A ball falls from a magnet but the magnet still exerts an upwards force against gravity yet the ball falls anyway. However, the ball slows down and thus the sound when it hits the floor is less signalling that some energy has been lost during its descent. What I'm wondering is where that energy has gone? Has the magnet gained magnet energy? Or has earth gained energy. Or has the ball not lost energy but its remaining energy just wasn't turned into sound upon contact with the ground? Or is it something else?
[Physics] Where is the energy transfer from a metal ball falling from a magnet
electromagnetismgravity
Related Solutions
Since gravity uses energy to push us down to earth
This is incorrect. Gravity does not use energy to pull in us.
If we started falling, then yes, gravity used energy do make us move. But that is only in the special case where gravity makes us move. In general, gravity spends no energy pulling in us.
In general, a force spends no energy. An apple lying on a table is both pulled down by gravity and held up by the table's normal force. Gravity spends no energy here. The normal force doesn't spend any energy either. This situation of apple-lying-still-on-table will stay like that forever. It will never change, since no energy can "run out" when no energy is spent.
The levitating magnet is the same case. No energy spent. Thus, this will theoretically remain forever. (Unless there are other forces acting as well, that do spend energy.)
As Dale points out there are tests of the weak equivalence principle that check that the acceleration of bodies of different composition, towards a large mass, are the same.
That checks that the 'passive gravitational mass' is equivalent to inertial mass. The experiments show that the equivalence principle is true to a high degree of accuracy.
It means that one aspect of Einstein's General Relativity seems to be valid. The motion of the masses can be modelled by a 'bending of space-time' by the large mass.
If you mean, in the question - Is there a way to check that the 'active gravitational mass' is equivalent to the inertial mass? Then it can't easily be accurately checked.
(the terms are explained here in the section weak equivalence principle)
It would mean checking that the amount that a mass bent space-time is proportional to it's inertial mass. As you say we can't know the inertial mass from the passive gravitational mass, so another means (electrostatic) would be needed to determine it .
That seems to be limit the objects mass. Then it seems that, even if the gravitational attraction from that mass could be measured, the accuracy would be limited by our knowledge of $G$, unfortunately $G$ is only known to about $0.6$%.
It could well be that this type of experiment has never been carried out, there are likely to be large uncertainties. It would be interesting to know to what extent the active gravitational mass has been found to be equivalent to inertial mass.
Perhaps an expert in General Relativity will comment whether the equivalence follows once GR is accepted, although it would be a theoretical justification and not an answer to your 'Has anyone directly observed...' question.
Best Answer
If the ball is made of iron
You put “magnetic” potential energy into the system when you brought the metal ball up to the magnet. The sign of that potential energy is negative indicating an attractive force.
When you drop the ball, the ball loses gravitational potential energy, but adds magnetic potential energy and kinetic energy. Therefore less energy was available for kinetic energy and the corresponding impact speed was less.
edit:
We can write this as an energy relationship: $$ \begin{align} \Delta E &= \Delta K + \Delta U \\ 0 &= (K_f-K_i) + \Delta U_G + \Delta U_{M} \\ K_f &= -\Delta U_G - \Delta U_M \end{align} $$ Where $K_i = \Delta E = 0$. In the situation where the ball falls the gravitational potential energy decreases ($\Delta U_G < 0$) but the magnetic potential energy increases ($\Delta U_M > 0$), since the metal ball has moved further from the magnet. The type of forces two magnets experience is a conservative force (since it's path independent) and so it makes sense to talk about a magnetic potential energy.
The ball would need to be iron (or one of its alloys like steel) because in terms of everday materials, iron is the only one that can be temporarily (induced) magnetized. For most other materials, $\Delta U_M \approx 0$.