Purchase Solution

Invariant mass of systems

Not what you're looking for?

Ask Custom Question

1. Consider two particles of equal mass m. Determine the system mass for each of the following cases.

(a) Both particles are moving in the x-direction with kinetic energies K=5m.
(b) One particle moves in the y-direction with K=5m and the other moves in the +x-direction with K=5m.
(c) Given that both systems contain two mass-m particles with K=5m, explain any difference between your answers to parts (a) and (b).

Note: in these units c=1, velocity is dimensionless, and thus energy has the same units as mass.

Purchase this Solution
Solution Summary

A detailed solution is given. The two particles of equal mass are determined.

Solution Preview

In some older textbooks "relativistic mass" is defined as total energy divided by c^2. But this is NOT the modern definition of mass. After the invention of relativity, it became clear that mass and energy are the same things; the equation E = m c^2 merely expresses this fact. The factor c^2 is only there because we still use our old units in which time and space are considered to be different quantities.

Today, the word "mass" in modern physics is reserved for the total energy in the rest frame of the system divided by c^2. Obviously this is an invariant quantity. If you and I are moving with respect to each other and there is some particle moving with some velocity w.r.t. me, then the mass is the energy/c^2 in the rest frame of that particle. I can calculate that if I know the energy and momentum of the particle. You can do that to with your figures, but we must both find the same value. Because of this invariance, the word "invariant mass" is sometimes used for the mass. The word "rest mass" is more often encountered in the older literature to distinguish it from the now obsolete term "relativistic mass". By putting c = 1, you can measure mass and energy in the same units.

So, how do we ...

Purchase this Solution
Free BrainMass Quizzes
Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

The Moon

Test your knowledge of moon phases and movement.

Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

Basic Physics

This quiz will test your knowledge about basic Physics.

View More Free Quizzes
Related BrainMass Solutions

  • Pion photo production

    If we square both sides, we get: q^2 = (q'_proton + q'_pion)^2 But since the square of 4-vectors are invariant, we can evaluate the right hand side in the center of mass frame and in that frame q'_proton + q'_pion = (m_proton,0) + (m_pion,0) =

  • Relativistic mechanics kinetic energy

    in the observer (lab) frame is: (1.6) Thus: (1.7) Or: (1.8) Newtonian momentum is defined as: (1.9) But since the real invariant is the proper time, the derivative at equation (1.9) becomes: (1.10)   If we expand the mass

  • Kinetic energy, rest energy and inelastic collisions

    It is again much more convenient to work with quantities that are invariant under Lorentz transformations. We have seen above that the square of a four-momentum is just the square of the rest mass.

  • Transfer Function

    The response of a system to an input is: What is the steady-state response? 1. Is the linear time-invariant continuous-time system with the impulse response h(t) = sin 2t for t ≥ 0 BIBO is stable? Explain.

  • Special Relativity - Energy Problems.

    c) before the collision is: The initial speed of the first particle is: The relation between momentum and energy of a particle is the invariant: Which here becomes: The initial momentum of the particle at

  • Discrete signals and systems problems

    The solution covers the problems of impulse response, periodicity and convolution for discrete signals and systems which are linear and time-invariant. It contains a detailed step-by-step guide with important calculations and illustrations.

  • Basis, Zero Subspace and Invariant Suspaces

    However, the characteristic equation does have two different COMPLEX roots, therefore it does have eigenvectors in C^2, and so each of the eigenvectors serves as a basis of a C^1 subspace of C^2 invariant under U.

  • signal and Laplace Transform

    The solution investigates the properties of the signal, such as linear, time invariant, causal, or memory-less. It also shows how to solve differential equation using Laplace transform. See attachments.

  • Canonical Transformation

    The solution shows how to obtain the generating function of a canonical invariant transformation.

View More Related Solutions