# Physics AS exam

1. May 10, 2004

i have just read while revising for my physics AS exam that

'Mass is the property of an object which resists change in motion'
'An object with larger mass will accelerate less than the object with smaller mass'

does this not imply that an object with zero mass will have infinite acceleration?
and does having infinite acceleration therefore imply the object has the ability to be everywhere at the same time??

2. May 10, 2004

### HallsofIvy

Staff Emeritus
Surely that quote should be 'An object with larger mass will accelerate less than the object with smaller mass WHEN SUBJECT TO THE SAME FORCE'

It implies that an object with zero mass COULD have infinite acceleration if it were affected by some force.

The only objects with zero mass are photons and they are not affected by forces- they have 0 acceleration.

3. May 10, 2004

### quantum mechanic

A photon is considered to have an actual mass of zero and a zero rest mass, but when the photon is moving, it assumes an apparent mass due to the velocity (m = E /C2). This apparent mass is significant enough to lend to uncertainties in momentum and position according to Heisenberg.

4. May 10, 2004

### pmb_phy

That is incorrect. A photon has a non-zero (relativistic) mass. Only its rest mass is zero. However this could be a disagreement in terms since the terms "apparent mass" and "actual mass" are not terms that are defined in relativity. At least not in the more well known literature.

Relativistic mass "m" equals the ratio of the magnitude of the particles momentim to its speed. I.e. m = p/v. For a photon v = c. Since E = pc => c/E then

m = p/c = (E/c)/c = E/c2

Pete

5. May 11, 2004

### Lorentz

Well if we stay at Newtons theory then the answer is clearly No.

F = m * a --> a = F/m if m = 0 we will divide by zero which isn't aloud.

There's no (classical) physical reality of an object with zero mass... it has no physical meaning. Something cannot have an infinite acceleration if it doesn't exist.

6. May 11, 2004

### arildno

Sure there is; fluid particles for example.
(They don't have infinite accelerations, though, since the sum of forces acting upon them is zero)

7. May 11, 2004

### pmb_phy

Fluid particles have mass. Anything that has momentum has mass (note: That
s mass, and not rest mass that I'm refering to).

Pete

8. May 11, 2004

### arildno

Any REAL fluid particle/collection of atoms have mass;
the mathematical abstraction known as a fluid particle (which is what I was talking about) occupies a single, spatial point, with a non-zero density value attached to it.
The mass of a fluid region V is given by:
$$M=\int_{V}\rho{dV}$$.
Going to the limit $$V\rightarrow0$$ yields the mass of a single, mathematical, fluid particle

9. May 11, 2004

### Lorentz

You say it yourself. It's a mathematical abstraction... in other words not to be confused with physical reality.

Do note that I don't know anything about the fluid particle you're talking about.

10. May 11, 2004

### arildno

You used the term (classical) physical reality, in the first place, and that's what I've referred to.
Up to the development of the atomic theory in the middle 19'th century,
"reality" consisted for physicists in the existence of continua/continuums,
in which such particles were thought to exist.
With the advent of the molecular model, the mathematics developed in earlier times could be overtaken almost unchanged; however, a lower limit of applicability of the continuum hypotheses had now to be introduced
(i.e. continuum mechanics do not accurately describe the behaviour at length scales comparable with the mean free path, for example).

11. May 11, 2004

### arildno

Have you ever calculated in solid mechanics the moment of inertia by integral?
If you have done so, you are using a continuum mechanics model of reality.