**Understanding Time Dilation and Distance in Relativity**In this educational exercise, we explore the concept of time dilation in special relativity through the example of a subatomic particle known as a pion. Pions are known to exist for a brief moment before decaying into other particles.**Scenario:**A pion is moving at a speed of 0.992c, where \( c \) is the speed of light. An observer stationary in a laboratory measures the pion's lifetime to be \( 2.7 \times 10^{-8} \) seconds.**Questions:**- (a) What is the lifetime of the pion according to a hypothetical person traveling with the pion?- (b) According to this hypothetical person, how far does the laboratory travel before the pion decays?Below the problem description are sections labeled (a) and (b), each containing fields for:- **Number**: Where the numeric answer is to be entered.- **Units**: A drop-down menu for selecting the appropriate unit (e.g., seconds, meters).This exercise illustrates how time and distance measurements change depending on the observer's frame of reference, a fundamental aspect of Einstein's theory of relativity.

A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.992c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 2.7 x 108 s. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart? (a) Number i (b) Number Units Units

A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.992c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 2.7 x 108 s. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart? (a) Number i (b) Number Units Units

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.

Question

**Understanding Time Dilation and Distance in Relativity**

In this educational exercise, we explore the concept of time dilation in special relativity through the example of a subatomic particle known as a pion. Pions are known to exist for a brief moment before decaying into other particles.

**Scenario:**
A pion is moving at a speed of 0.992c, where \( c \) is the speed of light. An observer stationary in a laboratory measures the pion's lifetime to be \( 2.7 \times 10^{-8} \) seconds.

**Questions:**
- (a) What is the lifetime of the pion according to a hypothetical person traveling with the pion?
- (b) According to this hypothetical person, how far does the laboratory travel before the pion decays?

Below the problem description are sections labeled (a) and (b), each containing fields for:
- **Number**: Where the numeric answer is to be entered.
- **Units**: A drop-down menu for selecting the appropriate unit (e.g., seconds, meters).

This exercise illustrates how time and distance measurements change depending on the observer's frame of reference, a fundamental aspect of Einstein's theory of relativity.

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