Does the mass of a brick increase when you lift it?

Question

If a person takes a brick, and lifts it to a height of 1 m, will the mass of the brick increase?

Technically this is a duplicate question: Does the mass of an object change as it moves away from the earth? However, that question contains several answers that disagree with each other, with no clear winner... — lemon, Jun 06 '16 at 11:21
Hi vladon, welcome to Physics SE! I will ask you a question: why do you ask? — Andrea, Jun 06 '16 at 11:26
@AndreaDiBiagio Because we discussed this topic at the lunch :-) — vladon, Jun 06 '16 at 11:27
The mass of an object at rest does not change if you change its position. — Andrea, Jun 06 '16 at 11:30

score 0 · Answer 1 · answered Jun 06 '16 at 11:24

0

No, mass does not increase when you lift an object. Potential energy increases, but that's because of the $\Delta h$ in $U_{\mathrm{grav}} = mg\Delta h$, not the $m$. Mass is, to put it a bit imprecisely, the amount of matter in an object. When you lift something, there doesn't become more of it.

(Note that I'm ignoring relativistic effects.)

answered Jun 06 '16 at 11:24

Deusovi

111

And what it will be when taking in account ther relativistic effects? – vladon Jun 06 '16 at 11:26
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@vladon Depends on your reference point. – Feyre Jun 06 '16 at 12:01

score 0 · Answer 2 · answered Jun 06 '16 at 13:28

If you have a proton (mass=$m_p$) and a neutron (mass=$m_n$) and allow them to join via the strong nuclear force the mass of the $^2_1H$ nucleus $m_{np}$ is less than the sum of the masses of the individual particles ($m_{np} \lt m_p + m_n$).
During this joining together the proton-neutron system loses potential energy and that energy is called the binding energy of the nucleus.

The same is true of your brick-Earth system except that now the mass of the brick-Earth system when the brick has been lifted a height $h$ is higher than that of the brick-Earth system before the brick was lifted up.
Work has had to be done to lift the brick and so the brick-Earth system has gained potential energy. The change in mass of the brick-Earth system is rather small $\approx 3 \times 10^{-16}$ kg for a 3 kg brick raised by 1 metre.
Even if you took the brick a long way away from the Earth (to "infinity") the brick-Earth system would only increase in mass by approximately $2 \times 10^{-9}$ kg.

The rest mass of the brick does not change.

What would happen, in your model, if you were to bring two rest masses closer and closer? As the potential energy decreases and decreases, does the combined mass also decrease and decrease, until it becomes massless? — Andrea, Jun 06 '16 at 15:51
Just as with bringing a neutron and a proton together one would imagine that the two masses would reach an equilibrium separation. — Farcher, Jun 06 '16 at 16:00

score -3 · Answer 3 · edited Jun 06 '16 at 13:25

-3

Mass certainly will change. In fact we have two connected bodies - brick and earth. The Hamiltonian (full energy operator) of a connected particle system is defined as: $H = H(brick) + H(earth) + V$, where $V$ is energy of interaction (potential energy in our case). Since potential energy will increase, mass inevitably increases due to the theory of special relativity.

edited Jun 06 '16 at 13:25

John Dumancic

3,937

answered Jun 06 '16 at 12:16

nmas

3

I do not think this is true.The Equation E=mc^2 is about rest energy for non-moving objects. That does not include potential energy in that form. – Physics Guy Jun 06 '16 at 12:49
Why do you use the Hamiltonian of a connected particle system to define potential energy by gravity? That's not necessary. – John Dumancic Jun 06 '16 at 13:19
well, I cant agree - for example nuclear power plant works because of mass defect in uranium-235 is less then in its decay products. And its all connected to potential energy of binding in atomic nuclei. – nmas Jun 06 '16 at 13:20
but thats for particles in a nucleus and not large multi-particle systems like the brick-earth system – Jaywalker Jun 06 '16 at 13:49
By how much does the mass increase then? By $.5 V/c^2$ perhaps? You cannot summon $E=mc^2$ for gravitational energy without careful treatment! The reason is that gravitational energy is a non-local property, and thus it is hard to apply relativity to it! Indeed, in general relativity there is no simple concept of gravitational potential energy. – Andrea Jun 06 '16 at 15:48
@AndreaDiBiagio What treatment is needed? Maybe in relativity theory there is smth about "types" of energy or interactions for which theory works or not? You mean that connection between mass and energy won't work here, maybe the law of conservation of energy will not work? We have here only mass (means energy) before lifting, and energy-mass after. – nmas Jun 06 '16 at 16:46
Indeed, energy is not generally conserved in general relativity! More broadly, some concepts of Newtonian physics do not carry immediately to general relativity. Gravitational potential energy is one of these. There are two options: work within Newtonian Physics (where the mass of the object is defined and constant) or in General Relativity (where the potential energy is not really defined, and the mass of a particle is also constant). In principle, you can probably calculate the "effective" mass of the combined system, as observed from far away. – Andrea Jun 06 '16 at 17:39

Does the mass of a brick increase when you lift it?

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