Archive for March, 2016

Kinetic Energy to Work, Work to Kinetic Energy

Thursday, March 24th, 2016

    Last time we watched our example ceramic coffee mug crash to a concrete floor, where its freefall kinetic energy performed the work of shattering it upon impact.   This is a scenario familiar to engineering experts like myself who are sometimes asked to reconstruct accidents and their aftermaths, otherwise known as forensic engineering.   Today we’ll take a look at what happens when the shattered mug’s pieces are freed from their formerly cozy, cohesive bond, and we’ll watch their transmutation from kinetic energy to work, and back to kinetic energy.

    As we watch our mug shatter on the floor, we notice that it breaks into different sized pieces that are broadcast in many directions around the point of impact.   Each piece has its own unique mass, m, travels at its own unique velocity, v, and has a unique and individualized amount of kinetic energy.   This is in accordance with the kinetic energy formula, shown here again:

KE = ½ × m × v2

    So where did that energy come from?

 The Scattering Pieces Have Kinetic Energy

The Scattering Pieces Have Kinetic Energy

   

    According to the Work-Energy Theorem, the shattered mug’s freefalling kinetic energy is transformed into the work that shatters the mug.   Once shattered, that work is transformed back into kinetic energy, the energy that fuels each piece as it skids across the floor.

    The pieces spray out from the point of the mug’s impact until they eventually come to rest nearby.   They succeed in traveling a fair distance, but eventually their kinetic energy is dissipated due to frictional force which slows and eventually stops them.

    The frictional force acting in opposition to the ceramic pieces’ travel is created when the weight of each fragment makes contact with the concrete floor’s rough surface, which creates a bumpy ride.   The larger the fragment, the more heavily it bears down on the concrete and the greater the frictional force working against it.   With this dynamic at play we see smaller, lighter fragments of broken ceramic cover a greater distance than their heavier counterparts.

    The Work-Energy Theorem holds that the kinetic energy of each piece equals the work of the frictional force acting against it to bring it to a stop.   We’ll talk more about this frictional force and its impact on the broken pieces’ distance traveled next time.

Copyright 2016 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog

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Mohs Scale of Hardness, Ceramic vs. Concrete

Tuesday, March 15th, 2016

    Last time we watched as the kinetic energy of our falling coffee mug was transformed into the work of creating a crater in a pan of soft kitty litter.   Shock absorbing materials are often placed strategically to cushion valuable objects should they fall, and as an engineering expert I’ve sometimes had to implement break-its-fall solutions.  Today we’ll place our mug into a less kind scenario, one in which it makes impact with the unforgiving hardness of a concrete floor.   In so doing we’ll compare the mug’s ceramic to the floor’s concrete, and we’ll familiarize ourselves with the Mohs Scale of Hardness.

The Mohs Scale of Hardness, Ceramic vs. Concrete

The Mohs Scale of Hardness, Ceramic vs. Concrete

   

    Material hardness is commonly measured by the Mohs Scale of Hardness, which ranks the relative hardness of a material by observing how resistant it is to scratching by other materials harder than itself.   This standard was developed by German mineralogist Friedrich Moh in 1812, and it rates objects’ hardness on a scale from 1.0, very soft, to 10.0, very hard.   A fingernail, for example, ranks 2.5 on the scale, while a diamond ranks 10.0.

    Now let’s take a look at the materials in our scenario, a ceramic mug and concrete floor, and see how they compare.   The mug’s ceramic was created by mixing together clay, water, and other materials and then heating them in a kiln, a process known as firing.   This firing causes a chemical reaction that bonds the individual materials tightly together, and when it cools it becomes the product we know as ceramic, a hard, brittle solid which registers at about 7.5 on the Mohs Scale.

    The floor the mug falls to is poured-in-place cement, a compound consisting of primarily limestone, clay, pebbles and sand.   When these materials are combined with water a chemical bonding takes place and forms the hard, stone-like matter we know as concrete, which comes in at about 8.0 on the Mohs Scale.

    Although the mug’s ceramic is comparably hard to the floor’s concrete, its inherent brittleness, along with certain design features, most notably its handle, causes it to be fragile.   Anyone broken a coffee mug lately?

    As for the concrete floor the mug falls onto, it won’t yield to the mug’s freefall kinetic energy and form a crater like the litter did.   So where does the mug’s energy go?

    According to the Work-Energy Theorem, most of the mug’s kinetic energy is still converted into work, just as it was when it met up with the litter, but because the concrete floor is harder and thicker than the mug’s thin ceramic, the mug’s kinetic energy at impact falls back on itself rather than transferring externally into the concrete.   The result is a shattered mug and a mess to clean up.

    But we haven’t yet accounted for all the mug’s energy.   We’ll find out what happens to the rest of it next time.

Copyright 2016 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog

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When Kinetic Energy Meets With Opposing Force

Tuesday, March 1st, 2016

    Objects in motion inevitably meet with opposing forces, a theme which I frequently encounter in my work as an engineering expert.   Today we’ll calculate the opposing force our exemplar coffee mug meets when it falls into a pan of kitty litter, thus transforming its freefalling kinetic energy into the work required to move through clay litter.

    Let’s revisit the Work-Energy Theorem formula, whose terms were explained in last week’s blog,

F × d = – ½ × m × v12          (1)

    The left side of this equation represents the mug’s work to move through the litter, while the right side represents its kinetic energy, which it gained through freefall.   To solve for F, the amount of force acting in opposition to the mug’s mass m as it plows a depth d into the litter, we’ll isolate it on one side of the equation, as shown here,

F = [- ½ × m × v12 ] ÷ d          (2)

    So how do we solve for F when we don’t know the value of v1, the mug’s freefall velocity at impact?   We’ll use the fact that The Law of Conservation of Energy tells us that all energies are equal, and we’ll eliminate the part of Equation (2) that contains this unknown variable, that is, the right side of the equation which deals with kinetic energy.   In its place we’ll substitute terms which represent the mug’s potential energy, that is, the latent energy held within it as it sat upon the shelf prior to falling.  Equation (2) then becomes,

F = [- m × g × h] ÷ d           (3)

where g is the Earth’s acceleration of gravity factor, a constant equal to 9.8 meters/sec2 , and h is the height from which the mug fell.

Kinetic Energy Meets With Opposing Force

Kinetic Energy Meets With Opposing Force

   

    So if we know the mug’s mass, the distance fallen, and the depth of the crater it made in the litter, we can determine the stopping force acting upon it at the time of impact.   It’s time to plug numbers.

    Let’s say our mug has a mass of 0.25 kg, it falls from a height of 2 meters, and it makes a crater 0.05 meters deep.   Then the stopping force acting upon it is,

F = [- (0.25 kg) × (9.8 meters/sec2) × (2 meters)] ÷ (0.05 meters)

=  – 98 Newtons

    The mug was subjected to -98 Newtons, or about -22 pounds of opposing force when it fell into the litter, that resistance being presented by the litter itself.

    Next time we’ll see what happens when our mug strikes a hard surface that fails to cushion its impact.    Energy is released, but where does it go?

Copyright 2016 – Philip J. O’Keefe, PE

Engineering Expert Witness Blog

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