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OK, so I know that with a 5mtr bar, and a 2kg weight at the long end, I have 10kg/metre, and as such need a 10kg weight 1mtr from the fulcrum on the short end to balance. That's schoolboy stuff.

I've also read that Newton-metre is roughly equal to 98.0 times the weight. But here's where I start to fall down.

If I position a gas lift arm 150cm from the fulcrum on the long side, how to calculate lift required. (ie weights have a downward force, a gas-lift an upward force)

My theory is that if I have (say) 5kg counterweight acting in a downward direction on the short end, a 5kg arm pushing UP on the long side would give a theoretical 10kg force. Or would one cancel the other?

Using the short arm for calcs as it's easier to visualise, I think that it would need 20kg at 0.5m, or 40kg at 0.25mtr or 80kg @ 0.125mtr. (0.125 being a metre divided by 8) So if this 80kg is transferred to the opposite side as an upward force, it should have enough force to lift.

Now- Newton-metre. This is obviously at one meter. If I halve the distance, does the number double or halve? (So it's either 12.25 or 784 - ie divided / multiplied by factor of 8) Multiply that by the 80kg force needed, and it becomes 980N/m or 62,720N/m. (If the latter is correct, I don't think a gas lift currently available would have that much force!! This assumes the whole weight is pushed by lift, but in reality it could be supplemented by the counterweights)

This is actually a crane arm. The pan head with motors weighs in at about 700g, a camera about 300g - 500g. The pole itself is 1kg over its 5mtr length. But I only have room in the case for 2x5kg plate weights, so am looking at alternative lift methods.

Of course, a very simple solution - which has only just occurred to me as I typed this - is to extend the counterbalance arm length! Oh well, makes for an interesting physics lesson for future use!

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Firstly, I think your units are wrong. Torque (the rotational ability of force/weight) is measured in newton-metre (as you have correctly written) or kg-metre not newton/metre or kg/metre(as you have incorrectly written). This is because the torque is directly proportional to both the amount of weight and the length of the lever-arm and so the two quantities are multiplied.

A body of mass $m$ (in kg) wieghs $9.8m$ newtons (because the acceleration due to gravity is $9.8ms^{-1}$) and therefore $1 kg-metre = 9.8 newton-metre$

When confused about whether two torques are cancelling or adding, determine whether the torque is trying to rotate the lever clockwise or counter-clockwise. Clockwise torque will cancel with the counter-clockwise torque.

Hope this helps. I don't really have a clear idea of what you were asking.

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