How do you find the tension in the real world? (Given a rope in a pulley system)

Question

I'm well aware of the formula to calculate tension, however, given a real world situation where you have a closed pulley system. How do you measure the force (i.e., tension) required to pull on the rope in the pulley?

I've thought of buying a portable luggage scale and affixing it onto a point on the rope and pulling the scale in parallel to the rope at a constant speed. This will give me a weight measurement, which I'll then be able to calculate the force from.

This seems like an awful way of measuring something. Can you describe some better ways of measuring, which will help me calculate the force required to pull on this pulley?

What if I wanted to pull on the pulley at a certain speed? How do I go about calculating that?

Answer 1

How accurate do you need to be? The problem with these calculations is that massless, frictionless pulleys are usually out of stock at Acme Mail Order.

High school physics will give you the tension in the rope, a different set of high school equations will tell you how much extra tension is needed for a certain acceleration. A rough metric is add 10% for friction losses, but if you need really accurate numbers you will have to do empirical measurements. Natural vs. synthetic fibre rope, weave pattern, pulley diameter and wether they've been greased recently will all affect the outcome.

The accuracy of the luggage scale will be sufficiently low that you can go back to the 10% guideline. Proper strain gauges are readily available in the gram-accurate range, and they won't break as easily. Remember to put a jumper across the gauge if you care about what's on the other end.