Happy Holidays from EngineeringExpert.net, LLC and the Engineering Expert Witness Blog.
Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |

Published by Philip J. O'Keefe, PE, MLE

Happy Holidays from EngineeringExpert.net, LLC and the Engineering Expert Witness Blog.
Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |

Last time we introduced the engineering concept of and how it affects his efforts.dynamic lifting
If you’ll recall from our last blog, Mr. Toga used a compound pulley to assist him in holding an urn stationary in space. To do so, he only needed to exert personal bicep force,
If the urn weighs 40 pounds, then he only needs to exert 20 Lbs of personal effort to keep it suspended. But when Mr. Toga uses more bicep power with that same compound pulley, he’s able to W ÷ 2. That relationship is represented by,
In the case of a 40 Lb urn, the lifting force Mr. Toga must exert to
where The net result is that the compound pulley enables the same Next time we’ll see how Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |

Last time we introduced the engineering expert. Today we’ll examine . We’ll begin with a the math behind the compound pulley representation and follow up with an active one in our next blog.static The F, _{1}F, and _{2}F. Together, these three forces work to offset the weight, _{3}W, of a suspended urn weighing 40 lbs. Weight itself is a downward pulling force due to the effects of gravity. To determine how our F, we must first calculate the tension forces _{3}F and _{1}F. To do so, we’ll use a _{2}free body diagram, shown in the green box, to display the forces’ relationship to one another.
The free body diagram only takes into consideration the forces inside the green box, namely F, and _{2}W. For the urn to remain suspended stationary in space, we know that F are each equal to one half the urn’s weight, because they’re spaced equidistant from the _{2} axle, which directly supports the weight of the urn. Mathematically this looks like,pulley’s
Because we know F, we also know the value of _{2}F, thanks to an engineering rule concerning _{3}. That is, when a single rope is used to support an object with pulleys, the tension force in each section of rope must be equal along the entire length of the rope, which means pulleysF. This rule holds true whether the rope is threaded through one simple pulley or a complex array of fixed and moveable simple pulleys within a _{1} = F_{2 }= F_{3}. If it wasn’t true, then unequal tension along the rope sections would result in some sections being taut and others limp, which would result in a situation which would not make lifting the urn any easier and thereby defeat the purpose of using compound pulley.pulleys If the urn’s weight,
÷ 2 = 20 poundsMr. Toga needs to exert a mere 20 pounds of personal effort to keep the immobile urn suspended above the ground. It’s the same effort he exerted when using the improved simple pulley in a previous blog, but this time he can do it from the comfort and safety of standing on the ground. Next time we’ll examine the math and mechanics behind an active _{1} , F_{2} , and F_{3.}
Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |

Sometimes one of something just isn’t enough, like one potato chip, one glass of wine… And when it comes to lifting massive objects one simple pulley isn’t going to be enough to get the job done. Even the improved simple pulley, which we introduced last week, is often not enough, a situation which I’ve run across in my career as an engineering expert. To get past the limitations of the simple pulley and improved simple pulley, ancient Greeks went on to devise
A system, a combination of fixed and moveable simple pulleys are used to lift objects. The scenario shown in our illustration features a the compound pulley consisting of two simple pulleys, one is stationary and affixed to a beam, the other hangs freely in space, riding on the rope connecting them. One end of the rope is held by Mr. Toga, the other end is affixed to the beam. In fact, all compound pulley require that at least one simple pulley be affixed to a stationary structure, and at least one other simple pulley must be free to move in space.compound pulleys When our toga clad friend pulls his end of the rope he exerts a force, affixed to the beam. This force transmits on to the pulley attached to the urn, which results in lifting the urn off the ground.pulley Next week we’ll calculate the force on Mr. Toga’s end, Fand_{1} F._{2}Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |

Last time we introduced the free body diagram, applied it to a simple pulley, and discovered that in so doing lifting objects required 50% less effort. As an engineering expert, I’ve sometimes put this to work for me in designs. We’ll do simple pulleythe math behind the today.improvement Here again is the improved as introduced last week.simple pulley
The illustration shows the three forces, F, and _{2}W, acting upon the simplewithin the highlighted free body diagram. Forces pulley F and _{1}F are exerted from above and act in opposition to the downward pull of gravity, represented by the weight of the urn, _{2}W. Forces F and _{1}Fare produced by that which holds onto either end of the rope that’s threaded through the _{2 } In our case those forces are supplied by a man in a toga and a beam. By engineering convention, these upward forces, pulley.F and _{1}F are considered positive, while the downward force, _{2,}W, is negative. In the arrangement shown in our illustration, the F and _{1}F are equal._{2} Now, according to the basic rule of F, _{1}F, and _{2}W must add up to zero in order for the to remain stationary. Put another way, if the pulley isn’t moving up or down, the positive forces pulleyF and _{1}F are balancing the negative force presented by the urn’s weight, _{2}W. this looks like,Mathematically
or, by rearranging terms,
We know that Fso we can substitute_{2}, F for _{1}F in the preceding equation to arrive at,_{2}
or,
Using algebra to divide both sides of the equation by 2, we get:
W ÷ 2Therefore,
F = _{2}W ÷ 2If the sum of the forces in a free body diagram do not equal zero, then the suspended object will move in space. In our situation the urn moves up if our toga-clad friend pulls on his end of the rope, and it moves down if Mr. Toga reduces his grip and allows the rope to slide through his hand under the influence of gravity. The net real world benefit to our Grecian friend is that the urn’s 20-pound weight is divided equally between him and the beam. He need only apply a force of 10 pounds to keep the urn suspended. Next time we’ll see how the improved Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |

