Archive for June, 2016

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.

The Simple Pulley

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



Magic as Performed by Pulleys

Friday, June 17th, 2016

    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 magically levitate off the ground, like in the famous magician’s trick.   That object with the spinning wheel is a pulley, a rather simple device which I as an engineering expert have often made use of in my designs.

So Where's The Pulley?

So Where’s The Pulley?


    We’ll be talking about the various types of pulleys and their uses in future blogs, beginning with an exploration of a simple pulley.

Copyright 2016 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog



Combining Kinetic Energy Formulas to Calculate Velocity

Monday, June 6th, 2016

    As an engineering expert, I often use the fact that formulas share a single common factor in order to set them equal to each other, which enables me to solve for a variable contained within one of them.   Using this approach we’ll calculate the velocity, 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 combining two equations which each solve for kinetic energy in their own way.

    Last time we used this formula to calculate the kinetic energy, KE, contained within the piece,

KE = FF × d            (1)

and we found that it stopped its movement across the floor when it had traveled a distance, d, of 2 meters.

    We also solved for the frictional force, FF, which hampered its free travel, and found that quantity to be 0.35 kilogram-meters/second2.   Thus the kinetic energy contained within that piece was calculated to be 0.70 kilogram-meters2/second2.

    Now we’ll put a second equation into play.   It, too, provides a way to solve for kinetic energy, but using different variables.   It’s the version of the formula that contains the variable we seek to calculate, v, for velocity.   If you’ll recall from a previous blog, that equation is,

KE = ½ × m × v2          (2)

    Of the variables present in this formula, we know the mass, m, of the piece is equal to 0.09 kilograms.   Knowing this quantity and the value derived for KE from formula (1), we’ll substitute known values into formula (2) and solve for v, the velocity, or traveling speed, of the piece at the beginning of its slide.

 Combining Kinetic Energy Formulas to Calculate Velocity

Combining Kinetic Energy Formulas to Calculate Velocity


    The ceramic piece’s velocity is thus calculated to be,

KE = ½ × m × v2

0.70 kilogram-meters2/second2=  ½ × (0.09 kilograms) × v2

now we’ll use algebra to rearrange things and isolate v to solve for it,

v2 = 2 × (0.70 kilogram-meters2/second2) ÷ (0.09 kilograms)

v = 3.94 meters/second =12.92 feet/second = 8.81 miles per hour

Our mug piece therefore began its slide across the floor at about the speed of an experienced jogger.

Engineering expert

    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