Tension at two points on a string? (Tension in general)

[RadiantL]

Alright tension has always got me confused... and takes up a lot of time because I have to think pretty hard about them. Anyway here's my question (s)

Say you have a hanging object, and connecting the object to the ceiling is a massless string. Will the tension near the object be the same as the tension near the ceiling?

Say I have two objects connected by a massless string, I hold object 1 and pull on it upwards with object 2 hanging from object 1 (using the massless string), will the tension force at object 1 be different from the tension force at object 2?

Will the tension across the string ever be different for any case (like at both sides of a string)?

And my book says that the the force is not labelled a tension if the string's mass is included, I don't understand what it means?

These are a lot of questions but it would help a lot with my understanding :)

THANKS!

 

[gsal]

Yes, the tension along the mass-less string is the same from the point it touches the lower object all the way to the point where it touches the higher object...

...if the string is not mass-less, then, as you move up in the string, the weight being carried the upper remaining portion of the string keeps increasing to the point where at the higher end of the string, the string is carrying the lower object, plus the weight of the string itself.

 

[torquil]

Say you have a hanging object, and connecting the object to the ceiling is a massless string. Will the tension near the object be the same as the tension near the ceiling?

Yes. Because if not, the string would experience an infinite vertical acceleration, by Newton's second law, since it is massless. The difference of endpoint tensions is the net force acting on the string. This must always be zero for a massless string to avoid infinite acceleration.

Say I have two objects connected by a massless string, I hold object 1 and pull on it upwards with object 2 hanging from object 1 (using the massless string), will the tension force at object 1 be different from the tension force at object 2?

No, they must be the same, for the same reason as above.

Will the tension across the string ever be different for any case (like at both sides of a string)?

Not for a massless string. Unless you want infinite acceleration of the string.

For a non-massless string, they will be different in all situations in which the string itself is accelerating (this includes gravity, which is equivalent to acceleration). All this follows from Newton's second law.

And my book says that the the force is not labelled a tension if the string's mass is included, I don't understand what it means?

Me neither. Is that the exact formulation from the book?

 

[AlephZero]

And my book says that the the force is not labelled a tension if the string's mass is included, I don't understand what it means?

I don't know what your book is trying to say there.

It might be saying that "tension" is not really something to do with the whole string, it is something to do with a single point along the string. If you cut the string at a point, you would have to apply equal and opposite forces T to the two cut ends, to have the same effect as the string.

If the string is massless, T is the same everywhere along the string, so it makes sense just to call T "the tension in the string" and not say which point you are referring to.

If the string has mass, usually T is different at different points along the string, because of the weight of the string, the forces needed to accelerate the string if it is moving, etc.

 

[RadiantL]

Hmm... I still don't quite understand why the string will have different tension about the string when it has mass...

 

[Number Nine]

Hmm... I still don't quite understand why the string will have different tension about the string when it has mass...

The lowest point on the string is carrying the weight of the object. The highest point on the string is carrying the weight of the object plus the weight of the lower portion of the string.

 

[RadiantL]

The lowest point on the string is carrying the weight of the object. The highest point on the string is carrying the weight of the object plus the weight of the lower portion of the string.

Haha, wow I can't believe I did not catch that,

THANKS everyone that posted, definitely improved my understanding :)

 

[JHamm]

wouldn't tension be directed towards the center of the string? In that case the tension isn't really the same through the entire string because the direction will change.