When is the tension the same on both sides?

[Lifeman]

---

Members don't see this ad.

-If we have two people pulling on a rope, the tension is the same on both ends.
-If we have a pulley on a cliff, the tension is the same on both ends.

But if we have someone walking on a tightrope, why is the tension not the same on either side of him?

 

[jungb024]

If the tightrope walker is standing in the center of the tight rope the tensions are equal, at any other point though they differ.

This is an equilibrium question. Every force on the system is canceled by another force. So to better analyze it break each force down into components. The rope will bow creating two geometric triangles, so the tension forces each have a vertical and horizontal component. However the gravitational force only has a vertical component.

The sum of the vertical components from the two tensions is equal in magnitude (opposite in direction) to the gravitational force from the tightrope walker. ( T1sinø1 + T2sinø2 = mg )

Since the gravitational force has no horizontal component, the horizontal components of the tensions cancel each other, or are equal to one another. Using this principle you get...

T1 cosø1 = T2 cosø2 (which can be rewritten) T1 = T2 cosø2/cosø1 (etc.)

I hope this helps / makes sense!