Posts Tagged ‘engineers’

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



Transistors – Voltage Regulation Part XIV

Monday, October 22nd, 2012

     As we’ve come to know through this series of blogs, all electronic components pose some degree of internal resistance to the electric current flowing through them.  This resistance results in electrical energy being converted into heat energy, heat which poses potential problems to sensitive components like electronic circuit boards.  If things get hot enough, components fail and fires may ignite. 

     To address these issues engineers design circuits with resistors whose job it is to limit the current flowing to electrical components.  In this article we’ll see how a limiting resistor protects a Zener diode from this fate, allowing it to continue doing its job of regulating voltage.    

     In our last blog we applied Ohm’s Law to our regulated power supply circuit, which makes use of a Zener diode.  See Figure 1.power supply

Figure 1


     Ohm’s Law gave us the following equation to determine the amount of current, IPS, flowing from the unregulated power supply portion, through the current limiting resistor RLimiting, and making its way into the rest of the circuit:

IPS = (VUnregulatedVZener) ÷ RLimiting

     We learned last week that for the circuit to work, the voltage of the unregulated power supply portion of the circuit, VUnregulated, must be greater than the Zener voltage, VZener.

     Looking at the equation above, we see that the voltage difference is divided by RLimiting, the value of the limiting resistor in the circuit.  This limiting resistor is there to constrain the current flowing to the Zener diode, allowing the diode to keep things under control within the circuit. 

     Basic mathematical principles hold that if a smaller number is divided by a bigger number, the resulting answer is an even smaller number.  Applying this principle to the equation above, if RLimiting is a big number, then IPS must be a smaller number.  On the other hand the smaller RLimiting gets, the bigger IPS becomes. 

     So what does it take for our circuit to fail?  Remove the limiting resistor as shown in Figure 2 and the value for RLimiting disappears.  In other words, RLimiting becomes zero.

zener diode with no limiting resistor

Figure 2


     In this case our Ohm’s Law equation becomes:

IPS = (VUnregulatedVZener) ÷ 0 =

     The resulting answer is said to go to infinity, or , as it is represented mathematically.  In other words, without a limiting resistor being employed within our circuit, IPS will become so large it will overwhelm the diode’s current handling capacity and lead to circuit failure. 

     Next time we’ll go over some advantages and disadvantages of this Zener diode voltage regulating circuit, and why the disadvantages outweigh the advantages for many applications.