How do mechanical (weighing) scales work?

[rudransh verma]

I want to understand how the weight machines work that we use in homes and shops. I have been working on force and motion chapter and I was curious how this weight machine actually push up and how it applies force to the feet of the person being weighed? What reading is this that we see in weight machines?

So if I am correct the reading that we see on scale is the force the spring applies back to counter the force of gravity. That is what we mean when we say the force applied by the scale in upward direction is equal to mg the weight of the person?

 

[Doc Al]

So if I am correct the reading that we see on scale is the force the spring applies back to counter the force of gravity.

The scale reads the force it exerts, which is, per Newton's 3rd law, equal to the force exerted on it. The scale doesn't "know" anything about gravity, it just knows that something is trying to squish it.

That is what we mean when we say the force applied by the scale in upward direction is equal to mg the weight of the person?

If a person stands on the scale and there is no acceleration, then the force the scale exerts is just enough to balance the force of gravity on the person and thus the scale reads the person's weight. Do the same thing in an accelerating elevator and the scale will read some different, depending on the direction of acceleration.

 

[Lnewqban]

The free end of the spring acts exactly like the free end of a cantilever beam.
Vertical deformation is proportional to excerted force.
In the case of our bathroom scale, the deformation has been translated onto a graphic or display that shows how much mg is standing still on the platform.
If you jump a little, the rate of deflection will change some.

 

[rudransh verma]

The scale reads the force it exerts

How can you say that for sure? I can equally say that it reads the force we exert on it.

 

[Doc Al]

How can you say that for sure? I can equally say that it reads the force we exert on it.

Realize that "the force it exerts" and "the force exerted on it" are just two sides of the same interaction. That's the meaning of Newton's third law.

 

[rudransh verma]

Realize that "the force it exerts" and "the force exerted on it" are just two sides of the same interaction. That's the meaning of Newton's third law.

I know that. But still the pointer is at its place because both of the forces are there in opposite direction.
Maybe because the pointer is connected to the spring so we can say it reads the force the spring applies back at us.

 

[sophiecentaur]

Realize that "the force it exerts" and "the force exerted on it" are just two sides of the same interaction. That's the meaning of Newton's third law.

A "Young Astronomer" (about ten years old) shouted out that answer whilst I was giving them a talk. That made my evening - even though he is a bit of a 'clever clogs'. He's one of those who holds his hand up before I have finished the question - bless him.

 

[Mister T]

I know that. But still the pointer is at its place because both of the forces are there in opposite direction.
Maybe because the pointer is connected to the spring so we can say it reads the force the spring applies back at us.

The two forces that are exerted in opposite directions to hold the pointer in place are not the two forces you were talking about.

The object hanging from the scale exerts a force on the scale. The scale exerts an equal but opposite force on the hanging object. These forces form a Third Law pair. They are equal but opposite even when the scale is not fixed in place.

The hanging object exerts a force on the scale. Something else exerts a force on the scale to hold it in place. These forces are equal but opposite only when the scale is held in place. They are not a Third Law pair of forces.

 

[sophiecentaur]

The scales in the OP are not for standing on. The design is more advanced than a 'Newton Meter' in which the pointer drags up and down a crude scale. It's not clear if the basics of Young's Constant is all that the OP (person) needs to have explained or if the details of that particular balance need explanation.

There are two coil springs which both act on the beam that moves the rack which turns the scale. The displacement of the rack is proportional to the sum of the forces on the two springs. The springs can each have half the spring constant of a single spring. I suggest that the two cams at the top ensure that the displacement of the two springs will be equal because the load difference is passed between them. The rack and pinion magnifies the displacement of the springs and allows a more compact design. Also, the balanced design does't need the suspension to be precisely vertical without drag.
The OP mentions scales you stand on. Bathroom scales are even more complicated with four levers which pivot and the sum of the forces on all four corners is what displaces a single heavy duty spring. It allows the user to stand a bit off-centre without affecting the measurement too much. This link describes the details of the mechanism. I remember taking one apart for interest and getting it back together was a real struggle, involving string to hold the levers in place and securing the spring. (V. satisfying).

 

[sophiecentaur]

These forces form a Third Law pair.

The relevant bit about those forces is Newton's first law. At equalibrium, the forces are equal and that's when the scale is reading your weight. Even when the spring is settling down, there are third law pairs all over the place.
It's very common for people to confuse equilibrium with N3.