Archive for July, 2016

Using a Free Body Diagram to Understand Simple Pulleys

Thursday, July 21st, 2016

    Sometimes the simplest alteration in design results in a huge improvement, a truth I’ve discovered more than a few times during my years as an engineering expert.   Last time we introduced the simple pulley and revealed that its usefulness was limited to the strength of the pulling force behind it.   Hundreds of years ago that force was most often supplied by a man and his biceps.   But ancient Greeks found an ingenious and simple way around this limitation, which we’ll highlight today by way of a modern design engineer’s tool, the free body diagram.

    Around 400 BC, the Greeks noticed that if they detached the simple pulley from the beam it was affixed to in our last blog and instead allowed it to be suspended in space with one of its rope ends fastened to a beam, the other rope end to a pulling force, something interesting happened.

The Simple Pulley Improved

The Simple Pulley Improved

    It was much easier to lift objects while suspended in air.  As a matter of fact, it took 50% less effort.   To understand why, let’s examine what engineers call a free body diagram of the pulley in our application, as shown in the blue inset box and in greater detail below.

Free Body Diagram of an Improved Simple Pulley

Using a Free Body Diagram to Understand Simple Pulleys

    The blue insert box in the first illustration highlights the subject at hand.   A free body diagram helps engineers analyze forces acting upon a stationary object suspended in space.   The forces acting upon the object, in our case a simple pulley, represent both positive and negative values.   The free body diagram above indicates that forces pointing up are, by engineering convention, considered to be positive, while downward forces are negative.   The basic rule of all free body diagrams is that in order for an object to remain suspended in a fixed position in space, the sum of all forces acting upon it must equal zero.

    We’ll see how the free body diagram concept is instrumental in understanding the improvement upon the action of a simple pulley next time, when we attack the math behind it.

Copyright 2016 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog

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The Simple Pulley Gives Us a Lift

Friday, July 8th, 2016

    Lifting heavy objects into position always presents a challenge, whether it’s a mom lifting a toddler to her hip or a construction worker lifting work materials to great heights.   During my career as an engineering expert I’ve dealt with similar challenges, some of which were handled quite nicely by incorporating a simple pulley, which we introduced last time, into my design.   But sometimes, due to certain restrictions, the addition of a simple pulley into the works isn’t enough to get the job done.   We’ll take a look at one of the restrictions working against the use of a simple pulley today.

    The simple pulley is believed to have first been used by the Greeks as far back as the 9th Century BC.   Back then it would have come in handy to lift cargo aboard ships, hoist sails on masts, and lift building materials high off the ground to supply workmen during the construction of temples and other marvels of ancient architecture.   In other words, pulleys literally saved ancient workers thousands of steps when it came to lifting things off the ground.

    Let’s return to ancient times for a moment to get an understanding of the mechanics behind the workings of the simple pulley as put to use in a basic lifting application.

 The Simple Pulley Gives Us a Lift

The Simple Pulley Gives Us a Lift

   

    With a simple pulley, the tension force F1 applied to the rope by the pull-er is equal to the tension force F2 exerted upon the object, the pull-ee.   Once lifted off the ground, these forces are also equal to the object’s weight, W, which gravity works upon to return the lifted object to its previous position on the ground.  All these forces come to bear upon whatever’s doing the pulling.   If this pull-er happens to be a human, then the simple pulley’s effectiveness to lift things is directly proportionate to that human’s strength.   In the case of the toga’d figure above, that would be about 10 pounds.   It’s this caveat that limits the usefulness of the simple pulley when relying on human power alone, particularly when it’s employed to lift extremely heavy objects like marble pillars.   A single human isn’t up to the task.

    Next time we’ll see how ancient Greeks overcame this limitation of the simple pulley by managing to cut in half the amount of brute force required to lift heavy objects.

Copyright 2016 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog

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Posted in Engineering and Science, Expert Witness, Forensic Engineering, Innovation and Intellectual Property, Personal Injury, Product Liability | Comments Off on The Simple Pulley Gives Us a Lift