Geometric and arithmetic series, pulleys in parallell
Resistances in series can be reduced to a unique resistance R such that
eq(1) R= r1 + r2 +...+ rn
in Parallel , we have
eq (2) 1/ (1/r1 +1/r2 +...+ 1/rn)
For the pulleys , to reduce the effort to keep a block and tackle (which has a mass M at he end) in equilibrium , the necessary force F to furnish is :
eq(3) F = W/2^n
Where n is the number of pulleys
By comparing the two examples we notice that eq(1) is an arithmetic series
Whereas eq(3) is a geometric series
Then find the equivalent relation of eq(2) but this time for a geometric series. To be clearer what would be a mathematical relation to represent in equation a "parallel" pulleys system.
Still to say it in another way ,
(2) is to (1)
what
"a certain equation" would be to (3)
What would be this equation?
https://brainmass.com/math/algebraic-geometry/geometric-and-arithmetic-series-pulleys-in-parallell-25293
Solution Preview
For equation (2), when each pulley carries a weight of W, each pulley will reduce the force ...