Relativistic Mass as described by Kenneth Krane in 'Modern Physics'

In summary, Mr. Krane describes a scenario in which two balls of equal mass, m1 and m2, collide inelastically with equal speed, v, resulting in a final speed of V = 0 and combined mass of M = m1 + m2. The proper mass of each ball is m0, and using the equation m' = m0 / sqrt(1 - u^2/c^2), the final mass can be calculated as 2m0 / sqrt(1-v^2/c^2). However, the observer argues that the mass of the two combined balls should simply be 2m0, as all the energy from the collision goes into their rest mass. Therefore, the concept of "
  • #1
arguellodw
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Homework Statement


Mr. Krane describes this scenario in a presentation of relativistic mass in his book
Modern Physics
John Wiley & Sons, Inc. 1983
p. 36-37

According to one observer, two balls of equal mass, m1 and m2, are approaching each other at equal speed, v. The proper mass of each is m0. They collide inelastically for a final speed of V = 0 and mass M = m1 + m2.


Homework Equations



m' = m0 / sqrt(1 - u^2/c^2)


The Attempt at a Solution



The conclusion is that the final the final mass of the two balls (stuck together) is:

M = m1 + m2 = m0/sqrt(1-v^2/c^2) + m0/sqrt(1-(-v)^2/c^2) = 2m0 / sqrt(1-v^2/c^2)

Instead, I argue that since two balls are now at rest in the reference frame of the observer, the mass of the two stuck balls is

M = 2m0

What am I missing here?
 
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  • #2
arguellodw said:
What am I missing here?
What happened to the kinetic energy of the masses? (The so-called 'relativistic mass' includes the kinetic energy of the masses.) Since the collision was totally inelastic, presumably all the energy goes into the rest mass of the two stuck balls.
 

1. What is relativistic mass?

Relativistic mass is a concept in modern physics that describes the increase in an object's mass as it approaches the speed of light. It is a result of the energy-mass equivalence principle, where mass and energy are interchangeable.

2. How is relativistic mass different from rest mass?

Rest mass is an object's mass when it is at rest, while relativistic mass takes into account the object's speed and increases as the object's speed approaches the speed of light. This means that an object's relativistic mass can never be less than its rest mass.

3. What is the formula for calculating relativistic mass?

The formula for calculating relativistic mass is m = m0/√(1 - v2/c2), where m0 is the rest mass, v is the velocity, and c is the speed of light (approximately 3 x 108 m/s).

4. Does relativistic mass affect an object's weight?

No, relativistic mass does not affect an object's weight. Weight is a measure of the force of gravity acting on an object, while mass is a measure of the amount of matter in an object. Relativistic mass does not change the amount of matter in an object, so it does not affect its weight.

5. What are some real-world applications of relativistic mass?

Relativistic mass is a fundamental concept in modern physics and has important applications in fields such as nuclear physics, particle accelerators, and space travel. It also plays a role in the understanding of the behavior of objects at high speeds, such as in the theory of relativity.

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