# Pushmi-pullyu

This is a pulley, pulled straight off Wikipedia:

On the test that my students had last week, there was a question involving pulleys connected in a sort of eclectic arrangement. The objective was to find the tension in certain ropes which were holding the pulleys up.

Imagine instead of being connected to the ceiling, the pulley in the picture is being held up by your hand. Hanging from the pulley is a heavy metal block, and the rope holding the block up is itself being temp taut by another person. So just like the picture, except for simplicity assume that the rope is not pulled at an angle as in the picture but instead has both ends pointing directly down.

And let's say the weight weighs 10 pounds. How much force do you have to apply to the pulley to hold it up?

The answer is 20 pounds. Lots of people got the equivalent of this question wrong. Some of my students too, I am sad to say. We never directly discussed pulleys so I suppose it's not a shock. The reason for the 20 pounds is this: there are two forces acting on the pulley: the weight down, and the person pulling the other end down. The person pulling the other end will clearly have to be applying 10 pounds to balance the weight, so the sum of those forces is 20 pounds. If it makes things any clearer, you can imagine that the person holding the rope could be replaced by another 10 pound weight.

So if you're ever using a pulley to haul buckets of concrete up to the roof, keep that in mind: a system like this has to support more than just the weight of the concrete load.

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And remember to give riggers their due. ;-)

And if the other end of the rope is tied to something?

Nice try.

I'd like to see that eclectic arrangement.

BTW: Students don't know anything about pulleys coming into a physics class and most books don't introduce the mechanical advantage of a block and tackle arrangement, while engineering classes often assume they have seen this before. It must be something that used to be in the physics or general physical science curriculum (or daily life experience) that is no longer taught to them.

PS - If you tie the other end of the rope to the ground and raise the concrete by lifting up on the pulley ... yur doin it wrng.

Hmm... we're having a dynamics unit test tomorrow. Maybe I should slip that one in there and see who really understands their free body diagrams...

Gee, I hope there are a total of three forces acting on that pulley!

So what force is required to accelerate the (massless) pulley upwards at 1g, assuming the person holding the rope does not let go? (hint - the mass accelerates upwards at 2g!)

The trick to these sorts of questions is to get the free body diagrams for the pulley and the mass so they include all the actual forces and accelerations with the correct signs. Then tension in the massless rope is constant over its length and everything falls out.

Note in the actual picture used, there is a definite torque on the pulley mounting bracket

Don't forget the mass of the rigging, mass of the arm, tilt of the skeleton, friction, elasticity of the rope, distance from the center of the earth, air density, temperature, humidity, childhood development of the foreman, etc. (I think my physics professors were sadists.) Fun science, though. Thanks.

By homostoicus (not verified) on 03 Apr 2009 #permalink