# How Scales Work: Exploring the Mechanics

• daniel_i_l
In summary, balance scales are used to weigh objects by placing them on one end of a rod with a pivot in the middle and a counterweight on the other end. The rod will swing all the way down unless the sides are balanced. This is achieved by moving the counterweight or changing the position of the pivot. The scale works by using moments of force acting around the pivot, and the ratio of the rod on either side of the pivot is also the ratio of the masses when balanced. This system has been used for hundreds, if not thousands, of years and was pioneered in China. The scales must be designed with the center of gravity below the pivot point to achieve a stable equilibrium.

#### daniel_i_l

Gold Member
I've never actually used something like this but in the "olden days" to weigh something they put the object on one end of a rod with a axis in the middle and a CW on the other end. (a scale) Then they checked how much the rod tilted to see how heavy the object was.
But I don't understand why the rod didn't just swing all the way down?
If one of the ends is heavier then why doesn't it swing all the way down? What's stopping after falling 5cm that wasn't there after 1cm?

In other words, if you have a rope around a pulley with a weight hanging on each end of the rope and one of the weights is heavier than the other one - won't the heavy one fall all the way down (untill the lighter weight hits the pulley or something)? Why is this different from a scale?
Thanks.

You add weights of known mass to one side until the scales balance; you then know how heavy the object is. The 'rod' will swing all the way down unless the sides balance.

Scales work by moving the counterbalance to the point that makes the rod perfectly level. If there is any imbalance, the heavy end will fall (until the rod hits some stop).

The rod scales that you still see used in markets across North Africa uses moments of force acting round the pivot. If you know the ratio of the rod on either side of the pivot then that is also the ratio of the masses when balanced. Therefore you can weigh heavy objects with a small set of lighter weights by changing the position of the pivot, or as DH said moving one weight along the rod until balance is achieved with a fixed pivot.

Most market balances I've seen have a set of hooks at fixed distances and the trader put various weights on at different points calculating all the different moments in their head to get an exact weight.

A very simple system that's been used for hundred if not thousands of years. IIRC it was pioneered in China where they used brass bells of different sizes as weights. These served both as fixed volume scoops and weights, and the cleverest bit was that the government inspectors could check them by ringing them and comparing the pitch to a standard set of bells of known weight and volume.

I don't think I've ever seen what the OP is describing as a method of measurement. I imagine that scales do tilt some, but only due to tiny imperfections that make a slight tilt favorable.

But reading this i though of something else:
If you have a scale like that, or anything balanced like a pencil on the side of your finger, then if you push it down a little it rocks from side to side until it comes to rest again. But if the system was balanced then why doesn't it keep falling? What's the restoring force?
Thanks.

The question is nice. The secret is that the scales pivot is designed some what higher than the line between the two scales. So when the two objects are equal in mass, the bar is horizontal and the angular momentums of them are mgd with d is the distance from the scales to the centre drop line.Those angular momentums are equal and opposite to each other so they cancel. If the left scale is heavier, it goes down until mg1d1=mg2d2 (1 indicates left and 2 for right) and stops there . This is because d1 decreases and d2 increases.
If the line between them intersects with the pivot, the left scale will go down until it hit something because distance d1 and d2 = constant. This case is similar to the pulley isn't it.

haiha

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daniel_i_l said:
But reading this i though of something else:
If you have a scale like that, or anything balanced like a pencil on the side of your finger, then if you push it down a little it rocks from side to side until it comes to rest again. But if the system was balanced then why doesn't it keep falling? What's the restoring force?
Thanks.
The center of gravity of the pencil is above your finger, so if the pencil is tilted, the cog moves away from the pivot point horizontally in the same direction it is tilting, increasing the torque in the direction it is moving. It's an unstable equilibrium.

So all it takes to get a stable equilibrium is the opposite: have the center of gravity below the pivot point. Then if you rotate left, the torque is to the right. If the pivot point is at the cog, you have a neutral equilibrium at all orientations.

Draw a picture! I'm in an argument on another forum with a guy who says it is impossible to balance a telescope, so I posted a picture. Soooo much can be figured out easily with a simple diagram.

