Eng: Block and tackle

From the oldest sailing ships to modern dinghies and yachts, people have used blocks and tackles to pull sails tighter, and to raise heavy loads. A “block” is what sailors call a pulley, or a set of pulleys, mounted like the 19^th century engraving on the left below, but the diagram version on the right is easier to work and plan with.

 

Pulley arrangements help us lift heavy loads.

In theory, the diagram on the right above shows a system that will lift a load six times the weight of a person hanging from the effort rope. We can calculate this ratio by looking at the number of strings (or ropes) supporting the load. The official way of describing this is to say the system has a mechanical advantage of six. (Strictly, it has a velocity ratio of six, with the mechanical advantage a little bit less, because of friction,)

You can use simple blocks from scraps of wood like this with screw eyes and hooks to make simple weight-lifting systems. You can get screw eyes and hooks at hardware stores, and screw them into the wood by hand, if you make a small starter hole with a gimlet, a nail, or best of all, a drill.

 

I used blind cord to get clearer pictures, but a finer thread is better!

In reality, the lower block weighs something, so the real mechanical advantage is a tiny bit less. Welcome to the world of ‘fairy physics’: in physics fairyland, horses are spherical and steel girders have negligible mass, but don’t worry about it.

The idea is to fit a thread like cotton or dental floss to link two of the blocks, as you can see in the picture on the right, above. Try making two blocks like this, set them up, and then test them to see how many standard masses you can lift with a single standard mass. There is more friction here than in a block and tackle with pulleys, but it still works fairly well.

With this arrangement, if you pull the outside line down one metre, the mass you are lifting will only go up 25 centimetres, because there are four strings supporting the lower block, and each one shortens by 25 cm.

We can lift about four times as much weight as we are pulling with, but only about four times as much.

A curious tackle

A puzzle.

I am still working on a possible intuitive solution to this, based on the idea that the supporting ropes are all getting shorter to the same extent (or do they?) as the weight rises. Quickly now: what is the velocity ratio of this rig?

Are you sure? Trying to work this one out hurt my brain, so I made a stand with scrap timber, and measured the rise and fall, but I'm not telling, but here is how it looked. With this, all I needed was a suitable measuring stick.

In this shot, the base is just a flat board with dowel-sized holes, so the whole stand pulls apart.

So I now know the answer, but I’m not telling. Science is often like that.

Note:  Engineers talk about mechanical advantage, calculated by dividing the weight that is moved by the weight needed to move it. They also talk about the velocity ratio, which compares the speeds of the load and effort. In an ideal world, with frictionless pulleys, the MA and the VR would be the same, but in reality, they never are.

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