Maths problem with pulleys

[Ebo100]

Firstly please excuse the photo; it was the closest to my problem I could find on google.



How can I calculate the vertical deflection of the centre weight?

In real life at the left side I have a furnace tube the expands vertically up, in normal operation the counterweight at the right side falls very nearly to the floor. However in the rare occasion where the plant is shut down the expansion is greater by approx 70mm and so there is a sag in the cable. We want to add a small weight to the cable to keep the cable in tension so the cable cannot jump off the pully.

If the distance between pully centres is 1700mm and we know that the sum of the two side of the triangle is 1770mm. The tension weight will be approx 400mm from the RHS pully how can I calculate the vertical deflection if I don't know any of the angles?

Any help would be appreciated.

[Ebo100]

Thanks for the reply, this was a case of trying to over-think a problem.

The forces in this case are not that important as our new tension weight is heavy enough to take up more than the weight of the anticipated sag of cable but acting against a 2 tonne counterweight.

I was getting hung up (no pun intended) on the position of the new tension weight being off centre, giving awkward angles. However the vertical deflection will be the same where-ever it will be applied across the 1700mm span. So applying it at the centre line gives two easily solvable triangles and a total vertical deflection of 260mm downward.

Thanks for the interest.