## Posts Tagged ‘compound pulley’

### Dynamic Lifting is Easier With a Compound Pulley

Friday, October 14th, 2016
 Last time we introduced the engineering concept of mechanical advantage, MA.   Thanks to its presence in our compound pulley arrangement, it made a Grecian man’s job of holding an urn suspended in space twice as easy as compared to when he used a mere simple pulley.   Today we’ll see what happens when our static scenario becomes active through dynamic lifting and how it affects his efforts. Dynamic Lifting is Easier With a Compound Pulley     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, F, equivalent to half the urn’s weight force, W, which meant he enjoyed a mechanical advantage of 2.  Mathematically that is represented by, F = W ÷ 2 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 dynamically raise its position in space until it eventually meets with the beam that supports it.   All the while he’ll be exerting a force greater than W ÷ 2.   That relationship is represented by, F > W ÷ 2     In the case of a 40 Lb urn, the lifting force Mr. Toga must exert to dynamically lift the urn is represented by, F > 40 Lbs ÷ 2 F > 20 Lbs where F represents a bicep force of at least 20 pounds.   Fortunately for him, his efforts will never have to extend much beyond 20 Lbs of effort to lift the urn to the beam.   That’s because gravity’s effect will remain nearly constant as the urn climbs, this being due to gravity’s influence upon objects decreasing by an insignificant amount over short distances above the Earth’s surface.   As a matter of fact, at an altitude of 3,280 feet, gravity’s pull decreases by a mere 0.2 %.     The net result is that the compound pulley enables the same mechanical advantage whether a static or dynamic scenario exists, that is, regardless of whether Mr. Toga is simply holding the urn stationary in space or he’s actively tugging on his end of the rope to lift it higher.     Next time we’ll see how mechanical advantage increases when we add more fixed and moveable pulleys to our compound pulley arrangement.  Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________

### Mechanical Advantage of a Compound Pulley

Thursday, September 29th, 2016
 In this blog series on pulleys we’ve gone from discussing the simple pulley to the improved simple pulley to an introduction to the complex world of compound pulleys, where we began with a static representation.   We’ve used the engineering tool of a free body diagram to help us understand things along the way, and today we’ll introduce another tool to prepare us for our later analysis of dynamic compound pulleys.   The tool we’re introducing today is the engineering concept of mechanical advantage, MA, as it applies to a compound pulley scenario.     The term mechanical advantage is used to describe the measure of force amplification achieved when humans use tools such as crowbars, pliers and the like to make the work of prying, lifting, pulling, bending, and cutting things easier.   Let’s see how it comes into play in our lifting scenario.     During our previous analysis of the simple pulley, we discovered that in order to keep the urn suspended, Mr. Toga had to employ personal effort, or force, equal to the entire weight of the urn. F = W                                    (1)     By comparison, our earlier discussion on the static compound pulley revealed that our Grecian friend need only exert an amount of personal force equal to 1/2 the suspended urn’s weight to keep it in its mid-air position.   The use of a compound pulley had effectively improved his ability to suspend the urn by a factor of 2.   Mathematically, this relationship is demonstrated by, F = W ÷ 2                              (2)     The factor of 2 in equation (2) represents the mechanical advantage Mr. Toga realizes by making use of a compound pulley.   It’s the ratio of the urn’s weight force, W, to the employed force, F.   This is represented mathematically as, MA = W ÷ F                            (3)     Substituting equation (2) into equation (3) we arrive at the mechanical advantage he enjoys by making use of a compound pulley, MA = W ÷ (W ÷ 2) = 2           (4) Mechanical Advantage of  a Compound Pulley     Next time we’ll apply what we’ve learned about mechanical advantage to a compound pulley used in a dynamic lifting scenario.                               Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________

### Archimedes and the Compound Pulley

Thursday, September 22nd, 2016
 Archimedes, a Greek mathematician of ancient times, is credited with inventing the compound pulley, a subject we’ve been exploring recently.  He was so confident in his invention, he’s said to have remarked, “I could move the Earth if given the right place to stand.” Archimedes and the Compound Pulley  Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________

### The Math Behind a Static Compound Pulley

Friday, September 9th, 2016
 Last time we introduced the compound pulley and saw how it improved upon a simple pulley, both of which I’ve engaged in my work as an engineering expert.  Today we’ll examine the math behind the compound pulley.   We’ll begin with a static representation and follow up with an active one in our next blog.     The compound pulley illustrated below contains three rope sections with three representative tension forces, F1, F2, and F3.   Together, these three forces work to offset the weight, 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 pulley scenario affects the man holding his section of rope and exerting force F3, we must first calculate the tension forces F1 and F2.   To do so, we’ll use a free body diagram, shown in the green box, to display the forces’ relationship to one another. The Math Behind a Static Compound Pulley     The free body diagram only takes into consideration the forces inside the green box, namely F1, F2, and W.     For the urn to remain suspended stationary in space, we know that F1 and F2 are each equal to one half the urn’s weight, because they’re spaced equidistant from the pulley’s axle, which directly supports the weight of the urn.  Mathematically this looks like, F1 = F2 = W ÷ 2     Because we know F1 and F2, we also know the value of F3, thanks to an engineering rule concerning pulleys.  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 F1 = F2 = F3.    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 compound pulley.   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 pulleys.     If the urn’s weight, W, is 40 pounds, then according to the aforementioned engineering rule, F1 = F2 = F3= W ÷ 2 F1 = F2 = F3 =  (40 pounds) ÷ 2 = 20 pounds     Mr. 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 compound pulley and see how movement affects F1 , F2 , and F3.   Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________

### The Compound Pulley

Saturday, August 13th, 2016
 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 the compound pulley, which we’ll introduce today. The Compound Pulley       A compound pulley, such as the one shown here, consists of two or more simple pulleys. In the compound pulley system, a combination of fixed and moveable simple pulleys are used to lift objects.   The scenario shown in our illustration features a 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 pulleys 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.     When our toga clad friend pulls his end of the rope he exerts a force, F3, via the pulley affixed to the beam.   This force transmits on to the pulley attached to the urn, which results in lifting the urn off the ground.     Next week we’ll calculate the force on Mr. Toga’s end, F3, as well as the other forces at play, F1 and F2. Copyright 2016 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________

### Simple Pulleys

Tuesday, June 28th, 2016
 Pulleys are simple 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 pulleys is to aid in lifting.   There are two types of pulleys for this purpose, simple or compound. We’ll start our discussion off by looking at the simple type today.     The simple pulley may have been an advanced application of the wheel.   It consists of a furrowed wheel on a shaft with some device for pulling threaded through it.   The pulley 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. Simple Pulley     Pulleys are believed to have first been used by the Greeks as early as the 9th 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 ____________________________________