marlyne montero villareal mscied physics ii july 16, 2011 mass

Marlyne Montero VillarealMSciEd Physics II

July 16, 2011

Mass

Make Physics as simple as possible, but no simpler.Albert Einstein

The ideal is to reach proofs by comprehension rather than by

computation.Bernhard Riemann

NEWTON’S THEORY OF MECHANICS AND GRAVITATION

►Inertial Mass – the ratio between force and acceleration in Newton’s Second Law and thus measure a particle’s resistance to acceleration

►Gravitational Mass-This is defined by the force of gravitation, which states that there is a gravitational force between any pair of objects, which is given by

Where G is the gravitational constant.Wolfgang Rindler

Relativity: Special, General and Cosmology 2nd Ed. (2006)

MASS IN THE SPECIAL RELATIVITY

3 Conservation Principles:

1.Conservation of Energy2.Conservation of Mass 3.Conservation of

Momentum

Relativistic Energy

2 Conditions:1.The total kinetic energy E of an isolated

system is conserved2.E will approach the classical value when

u/c approaches zero.

Paul A.Tipler & Ralph A. LlewellynModern Physics 2nd Ed. (1999

Relativistic total energy is then defined as the sum of KE and the rest energy

Paul A.Tipler & Ralph A. LlewellynModern Physics 2nd Ed. (1999)

“rest mass” (velocity-independent)

“relativistic mass” (velocity-dependent)

Guide questions:

1.Does mass depend on velocity?2.Is mass invariant?3.Should using the term

“relativistic mass” be discontinued?

Does mass depend on velocity, dad?

The notion of the dependence of mass on velocity as introduced by Lorentz in 1899 and then developed by him and others in the years preceding Einstein’s years.

Transverse mass; F is perpendicular to v

Longitudinal mass; F is parallel to v

Lev B. OkunThe Concept of Mass

Physics Today. June 1989

In accordance with the theory of relativity the kineticenergy of a material point of mass m is no longer given by the well-knownexpression

but by the expression

This expression approaches infinity as the velocity v approaches thevelocity of light c. The velocity must therefore always remain lessthan c, however great may be the energies used to produce theacceleration

Albert EinsteinThe Special and General Theory of Relativity.1920

If we develop the expression for the kinetic energy inthe form of a series, we obtain

The first term does not contain the velocity, and requires no consideration if we are only dealing with the question as to how the energy of a point-mass depends on the velocity.

The most important result of a general character to which thespecial theory of relativity has led is concerned with the conception ofmass. Before the advent of relativity, physics recognised twoconservation laws of fundamental importance, namely, the law of theconservation of energy and the law of the conservation of mass; thesetwo fundamental laws appeared to be quite independent of each other.By means of the theory of relativity they have been united into onelaw


Arthur BeiserConcepts of Modern Physics, 6th Ed. (2003)

The total energy and momentum are conserved in an isolated system, and the rest energy of particle is invariant.

Arthur BeiserConcepts of Modern Physics, 6th Ed. (2003)Paul A.Tipler & Ralph A. Llewellyn

Modern Physics 2nd Ed. (1999

Four-vector

In relativistic energy and momentum we components of another four vector

The magnitude of the invariant energy/momentum four-vector is the rest energy of the mass m. Thus, observers in all inertial frame will measure the same value for the rest mass.


Note:1. It is the rest energy of any isolated system be a single

atom or the entire universe that is conserved.2. The system’s rest energy may be greater than, equal

to, or less than the sum of the rest energies of the constituents depending on their relative velocities and the detailed character of any interaction between them

An important case, in which the system rest energy is less that the rest energies of its members is that of a system of particles held together by attractive forces, such as the neutrons and protons in a atomic nucleus. The rest energy of a nucleus (except that of ordinary hydrogen, which is a single proton) is less than the total rest energies of its constituent particles.

The difference is called the binding energy of the nucleus. To break a nucleus up completely calls for an amount of energy at least equal to its binding energy.


Massless particle

Can a massless particle exist?

The conclusion is not that massless particles necessarily occur, only that the laws of physics do not exclude the possibility as long as v=c and E=pc for them, In fact, a massless particle – the photon – indeed exists and its behaviour is as expected.


A debate of the subject surfaced in Physics Today in 1989 when Lev Okun wrote an article urging that relativistic mass should no longer be taught . Wolfgang Rindler responded with a letter to the editors defending its continued use. In 1991 Tom Sandin wrote an article in the American Journal of Physics that argued in favour of relativistic mass.

In a 1948 letter to Lincoln Barnett, Einstein wrote

"It is not good to introduce the concept of the mass M = m/(1-v2/c2)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than `the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion."

Cited in: Lev B. Okun

The Concept of MassPhysics Today. June 1989

marlyne montero villareal mscied physics ii july 16, 2011 mass

Documents

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