What's the "d" in that formula? (work formula)

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In summary, the "d" in the formula represents a change, specifically in terms of time, and is a basic calculus term known as "differential" or "delta". It is used to find W by integrating F over a range of dr, assuming that F is approximately constant during the displacement. However, when evaluated over a path, both F and dr can vary. It is important to note that dW is not a differential of W, as the work done generally depends on the path. In thermodynamics, it may be written as đW.
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Austin Gibson
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What's the definition of the "d" in that formula?

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  • #3
.Scott said:
It a basic calculus term: "differential" or "delta". It indicates a change.
In this case, most likely a change as a function of time.

https://en.wikipedia.org/wiki/Differential_calculus
This equation assumes a constant force?
 
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Austin Gibson said:
This equation assumes a constant force?

No it doesn't. This is because to find W, you have to integrate F over the appropriate range of dr.

Zz.
 
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[itex]dW=\vec F \cdot d\vec r [/itex] is an infinitesimal amount work done over the infinitesimal displacement [itex]d\vec r [/itex],
where [itex] \vec F [/itex] is approximately constant during that displacement.

When this is evaluated over a path, then [itex]\vec F[/itex] and [itex]d\vec r [/itex] will vary as you progress along the path.

It's probably not a good idea to think of these [itex]d[/itex]'s as differentials (as in [itex]dW[/itex] is a differential of [itex]W[/itex]
since there is generally no such [itex]W[/itex] because the work done generally depends on the path. In thermodynamics books, this is sometimes written as [itex]đW [/itex].)
 
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What is the "d" in the work formula?

The "d" in the work formula represents the displacement or distance traveled by an object. It is usually measured in meters (m) or feet (ft).

Why is the "d" important in the work formula?

The "d" is important because it tells us the distance that an object has moved. This is a crucial factor in calculating the amount of work done on an object.

How is the "d" related to the other variables in the work formula?

The "d" is directly related to the force (F) and the angle (θ) in the work formula. It is also indirectly related to the amount of work (W) done on an object.

What happens if the "d" is zero in the work formula?

If the "d" is zero, it means that there is no displacement or movement of the object. In this case, the work done on the object is also zero, since work is defined as force multiplied by distance.

Can the "d" in the work formula be negative?

Yes, the "d" in the work formula can be negative. This indicates that the object is moving in the opposite direction of the applied force. The negative sign is important in determining the direction of the work done on the object.

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