# Measuring Weight with Multiple Scales

If I am weighting a long tube of (nearly) uniform weight with multiple hang-scales (really a 10-ft long Helical Antenna), how do I calculate the total weight from the multiple scales?

• Can I just add the measured weights at each point regardless of the spacing?
• If the spacing is non-uniform, does the total weight calculation change?

Assuming that

• antenna is in static equilibrium (i.e. not moving)
• the only forces holding it up are forces exerted by the scales,
• the forces applied by the scale are applied directly upwards (this one is important!)

then the weight will in fact equal the sum of the forces exerted by each scale. So you can sum up all the measurements of each scale.

The spacing does not matter, but, again, ensure that the strings holding up the antenna are pointing straight up (anti-parallel to gravity force). Otherwise, you will have to measure the angle at which these forces are applied, and account for that.

If you want to test out the accuracy of this technique (which I strongly recommend -- just because this is sound on paper does not mean it'll work well given the outlined constraints), I would suggest to weigh a more lightweight object (like a plank, similar length to your antenna) with initially 1 scale, then 2 scales, then 3, etc. and see how much each set of results deviates.

EDIT: user alephzero makes some excellent suggestions in the comments.

• We use this as a technique at work to measure the mass of large irregular shaped objects. As a practical tip, use very flexible cords between the scales and the object. (We use bungee cords but we are usually weighing things of the order of a few tonnes - you might find elastic bands work well for a light weight antenna.) The reason is that if you need to adjust the suspension system to get all the cords vertical, changing the length of one flexible cord does not have much effect on the load it supports, and therefore doesn't mess up the position of all the other cords. Commented Dec 28, 2020 at 2:43
• I had a typo in my post. To clarify, spacing between each strong does not matter. Commented Dec 28, 2020 at 2:47
• ... Using this technique for heavy objects, the procedure we use is to suspend the scales (or load cells) by wire ropes from cranes, and the object by flexible cords from the load cells. First position the ropes vertically with the object resting on the ground. Then winch up the wire ropes in small increments, until the object is lifted off the ground - but with only 2 or 3 mm clearance, so there will not be a disaster if something unexpected happens. Of course you may not need to be so careful. Commented Dec 28, 2020 at 3:06