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How Balance Scales Work

I have been a collector and restorer of balance scales, among other things, for many years now and I must admit that I am not 100% sure how they work. The original question is deceptively difficult to answer. Typical balance scales have a small linear tilt range on each side of the zero point and this small range is the point of interest. The balance has a knife edge pivot resting in a v-block. If the knife edge was perfectly sharp, I would expect any unbalance to cause the beam to tilt one way or the other until it hit the stop. Since this doesn't happen, there must be some other mechanism restoring equilibrium to the beam. I believe that this mechanism is the slight movement of the center of support in the direction of the tilt when the beam tilts slightly to one side. The knife edge has a slight radius--it is not perfectly sharp so when the beam tilts, it is actually rotating on the radius of the knife edge thus moving the center of support. The v-block is also not sharp at the bottom and effectively gives the knife edge a flat surface to rotate on. The sharper the knife edge the more sensitive the scale. As the knife edge rounds off from years of use, or due to corrosion, the scale becomes less and less sensitive. In fact, pharmacists that routinely weigh corrosive compounds do not use traditional balance scales because of their short life in that environment. Instead, they typically use "Torsion Balance" scales that get their restoring force from the torsion of metal bands that support the beam.

The same thing applies to a pencil balanced on your finger. As it rotates to one side it also moves it's center of support in that direction thus creating a restoring force that keeps the pencil from simply rotating until it falls.

Since the scale is typically "balanced" by moving counterweights until the pointer reads zero, the effects of moving the center of support are eliminated and the object being weighed is weighed accurately. I have observed that this type of scale has lower sensitivity when larger weights are being weighed but some more complex designs (multiple beams and pivots) do not exhibit this behavior. I still don't understand why.

russ_watters said:
The center of gravity of the pencil is above your finger, so if the pencil is tilted, the cog moves away from the pivot point horizontally in the same direction it is tilting, increasing the torque in the direction it is moving. It's an unstable equilibrium.

So all it takes to get a stable equilibrium is the opposite: have the center of gravity below the pivot point. Then if you rotate left, the torque is to the right. If the pivot point is at the cog, you have a neutral equilibrium at all orientations.

Draw a picture! I'm in an argument on another forum with a guy who says it is impossible to balance a telescope, so I posted a picture. Soooo much can be figured out easily with a simple diagram.

Russ,
Here's a neat picture showing your point.
http://www.gilai.com/scripts/more/sbe200-scales_equal-Equal+Armed+Scales-no.html

In response to TVP45, I still cannot see your point about the cog being below the pivot point. If the pivot point is basically fixed at the center of the beam and a small weight is added at either side, I would expect the beam to rotate to the "bottom" or until it hits a stop since I don't see any other restoring torque coming into play. I will give it some more thought--maybe it will sink in.

Ah, that's what you didn't see. The pivot is at the very top where there is something that looks like 2 thumbscrews.

[nitpick]
By the way, what you are describing here is properly called a "balance" (or occasionally a "balance scale"), which measures mass and would get the same result on the moon. A "scale" usually refers to a device which measures force (weight) typically using a spring or something similar, and it would get a smaller measurement on the moon.
[\nitpick]

jimhook - The balance scale has a range of stability because the COG is below the knife-edge. As it swings, the COG shifts back toward the knife edge instead of away from it. Technically-speaking, it will always be stable - it'll just require a large tilt angle (and the stops prevent that) to move the COG back to the center.

Draw a picture! The balance will look like an elongated, inverted "T". In fact, make it T shaped to exagerrate the effect of suspending the bar below the pivot point. Then you should easily be able to see that the maximum deflection angle is the angle between the two points on one side of the T (one short side and the long side).

TVP, I can't see the pivot point on that pic - is it at the top of the frame?

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Sorry to quote myself, but...
russ_watters said:
Draw a picture! The balance will look like an elongated, inverted "T". In fact, make it T shaped to exagerrate the effect of suspending the bar below the pivot point. Then you should easily be able to see that the maximum deflection angle is the angle between the two points on one side of the T (one short side and the long side).
The ratio of the lengths is what determines the stability of the scale. The longer the center section, the more stable the scale. You don't want it too stable, otherwise you won't be able to fine-tune the balance. But if you have it inherrently unstable, there won't be any balance point at all - you wouldn't ever be able to tell if your weights were balanced.

The secret that scales can stay in balance is that the center of mass is made somewhat lower than the pivot. The closer the center of mass to the pivot, the more sensitive the scales (and of course the less stable).

Ok--maybe we are talking about two different types of balances. The balance I was talking about has a center pivot with arms that go out several inches to two flat porcelain plates--one for the item being weighed and the other for calibrated weights. Below each plate is a vertical member (supported by another pivot) that goes down through the top of the base and connects to a horizontal shaft that is connected to the center of the frame. These members keep the platforms flat as the scale tilts from side to side. In this scale, the cog may be lower than the pivot with nothing on the plates but when I put a 1 lb calibration weight on each plate, the cog is definitely above the center pivot. In this state, the scale still behaves the same--it has a small linear range (about 1.5gm) on each side of center balance and is very stable. I also have an analytical balance. I will look at it and see if it relies on a different method for stabilization.

russ_watters said: