates the principles of special relativity, specifically the concept of time dilation and length contraction. It shows that time and space are relative and can change depending on the observer's frame of reference.

4. What are some possible solutions to the "Berlin-Paris Train Problem"?

There are several possible solutions to the "Berlin-Paris Train Problem" depending on the frame of reference and assumptions made. Some solutions involve using the equations of special relativity to calculate the time and distance measurements, while others may involve using thought experiments to visualize the scenario.

5. How does the "Berlin-Paris Train Problem" challenge our understanding of physics?

The "Berlin-Paris Train Problem" challenges our understanding of physics by demonstrating the counterintuitive effects of relative motion on time and space. It also highlights the importance of considering the observer's frame of reference when making measurements and calculations. This thought experiment played a crucial role in the development of the theory of relativity and continues to challenge our understanding of the universe.

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