A ball of mass m traveling at a speed of 0.80c has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass 2m departs the collision with a speed of 0.40c. Let's do a relativistic collision analysis to determine the mass and speed of the ball after the collision. Part C What is the initial total energy? Give your answer as a fraction times mc². Don't forget that there are two balls. Express your answer in terms of c and m. 15. ΑΣΦ E= Submit Part D U₁ = Request Answer Because energy can be transformed into mass, and vice versa, you cannot assume that the final mass is 2m. Instead, I the final state of the system be an unknown mass M traveling at the unknown speed up. You have two conservation law Find us. Express your answer in terms of c and m. Submit Π ΑΣΦ ? Request Answer

A ball of mass m traveling at a speed of 0.80c has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass 2m departs the collision with a speed of 0.40c. Let's do a relativistic collision analysis to determine the mass and speed of the ball after the collision. Part C What is the initial total energy? Give your answer as a fraction times mc². Don't forget that there are two balls. Express your answer in terms of c and m. 15. ΑΣΦ E= Submit Part D U₁ = Request Answer Because energy can be transformed into mass, and vice versa, you cannot assume that the final mass is 2m. Instead, I the final state of the system be an unknown mass M traveling at the unknown speed up. You have two conservation law Find us. Express your answer in terms of c and m. Submit Π ΑΣΦ ? Request Answer

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter9: Relativity

Section: Chapter Questions

Problem 54P

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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

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**Relativistic Collision Analysis**

A ball of mass \( m \) traveling at a speed of \( 0.80c \) has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass \( 2m \) departs the collision with a speed of \( 0.40c \). Let's do a relativistic collision analysis to determine the mass and speed of the ball after the collision.

**Part C**

What is the initial total energy? Give your answer as a fraction times \( mc^2 \). Don't forget that there are two balls.

*Express your answer in terms of \( c \) and \( m \).*

\[ E = \]
[Input box]
[Submit] [Request Answer]

**Part D**

Because energy can be transformed into mass, and vice versa, you cannot assume that the final mass is \( 2m \). Instead, let the final state of the system be an unknown mass \( M \) traveling at the unknown speed \( u_f \). You have two conservation laws. Find \( u_f \).

*Express your answer in terms of \( c \) and \( m \).*

\[ u_f = \]
[Input box]
[Submit]

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