# Special Relativity transformations

• Icaro Amorim
In summary: It was Bergmann's classic on SR and GR. I worked through every problem in it in high school with no one available to help.I understand Resnick has passed on in late January. He will be missed. I am surprised I have not seen this mentioned in any physics forum columns.
Icaro Amorim

## Homework Statement

A rod of rest length 1,0m is moving longitudinally on a smooth table with a velocity 0,8c relative to the table. A circular hole of rest diameter 1,0 m lies in its path. The diameter of the hole as seen by the rod is going to be larger?

## The Attempt at a Solution

I guess no, because the length of a moving object relative to another at rest is smaller, from the contraction of length in relativity, but the asnwer is a larger length (1,667m). Why doest it happen?

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Icaro Amorim said:
I guess no, because the length of moving object relative to another at rest is smaller, from the contraction of length in relativity, but the asnwer is a larger length (1,667m). Why doest it happen?
I'd say you were correct and the answer given is incorrect. Is this from a textbook?

Thank you!
Yes, it is from a textbook. From Resnick, Introduction to Relativity.

Icaro Amorim said:
Thank you!
Yes, it is from a textbook. From Resnick, Introduction to Relativity.

I'd have to see a snapshot or scan to believe it. I agree with the OP and Doc.

I also agree with OP and Doc Al, and other posters. Further, this is a classic scenario in SR.

What is true is that everyone agrees that the rod will hit the far edge of the hole. For the table frame, this is because the rod is smaller than the hole, and has a brief moment to fall so as to clip the edge of the hole. For the rod, the hole is small, but (using gravity as a force + SR) but moving upwards, bending the rod and hitting the edge of the rod.

Note, you don't need any theory of matter or gravity to explain this. If you posit what happens in the table frame, a Lorentz transform to the Rod frame gives you all the rest (that he far side of hole and rod collide, that the rod bends, etc.).

I also would like to see a scan of the text. I think it is more likely that OP is misinterpreting something than that a standard text like this can be in error on such a classic SR problem.

rude man said:
I'd have to see a snapshot or scan to believe it. I agree with the OP and Doc.

I also wondered if such an error existed in Resnick's text. Wonder no more.

#### Attachments

• Resnick Prob 2_26.png
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Wow, the text is wrong and disagrees with its references. That is really shocking.

The first book I used when I was self-learning SR was Resnick's text. In retrospect, I feel that it was awful.

Chet

Chestermiller, can you advise me a better book for the same subject?

Thank you all guys for the support. It was really helpful. I'm learning by myself and I thought I had misunderstood. I appreciate. :)

Greetings from Brazil.

Icaro Amorim said:
Chestermiller, can you advise me a better book for the same subject?

Thank you all guys for the support. It was really helpful. I'm learning by myself and I thought I had misunderstood. I appreciate. :)

Greetings from Brazil.

See our textbook subforum! The following gets the most votes in that forum:

(I can't say anything personally; I don't own it, and learned initially from a 1942 textbook; no, I'm not that old, just the book was).

PAllen said:
Wow, the text is wrong and disagrees with its references. That is really shocking.

Quite amazing. Although I didn't use Resnick & Halliday for introductory physics in school I liked their book so much I went & bought it well after graduation - so this is indeed a shocker.

We need to inform Dr. Resnick if we still can, don't know if he's still with Rensselaer Poly.

Or maybe this is his son or ...? (The Resnick of R&H is Robert Resnick. PAllen, what's the name in your SR text?).

rude man said:
Quite amazing. Although I didn't use Resnick & Halliday for introductory physics in school I liked their book so much I went & bought it well after graduation - so this is indeed a shocker.

We need to inform Dr. Resnick if we still can, don't know if he's still with Rensselaer Poly.

Or maybe this is his son or ...? (The Resnick of R&H is Robert Resnick. PAllen, what's the name in your SR text?).

It was Bergmann's classic on SR and GR. I worked through every problem in it in high school with no one available to help.

I understand Resnick has passed on in late January. He will be missed. I am surprised I have not seen this mentioned in any physics forum columns.

## What is "Special Relativity transformations"?

"Special Relativity transformations" refers to the equations and principles developed by Albert Einstein in his theory of Special Relativity. These transformations describe how space and time are relative and how they are affected by the speed of an object.

## What is the significance of "Special Relativity transformations"?

"Special Relativity transformations" revolutionized our understanding of space and time, showing that they are not absolute concepts but are relative to an observer's frame of reference. This theory has had a significant impact on modern physics and has been verified by numerous experiments.

## What is the difference between "Special Relativity transformations" and "General Relativity transformations"?

The main difference between these two is that Special Relativity transformations only apply to objects moving at a constant speed in a straight line, while General Relativity transformations take into account acceleration and gravity. General Relativity is an extension of Special Relativity and provides a more complete understanding of the universe.

## How do "Special Relativity transformations" affect time and space?

According to Special Relativity, time and space are not absolute but are relative to an observer's frame of reference. This means that the length of an object and the passage of time can appear different to different observers depending on their relative motion. Additionally, Special Relativity predicts that time and space can be warped by gravity and acceleration.

## How have "Special Relativity transformations" been proven?

Special Relativity has been extensively tested and confirmed through various experiments, such as the Michelson-Morley experiment, which showed that the speed of light is constant for all observers. Additionally, the predictions of Special Relativity have been used to make precise measurements and calculations in fields such as particle physics and astrophysics.

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