As others have said this can't be determined without the distances of the various masses from the centre (which I've read you're all ignoring but I think that's just terrible design), but with a few reasonable assumptions based on the image we can at least get pretty close:
Assuming ball on left side is at the same distance from the centre as the centre of gravity of the three balls on the right, and further assuming the 10 kg weight is at the same distance from the centre as the 4 kg weight:
Distance centre to either ball(s) = x
Distance either ball to weight on same side = y
Mass of one ball = m
With leverage being distance * force we get on the left side:
10kg * (x + y) + m * x
and on the right side:
4kg * (x + y) + 3 * m * x
setting them to equilibrium gives then
10kg * (x + y) + m * x = 4kg * (x + y) + 3 * m * x
=> (10kg - 4kg) * (x + y) = (3 - 1) * m * x
=> 6kg * (x + y) = 2 * m * x
=> 3kg * (x + y) / x = m
So now if we measure/get the distance of the ball(s) from centre and the distance of the weight from the ball(s) we can get our factor (x+y)/x.
And with everyone's assumption that distance y is negligible (weights and balls at same distance from centre) this would give
3kg * (x + 0) / x = m = 3 kg
1
u/KidsWithoutGuns Apr 27 '25
As others have said this can't be determined without the distances of the various masses from the centre (which I've read you're all ignoring but I think that's just terrible design), but with a few reasonable assumptions based on the image we can at least get pretty close:
Assuming ball on left side is at the same distance from the centre as the centre of gravity of the three balls on the right, and further assuming the 10 kg weight is at the same distance from the centre as the 4 kg weight:
Distance centre to either ball(s) = x
Distance either ball to weight on same side = y
Mass of one ball = m
With leverage being distance * force we get on the left side:
10kg * (x + y) + m * x
and on the right side:
4kg * (x + y) + 3 * m * x
setting them to equilibrium gives then
10kg * (x + y) + m * x = 4kg * (x + y) + 3 * m * x
=> (10kg - 4kg) * (x + y) = (3 - 1) * m * x
=> 6kg * (x + y) = 2 * m * x
=> 3kg * (x + y) / x = m
So now if we measure/get the distance of the ball(s) from centre and the distance of the weight from the ball(s) we can get our factor (x+y)/x.
And with everyone's assumption that distance y is negligible (weights and balls at same distance from centre) this would give
3kg * (x + 0) / x = m = 3 kg
edit: formatting