We’ve
been discussing the different forms energy takes, delving deeply into de
Coriolis’ claim that energy doesn’t ever die or disappear, it simply changes
forms depending on the tasks it’s
performing. here we’ll combine
mathematical formulas to derive an equation specific to our needs, an
activity my work as an engineer frequently requires of
me. Our task today is to find a means to calculate the
amount of kinetic energy contained
within a piece of ceramic skidding across a concrete
floor. To do so we’ll combine the frictional
force and Work-Energy Theorem formulas to observe the interplay between work
and kinetic energy. As we
learned studying the math behind the Work-Energy Theorem, it takes work to slow a moving object. Work is
present in our example due to the friction that’s created when the broken
piece moves across the floor. The formula to calculate the
amount of work being performed in this situation is written as, W = FF ×d (1) where, d is
the distance the piece travels before it stops, and FF is the
frictional force that stops it. We
established last time that our
ceramic piece has a mass of 0.09 kilograms and the friction created between
it and the floor was calculated to be 0.35 kilogram-meters/second2. We’ll
use this information to calculate the amount of kinetic energy it contains. Here again is the
kinetic energy formula, as presented previously, KE =
½ × m × v2 (2) where m
represents the broken piece’s mass and v its velocity when it first begins to
move across the floor.
The Interplay of Work and Kinetic Energy The Work-Energy
Theorem states that the work, W, required to
stop the piece’s travel is equal to its kinetic energy, KE, while in
motion. This relationship is expressed as, KE =
W (3) Substituting
terms from equation (1) into equation (3), we derive a formula that allows us
to calculate the kinetic energy of our broken piece if we know the frictional
force, FF, acting upon it which causes
it to stop within a distance, d, KE =
FF × d Next
time we’ll use this newly derived formula, and the value we found for FF in
our previous article, to crunch numbers and calculate the exact amount of
kinetic energy contained with our ceramic piece. |