Originally Posted by

**William McCormick**
Originally Posted by

**MagiMaster**
William, this is exactly why math is important. We can sit here and argue about this until our keyboards break, or we can just do the math and be done with it. But you don't like math, and you'd never believe something that was explained with equations, meaning we'll have to sit here and argue about this until our keyboards break.

You could not do the math on that because you do not even understand it.

Since you insist, I will do the math.

The system for this will be two 25 lbs weights on each end of a rope over two pulleys, very similar to what's been drawn so far. First, let's seperate the system into two parts, seperated between the two pulleys.

- The first part consists of the left weight, the left pulley and the left half of the rope.

- The second part is everything else.

Additionally, to avoid complicating things unnecessarily, we'll assume a weightless rope. This should closely approximate a real test using as light a rope as possible.

Since nothing's moving, all forces must be in balance. The forces in question are simply gravity and tension. Tension is uniform throughout the rope under these conditions.

First we'll consider what things would be like if the pulley were a fixture instead. Since lbs is a measure of force, a 25 lbs weight simply exerts 25 lbs on the rope in the down direction. This means that the rope between the block and the pulley is exerting 25 lbs of force on the block. This must be so, otherwise something would be moving. This causes the fixture to exert 25 lbs of reactionary force on the rope. Again, this must be so since nothing's moving. (If the fixture exerted no force, the rope would fall.) Now, the fixture isn't causing the rope to exert a further 25 lbs on the block, since then the block would be rising off the floor.

Now, when we change the fixture back to a pulley, the reactionary force is replaced by a 25 lbs force from the other half of the system. Again, this doesn't exert a further 25 lbs on the first part of the rope.

Having worked through this, I think I can point out the real problem here. We're working on two different definitions of tension here. Your definition is the sum of the absolute value of the parallel forces acting on the rope. Mine is the force the rope is exerting. I think we may actually agree on what's going on, just not what we call tension.

Since arguments about definitions never get anywhere, I think we can drop this here, unless you think I got something in my math wrong.