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# Pulley problem

• #2
Registered Users Posts: 29,563 ✭✭✭✭

Engineers, I need your brains cos mine isn't working. This is a trivial problem for you, but I left school a long time ago.

The requirement for the following design is to lift a heavy beam perpendicular to its long axis, i.e. without it tilting as it rises. The whole system is effectively acting as a wide pulley block.

I think that, simplifying using g=10 and ignoring the horizontal component of forces, that

f = 10,000N = sum(f2,f4,f6,f8,f10)
t0 = t1 = ...t9 = 1,000N
f2 = t1+t2 = 2,000N

So each pulley deals with the same 1/5 of the load, and the tension in all sections of the rope is the same 1/10 of the load (for a point beam of zero length).

If we consider a non-zero beam length, then as the beam gets longer the tensions increase, because the vertical component of the vector tension is a relatively smaller fraction of the load at the pulley fixture.

I think that the free beam will rise parallel to the fixed beam. What do you think?

• #2

Empiricism FTW.

I'm not sure staples are a good model for pulleys but....oh.

• #2

• #2

The beam has an unconstrained rotational DOF, which is why you got the torque effect in your first (very nifty) model. Making the whole thing symmetrical about the middle of the beam might get around this.

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