Last time we began demonstration and engineering analysis of the inequality of work input and output as experienced by our example persona, an ancient Greek lifting an urn. Today we’ll get two steps closer to demonstrating this reality as we numerical shuffling equations like a Rubik’s Cube to arrive at values for two variables crucial to our analysis, work a compound pulley’s numerical puzzle, d, the length of rope he extracts from the _{2} while lifting, and pulleyF, the force/effort required to lift the urn in an idealized situation where no friction exists.
We’ll continue manipulating the work input equation, F and d._{2} + (F _{F}× d) (1)_{2} Previously we learned that when friction is present, work output,
d) (2)_{2} We also previously calculated WO, we substitute Equation (1) into Equation (2) and arrive at,80 + (F _{F}× d)_{2} – (F) (3)_{F} × d_{2}simplified this becomes, 80 To find the value of mechanical advantage, MA. That is,
d(5)_{1 }= _{ }MA_{ }And because in our example four ropes are used to support the weight of the urn, we know that d_{2},
ft(6)_{ }= _{ }4
= 4 × 2 ft (7)
ft (8) Substituting Equation (8) into Equation (4), we solve for 80
Now that we know F, the amount of extra effort required by man or machine to overcome friction in a _{F} assembly. It’s the final piece in the compound pulley which will then allow us to compare work input to output.numerical puzzleCopyright 2017 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |