# Why is the parallelogram rule for the addition of forces as it is?

• zexott
In summary, the parallelogram rule for the addition of forces is based on the observation of ropes and the rule of linear superposition. This rule has been around since at least the first century BC and has been written about by philosophers. The full text of the rule is available at the web link provided.
zexott
Why is the parallelogram rule for the addition of forces as it is?
I feel it must have some deep origin and pointing to something fundamental. Though I know this problem may have no answer: God design it as such.
But I wonder how the first person came up with this rule, where does his/her intuition come from?
Are there something that addition of forces simply must obey due to logic itself?
Are there active research going on that is investigating this?

Would you accept vector addition as being the logic?

It is likely that it arose because, at the time this was being developed, probably at the time of people like Stevens (1548 - 1620) most mathematics was carried out geometrically. So the parallelogram construction was the natural mode of working.

Whoops, autocorrect jumped in. I mean Stevenus .

Use the Edit button to correct it.

All the parallelogram rule does is to enforce that the addition of two vectors actually add their components.

Historically it was an observation about ropes. The rule is equivalent assuming the rule of linear superposition of forces ... that is, application of one force does not interfere with any other. This means that forces form a linear vector space.

The rule dates back to at least the first century BC; it appears in Heron's "Mechanics". But it is probably older.

UltrafastPED said:
Historically it was an observation about ropes. The rule is equivalent assuming the rule of linear superposition of forces ... that is, application of one force does not interfere with any other. This means that forces form a linear vector space.

The rule dates back to at least the first century BC; it appears in Heron's "Mechanics". But it is probably older.

Ah, observation of ropes, that's how their intuition comes. Now it seems conceivable for me. Your information is very detailed and now I guess I can trace it down. Thank you so much! And thank you all for your time and attention!

UltrafastPED said:

Don't you have a web link?

Last edited:

## 1. How does the parallelogram rule for addition of forces work?

The parallelogram rule states that when two forces are acting on an object at the same time, the resulting force can be found by creating a parallelogram with the two forces as adjacent sides. The diagonal of the parallelogram represents the magnitude and direction of the resulting force.

## 2. Why is the parallelogram rule used for addition of forces?

The parallelogram rule is used because it takes into account both the magnitude and direction of the forces, which are vector quantities. This allows for a more accurate representation of the resulting force on an object.

## 3. How is the parallelogram rule related to Newton's laws of motion?

The parallelogram rule is related to Newton's laws of motion, specifically the second law which states that the net force on an object is equal to its mass multiplied by its acceleration. By using the parallelogram rule, we can accurately determine the net force acting on an object.

## 4. Can the parallelogram rule be used for more than two forces?

Yes, the parallelogram rule can be extended to include more than two forces. Each force can be represented by a side of the parallelogram and the resulting force can be found by drawing the diagonal of the parallelogram.

## 5. Are there any limitations to the parallelogram rule for addition of forces?

While the parallelogram rule is a useful tool for finding the resulting force of two or more forces, it does have limitations. It only applies to forces acting on a single point and it assumes that the forces are acting on the same plane. Additionally, the rule does not take into account rotational forces.

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