Confirming if Friction is a Scalar: Examining the Work Energy Theorem

[Timothy S]

In examining the work energy theorem on vector fields, I have concluded that friction must be a scalar field with a negative value. This is because one must integrate the line integral with respect to ds instead of the function dotted with dr. Am I correct in my understanding or am I missing something?

 

[Vanadium 50]

"Friction" is a phenomenon, not a quantity So what you wrote cannot be what you mean.

 

[Timothy S]

All physical Phenomena are quantities

 

[robphy]

Is friction dependent on location alone (as might be expected for a scalar field)?
If it did, wouldn't it be associated with a conservative field?

 

[Vanadium 50]

All physical Phenomena are quantities

Nonsense. "Motion" is not a quantity, but "velocity" is. "Space" is not a quantity, but "length" and "volume" are.

You started this thread with a title that is incorrect, and in message 3, your entire message was an incorrect statement. Making incorrect statements hoping that someone will correct you is a frustrating and inefficient way to learn.

 

[Timothy S]

I think I understand. Is there a unit vector which can be used to signify that friction is opposite to the direction of motion?

 

[Timothy S]

Now I see my ignorance. My assumption was that the scalar form of friction was the Vector form of friction. I realize now that friction needs to be multiplied by the unit tangent vector. Thanks for correcting me.

 

[nasu]

There is "friction", a phenomenon, and there is the "friction force". The first is neither vector nor scalar. The second is a vector, as any type of force.
Same as "gravity" is a phenomenon and the weight or "force of gravity" is a force. People (especially students) tend to use "gravity" when they mean the force of attraction.
This is OK in general but it may create confusion sometimes.

Multiplying the friction by a unit vector (or by anything else) is not a valid operation.
You can multiply the magnitude of the friction force by a unit vector, if you wish. Indeed the friction force is tangent to the surfaces in contact.

And I think I understand (maybe) your problem.
If you look at the equation
F_f=μN, it makes sense for the magnitudes of the forces but not in vector form. The friction force is not parallel to the normal force.

 

[Timothy S]

yes but the normal force in this situation is not a vector in this sense but simply a coefficient.

 

[Vanadium 50]

No, the normal force is a force. And force is a vector.