Sometimes 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 way around this limitation, which we’ll highlight today by way of a modern design engineer’s tool, the simplefree body diagram. Around 400 BC, the Greeks noticed that if they detached the
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 in our application, as shown in the blue inset box and in greater detail below.pulley
The blue insert box in the first illustration highlights the subject at hand. A represent both positive and negative values. The simple pulley,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 diagram 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.free body diagrams We’ll see how the next time, when we attack the math behind it.simple pulleyCopyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |

Lifting heavy objects into position always presents a challenge, whether it’s a mom 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 lifting 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.simple pulley The ^{th} Century BC. Back then it would have come in handy to lift cargo aboard ships, hoist sails on masts, and building materials high off the ground to supply workmen during the construction of temples and other marvels of ancient architecture. In other words, lift literally saved ancient workers thousands of steps when it came to pulleys things off the ground.lifting Let’s return to ancient times for a moment to get an understanding of the mechanics behind the workings of the application.lifting
With a F applied to the rope by the pull-er is equal to the tension force _{1}F exerted upon the object, the pull-ee. Once lifted off the ground, these forces are also equal to the object’s weight, _{2}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 effectiveness to simple pulley’s 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 lift when relying on human power alone, particularly when it’s employed to simple pulley extremely heavy objects like marble pillars. A single human isn’t up to the task.lift Next time we’ll see how ancient Greeks overcame this limitation of the heavy objects.liftCopyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |

devices with many uses, and as an engineering expert, I’ve often incorporated them into mechanical designs. They’re used in machinery to transmit mechanical power from electric motors and engines to devices like blowers and pumps. Another common usage for simpleis to aid in lifting. There are two types of pulleys for this purpose, pulleys or compound. We’ll start our discussion off by looking at the simple type today.simple The wheel supports and guides the movement of a rope, cable, or other pulling device around its circumference. The pulling device runs between a pull-ee and pull-er, that is, the object to be moved and the source of pulling power, with the pulley itself situated somewhere between them.pulley
^{th} Century BC. We’ll look into how they put them to use next time.Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |

Ever seen that old movie where they’re lifting a grand piano to the top floor of a tall building with ropes? The huge piano dangles precariously in mid air by the ropes, which are attached to a rather simple looking wheeled device that’s situated at the top of the building. As men on the ground tug on the ropes, they hoist the piano higher and higher by increments of inches as the wheeled device the rope is threaded through spins madly. The piano’s formidable size appears to trick. That object with the spinning wheel is a magician’s a rather simple device which I as an engineering expert have often made use of in my designs.pulley,
We’ll be talking about the various types of pulley.Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |

As an engineering expert, I often use the fact that the calculate or speed, at which the broken bit of ceramic from the coffee mug we’ve been following slides across the floor until it’s finally brought to a stop by friction between it and the floor. We’ll do so by velocity, two equations which each solve for combiningin their own way.kinetic energy Last time we used this the kinetic energy, calculateKE, contained within the piece,
d (1)and we found that it stopped its movement across the floor when it had traveled a distance, We also solved for the frictional force, ^{2}. Thus the contained within that piece was kinetic energy to be 0.70 kilogram-meterscalculated^{2}/second^{2}. Now we’ll put a second equation into play. It, too, provides a way to solve for calculate,v, for . If you’ll recall from a previous blog, that equation is,velocity
Of the variables present in this m, of the piece is equal to 0.09 kilograms. Knowing this quantity and the value derived for KE from (1), we’ll substitute known values into formula(2) and solve for formula v, the or traveling speed, of the piece at the beginning of its slide.velocity,
The ceramic piece’s to be,calculated
0.70 kilograms) × v^{2}now we’ll use algebra to rearrange things and isolate
× (0.70 kilogram-meters) ÷ (0.09 ^{2}/second^{2}kilograms)
Our mug piece therefore began its slide across the floor at about the speed of an experienced jogger. This ends our series on the interrelationship of energy and work. Next time we’ll begin a new topic, namely, how pulleys make the work of lifting objects and driving machines easier. Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |