- #1
Pepon
What can you tell me about the tension in a string? Why is it equal over the string? Why is the direction of the tension over the ends of the string opposite?
Danger said:Arildno, that's just about the best explanation of the situation that I've ever seen.
Pepon said:What can you tell me about the tension in a string? Why is it equal over the string? Why is the direction of the tension over the ends of the string opposite?
The reason is that a tension is, strictly speaking, not a force, but a tensor (a second-order tensor).
How does this contradict the line you just quoted?cyrusabdollahi said:I don't understand. Stress is a tensor, but force is a vector, by definition.
Gokul43201 said:How does this contradict the line you just quoted?
But to differ slightly from vanesch, I'd add that tension is not a tensor, but one of the positive components of the stress tensor that lie along its principal diagonal.
vanesch said:The point I wanted simply to make, is the origin of the "flip of sign" of the "force of tension" on both sides of the string, which was one of the questions of the OP. I was pointing out that what was constant along the string was the "situation of stress" which is described by the stress tensor (forgive me any erroneous nomenclature), and that this is a beast that gives you a force when you give it a direction in which you want to know the force.
Now, as on both sides of the string, one wants to know the force in OPPOSITE DIRECTIONS, you have to feed two opposite normal vectors to the stress tensor, and hence it will spit out two opposite forces.
So it is not (as I understood the problem of the OP, but I might be wrong) that "somewhere along the string, the "force of tension flips sign". But maybe I was addressing a non-existent problem...
Swapnil said:The whole concept of masslessness (even for an approximation) doesn't make sense to me. I mean, it has zero mass and so no matter what the acceleration is, the force on the rope would alwasy be zero, right? So...
Aero said:So what happens if you give a non-unit vector? Doesn't the magnitude of the normal vector give the area of the associated plane segment? But then wouldn't we be involving pressure, as force divided by area?
Tension in a string is the force applied to a string that causes it to stretch or become taut. It is typically measured in units of Newtons (N).
The tension in a string is affected by the magnitude of the force applied, the length of the string, and the properties of the material the string is made of (such as elasticity and density).
The tension in a string is directly proportional to the frequency of its vibrations. This means that as tension increases, the frequency of the vibrations also increases, and vice versa.
If a string is stretched, the tension will increase. If a string is compressed, the tension will decrease. This is because the length of the string affects the force required to keep it taut.
Yes, tension in a string can also be changed by altering the length or material of the string. For example, a shorter and thicker string will have a higher tension than a longer and thinner string, even if the same force is applied.